A, Z, N, EBE, EBE/a, # up quarks, # down quarks, # possible bonds, and non-quantum calculated binding energy (classical CBE) for a representative sample of nuclides.
\\n\\n
IntechOpen was founded by scientists, for scientists, in order to make book publishing accessible around the globe. Over the last two decades, this has driven Open Access (OA) book publishing whilst levelling the playing field for global academics. Through our innovative publishing model and the support of the research community, we have now published over 5,700 Open Access books and are visited online by over three million academics every month. These researchers are increasingly working in broad technology-based subjects, driving multidisciplinary academic endeavours into human health, environment, and technology.
\\n\\nBy listening to our community, and in order to serve these rapidly growing areas which lie at the core of IntechOpen's expertise, we are launching a portfolio of Open Science journals:
\\n\\nAll three journals will publish under an Open Access model and embrace Open Science policies to help support the changing needs of academics in these fast-moving research areas. There will be direct links to preprint servers and data repositories, allowing full reproducibility and rapid dissemination of published papers to help accelerate the pace of research. Each journal has renowned Editors in Chief who will work alongside a global Editorial Board, delivering robust single-blind peer review. Supported by our internal editorial teams, this will ensure our authors will receive a quick, user-friendly, and personalised publishing experience.
\\n\\n"By launching our journals portfolio we are introducing new, dedicated homes for interdisciplinary technology-focused researchers to publish their work, whilst embracing Open Science and creating a unique global home for academics to disseminate their work. We are taking a leap toward Open Science continuing and expanding our fundamental commitment to openly sharing scientific research across the world, making it available for the benefit of all." Dr. Sara Uhac, IntechOpen CEO
\\n\\n"Our aim is to promote and create better science for a better world by increasing access to information and the latest scientific developments to all scientists, innovators, entrepreneurs and students and give them the opportunity to learn, observe and contribute to knowledge creation. Open Science promotes a swifter path from research to innovation to produce new products and services." Alex Lazinica, IntechOpen founder
\\n\\nIn conclusion, Natalia Reinic Babic, Head of Journal Publishing and Open Science at IntechOpen adds:
\\n\\n“On behalf of the journal team I’d like to thank all our Editors in Chief, Editorial Boards, internal supporting teams, and our scientific community for their continuous support in making this portfolio a reality - we couldn’t have done it without you! With your support in place, we are confident these journals will become as impactful and successful as our book publishing program and bring us closer to a more open (science) future.”
\\n\\nWe invite you to visit the journals homepage and learn more about the journal’s Editorial Boards, scope and vision as all three journals are now open for submissions.
\\n\\nFeel free to share this news on social media and help us mark this memorable moment!
\\n\\n\\n"}]',published:!0,mainMedia:{caption:"",originalUrl:"/media/original/237"}},components:[{type:"htmlEditorComponent",content:'
After years of being acknowledged as the world's leading publisher of Open Access books, today, we are proud to announce we’ve successfully launched a portfolio of Open Science journals covering rapidly expanding areas of interdisciplinary research.
\n\n\n\nIntechOpen was founded by scientists, for scientists, in order to make book publishing accessible around the globe. Over the last two decades, this has driven Open Access (OA) book publishing whilst levelling the playing field for global academics. Through our innovative publishing model and the support of the research community, we have now published over 5,700 Open Access books and are visited online by over three million academics every month. These researchers are increasingly working in broad technology-based subjects, driving multidisciplinary academic endeavours into human health, environment, and technology.
\n\nBy listening to our community, and in order to serve these rapidly growing areas which lie at the core of IntechOpen's expertise, we are launching a portfolio of Open Science journals:
\n\nAll three journals will publish under an Open Access model and embrace Open Science policies to help support the changing needs of academics in these fast-moving research areas. There will be direct links to preprint servers and data repositories, allowing full reproducibility and rapid dissemination of published papers to help accelerate the pace of research. Each journal has renowned Editors in Chief who will work alongside a global Editorial Board, delivering robust single-blind peer review. Supported by our internal editorial teams, this will ensure our authors will receive a quick, user-friendly, and personalised publishing experience.
\n\n"By launching our journals portfolio we are introducing new, dedicated homes for interdisciplinary technology-focused researchers to publish their work, whilst embracing Open Science and creating a unique global home for academics to disseminate their work. We are taking a leap toward Open Science continuing and expanding our fundamental commitment to openly sharing scientific research across the world, making it available for the benefit of all." Dr. Sara Uhac, IntechOpen CEO
\n\n"Our aim is to promote and create better science for a better world by increasing access to information and the latest scientific developments to all scientists, innovators, entrepreneurs and students and give them the opportunity to learn, observe and contribute to knowledge creation. Open Science promotes a swifter path from research to innovation to produce new products and services." Alex Lazinica, IntechOpen founder
\n\nIn conclusion, Natalia Reinic Babic, Head of Journal Publishing and Open Science at IntechOpen adds:
\n\n“On behalf of the journal team I’d like to thank all our Editors in Chief, Editorial Boards, internal supporting teams, and our scientific community for their continuous support in making this portfolio a reality - we couldn’t have done it without you! With your support in place, we are confident these journals will become as impactful and successful as our book publishing program and bring us closer to a more open (science) future.”
\n\nWe invite you to visit the journals homepage and learn more about the journal’s Editorial Boards, scope and vision as all three journals are now open for submissions.
\n\nFeel free to share this news on social media and help us mark this memorable moment!
\n\n\n'}],latestNews:[{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"},{slug:"introducing-intechopen-book-series-a-new-publishing-format-for-oa-books-20210915",title:"Introducing IntechOpen Book Series - A New Publishing Format for OA Books"}]},book:{item:{type:"book",id:"412",leadTitle:null,fullTitle:"Biosensors for Health, Environment and Biosecurity",title:"Biosensors for Health, Environment and Biosecurity",subtitle:null,reviewType:"peer-reviewed",abstract:"A biosensor is a detecting device that combines a transducer with a biologically sensitive and selective component. Biosensors can measure compounds present in the environment, chemical processes, food and human body at low cost if compared with traditional analytical techniques. This book covers a wide range of aspects and issues related to biosensor technology, bringing together researchers from 16 different countries. 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Binding",doi:"10.5772/intechopen.94377",slug:"the-inter-nucleon-up-to-down-quark-bond-and-its-implications-for-nuclear-binding",body:'
The nuclear force is defined as the force which binds the protons and neutrons together within a nucleus. One of the currently accepted models of the nuclear force is the liquid drop model [1]. This model of the nuclear force uses the Weizsäcker formula to predict the binding energies of nuclides. The Weizsäcker formula is a curve-fitting formula that uses five parameters, plus one conditional logic statement, in order to achieve its results [2]. These parameters are selected to empirically curve-fit an equation to match the experimental data. The liquid drop model is considered to be a “semi-classical” model of the nuclear force, rather than a quantum model [3].
Another currently accepted model of the nuclear force is the shell model, which uses magic numbers to explain certain nuclear behavior. The nuclear shell model is similar to the electronic shell model, which describes the electrons orbiting around an atom. However, the nuclear shell model does not predict the nuclear binding energy, rather the shell model defers back to the Weizsäcker formula for binding energy calculations.
A third currently accepted model of the nuclear force is the residual chromo-dynamic force (RCDF) model, also known as the residual strong force model. Before describing this residual chromodynamic force, it is useful to mention a few specifics about quantum chromodynamics (QCD). Quantum chromodynamics postulates that the three valance quarks of protons and neutrons possess an attribute called “color charge.” Historically, a contradiction of the quantum mechanical basis of nucleon properties with the Pauli Exclusion Principle led to the concept of the color charge for quarks [4]. The color charges of the quarks are considered to be either red, green, or blue. The words red, green, and blue are simply the names of the color charges and do not imply any type of physically visual hue for the quarks. Also, the term “charge”, when referring specifically to the color charge, is not related to electric charge, which unfortunately can often be a point of confusion. Quantum chromodynamics states that a very strong bond is formed among the three color charges of the quarks inside the nucleon [5]. Both protons and neutrons have all three colors inside the nucleon.
The residual chromodynamic force model assumes that the chromodynamic force also has a weaker
An illustrative representation showing both the chromodynamic force and the residual chromodynamic force.
In Figure 1, the bold black line represents the chromodynamic force inside the nucleon, and the dotted gray line represents the residual chromodynamic force between two nucleons. (Note that quarks are considered to be point-like particles. Thus this drawing is not meant to be a scaled representation of the quarks, rather it is meant for illustrative purposes only.) The residual chromodynamic bond can be between any two quarks of different colors, such as between a red and blue, a green and red, or a blue and green. The residual chromodynamic bond can be between a neutron and a neutron, a proton and a neutron, or a proton and another proton.
While the RCDF model is considered to be the mechanism for nuclear bonding, the model is unable to duplicate the experimental binding energy curve. This inability of the RCDF model to reproduce this nuclear behavior is currently attributed to the extreme difficulty of modeling the multi-body interactions of the three color charges [6, 7]. This difficulty with the derivation of the nuclear binding forces from the residual chromodynamic force model is two-fold. First, each nucleon consists of three quarks, which means that a system of two nucleons is already a six-body problem. Second, because the chromodynamic force between quarks inside the nucleons has the feature of being very strong compared to the residual chromodynamic force outside the nucleons, this disproportionate ratio of strength makes a converging solution for the complicated mathematical calculations difficult to find. For nuclides with a small number of nucleons, the problem can be solved with brute-force computing power by putting each of the quarks into a four-dimensional lattice of discrete points: three dimensions of space and one of time. This method is known as lattice quantum chromodynamics, or lattice QCD. This brute-force method for the computer calculations in lattice QCD iterates the position of each quark by assigning an x, y, z, and t position to it, calculating the resulting forces on each quark, allowing their position to change as a result of these forces, and then iterating this procedure until a resulting converging solution is found. If a converging solution is found, then these calculations are able to determine the binding energy of the nuclide in question. These computer calculations are done through extremely complex mathematical models, often using Monte-Carlo simulations [8]. Because of these computational difficulties, modeling the binding energies of only the smallest nuclides has been achieved.
However, such calculations are computationally expensive, requiring very large computers. Because of these complications, this modeling method is not normally used as a standard nuclear physics tool [7] .Thus, the RCDF model remains largely unverified when testing its binding energy predictions against experimental data.
Besides having the attribute of color charge, there is also another attribute of quarks called flavor. From QCD theory, we know there are six different flavors of quarks: up, down, strange, charm, top, and bottom. Of these six different flavors, only two flavors are found in the stable matter of neutrons and protons: the up and down quarks [9]. (The terms of up and down do not imply any specific orientation with regard to spatial direction, and are simply the names of these types of quarks).
An up quark has an electric charge that is +2/3 the charge of a proton, and it also contains a positive magnetic moment. The up quark has a spin of ½ and a mass of about 0.3% of the proton. The color of an up quark can be either red, green, or blue. A down quark has an electric charge that is −1/3 the charge of a proton, and it contains a negative magnetic moment, which is anti-parallel to of the spin of the nuclide. The down quark has a spin of ½, and a mass of about 0.6% of the proton. The color of a down quark can be either red, green, or blue.
The magnetic moments of an up quark is estimated to be +1.85 and the magnetic moments of a down quark is estimated to be −0.97, both in units of nuclear magnetons. The electric charges of the proton and neutron are completely contained within the quarks. The proton is comprised of two up quarks and one down quark, giving it a net charge of one (2/3 + 2/3 -1/3 = 1). The neutron is comprised of one up quark and two down quarks, giving it a net charge of zero (2/3 -1/3 -1/3 = 0). Figure 2 illustrates these properties.
An illustrative representation of the up and down quarks in a proton and neutron.
The quarks inside of a proton and neutron have both attributes of flavor (up or down) and color (red, green, or blue). Thus, each quark inside of a proton or neutron is one of six types: up and red, up and green, up and blue, down and red, down and green, or down and blue [5]. Since both the neutron and the proton contain all three different colors, there is no difference between the proton and the neutron with regard to the attribute of color charges. The only difference in the quark characteristics between a proton or a neutron resides in the number of up and down quarks. Therefore, any bond between the different colors is also inherently a bond between some combination of the up and down quarks. Hence, the quantum assumptions that are made in the RCDF model about the possibility of an internucleon bond between the residual colors of quarks are also inherently applicable to the formation of an internucleon bond between up and down quarks.
Figure 3 shows three possible bonds, all of which are allowed in the RCDF model: a bond between two up quarks, between two down quarks, and between an up and a down quark. In the RCDF model, as long as the bond is between different colors of quarks, the up or down flavor of the quarks, is considered relatively unimportant.
Possible bonds in the RCDF model. A bond can be formed regardless of the flavor (up or down) of the quark.
Although it is considered relatively unimportant in the RCDF model, the up or down flavor of the quarks does indeed cause an energy difference among the three types of bonds that are illustrated in Figure 3. If there is an internucleon bond between two up quarks or between two down quarks, then the intrinsic electro-magnetic force between these quarks is repulsive. Conversely, if there is an internucleon bond between an up quark and a down quark, then the intrinsic electromagnetic force between these quarks is attractive. Among the three types of bonds shown in Figure 3, this inherent difference in the electromagnetic energy may cause the two repulsive bonds to be less probable or less stable, producing a situation in which the up-to-down quark bond would be more prevalent in stable matter.
As mentioned previously, the color charges of the quarks contained within a nucleon do not inherently distinguish between a neutron or proton; it is only the up and down attribute of the quarks that distinguish between the two types of stable nucleons. Thus, an examination of an internucleon bond being formed only between an up and a down quark is an appropriate possibility to explore. Specifically, this additional constraint is that not only must the internucleon quark-to-quark bond be between different colors, but also it must be between only an up and a down quark; specifically, it cannot be between two up quarks or two down quarks. If this quite reasonable constraint is made to the RCDF model, a quick calculation of the allowed bonds can be easily made. By using the currently accepted RCDF concept of the internucleon quark-to-quark bond, and applying this additional constraint, in which bonds are only formed between up and down quarks, an interesting and potentially significant set of data emerges.
For any given nuclide, the number of internucleon up-to-down quark pairs can be determined, based on how many up and down quarks each nuclide has. This calculation, as shown in Eq. (1), is made for each nuclide.
For simplicity of this very quick and easy calculation, it is assumed that every bonded pair of up-to-down quarks has the same bonding energy. Thus, just for this simple calculation, the equation for the calculated binding energy (CBE) of a non-quantum nuclide is the number of internucleon up-to-down quark pairs times the binding energy per pair, as shown in Eq. (2).
For a representative sample of stable nuclides, this information is also shown in Table 1. For values of mass number with two stable nuclides, such as A = 40, both stable nuclides are shown. The following information is listed:
The nuclide name
The number of nucleons, A
The number of protons, Z
The number of neutrons, N
The experimental binding energy (EBE) in units of MeV, as obtained from the nuclear tables in Ref. [10].
The experimental binding energy per nucleon (EBE/A)
The number of up quarks in the nuclide
The number of down quarks in the nuclide
The number or possible pairs between up and down quarks for the nuclide
The classical (non-quantum) calculated binding energy (CBE) in MeV of the nuclide, for a fixed energy (6.000 MeV) per bond.
Nuclide | A | Z | N | EBE in MeV | EBE/A | # Of up quarks | # Of down quarks | # Of updown bonds, classical | Classical CBE/A |
---|---|---|---|---|---|---|---|---|---|
H2 | 2 | 1 | 1 | 2.225 | 1.11 | 3 | 3 | 3 | 9 |
He3 | 3 | 2 | 1 | 7.718 | 2.57 | 5 | 4 | 4 | 8 |
He4 | 4 | 2 | 2 | 28.296 | 7.07 | 6 | 6 | 6 | 9 |
He5 | 5 | 2 | 3 | 26.626 | 5.33 | 7 | 8 | 7 | 8.4 |
Li6 | 6 | 3 | 3 | 31.995 | 5.33 | 9 | 9 | 9 | 9 |
Li7 | 7 | 3 | 4 | 39.245 | 5.61 | 10 | 11 | 10 | 8.571 |
Be8 | 8 | 4 | 4 | 56.5 | 7.06 | 12 | 12 | 12 | 9 |
Be9 | 9 | 4 | 5 | 58.165 | 6.46 | 13 | 14 | 13 | 8.667 |
B10 | 10 | 5 | 5 | 64.751 | 6.48 | 15 | 15 | 15 | 9 |
B11 | 11 | 5 | 6 | 76.205 | 6.93 | 16 | 17 | 16 | 8.727 |
C12 | 12 | 6 | 6 | 92.162 | 7.68 | 18 | 18 | 18 | 9 |
C13 | 13 | 6 | 7 | 97.108 | 7.47 | 19 | 20 | 19 | 8.769 |
N14 | 14 | 7 | 7 | 104.659 | 7.48 | 21 | 21 | 21 | 9 |
N15 | 15 | 7 | 8 | 115.492 | 7.7 | 22 | 23 | 22 | 8.8 |
O16 | 16 | 8 | 8 | 127.619 | 7.98 | 24 | 24 | 24 | 9 |
O17 | 17 | 8 | 9 | 131.762 | 7.75 | 25 | 26 | 25 | 8.824 |
O18 | 18 | 8 | 10 | 139.808 | 7.77 | 26 | 28 | 26 | 8.667 |
F19 | 19 | 9 | 10 | 147.801 | 7.78 | 28 | 29 | 28 | 8.842 |
Ne20 | 20 | 10 | 10 | 160.65 | 8.03 | 30 | 30 | 30 | 9 |
Ne21 | 21 | 10 | 11 | 167.406 | 7.97 | 31 | 32 | 31 | 8.857 |
Ne22 | 22 | 10 | 12 | 177.77 | 8.08 | 32 | 34 | 32 | 8.727 |
Na23 | 23 | 11 | 12 | 186.564 | 8.11 | 34 | 35 | 34 | 8.87 |
Mg24 | 24 | 12 | 12 | 198.257 | 8.26 | 36 | 36 | 36 | 9 |
Mg25 | 25 | 12 | 13 | 205.587 | 8.22 | 37 | 38 | 37 | 8.88 |
Mg26 | 26 | 12 | 14 | 216.681 | 8.33 | 38 | 40 | 38 | 8.769 |
Al27 | 27 | 13 | 14 | 224.952 | 8.33 | 40 | 41 | 40 | 8.889 |
Si28 | 28 | 14 | 14 | 236.537 | 8.45 | 42 | 42 | 42 | 9 |
Si29 | 29 | 14 | 15 | 245.01 | 8.45 | 43 | 44 | 43 | 8.897 |
Si30 | 30 | 14 | 16 | 255.62 | 8.52 | 44 | 46 | 44 | 8.8 |
P31 | 31 | 15 | 16 | 262.917 | 8.48 | 46 | 47 | 46 | 8.903 |
S32 | 32 | 16 | 16 | 271.78 | 8.49 | 48 | 48 | 48 | 9 |
S33 | 33 | 16 | 17 | 280.422 | 8.5 | 49 | 50 | 49 | 8.909 |
S34 | 34 | 16 | 18 | 291.839 | 8.58 | 50 | 52 | 50 | 8.824 |
Cl35 | 35 | 17 | 18 | 298.21 | 8.52 | 52 | 53 | 52 | 8.914 |
S36 | 36 | 16 | 20 | 308.71 | 8.58 | 52 | 56 | 52 | 8.667 |
Ar36 | 36 | 18 | 18 | 306.716 | 8.52 | 54 | 54 | 54 | 9 |
Cl37 | 37 | 17 | 20 | 318.784 | 8.62 | 54 | 57 | 54 | 8.757 |
Ar38 | 38 | 18 | 20 | 327.343 | 8.61 | 56 | 58 | 56 | 8.842 |
K39 | 39 | 19 | 20 | 333.724 | 8.56 | 58 | 59 | 58 | 8.923 |
Ar40 | 40 | 18 | 22 | 343.81 | 8.6 | 58 | 62 | 58 | 8.7 |
Ca40 | 40 | 20 | 20 | 342.053 | 8.55 | 60 | 60 | 60 | 9 |
K41 | 41 | 19 | 22 | 351.619 | 8.58 | 60 | 63 | 60 | 8.78 |
Ca42 | 42 | 20 | 22 | 361.895 | 8.62 | 62 | 64 | 62 | 8.857 |
Ca43 | 43 | 20 | 23 | 369.828 | 8.6 | 63 | 66 | 63 | 8.791 |
Ca44 | 44 | 20 | 24 | 380.96 | 8.66 | 64 | 68 | 64 | 8.727 |
Sc45 | 45 | 21 | 24 | 387.849 | 8.62 | 66 | 69 | 66 | 8.8 |
Ca46 | 46 | 20 | 26 | 398.772 | 8.67 | 66 | 72 | 66 | 8.609 |
Ti46 | 46 | 22 | 24 | 398.194 | 8.66 | 68 | 70 | 68 | 8.87 |
Ti47 | 47 | 22 | 25 | 407.072 | 8.66 | 69 | 72 | 69 | 8.809 |
Ca48 | 48 | 20 | 28 | 415.992 | 8.67 | 68 | 76 | 68 | 8.5 |
Ti48 | 48 | 22 | 26 | 418.699 | 8.72 | 70 | 74 | 70 | 8.75 |
Ti49 | 49 | 22 | 27 | 426.841 | 8.71 | 71 | 76 | 71 | 8.694 |
Ti50 | 50 | 22 | 28 | 437.78 | 8.76 | 72 | 78 | 72 | 8.64 |
Cr50 | 50 | 24 | 26 | 435.047 | 8.7 | 74 | 76 | 74 | 8.88 |
V51 | 51 | 23 | 28 | 445.842 | 8.74 | 74 | 79 | 74 | 8.706 |
Cr52 | 52 | 24 | 28 | 456.345 | 8.78 | 76 | 80 | 76 | 8.769 |
Cr53 | 53 | 24 | 29 | 464.287 | 8.76 | 77 | 82 | 77 | 8.717 |
Cr54 | 54 | 24 | 30 | 474.009 | 8.78 | 78 | 84 | 78 | 8.667 |
Fe54 | 54 | 26 | 28 | 471.765 | 8.74 | 80 | 82 | 80 | 8.889 |
Mn55 | 55 | 25 | 30 | 482.075 | 8.77 | 80 | 85 | 80 | 8.727 |
Fe56 | 56 | 26 | 30 | 492.257 | 8.79 | 82 | 86 | 82 | 8.786 |
Fe57 | 57 | 26 | 31 | 499.905 | 8.77 | 83 | 88 | 83 | 8.737 |
Fe58 | 58 | 26 | 32 | 509.945 | 8.79 | 84 | 90 | 84 | 8.69 |
Ni58 | 58 | 28 | 30 | 506.456 | 8.73 | 86 | 88 | 86 | 8.897 |
Co59 | 59 | 27 | 32 | 517.314 | 8.77 | 86 | 91 | 86 | 8.746 |
Ni60 | 60 | 28 | 32 | 526.842 | 8.78 | 88 | 92 | 88 | 8.8 |
Zn70 | 70 | 30 | 40 | 611.08 | 8.73 | 100 | 110 | 100 | 8.571 |
Ge70 | 70 | 32 | 38 | 610.519 | 8.72 | 102 | 108 | 102 | 8.743 |
Se80 | 80 | 34 | 46 | 696.867 | 8.71 | 114 | 126 | 114 | 8.55 |
Kr80 | 80 | 36 | 44 | 695.438 | 8.69 | 116 | 124 | 116 | 8.7 |
Zr90 | 90 | 40 | 50 | 783.895 | 8.71 | 130 | 140 | 130 | 8.667 |
Ru100 | 100 | 44 | 56 | 861.929 | 8.62 | 144 | 156 | 144 | 8.64 |
Cd113 | 113 | 48 | 65 | 963.557 | 8.53 | 161 | 178 | 161 | 8.549 |
In113 | 113 | 49 | 64 | 963.091 | 8.52 | 162 | 177 | 162 | 8.602 |
Sn117 | 117 | 50 | 67 | 995.623 | 8.51 | 167 | 184 | 167 | 8.564 |
Xe129 | 129 | 54 | 75 | 1087.648 | 8.43 | 183 | 204 | 183 | 8.512 |
Ce142 | 142 | 58 | 84 | 1185.28 | 8.35 | 200 | 226 | 200 | 8.451 |
Nd142 | 142 | 60 | 82 | 1185.148 | 8.35 | 202 | 224 | 202 | 8.535 |
Sm150 | 150 | 62 | 88 | 1239.253 | 8.26 | 212 | 238 | 212 | 8.48 |
Gd150 | 150 | 64 | 86 | 1236.39 | 8.24 | 214 | 236 | 214 | 8.56 |
Dy162 | 162 | 66 | 96 | 1323.884 | 8.17 | 228 | 258 | 228 | 8.444 |
Yb172 | 172 | 70 | 102 | 1392.764 | 8.1 | 242 | 274 | 242 | 8.442 |
W183 | 183 | 74 | 109 | 1465.526 | 8.01 | 257 | 292 | 257 | 8.426 |
Pt194 | 194 | 78 | 116 | 1539.578 | 7.94 | 272 | 310 | 272 | 8.412 |
Au197 | 197 | 79 | 118 | 1559.397 | 7.92 | 276 | 315 | 276 | 8.406 |
Hg200 | 200 | 80 | 120 | 1581.207 | 7.91 | 280 | 320 | 280 | 8.4 |
Hg204 | 204 | 80 | 124 | 1608.65 | 7.89 | 284 | 328 | 284 | 8.353 |
Pb204 | 204 | 82 | 122 | 1605.343 | 7.87 | 286 | 326 | 286 | 8.412 |
A, Z, N, EBE, EBE/a, # up quarks, # down quarks, # possible bonds, and non-quantum calculated binding energy (classical CBE) for a representative sample of nuclides.
Figure 4 is a plot for this same a representative sample of nuclides, showing both the experimental binding energy per nucleon (EBE/A) and the non-quantum calculated binding energy per nucleon (CBE/A) for an object with a fixed energy (6.000 MeV) per bond. For this quick calculation, neither the type of bond nor the structure of these bonds comes into consideration. Simply stated, this is a theory-independent calculation of the number of possible bonded pairs times a fixed binding energy per bonded pair.
In blue, a plot of the experimental binding energy (EBE) per nucleon. In orange, a plot of the calculated binding energy (CBE) per nucleon, based on the number of possible non-quantum up-to-down quark pairs and a fixed binding energy per bonded pair.
A nucleus is a quantum object, and being so, certain quantum rules must apply. A known phenomenological feature of the nuclear force is the QCD hard-core repulsion. The hard-core repulsion states that nucleons, such as a proton or neutron, cannot overlap in their spatial location [11, 12]. If too many bonds are formed for either 2H or 3H or 3He, overlap will occur. This overlap is illustrated in Figure 5.
An illustration of the overlapping nucleons if too many bonds are attempted. For the nuclide 2H, if two or three bonds are attempted, indicated by the red bonds, an overlap occurs. Similarly, 3He can form only three bonds. If four or five are attempted, an overlap occurs in three dimensions.
To prevent this overlap, hydrogen 2H can have only one bond instead of two or three. Similarly, helium 3He (as well as hydrogen 3H) can have only three bonds instead of four or five. Three other nuclides are subject to this constraint, those with odd-odd configurations: 6Li, 10B, and 14N. Specifically, the odd neutron and the odd proton cannot bond twice to either each other or to another nucleon. Other stable nuclides are not affected by the application of this rule, since there are enough nucleons to prevent an overlap from occurring for the larger nuclides.
Quantum mechanics also states there can be no net electric dipole moment for the nuclide [13, 14]. For this second quantum rule, three more bonds must be subtracted from the number of bonds available, in order to remove the electric dipole moment. Without stating any specific configuration for the nuclide, this reduction of bonds can be best understood from the fact that the electric charge distribution of the nuclide must not have a net asymmetry in electrical charge for any of the three spatial dimensions, x, y, or z. To prevent an electric dipole moment, a bond is broken in each of these three dimensions, so that the net charge is symmetric about the x, y, and z axes. This quantum requirement removes three of the classically-allowed bonds. This rule applies to all stable nuclides, except for the three very smallest stable nuclides, 2H, 3He, and 4He.
The inclusion of these two quantum rules is shown in Table 2. The first 8 columns of Table 2 are similar to the first 8 columns of Table 1. Also shown in Table 2 is the number of possible quantum bonds for each nuclide, taking into consideration the two above mentioned quantum rules. The last three columns of Table 2 show the quantum calculated binding energy, the CBE/A, and the percent error of that calculated energy, as compared with the experimental binding energy.
Nuclide | A | Z | N | EBE in MeV | EBE/A | # Of up quarks | # Of down quarks | # Of updown bonds, classical | # Of updown bonds, quantum | Calculated binding energy (CBE) in MeV | CBE/A | %Error |
---|---|---|---|---|---|---|---|---|---|---|---|---|
H2 | 2 | 1 | 1 | 2.225 | 1.11 | 3 | 3 | 3 | 1 | 6 | 3 | −169.66 |
He3 | 3 | 2 | 1 | 7.718 | 2.57 | 5 | 4 | 4 | 3 | 18 | 6 | −133.22 |
He4 | 4 | 2 | 2 | 28.296 | 7.07 | 6 | 6 | 6 | 6 | 36 | 9 | −27.23 |
He5 | 5 | 2 | 3 | 26.626 | 5.33 | 7 | 8 | 7 | 4 | 24 | 4.8 | 9.86 |
Li6 | 6 | 3 | 3 | 31.995 | 5.33 | 9 | 9 | 9 | 5 | 30 | 5 | 6.24 |
Li7 | 7 | 3 | 4 | 39.245 | 5.61 | 10 | 11 | 10 | 7 | 42 | 6 | −7.02 |
Be8 | 8 | 4 | 4 | 56.5 | 7.06 | 12 | 12 | 12 | 9 | 54 | 6.75 | 4.42 |
Be9 | 9 | 4 | 5 | 58.165 | 6.46 | 13 | 14 | 13 | 10 | 60 | 6.667 | −3.15 |
B10 | 10 | 5 | 5 | 64.751 | 6.48 | 15 | 15 | 15 | 11 | 66 | 6.6 | −1.93 |
B11 | 11 | 5 | 6 | 76.205 | 6.93 | 16 | 17 | 16 | 13 | 78 | 7.091 | −2.36 |
C12 | 12 | 6 | 6 | 92.162 | 7.68 | 18 | 18 | 18 | 15 | 90 | 7.5 | 2.35 |
C13 | 13 | 6 | 7 | 97.108 | 7.47 | 19 | 20 | 19 | 16 | 96 | 7.385 | 1.14 |
N14 | 14 | 7 | 7 | 104.659 | 7.48 | 21 | 21 | 21 | 17 | 102 | 7.286 | 2.54 |
N15 | 15 | 7 | 8 | 115.492 | 7.7 | 22 | 23 | 22 | 19 | 114 | 7.6 | 1.29 |
O16 | 16 | 8 | 8 | 127.619 | 7.98 | 24 | 24 | 24 | 21 | 126 | 7.875 | 1.27 |
O17 | 17 | 8 | 9 | 131.762 | 7.75 | 25 | 26 | 25 | 22 | 132 | 7.765 | −0.18 |
O18 | 18 | 8 | 10 | 139.808 | 7.77 | 26 | 28 | 26 | 23 | 138 | 7.667 | 1.29 |
F19 | 19 | 9 | 10 | 147.801 | 7.78 | 28 | 29 | 28 | 25 | 150 | 7.895 | −1.49 |
Ne20 | 20 | 10 | 10 | 160.65 | 8.03 | 30 | 30 | 30 | 27 | 162 | 8.1 | −0.84 |
Ne21 | 21 | 10 | 11 | 167.406 | 7.97 | 31 | 32 | 31 | 28 | 168 | 8 | −0.35 |
Ne22 | 22 | 10 | 12 | 177.77 | 8.08 | 32 | 34 | 32 | 29 | 174 | 7.909 | 2.12 |
Na23 | 23 | 11 | 12 | 186.564 | 8.11 | 34 | 35 | 34 | 31 | 186 | 8.087 | 0.3 |
Mg24 | 24 | 12 | 12 | 198.257 | 8.26 | 36 | 36 | 36 | 33 | 198 | 8.25 | 0.13 |
Mg25 | 25 | 12 | 13 | 205.587 | 8.22 | 37 | 38 | 37 | 34 | 204 | 8.16 | 0.77 |
Mg26 | 26 | 12 | 14 | 216.681 | 8.33 | 38 | 40 | 38 | 35 | 210 | 8.077 | 3.08 |
Al27 | 27 | 13 | 14 | 224.952 | 8.33 | 40 | 41 | 40 | 37 | 222 | 8.222 | 1.31 |
Si28 | 28 | 14 | 14 | 236.537 | 8.45 | 42 | 42 | 42 | 39 | 234 | 8.357 | 1.07 |
Si29 | 29 | 14 | 15 | 245.01 | 8.45 | 43 | 44 | 43 | 40 | 240 | 8.276 | 2.04 |
Si30 | 30 | 14 | 16 | 255.62 | 8.52 | 44 | 46 | 44 | 41 | 246 | 8.2 | 3.76 |
P31 | 31 | 15 | 16 | 262.917 | 8.48 | 46 | 47 | 46 | 43 | 258 | 8.323 | 1.87 |
S32 | 32 | 16 | 16 | 271.78 | 8.49 | 48 | 48 | 48 | 45 | 270 | 8.438 | 0.65 |
S33 | 33 | 16 | 17 | 280.422 | 8.5 | 49 | 50 | 49 | 46 | 276 | 8.364 | 1.58 |
S34 | 34 | 16 | 18 | 291.839 | 8.58 | 50 | 52 | 50 | 47 | 282 | 8.294 | 3.37 |
Cl35 | 35 | 17 | 18 | 298.21 | 8.52 | 52 | 53 | 52 | 49 | 294 | 8.4 | 1.41 |
S36 | 36 | 16 | 20 | 308.71 | 8.58 | 52 | 56 | 52 | 49 | 294 | 8.167 | 4.76 |
Ar36 | 36 | 18 | 18 | 306.716 | 8.52 | 54 | 54 | 54 | 51 | 306 | 8.5 | 0.23 |
Cl37 | 37 | 17 | 20 | 318.784 | 8.62 | 54 | 57 | 54 | 51 | 306 | 8.27 | 4.01 |
Ar38 | 38 | 18 | 20 | 327.343 | 8.61 | 56 | 58 | 56 | 53 | 318 | 8.368 | 2.85 |
K39 | 39 | 19 | 20 | 333.724 | 8.56 | 58 | 59 | 58 | 55 | 330 | 8.462 | 1.12 |
Ar40 | 40 | 18 | 22 | 343.81 | 8.6 | 58 | 62 | 58 | 55 | 330 | 8.25 | 4.02 |
Ca40 | 40 | 20 | 20 | 342.053 | 8.55 | 60 | 60 | 60 | 57 | 342 | 8.55 | 0.02 |
K41 | 41 | 19 | 22 | 351.619 | 8.58 | 60 | 63 | 60 | 57 | 342 | 8.341 | 2.74 |
Ca42 | 42 | 20 | 22 | 361.895 | 8.62 | 62 | 64 | 62 | 59 | 354 | 8.429 | 2.18 |
Ca43 | 43 | 20 | 23 | 369.828 | 8.6 | 63 | 66 | 63 | 60 | 360 | 8.372 | 2.66 |
Ca44 | 44 | 20 | 24 | 380.96 | 8.66 | 64 | 68 | 64 | 61 | 366 | 8.318 | 3.93 |
Sc45 | 45 | 21 | 24 | 387.849 | 8.62 | 66 | 69 | 66 | 63 | 378 | 8.4 | 2.54 |
Ca46 | 46 | 20 | 26 | 398.772 | 8.67 | 66 | 72 | 66 | 63 | 378 | 8.217 | 5.21 |
Ti46 | 46 | 22 | 24 | 398.194 | 8.66 | 68 | 70 | 68 | 65 | 390 | 8.478 | 2.06 |
Ti47 | 47 | 22 | 25 | 407.072 | 8.66 | 69 | 72 | 69 | 66 | 396 | 8.426 | 2.72 |
Ca48 | 48 | 20 | 28 | 415.992 | 8.67 | 68 | 76 | 68 | 65 | 390 | 8.125 | 6.25 |
Ti48 | 48 | 22 | 26 | 418.699 | 8.72 | 70 | 74 | 70 | 67 | 402 | 8.375 | 3.99 |
Ti49 | 49 | 22 | 27 | 426.841 | 8.71 | 71 | 76 | 71 | 68 | 408 | 8.327 | 4.41 |
Ti50 | 50 | 22 | 28 | 437.78 | 8.76 | 72 | 78 | 72 | 69 | 414 | 8.28 | 5.43 |
Cr50 | 50 | 24 | 26 | 435.047 | 8.7 | 74 | 76 | 74 | 71 | 426 | 8.52 | 2.08 |
V51 | 51 | 23 | 28 | 445.842 | 8.74 | 74 | 79 | 74 | 71 | 426 | 8.353 | 4.45 |
Cr52 | 52 | 24 | 28 | 456.345 | 8.78 | 76 | 80 | 76 | 73 | 438 | 8.423 | 4.02 |
Cr53 | 53 | 24 | 29 | 464.287 | 8.76 | 77 | 82 | 77 | 74 | 444 | 8.377 | 4.37 |
Cr54 | 54 | 24 | 30 | 474.009 | 8.78 | 78 | 84 | 78 | 75 | 450 | 8.333 | 5.07 |
Fe54 | 54 | 26 | 28 | 471.765 | 8.74 | 80 | 82 | 80 | 77 | 462 | 8.556 | 2.07 |
Mn55 | 55 | 25 | 30 | 482.075 | 8.77 | 80 | 85 | 80 | 77 | 462 | 8.4 | 4.16 |
Fe56 | 56 | 26 | 30 | 492.257 | 8.79 | 82 | 86 | 82 | 79 | 474 | 8.464 | 3.71 |
Fe57 | 57 | 26 | 31 | 499.905 | 8.77 | 83 | 88 | 83 | 80 | 480 | 8.421 | 3.98 |
Fe58 | 58 | 26 | 32 | 509.945 | 8.79 | 84 | 90 | 84 | 81 | 486 | 8.379 | 4.7 |
Ni58 | 58 | 28 | 30 | 506.456 | 8.73 | 86 | 88 | 86 | 83 | 498 | 8.586 | 1.67 |
Co59 | 59 | 27 | 32 | 517.314 | 8.77 | 86 | 91 | 86 | 83 | 498 | 8.441 | 3.73 |
Ni60 | 60 | 28 | 32 | 526.842 | 8.78 | 88 | 92 | 88 | 85 | 510 | 8.5 | 3.2 |
Zn70 | 70 | 30 | 40 | 611.08 | 8.73 | 100 | 110 | 100 | 97 | 582 | 8.314 | 4.76 |
Ge70 | 70 | 32 | 38 | 610.519 | 8.72 | 102 | 108 | 102 | 99 | 594 | 8.486 | 2.71 |
Se80 | 80 | 34 | 46 | 696.867 | 8.71 | 114 | 126 | 114 | 111 | 666 | 8.325 | 4.43 |
Kr80 | 80 | 36 | 44 | 695.438 | 8.69 | 116 | 124 | 116 | 113 | 678 | 8.475 | 2.51 |
Zr90 | 90 | 40 | 50 | 783.895 | 8.71 | 130 | 140 | 130 | 127 | 762 | 8.467 | 2.79 |
Ru100 | 100 | 44 | 56 | 861.929 | 8.62 | 144 | 156 | 144 | 141 | 846 | 8.46 | 1.85 |
Cd113 | 113 | 48 | 65 | 963.557 | 8.53 | 161 | 178 | 161 | 158 | 948 | 8.389 | 1.61 |
In113 | 113 | 49 | 64 | 963.091 | 8.52 | 162 | 177 | 162 | 159 | 954 | 8.442 | 0.94 |
Sn117 | 117 | 50 | 67 | 995.623 | 8.51 | 167 | 184 | 167 | 164 | 984 | 8.41 | 1.17 |
Xe129 | 129 | 54 | 75 | 1087.648 | 8.43 | 183 | 204 | 183 | 180 | 1080 | 8.372 | 0.7 |
Ce142 | 142 | 58 | 84 | 1185.28 | 8.35 | 200 | 226 | 200 | 197 | 1182 | 8.324 | 0.28 |
Nd142 | 142 | 60 | 82 | 1185.148 | 8.35 | 202 | 224 | 202 | 199 | 1194 | 8.408 | −0.75 |
Sm150 | 150 | 62 | 88 | 1239.253 | 8.26 | 212 | 238 | 212 | 209 | 1254 | 8.36 | −1.19 |
Gd150 | 150 | 64 | 86 | 1236.39 | 8.24 | 214 | 236 | 214 | 211 | 1266 | 8.44 | −2.39 |
Dy162 | 162 | 66 | 96 | 1323.884 | 8.17 | 228 | 258 | 228 | 225 | 1350 | 8.333 | −1.97 |
Yb172 | 172 | 70 | 102 | 1392.764 | 8.1 | 242 | 274 | 242 | 239 | 1434 | 8.337 | −2.96 |
W183 | 183 | 74 | 109 | 1465.526 | 8.01 | 257 | 292 | 257 | 254 | 1524 | 8.328 | −3.99 |
Pt194 | 194 | 78 | 116 | 1539.578 | 7.94 | 272 | 310 | 272 | 269 | 1614 | 8.32 | −4.83 |
Au197 | 197 | 79 | 118 | 1559.397 | 7.92 | 276 | 315 | 276 | 273 | 1638 | 8.315 | −5.04 |
Hg200 | 200 | 80 | 120 | 1581.207 | 7.91 | 280 | 320 | 280 | 277 | 1662 | 8.31 | −5.11 |
Hg204 | 204 | 80 | 124 | 1608.65 | 7.89 | 284 | 328 | 284 | 281 | 1686 | 8.265 | −4.81 |
Pb204 | 204 | 82 | 122 | 1605.343 | 7.87 | 286 | 326 | 286 | 283 | 1698 | 8.324 | −5.77 |
A representative sample of nuclides, showing quantum-allowed bonded up-to-down quark pairs for each nuclide.
As before for this simple calculation, the calculated binding energy is the number of bonds times a fixed energy per bond. The energy per bond is the only selected parameter; for this simple calculation, it is 6.000 MeV per bond. These plots take into consideration the quantum rules of hard-core repulsion and zero electric dipole moment. These data are plotted in Figures 6 and 7. In Figure 6, a representative sample of all of the stable nuclides is shown, out to lead 204Pb. In Figure 7, only the first 60 nuclides are plotted, to show the detail. As before, when there is more than one stable nuclide for a given mass number, these additional points are plotted as well.
A plot of the experimental nuclear binding energy per nucleon (blue) and the simple quantum calculated binding energy (orange).
A plot of the experimental nuclear binding energy per nucleon (blue) and the simple quantum calculated binding energy (orange) for only the first 60 nuclides.
To reiterate, this is a very quick and easy calculation, only involving a simple numerical count of quantum-allowed internucleon up-to-down quark pairs. This calculation does not specify the arrangement of the nucleons or the mechanism of the bond. It is simply a count of the quantum-allowed up-to-down quark bonds. Other than being quantum, this calculation is theory independent, and as such, it is not subject to theoretical criticisms or theoretical differences of opinion.
The excellent reproduction of the experimental data for these calculated results is impressive, especially considering that there is only one empirically-selected variable for this calculation, the value of 6.000 MeV for the bond energy, instead of the five empirically-selected variables for the Weizsäcker formula. This reproduction of the experimental data is especially impressive considering that other currently accepted nuclear theories cannot easily duplicate this curve.
In terms of the possible mechanism for the bond, the residual chromodynamic force between the color charges for internucleon quark-to-quark bonding is one possibility. Another possibility for this bond becomes apparent when it is recalled that the up quark has an electric charge +2/3 the charge of a proton, the down quark has an electric charge of −1/3 the charge of a proton, and both quarks carry a magnetic moment. These electromagnetic properties of the up and down quarks create a strong attractive electromagnetic force between the up and the down quarks; the strength of this electromagnetic force is dependent only on the minimum proximity between the up and down quarks engaged in the bond. Historically, it was believed that the strength of the electromagnetic force had an upper limit, based on the misconceptions that protons were homogeneously charged and that quarks did not exist. However, these misconceived notions are invalid when quarks, which contain all of the electric charge for the nucleons, are taken into consideration.
The internuclear quark-to-quark bond is most likely some combination of both the electromagnetic charge and the color charge of the quarks, but the relative percentages of these two contributions is not postulated here. Regardless of the relative percentages, the electromagnetic component of this bond should not be ignored--as is usually the case in current theories. When any internucleon quark-to-quark bond is considered, the electromagnetic component must be taken into full account, rather than being considered relatively unimportant. A more detailed analysis of the electromagnetic contribution of this internucleon up-to-down quark bonding can easily be made by using the standard electromagnetic Eqs. A detailed analysis would include the addition of the energy due to all electric charges interacting with each other. In other words, this would be a double summation of the interaction for each electric charge of each quark with every other electric charge on all other quarks [15]. This double summation calculation would inherently include the Coulomb energy of the net repulsive electric energies among the protons.
Similarly, a more detailed electromagnetic analysis would also include the variation of the electromagnetic bond due to the vector orientation of the magnetic moments of the quarks. The energy of the magnetic moments interacting with each other should be included, which again would be a double summation for the magnetic interaction for all of the magnetic moment vectors [16]. Finally, the kinetic energy of the quantum spin of the nuclide should also be included in this more detailed binding energy calculation [17, 18]. However, for this more detailed and accurate calculation to be done, the lowest energy configuration of the nuclide must be determined and specified before the electromagnetic interaction energies can be accurately calculated.
An extremely simple calculation of the internucleon up-to-down quark bonding has been made, giving excellent results in duplicating the nuclear binding energy curve, using only one parameter rather than five. The resulting errors for nuclides going up to lead 204Pb are only few percent. The average error, going from A = 10 to A = 60, is only 2.32% with a standard deviation for that error of only 1.91%. Also, due to the inherent similarities of this concept to the currently accepted residual chromodynamic force model, with its quark-to-quark internucleon bonding, the existence of an internucleon up-to-down quark bond cannot be relegated as implausible.
An obvious implication of these results is that a significant part of the nuclear force is electromagnetic. To some, this may be an unexpected implication, but not unfeasible, especially when the electromagnetic attraction of the up-to-down quarks is considered. If one only considers, as is the case historically, that homogenously charged protons cannot bond to other homogeneously charged protons, then the concept that the nuclear force could be partially electromagnetic is deemed implausible. However, with the understanding that the electrical charges of the up and down quarks are able to attract each other and bond to each other, and given that the RCDF allows a quark-to-quark internucleon bond to occur, such restrictions about the nuclear force being partly electromagnetic are no longer relevant.
The excellent reproduction of experimental binding energy data with only one empirically-selected variable strongly suggests that the internucleon up-to-down quark bonding is a concept that should be seriously considered and more thoroughly examined by nuclear physicists.
The nuclear force is defined as the force which binds the protons and neutrons together within a nucleus. One of the currently accepted models of the nuclear force is the liquid drop model [1]. This model of the nuclear force uses the Weizsäcker formula to predict the binding energies of nuclides. The Weizsäcker formula is a curve-fitting formula that uses five parameters, plus one conditional logic statement, in order to achieve its results [2]. These parameters are selected to empirically curve-fit an equation to match the experimental data. The liquid drop model is considered to be a “semi-classical” model of the nuclear force, rather than a quantum model [3].
Another currently accepted model of the nuclear force is the shell model, which uses magic numbers to explain certain nuclear behavior. The nuclear shell model is similar to the electronic shell model, which describes the electrons orbiting around an atom. However, the nuclear shell model does not predict the nuclear binding energy, rather the shell model defers back to the Weizsäcker formula for binding energy calculations.
A third currently accepted model of the nuclear force is the residual chromo-dynamic force (RCDF) model, also known as the residual strong force model. Before describing this residual chromodynamic force, it is useful to mention a few specifics about quantum chromodynamics (QCD). Quantum chromodynamics postulates that the three valance quarks of protons and neutrons possess an attribute called “color charge.” Historically, a contradiction of the quantum mechanical basis of nucleon properties with the Pauli Exclusion Principle led to the concept of the color charge for quarks [4]. The color charges of the quarks are considered to be either red, green, or blue. The words red, green, and blue are simply the names of the color charges and do not imply any type of physically visual hue for the quarks. Also, the term “charge”, when referring specifically to the color charge, is not related to electric charge, which unfortunately can often be a point of confusion. Quantum chromodynamics states that a very strong bond is formed among the three color charges of the quarks inside the nucleon [5]. Both protons and neutrons have all three colors inside the nucleon.
The residual chromodynamic force model assumes that the chromodynamic force also has a weaker
An illustrative representation showing both the chromodynamic force and the residual chromodynamic force.
In Figure 1, the bold black line represents the chromodynamic force inside the nucleon, and the dotted gray line represents the residual chromodynamic force between two nucleons. (Note that quarks are considered to be point-like particles. Thus this drawing is not meant to be a scaled representation of the quarks, rather it is meant for illustrative purposes only.) The residual chromodynamic bond can be between any two quarks of different colors, such as between a red and blue, a green and red, or a blue and green. The residual chromodynamic bond can be between a neutron and a neutron, a proton and a neutron, or a proton and another proton.
While the RCDF model is considered to be the mechanism for nuclear bonding, the model is unable to duplicate the experimental binding energy curve. This inability of the RCDF model to reproduce this nuclear behavior is currently attributed to the extreme difficulty of modeling the multi-body interactions of the three color charges [6, 7]. This difficulty with the derivation of the nuclear binding forces from the residual chromodynamic force model is two-fold. First, each nucleon consists of three quarks, which means that a system of two nucleons is already a six-body problem. Second, because the chromodynamic force between quarks inside the nucleons has the feature of being very strong compared to the residual chromodynamic force outside the nucleons, this disproportionate ratio of strength makes a converging solution for the complicated mathematical calculations difficult to find. For nuclides with a small number of nucleons, the problem can be solved with brute-force computing power by putting each of the quarks into a four-dimensional lattice of discrete points: three dimensions of space and one of time. This method is known as lattice quantum chromodynamics, or lattice QCD. This brute-force method for the computer calculations in lattice QCD iterates the position of each quark by assigning an x, y, z, and t position to it, calculating the resulting forces on each quark, allowing their position to change as a result of these forces, and then iterating this procedure until a resulting converging solution is found. If a converging solution is found, then these calculations are able to determine the binding energy of the nuclide in question. These computer calculations are done through extremely complex mathematical models, often using Monte-Carlo simulations [8]. Because of these computational difficulties, modeling the binding energies of only the smallest nuclides has been achieved.
However, such calculations are computationally expensive, requiring very large computers. Because of these complications, this modeling method is not normally used as a standard nuclear physics tool [7] .Thus, the RCDF model remains largely unverified when testing its binding energy predictions against experimental data.
Besides having the attribute of color charge, there is also another attribute of quarks called flavor. From QCD theory, we know there are six different flavors of quarks: up, down, strange, charm, top, and bottom. Of these six different flavors, only two flavors are found in the stable matter of neutrons and protons: the up and down quarks [9]. (The terms of up and down do not imply any specific orientation with regard to spatial direction, and are simply the names of these types of quarks).
An up quark has an electric charge that is +2/3 the charge of a proton, and it also contains a positive magnetic moment. The up quark has a spin of ½ and a mass of about 0.3% of the proton. The color of an up quark can be either red, green, or blue. A down quark has an electric charge that is −1/3 the charge of a proton, and it contains a negative magnetic moment, which is anti-parallel to of the spin of the nuclide. The down quark has a spin of ½, and a mass of about 0.6% of the proton. The color of a down quark can be either red, green, or blue.
The magnetic moments of an up quark is estimated to be +1.85 and the magnetic moments of a down quark is estimated to be −0.97, both in units of nuclear magnetons. The electric charges of the proton and neutron are completely contained within the quarks. The proton is comprised of two up quarks and one down quark, giving it a net charge of one (2/3 + 2/3 -1/3 = 1). The neutron is comprised of one up quark and two down quarks, giving it a net charge of zero (2/3 -1/3 -1/3 = 0). Figure 2 illustrates these properties.
An illustrative representation of the up and down quarks in a proton and neutron.
The quarks inside of a proton and neutron have both attributes of flavor (up or down) and color (red, green, or blue). Thus, each quark inside of a proton or neutron is one of six types: up and red, up and green, up and blue, down and red, down and green, or down and blue [5]. Since both the neutron and the proton contain all three different colors, there is no difference between the proton and the neutron with regard to the attribute of color charges. The only difference in the quark characteristics between a proton or a neutron resides in the number of up and down quarks. Therefore, any bond between the different colors is also inherently a bond between some combination of the up and down quarks. Hence, the quantum assumptions that are made in the RCDF model about the possibility of an internucleon bond between the residual colors of quarks are also inherently applicable to the formation of an internucleon bond between up and down quarks.
Figure 3 shows three possible bonds, all of which are allowed in the RCDF model: a bond between two up quarks, between two down quarks, and between an up and a down quark. In the RCDF model, as long as the bond is between different colors of quarks, the up or down flavor of the quarks, is considered relatively unimportant.
Possible bonds in the RCDF model. A bond can be formed regardless of the flavor (up or down) of the quark.
Although it is considered relatively unimportant in the RCDF model, the up or down flavor of the quarks does indeed cause an energy difference among the three types of bonds that are illustrated in Figure 3. If there is an internucleon bond between two up quarks or between two down quarks, then the intrinsic electro-magnetic force between these quarks is repulsive. Conversely, if there is an internucleon bond between an up quark and a down quark, then the intrinsic electromagnetic force between these quarks is attractive. Among the three types of bonds shown in Figure 3, this inherent difference in the electromagnetic energy may cause the two repulsive bonds to be less probable or less stable, producing a situation in which the up-to-down quark bond would be more prevalent in stable matter.
As mentioned previously, the color charges of the quarks contained within a nucleon do not inherently distinguish between a neutron or proton; it is only the up and down attribute of the quarks that distinguish between the two types of stable nucleons. Thus, an examination of an internucleon bond being formed only between an up and a down quark is an appropriate possibility to explore. Specifically, this additional constraint is that not only must the internucleon quark-to-quark bond be between different colors, but also it must be between only an up and a down quark; specifically, it cannot be between two up quarks or two down quarks. If this quite reasonable constraint is made to the RCDF model, a quick calculation of the allowed bonds can be easily made. By using the currently accepted RCDF concept of the internucleon quark-to-quark bond, and applying this additional constraint, in which bonds are only formed between up and down quarks, an interesting and potentially significant set of data emerges.
For any given nuclide, the number of internucleon up-to-down quark pairs can be determined, based on how many up and down quarks each nuclide has. This calculation, as shown in Eq. (1), is made for each nuclide.
For simplicity of this very quick and easy calculation, it is assumed that every bonded pair of up-to-down quarks has the same bonding energy. Thus, just for this simple calculation, the equation for the calculated binding energy (CBE) of a non-quantum nuclide is the number of internucleon up-to-down quark pairs times the binding energy per pair, as shown in Eq. (2).
For a representative sample of stable nuclides, this information is also shown in Table 1. For values of mass number with two stable nuclides, such as A = 40, both stable nuclides are shown. The following information is listed:
The nuclide name
The number of nucleons, A
The number of protons, Z
The number of neutrons, N
The experimental binding energy (EBE) in units of MeV, as obtained from the nuclear tables in Ref. [10].
The experimental binding energy per nucleon (EBE/A)
The number of up quarks in the nuclide
The number of down quarks in the nuclide
The number or possible pairs between up and down quarks for the nuclide
The classical (non-quantum) calculated binding energy (CBE) in MeV of the nuclide, for a fixed energy (6.000 MeV) per bond.
Nuclide | A | Z | N | EBE in MeV | EBE/A | # Of up quarks | # Of down quarks | # Of updown bonds, classical | Classical CBE/A |
---|---|---|---|---|---|---|---|---|---|
H2 | 2 | 1 | 1 | 2.225 | 1.11 | 3 | 3 | 3 | 9 |
He3 | 3 | 2 | 1 | 7.718 | 2.57 | 5 | 4 | 4 | 8 |
He4 | 4 | 2 | 2 | 28.296 | 7.07 | 6 | 6 | 6 | 9 |
He5 | 5 | 2 | 3 | 26.626 | 5.33 | 7 | 8 | 7 | 8.4 |
Li6 | 6 | 3 | 3 | 31.995 | 5.33 | 9 | 9 | 9 | 9 |
Li7 | 7 | 3 | 4 | 39.245 | 5.61 | 10 | 11 | 10 | 8.571 |
Be8 | 8 | 4 | 4 | 56.5 | 7.06 | 12 | 12 | 12 | 9 |
Be9 | 9 | 4 | 5 | 58.165 | 6.46 | 13 | 14 | 13 | 8.667 |
B10 | 10 | 5 | 5 | 64.751 | 6.48 | 15 | 15 | 15 | 9 |
B11 | 11 | 5 | 6 | 76.205 | 6.93 | 16 | 17 | 16 | 8.727 |
C12 | 12 | 6 | 6 | 92.162 | 7.68 | 18 | 18 | 18 | 9 |
C13 | 13 | 6 | 7 | 97.108 | 7.47 | 19 | 20 | 19 | 8.769 |
N14 | 14 | 7 | 7 | 104.659 | 7.48 | 21 | 21 | 21 | 9 |
N15 | 15 | 7 | 8 | 115.492 | 7.7 | 22 | 23 | 22 | 8.8 |
O16 | 16 | 8 | 8 | 127.619 | 7.98 | 24 | 24 | 24 | 9 |
O17 | 17 | 8 | 9 | 131.762 | 7.75 | 25 | 26 | 25 | 8.824 |
O18 | 18 | 8 | 10 | 139.808 | 7.77 | 26 | 28 | 26 | 8.667 |
F19 | 19 | 9 | 10 | 147.801 | 7.78 | 28 | 29 | 28 | 8.842 |
Ne20 | 20 | 10 | 10 | 160.65 | 8.03 | 30 | 30 | 30 | 9 |
Ne21 | 21 | 10 | 11 | 167.406 | 7.97 | 31 | 32 | 31 | 8.857 |
Ne22 | 22 | 10 | 12 | 177.77 | 8.08 | 32 | 34 | 32 | 8.727 |
Na23 | 23 | 11 | 12 | 186.564 | 8.11 | 34 | 35 | 34 | 8.87 |
Mg24 | 24 | 12 | 12 | 198.257 | 8.26 | 36 | 36 | 36 | 9 |
Mg25 | 25 | 12 | 13 | 205.587 | 8.22 | 37 | 38 | 37 | 8.88 |
Mg26 | 26 | 12 | 14 | 216.681 | 8.33 | 38 | 40 | 38 | 8.769 |
Al27 | 27 | 13 | 14 | 224.952 | 8.33 | 40 | 41 | 40 | 8.889 |
Si28 | 28 | 14 | 14 | 236.537 | 8.45 | 42 | 42 | 42 | 9 |
Si29 | 29 | 14 | 15 | 245.01 | 8.45 | 43 | 44 | 43 | 8.897 |
Si30 | 30 | 14 | 16 | 255.62 | 8.52 | 44 | 46 | 44 | 8.8 |
P31 | 31 | 15 | 16 | 262.917 | 8.48 | 46 | 47 | 46 | 8.903 |
S32 | 32 | 16 | 16 | 271.78 | 8.49 | 48 | 48 | 48 | 9 |
S33 | 33 | 16 | 17 | 280.422 | 8.5 | 49 | 50 | 49 | 8.909 |
S34 | 34 | 16 | 18 | 291.839 | 8.58 | 50 | 52 | 50 | 8.824 |
Cl35 | 35 | 17 | 18 | 298.21 | 8.52 | 52 | 53 | 52 | 8.914 |
S36 | 36 | 16 | 20 | 308.71 | 8.58 | 52 | 56 | 52 | 8.667 |
Ar36 | 36 | 18 | 18 | 306.716 | 8.52 | 54 | 54 | 54 | 9 |
Cl37 | 37 | 17 | 20 | 318.784 | 8.62 | 54 | 57 | 54 | 8.757 |
Ar38 | 38 | 18 | 20 | 327.343 | 8.61 | 56 | 58 | 56 | 8.842 |
K39 | 39 | 19 | 20 | 333.724 | 8.56 | 58 | 59 | 58 | 8.923 |
Ar40 | 40 | 18 | 22 | 343.81 | 8.6 | 58 | 62 | 58 | 8.7 |
Ca40 | 40 | 20 | 20 | 342.053 | 8.55 | 60 | 60 | 60 | 9 |
K41 | 41 | 19 | 22 | 351.619 | 8.58 | 60 | 63 | 60 | 8.78 |
Ca42 | 42 | 20 | 22 | 361.895 | 8.62 | 62 | 64 | 62 | 8.857 |
Ca43 | 43 | 20 | 23 | 369.828 | 8.6 | 63 | 66 | 63 | 8.791 |
Ca44 | 44 | 20 | 24 | 380.96 | 8.66 | 64 | 68 | 64 | 8.727 |
Sc45 | 45 | 21 | 24 | 387.849 | 8.62 | 66 | 69 | 66 | 8.8 |
Ca46 | 46 | 20 | 26 | 398.772 | 8.67 | 66 | 72 | 66 | 8.609 |
Ti46 | 46 | 22 | 24 | 398.194 | 8.66 | 68 | 70 | 68 | 8.87 |
Ti47 | 47 | 22 | 25 | 407.072 | 8.66 | 69 | 72 | 69 | 8.809 |
Ca48 | 48 | 20 | 28 | 415.992 | 8.67 | 68 | 76 | 68 | 8.5 |
Ti48 | 48 | 22 | 26 | 418.699 | 8.72 | 70 | 74 | 70 | 8.75 |
Ti49 | 49 | 22 | 27 | 426.841 | 8.71 | 71 | 76 | 71 | 8.694 |
Ti50 | 50 | 22 | 28 | 437.78 | 8.76 | 72 | 78 | 72 | 8.64 |
Cr50 | 50 | 24 | 26 | 435.047 | 8.7 | 74 | 76 | 74 | 8.88 |
V51 | 51 | 23 | 28 | 445.842 | 8.74 | 74 | 79 | 74 | 8.706 |
Cr52 | 52 | 24 | 28 | 456.345 | 8.78 | 76 | 80 | 76 | 8.769 |
Cr53 | 53 | 24 | 29 | 464.287 | 8.76 | 77 | 82 | 77 | 8.717 |
Cr54 | 54 | 24 | 30 | 474.009 | 8.78 | 78 | 84 | 78 | 8.667 |
Fe54 | 54 | 26 | 28 | 471.765 | 8.74 | 80 | 82 | 80 | 8.889 |
Mn55 | 55 | 25 | 30 | 482.075 | 8.77 | 80 | 85 | 80 | 8.727 |
Fe56 | 56 | 26 | 30 | 492.257 | 8.79 | 82 | 86 | 82 | 8.786 |
Fe57 | 57 | 26 | 31 | 499.905 | 8.77 | 83 | 88 | 83 | 8.737 |
Fe58 | 58 | 26 | 32 | 509.945 | 8.79 | 84 | 90 | 84 | 8.69 |
Ni58 | 58 | 28 | 30 | 506.456 | 8.73 | 86 | 88 | 86 | 8.897 |
Co59 | 59 | 27 | 32 | 517.314 | 8.77 | 86 | 91 | 86 | 8.746 |
Ni60 | 60 | 28 | 32 | 526.842 | 8.78 | 88 | 92 | 88 | 8.8 |
Zn70 | 70 | 30 | 40 | 611.08 | 8.73 | 100 | 110 | 100 | 8.571 |
Ge70 | 70 | 32 | 38 | 610.519 | 8.72 | 102 | 108 | 102 | 8.743 |
Se80 | 80 | 34 | 46 | 696.867 | 8.71 | 114 | 126 | 114 | 8.55 |
Kr80 | 80 | 36 | 44 | 695.438 | 8.69 | 116 | 124 | 116 | 8.7 |
Zr90 | 90 | 40 | 50 | 783.895 | 8.71 | 130 | 140 | 130 | 8.667 |
Ru100 | 100 | 44 | 56 | 861.929 | 8.62 | 144 | 156 | 144 | 8.64 |
Cd113 | 113 | 48 | 65 | 963.557 | 8.53 | 161 | 178 | 161 | 8.549 |
In113 | 113 | 49 | 64 | 963.091 | 8.52 | 162 | 177 | 162 | 8.602 |
Sn117 | 117 | 50 | 67 | 995.623 | 8.51 | 167 | 184 | 167 | 8.564 |
Xe129 | 129 | 54 | 75 | 1087.648 | 8.43 | 183 | 204 | 183 | 8.512 |
Ce142 | 142 | 58 | 84 | 1185.28 | 8.35 | 200 | 226 | 200 | 8.451 |
Nd142 | 142 | 60 | 82 | 1185.148 | 8.35 | 202 | 224 | 202 | 8.535 |
Sm150 | 150 | 62 | 88 | 1239.253 | 8.26 | 212 | 238 | 212 | 8.48 |
Gd150 | 150 | 64 | 86 | 1236.39 | 8.24 | 214 | 236 | 214 | 8.56 |
Dy162 | 162 | 66 | 96 | 1323.884 | 8.17 | 228 | 258 | 228 | 8.444 |
Yb172 | 172 | 70 | 102 | 1392.764 | 8.1 | 242 | 274 | 242 | 8.442 |
W183 | 183 | 74 | 109 | 1465.526 | 8.01 | 257 | 292 | 257 | 8.426 |
Pt194 | 194 | 78 | 116 | 1539.578 | 7.94 | 272 | 310 | 272 | 8.412 |
Au197 | 197 | 79 | 118 | 1559.397 | 7.92 | 276 | 315 | 276 | 8.406 |
Hg200 | 200 | 80 | 120 | 1581.207 | 7.91 | 280 | 320 | 280 | 8.4 |
Hg204 | 204 | 80 | 124 | 1608.65 | 7.89 | 284 | 328 | 284 | 8.353 |
Pb204 | 204 | 82 | 122 | 1605.343 | 7.87 | 286 | 326 | 286 | 8.412 |
A, Z, N, EBE, EBE/a, # up quarks, # down quarks, # possible bonds, and non-quantum calculated binding energy (classical CBE) for a representative sample of nuclides.
Figure 4 is a plot for this same a representative sample of nuclides, showing both the experimental binding energy per nucleon (EBE/A) and the non-quantum calculated binding energy per nucleon (CBE/A) for an object with a fixed energy (6.000 MeV) per bond. For this quick calculation, neither the type of bond nor the structure of these bonds comes into consideration. Simply stated, this is a theory-independent calculation of the number of possible bonded pairs times a fixed binding energy per bonded pair.
In blue, a plot of the experimental binding energy (EBE) per nucleon. In orange, a plot of the calculated binding energy (CBE) per nucleon, based on the number of possible non-quantum up-to-down quark pairs and a fixed binding energy per bonded pair.
A nucleus is a quantum object, and being so, certain quantum rules must apply. A known phenomenological feature of the nuclear force is the QCD hard-core repulsion. The hard-core repulsion states that nucleons, such as a proton or neutron, cannot overlap in their spatial location [11, 12]. If too many bonds are formed for either 2H or 3H or 3He, overlap will occur. This overlap is illustrated in Figure 5.
An illustration of the overlapping nucleons if too many bonds are attempted. For the nuclide 2H, if two or three bonds are attempted, indicated by the red bonds, an overlap occurs. Similarly, 3He can form only three bonds. If four or five are attempted, an overlap occurs in three dimensions.
To prevent this overlap, hydrogen 2H can have only one bond instead of two or three. Similarly, helium 3He (as well as hydrogen 3H) can have only three bonds instead of four or five. Three other nuclides are subject to this constraint, those with odd-odd configurations: 6Li, 10B, and 14N. Specifically, the odd neutron and the odd proton cannot bond twice to either each other or to another nucleon. Other stable nuclides are not affected by the application of this rule, since there are enough nucleons to prevent an overlap from occurring for the larger nuclides.
Quantum mechanics also states there can be no net electric dipole moment for the nuclide [13, 14]. For this second quantum rule, three more bonds must be subtracted from the number of bonds available, in order to remove the electric dipole moment. Without stating any specific configuration for the nuclide, this reduction of bonds can be best understood from the fact that the electric charge distribution of the nuclide must not have a net asymmetry in electrical charge for any of the three spatial dimensions, x, y, or z. To prevent an electric dipole moment, a bond is broken in each of these three dimensions, so that the net charge is symmetric about the x, y, and z axes. This quantum requirement removes three of the classically-allowed bonds. This rule applies to all stable nuclides, except for the three very smallest stable nuclides, 2H, 3He, and 4He.
The inclusion of these two quantum rules is shown in Table 2. The first 8 columns of Table 2 are similar to the first 8 columns of Table 1. Also shown in Table 2 is the number of possible quantum bonds for each nuclide, taking into consideration the two above mentioned quantum rules. The last three columns of Table 2 show the quantum calculated binding energy, the CBE/A, and the percent error of that calculated energy, as compared with the experimental binding energy.
Nuclide | A | Z | N | EBE in MeV | EBE/A | # Of up quarks | # Of down quarks | # Of updown bonds, classical | # Of updown bonds, quantum | Calculated binding energy (CBE) in MeV | CBE/A | %Error |
---|---|---|---|---|---|---|---|---|---|---|---|---|
H2 | 2 | 1 | 1 | 2.225 | 1.11 | 3 | 3 | 3 | 1 | 6 | 3 | −169.66 |
He3 | 3 | 2 | 1 | 7.718 | 2.57 | 5 | 4 | 4 | 3 | 18 | 6 | −133.22 |
He4 | 4 | 2 | 2 | 28.296 | 7.07 | 6 | 6 | 6 | 6 | 36 | 9 | −27.23 |
He5 | 5 | 2 | 3 | 26.626 | 5.33 | 7 | 8 | 7 | 4 | 24 | 4.8 | 9.86 |
Li6 | 6 | 3 | 3 | 31.995 | 5.33 | 9 | 9 | 9 | 5 | 30 | 5 | 6.24 |
Li7 | 7 | 3 | 4 | 39.245 | 5.61 | 10 | 11 | 10 | 7 | 42 | 6 | −7.02 |
Be8 | 8 | 4 | 4 | 56.5 | 7.06 | 12 | 12 | 12 | 9 | 54 | 6.75 | 4.42 |
Be9 | 9 | 4 | 5 | 58.165 | 6.46 | 13 | 14 | 13 | 10 | 60 | 6.667 | −3.15 |
B10 | 10 | 5 | 5 | 64.751 | 6.48 | 15 | 15 | 15 | 11 | 66 | 6.6 | −1.93 |
B11 | 11 | 5 | 6 | 76.205 | 6.93 | 16 | 17 | 16 | 13 | 78 | 7.091 | −2.36 |
C12 | 12 | 6 | 6 | 92.162 | 7.68 | 18 | 18 | 18 | 15 | 90 | 7.5 | 2.35 |
C13 | 13 | 6 | 7 | 97.108 | 7.47 | 19 | 20 | 19 | 16 | 96 | 7.385 | 1.14 |
N14 | 14 | 7 | 7 | 104.659 | 7.48 | 21 | 21 | 21 | 17 | 102 | 7.286 | 2.54 |
N15 | 15 | 7 | 8 | 115.492 | 7.7 | 22 | 23 | 22 | 19 | 114 | 7.6 | 1.29 |
O16 | 16 | 8 | 8 | 127.619 | 7.98 | 24 | 24 | 24 | 21 | 126 | 7.875 | 1.27 |
O17 | 17 | 8 | 9 | 131.762 | 7.75 | 25 | 26 | 25 | 22 | 132 | 7.765 | −0.18 |
O18 | 18 | 8 | 10 | 139.808 | 7.77 | 26 | 28 | 26 | 23 | 138 | 7.667 | 1.29 |
F19 | 19 | 9 | 10 | 147.801 | 7.78 | 28 | 29 | 28 | 25 | 150 | 7.895 | −1.49 |
Ne20 | 20 | 10 | 10 | 160.65 | 8.03 | 30 | 30 | 30 | 27 | 162 | 8.1 | −0.84 |
Ne21 | 21 | 10 | 11 | 167.406 | 7.97 | 31 | 32 | 31 | 28 | 168 | 8 | −0.35 |
Ne22 | 22 | 10 | 12 | 177.77 | 8.08 | 32 | 34 | 32 | 29 | 174 | 7.909 | 2.12 |
Na23 | 23 | 11 | 12 | 186.564 | 8.11 | 34 | 35 | 34 | 31 | 186 | 8.087 | 0.3 |
Mg24 | 24 | 12 | 12 | 198.257 | 8.26 | 36 | 36 | 36 | 33 | 198 | 8.25 | 0.13 |
Mg25 | 25 | 12 | 13 | 205.587 | 8.22 | 37 | 38 | 37 | 34 | 204 | 8.16 | 0.77 |
Mg26 | 26 | 12 | 14 | 216.681 | 8.33 | 38 | 40 | 38 | 35 | 210 | 8.077 | 3.08 |
Al27 | 27 | 13 | 14 | 224.952 | 8.33 | 40 | 41 | 40 | 37 | 222 | 8.222 | 1.31 |
Si28 | 28 | 14 | 14 | 236.537 | 8.45 | 42 | 42 | 42 | 39 | 234 | 8.357 | 1.07 |
Si29 | 29 | 14 | 15 | 245.01 | 8.45 | 43 | 44 | 43 | 40 | 240 | 8.276 | 2.04 |
Si30 | 30 | 14 | 16 | 255.62 | 8.52 | 44 | 46 | 44 | 41 | 246 | 8.2 | 3.76 |
P31 | 31 | 15 | 16 | 262.917 | 8.48 | 46 | 47 | 46 | 43 | 258 | 8.323 | 1.87 |
S32 | 32 | 16 | 16 | 271.78 | 8.49 | 48 | 48 | 48 | 45 | 270 | 8.438 | 0.65 |
S33 | 33 | 16 | 17 | 280.422 | 8.5 | 49 | 50 | 49 | 46 | 276 | 8.364 | 1.58 |
S34 | 34 | 16 | 18 | 291.839 | 8.58 | 50 | 52 | 50 | 47 | 282 | 8.294 | 3.37 |
Cl35 | 35 | 17 | 18 | 298.21 | 8.52 | 52 | 53 | 52 | 49 | 294 | 8.4 | 1.41 |
S36 | 36 | 16 | 20 | 308.71 | 8.58 | 52 | 56 | 52 | 49 | 294 | 8.167 | 4.76 |
Ar36 | 36 | 18 | 18 | 306.716 | 8.52 | 54 | 54 | 54 | 51 | 306 | 8.5 | 0.23 |
Cl37 | 37 | 17 | 20 | 318.784 | 8.62 | 54 | 57 | 54 | 51 | 306 | 8.27 | 4.01 |
Ar38 | 38 | 18 | 20 | 327.343 | 8.61 | 56 | 58 | 56 | 53 | 318 | 8.368 | 2.85 |
K39 | 39 | 19 | 20 | 333.724 | 8.56 | 58 | 59 | 58 | 55 | 330 | 8.462 | 1.12 |
Ar40 | 40 | 18 | 22 | 343.81 | 8.6 | 58 | 62 | 58 | 55 | 330 | 8.25 | 4.02 |
Ca40 | 40 | 20 | 20 | 342.053 | 8.55 | 60 | 60 | 60 | 57 | 342 | 8.55 | 0.02 |
K41 | 41 | 19 | 22 | 351.619 | 8.58 | 60 | 63 | 60 | 57 | 342 | 8.341 | 2.74 |
Ca42 | 42 | 20 | 22 | 361.895 | 8.62 | 62 | 64 | 62 | 59 | 354 | 8.429 | 2.18 |
Ca43 | 43 | 20 | 23 | 369.828 | 8.6 | 63 | 66 | 63 | 60 | 360 | 8.372 | 2.66 |
Ca44 | 44 | 20 | 24 | 380.96 | 8.66 | 64 | 68 | 64 | 61 | 366 | 8.318 | 3.93 |
Sc45 | 45 | 21 | 24 | 387.849 | 8.62 | 66 | 69 | 66 | 63 | 378 | 8.4 | 2.54 |
Ca46 | 46 | 20 | 26 | 398.772 | 8.67 | 66 | 72 | 66 | 63 | 378 | 8.217 | 5.21 |
Ti46 | 46 | 22 | 24 | 398.194 | 8.66 | 68 | 70 | 68 | 65 | 390 | 8.478 | 2.06 |
Ti47 | 47 | 22 | 25 | 407.072 | 8.66 | 69 | 72 | 69 | 66 | 396 | 8.426 | 2.72 |
Ca48 | 48 | 20 | 28 | 415.992 | 8.67 | 68 | 76 | 68 | 65 | 390 | 8.125 | 6.25 |
Ti48 | 48 | 22 | 26 | 418.699 | 8.72 | 70 | 74 | 70 | 67 | 402 | 8.375 | 3.99 |
Ti49 | 49 | 22 | 27 | 426.841 | 8.71 | 71 | 76 | 71 | 68 | 408 | 8.327 | 4.41 |
Ti50 | 50 | 22 | 28 | 437.78 | 8.76 | 72 | 78 | 72 | 69 | 414 | 8.28 | 5.43 |
Cr50 | 50 | 24 | 26 | 435.047 | 8.7 | 74 | 76 | 74 | 71 | 426 | 8.52 | 2.08 |
V51 | 51 | 23 | 28 | 445.842 | 8.74 | 74 | 79 | 74 | 71 | 426 | 8.353 | 4.45 |
Cr52 | 52 | 24 | 28 | 456.345 | 8.78 | 76 | 80 | 76 | 73 | 438 | 8.423 | 4.02 |
Cr53 | 53 | 24 | 29 | 464.287 | 8.76 | 77 | 82 | 77 | 74 | 444 | 8.377 | 4.37 |
Cr54 | 54 | 24 | 30 | 474.009 | 8.78 | 78 | 84 | 78 | 75 | 450 | 8.333 | 5.07 |
Fe54 | 54 | 26 | 28 | 471.765 | 8.74 | 80 | 82 | 80 | 77 | 462 | 8.556 | 2.07 |
Mn55 | 55 | 25 | 30 | 482.075 | 8.77 | 80 | 85 | 80 | 77 | 462 | 8.4 | 4.16 |
Fe56 | 56 | 26 | 30 | 492.257 | 8.79 | 82 | 86 | 82 | 79 | 474 | 8.464 | 3.71 |
Fe57 | 57 | 26 | 31 | 499.905 | 8.77 | 83 | 88 | 83 | 80 | 480 | 8.421 | 3.98 |
Fe58 | 58 | 26 | 32 | 509.945 | 8.79 | 84 | 90 | 84 | 81 | 486 | 8.379 | 4.7 |
Ni58 | 58 | 28 | 30 | 506.456 | 8.73 | 86 | 88 | 86 | 83 | 498 | 8.586 | 1.67 |
Co59 | 59 | 27 | 32 | 517.314 | 8.77 | 86 | 91 | 86 | 83 | 498 | 8.441 | 3.73 |
Ni60 | 60 | 28 | 32 | 526.842 | 8.78 | 88 | 92 | 88 | 85 | 510 | 8.5 | 3.2 |
Zn70 | 70 | 30 | 40 | 611.08 | 8.73 | 100 | 110 | 100 | 97 | 582 | 8.314 | 4.76 |
Ge70 | 70 | 32 | 38 | 610.519 | 8.72 | 102 | 108 | 102 | 99 | 594 | 8.486 | 2.71 |
Se80 | 80 | 34 | 46 | 696.867 | 8.71 | 114 | 126 | 114 | 111 | 666 | 8.325 | 4.43 |
Kr80 | 80 | 36 | 44 | 695.438 | 8.69 | 116 | 124 | 116 | 113 | 678 | 8.475 | 2.51 |
Zr90 | 90 | 40 | 50 | 783.895 | 8.71 | 130 | 140 | 130 | 127 | 762 | 8.467 | 2.79 |
Ru100 | 100 | 44 | 56 | 861.929 | 8.62 | 144 | 156 | 144 | 141 | 846 | 8.46 | 1.85 |
Cd113 | 113 | 48 | 65 | 963.557 | 8.53 | 161 | 178 | 161 | 158 | 948 | 8.389 | 1.61 |
In113 | 113 | 49 | 64 | 963.091 | 8.52 | 162 | 177 | 162 | 159 | 954 | 8.442 | 0.94 |
Sn117 | 117 | 50 | 67 | 995.623 | 8.51 | 167 | 184 | 167 | 164 | 984 | 8.41 | 1.17 |
Xe129 | 129 | 54 | 75 | 1087.648 | 8.43 | 183 | 204 | 183 | 180 | 1080 | 8.372 | 0.7 |
Ce142 | 142 | 58 | 84 | 1185.28 | 8.35 | 200 | 226 | 200 | 197 | 1182 | 8.324 | 0.28 |
Nd142 | 142 | 60 | 82 | 1185.148 | 8.35 | 202 | 224 | 202 | 199 | 1194 | 8.408 | −0.75 |
Sm150 | 150 | 62 | 88 | 1239.253 | 8.26 | 212 | 238 | 212 | 209 | 1254 | 8.36 | −1.19 |
Gd150 | 150 | 64 | 86 | 1236.39 | 8.24 | 214 | 236 | 214 | 211 | 1266 | 8.44 | −2.39 |
Dy162 | 162 | 66 | 96 | 1323.884 | 8.17 | 228 | 258 | 228 | 225 | 1350 | 8.333 | −1.97 |
Yb172 | 172 | 70 | 102 | 1392.764 | 8.1 | 242 | 274 | 242 | 239 | 1434 | 8.337 | −2.96 |
W183 | 183 | 74 | 109 | 1465.526 | 8.01 | 257 | 292 | 257 | 254 | 1524 | 8.328 | −3.99 |
Pt194 | 194 | 78 | 116 | 1539.578 | 7.94 | 272 | 310 | 272 | 269 | 1614 | 8.32 | −4.83 |
Au197 | 197 | 79 | 118 | 1559.397 | 7.92 | 276 | 315 | 276 | 273 | 1638 | 8.315 | −5.04 |
Hg200 | 200 | 80 | 120 | 1581.207 | 7.91 | 280 | 320 | 280 | 277 | 1662 | 8.31 | −5.11 |
Hg204 | 204 | 80 | 124 | 1608.65 | 7.89 | 284 | 328 | 284 | 281 | 1686 | 8.265 | −4.81 |
Pb204 | 204 | 82 | 122 | 1605.343 | 7.87 | 286 | 326 | 286 | 283 | 1698 | 8.324 | −5.77 |
A representative sample of nuclides, showing quantum-allowed bonded up-to-down quark pairs for each nuclide.
As before for this simple calculation, the calculated binding energy is the number of bonds times a fixed energy per bond. The energy per bond is the only selected parameter; for this simple calculation, it is 6.000 MeV per bond. These plots take into consideration the quantum rules of hard-core repulsion and zero electric dipole moment. These data are plotted in Figures 6 and 7. In Figure 6, a representative sample of all of the stable nuclides is shown, out to lead 204Pb. In Figure 7, only the first 60 nuclides are plotted, to show the detail. As before, when there is more than one stable nuclide for a given mass number, these additional points are plotted as well.
A plot of the experimental nuclear binding energy per nucleon (blue) and the simple quantum calculated binding energy (orange).
A plot of the experimental nuclear binding energy per nucleon (blue) and the simple quantum calculated binding energy (orange) for only the first 60 nuclides.
To reiterate, this is a very quick and easy calculation, only involving a simple numerical count of quantum-allowed internucleon up-to-down quark pairs. This calculation does not specify the arrangement of the nucleons or the mechanism of the bond. It is simply a count of the quantum-allowed up-to-down quark bonds. Other than being quantum, this calculation is theory independent, and as such, it is not subject to theoretical criticisms or theoretical differences of opinion.
The excellent reproduction of the experimental data for these calculated results is impressive, especially considering that there is only one empirically-selected variable for this calculation, the value of 6.000 MeV for the bond energy, instead of the five empirically-selected variables for the Weizsäcker formula. This reproduction of the experimental data is especially impressive considering that other currently accepted nuclear theories cannot easily duplicate this curve.
In terms of the possible mechanism for the bond, the residual chromodynamic force between the color charges for internucleon quark-to-quark bonding is one possibility. Another possibility for this bond becomes apparent when it is recalled that the up quark has an electric charge +2/3 the charge of a proton, the down quark has an electric charge of −1/3 the charge of a proton, and both quarks carry a magnetic moment. These electromagnetic properties of the up and down quarks create a strong attractive electromagnetic force between the up and the down quarks; the strength of this electromagnetic force is dependent only on the minimum proximity between the up and down quarks engaged in the bond. Historically, it was believed that the strength of the electromagnetic force had an upper limit, based on the misconceptions that protons were homogeneously charged and that quarks did not exist. However, these misconceived notions are invalid when quarks, which contain all of the electric charge for the nucleons, are taken into consideration.
The internuclear quark-to-quark bond is most likely some combination of both the electromagnetic charge and the color charge of the quarks, but the relative percentages of these two contributions is not postulated here. Regardless of the relative percentages, the electromagnetic component of this bond should not be ignored--as is usually the case in current theories. When any internucleon quark-to-quark bond is considered, the electromagnetic component must be taken into full account, rather than being considered relatively unimportant. A more detailed analysis of the electromagnetic contribution of this internucleon up-to-down quark bonding can easily be made by using the standard electromagnetic Eqs. A detailed analysis would include the addition of the energy due to all electric charges interacting with each other. In other words, this would be a double summation of the interaction for each electric charge of each quark with every other electric charge on all other quarks [15]. This double summation calculation would inherently include the Coulomb energy of the net repulsive electric energies among the protons.
Similarly, a more detailed electromagnetic analysis would also include the variation of the electromagnetic bond due to the vector orientation of the magnetic moments of the quarks. The energy of the magnetic moments interacting with each other should be included, which again would be a double summation for the magnetic interaction for all of the magnetic moment vectors [16]. Finally, the kinetic energy of the quantum spin of the nuclide should also be included in this more detailed binding energy calculation [17, 18]. However, for this more detailed and accurate calculation to be done, the lowest energy configuration of the nuclide must be determined and specified before the electromagnetic interaction energies can be accurately calculated.
An extremely simple calculation of the internucleon up-to-down quark bonding has been made, giving excellent results in duplicating the nuclear binding energy curve, using only one parameter rather than five. The resulting errors for nuclides going up to lead 204Pb are only few percent. The average error, going from A = 10 to A = 60, is only 2.32% with a standard deviation for that error of only 1.91%. Also, due to the inherent similarities of this concept to the currently accepted residual chromodynamic force model, with its quark-to-quark internucleon bonding, the existence of an internucleon up-to-down quark bond cannot be relegated as implausible.
An obvious implication of these results is that a significant part of the nuclear force is electromagnetic. To some, this may be an unexpected implication, but not unfeasible, especially when the electromagnetic attraction of the up-to-down quarks is considered. If one only considers, as is the case historically, that homogenously charged protons cannot bond to other homogeneously charged protons, then the concept that the nuclear force could be partially electromagnetic is deemed implausible. However, with the understanding that the electrical charges of the up and down quarks are able to attract each other and bond to each other, and given that the RCDF allows a quark-to-quark internucleon bond to occur, such restrictions about the nuclear force being partly electromagnetic are no longer relevant.
The excellent reproduction of experimental binding energy data with only one empirically-selected variable strongly suggests that the internucleon up-to-down quark bonding is a concept that should be seriously considered and more thoroughly examined by nuclear physicists.
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Therefore, we aimed to study cerebral activity during the performance of diagonal and vertical movements (DM and VM, respectively), through EEG recording focusing on theta, alpha, and beta frequency bands. Following independent component analysis, we computed time-frequency and source localization analysis. We found that (1) increased frontal theta during the initiation of DM was possibly related to the computational effort; (2) a biphasic pattern of frontoparietal alpha/beta modulations was found during VM; and in addition, (3) source localization showed increased frontal theta during DM generated in the middle frontal cortex. We will discuss the current results and their implications in relation to task difficulty, spatial and temporal computation.",book:{id:"8851",slug:"advances-in-neural-signal-processing",title:"Advances in Neural Signal Processing",fullTitle:"Advances in Neural Signal Processing"},signatures:"Fabio Marson, Patrizio Paoletti, Stefano Lasaponara, Joseph Glicksohn, Antonio De Fano and Tal Dotan Ben-Soussan",authors:[{id:"191040",title:"Dr.",name:"Tal",middleName:null,surname:"Dotan Ben-Soussan",slug:"tal-dotan-ben-soussan",fullName:"Tal Dotan Ben-Soussan"},{id:"195042",title:"Prof.",name:"Joseph",middleName:null,surname:"Glicksohn",slug:"joseph-glicksohn",fullName:"Joseph Glicksohn"},{id:"309442",title:"Dr.",name:"Fabio",middleName:null,surname:"Marson",slug:"fabio-marson",fullName:"Fabio Marson"},{id:"309443",title:"Dr.",name:"Patrizio",middleName:null,surname:"Paoletti",slug:"patrizio-paoletti",fullName:"Patrizio Paoletti"},{id:"309444",title:"Dr.",name:"Stefano",middleName:null,surname:"Lasaponara",slug:"stefano-lasaponara",fullName:"Stefano Lasaponara"},{id:"309445",title:"Dr.",name:"Antonio",middleName:null,surname:"De Fano",slug:"antonio-de-fano",fullName:"Antonio De Fano"}]},{id:"73674",title:"Basic Electroencephalogram and Its Common Clinical Applications in Children",slug:"basic-electroencephalogram-and-its-common-clinical-applications-in-children",totalDownloads:561,totalCrossrefCites:0,totalDimensionsCites:2,abstract:"Electroencephalography (EEG) is a non-invasive neurophysiological study that monitors electrical activity of the brain. EEG is an essential investigational tool to analyze and record electrical impulses of the brain and considered to be the gold standard electrophysiological test which can be used to help diagnose epilepsy. EEG can also be used to diagnose and evaluate other conditions such as sleep disorders, neurometabolic diseases with encephalopathy and neuropsychiatric disorders. It is also an essential ancillary test in other conditions such as brain death assessment. However, it is essential not to entirely rely on EEG for an absolute diagnosis of epilepsy as the main indication of EEG in general and in Pediatric age group in particular is to categorize different types of seizure and epilepsy syndromes for further evaluation and management.",book:{id:"9629",slug:"electroencephalography-from-basic-research-to-clinical-applications",title:"Electroencephalography",fullTitle:"Electroencephalography - From Basic Research to Clinical Applications"},signatures:"Raafat Hammad Seroor Jadah",authors:[{id:"314907",title:"Dr.",name:"Raafat Hammad Seroor",middleName:null,surname:"Jadah",slug:"raafat-hammad-seroor-jadah",fullName:"Raafat Hammad Seroor Jadah"}]},{id:"75015",title:"Periodic EEG Patterns in the Intensive Care Unit (ICU): Definition, Recognition and Clinical Significance",slug:"periodic-eeg-patterns-in-the-intensive-care-unit-icu-definition-recognition-and-clinical-significanc",totalDownloads:440,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"Periodic electroencephalographic (EEG) patterns are frequently recorded during ICU EEG monitoring in patients with altered mental status; these EEG features represent electrical discharges, ictal in appearance, occuring at regular intervals. They are known as lateralized periodic discharges (LPDs), bilateral independent periodic discharges (BIPDS), generalized periodic discharges (GPDs), continuous 2/s GPDs with triphasic morphology or triphasic waves (TWs) and Stimulus Induced Evolving Lateralized Rhytmic delta activity or Si-Evolving LRDA (previously SIRPIDS); other periodic, rhythmic patterns are Occasional frontally predominant brief 2/s GRDA (FIRDA previously), Lateralized rhythmic delta activity (LRDA) and Brief potentially ictal rhythmic discharges or B (I)RDs. The role of most (not all) of these EEG patterns is controversial; there is no consensus on which patterns are associated with ongoing seizure injury, which patterns need to be treated, and how aggressively they should be treated. Many authors consider these patterns as an unstable state on an ictal-interictal EEG continuum; the aim of the present chapter is to gain knowledge of these EEG features, show their association with known neurologic pathologies/syndromes and finally how to manage them.",book:{id:"9629",slug:"electroencephalography-from-basic-research-to-clinical-applications",title:"Electroencephalography",fullTitle:"Electroencephalography - From Basic Research to Clinical Applications"},signatures:"Boulenouar Mesraoua, Musab Abdalhalim Ali, Rola Hosni Mohamed Hashem Khodair, Yazan Nofal, Dirk Theophiel O. 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He also obtained an MSc in Molecular and Genetic Medicine, and a Ph.D. in Clinical Immunology and Human Genetics from the University of Sheffield, UK. He also completed a short-term fellowship in Pediatric Clinical Immunology and Bone Marrow Transplantation at Newcastle General Hospital, England. Dr. Rezaei is a Full Professor of Immunology and Vice Dean of International Affairs and Research, at the School of Medicine, Tehran University of Medical Sciences, and the co-founder and head of the Research Center for Immunodeficiencies. He is also the founding president of the Universal Scientific Education and Research Network (USERN). Dr. Rezaei has directed more than 100 research projects and has designed and participated in several international collaborative projects. He is an editor, editorial assistant, or editorial board member of more than forty international journals. He has edited more than 50 international books, presented more than 500 lectures/posters in congresses/meetings, and published more than 1,100 scientific papers in international journals.",institutionString:"Tehran University of Medical Sciences",institution:{name:"Tehran University of Medical Sciences",country:{name:"Iran"}}},{id:"180733",title:"Dr.",name:"Jean",middleName:null,surname:"Engohang-Ndong",slug:"jean-engohang-ndong",fullName:"Jean Engohang-Ndong",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/180733/images/system/180733.png",biography:"Dr. Jean Engohang-Ndong was born and raised in Gabon. After obtaining his Associate Degree of Science at the University of Science and Technology of Masuku, Gabon, he continued his education in France where he obtained his BS, MS, and Ph.D. in Medical Microbiology. He worked as a post-doctoral fellow at the Public Health Research Institute (PHRI), Newark, NJ for four years before accepting a three-year faculty position at Brigham Young University-Hawaii. Dr. Engohang-Ndong is a tenured faculty member with the academic rank of Full Professor at Kent State University, Ohio, where he teaches a wide range of biological science courses and pursues his research in medical and environmental microbiology. Recently, he expanded his research interest to epidemiology and biostatistics of chronic diseases in Gabon.",institutionString:"Kent State University",institution:{name:"Kent State University",country:{name:"United States of America"}}},{id:"188773",title:"Prof.",name:"Emmanuel",middleName:null,surname:"Drouet",slug:"emmanuel-drouet",fullName:"Emmanuel Drouet",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/188773/images/system/188773.png",biography:"Emmanuel Drouet, PharmD, is a Professor of Virology at the Faculty of Pharmacy, the University Grenoble-Alpes, France. As a head scientist at the Institute of Structural Biology in Grenoble, Dr. Drouet’s research investigates persisting viruses in humans (RNA and DNA viruses) and the balance with our host immune system. He focuses on these viruses’ effects on humans (both their impact on pathology and their symbiotic relationships in humans). He has an excellent track record in the herpesvirus field, and his group is engaged in clinical research in the field of Epstein-Barr virus diseases. He is the editor of the online Encyclopedia of Environment and he coordinates the Universal Health Coverage education program for the BioHealth Computing Schools of the European Institute of Science.",institutionString:null,institution:{name:"Grenoble Alpes University",country:{name:"France"}}},{id:"131400",title:"Prof.",name:"Alfonso J.",middleName:null,surname:"Rodriguez-Morales",slug:"alfonso-j.-rodriguez-morales",fullName:"Alfonso J. Rodriguez-Morales",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/131400/images/system/131400.png",biography:"Dr. Rodriguez-Morales is an expert in tropical and emerging diseases, particularly zoonotic and vector-borne diseases (especially arboviral diseases). He is the president of the Travel Medicine Committee of the Pan-American Infectious Diseases Association (API), as well as the president of the Colombian Association of Infectious Diseases (ACIN). He is a member of the Committee on Tropical Medicine, Zoonoses, and Travel Medicine of ACIN. He is a vice-president of the Latin American Society for Travel Medicine (SLAMVI) and a Member of the Council of the International Society for Infectious Diseases (ISID). Since 2014, he has been recognized as a Senior Researcher, at the Ministry of Science of Colombia. He is a professor at the Faculty of Medicine of the Fundacion Universitaria Autonoma de las Americas, in Pereira, Risaralda, Colombia. He is an External Professor, Master in Research on Tropical Medicine and International Health, Universitat de Barcelona, Spain. He is also a professor at the Master in Clinical Epidemiology and Biostatistics, Universidad Científica del Sur, Lima, Peru. In 2021 he has been awarded the “Raul Isturiz Award” Medal of the API. Also, in 2021, he was awarded with the “Jose Felix Patiño” Asclepius Staff Medal of the Colombian Medical College, due to his scientific contributions to COVID-19 during the pandemic. He is currently the Editor in Chief of the journal Travel Medicine and Infectious Diseases. His Scopus H index is 47 (Google Scholar H index, 68).",institutionString:"Institución Universitaria Visión de las Américas, Colombia",institution:null},{id:"332819",title:"Dr.",name:"Chukwudi Michael",middleName:"Michael",surname:"Egbuche",slug:"chukwudi-michael-egbuche",fullName:"Chukwudi Michael Egbuche",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/332819/images/14624_n.jpg",biography:"I an Dr. Chukwudi Michael Egbuche. I am a Senior Lecturer in the Department of Parasitology and Entomology, Nnamdi Azikiwe University, Awka.",institutionString:null,institution:{name:"Nnamdi Azikiwe University",country:{name:"Nigeria"}}},{id:"284232",title:"Mr.",name:"Nikunj",middleName:"U",surname:"Tandel",slug:"nikunj-tandel",fullName:"Nikunj Tandel",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/284232/images/8275_n.jpg",biography:'Mr. Nikunj Tandel has completed his Master\'s degree in Biotechnology from VIT University, India in the year of 2012. He is having 8 years of research experience especially in the field of malaria epidemiology, immunology, and nanoparticle-based drug delivery system against the infectious diseases, autoimmune disorders and cancer. He has worked for the NIH funded-International Center of Excellence in Malaria Research project "Center for the study of complex malaria in India (CSCMi)" in collaboration with New York University. The preliminary objectives of the study are to understand and develop the evidence-based tools and interventions for the control and prevention of malaria in different sites of the INDIA. Alongside, with the help of next-generation genomics study, the team has studied the antimalarial drug resistance in India. Further, he has extended his research in the development of Humanized mice for the study of liver-stage malaria and identification of molecular marker(s) for the Artemisinin resistance. At present, his research focuses on understanding the role of B cells in the activation of CD8+ T cells in malaria. Received the CSIR-SRF (Senior Research Fellow) award-2018, FIMSA (Federation of Immunological Societies of Asia-Oceania) Travel Bursary award to attend the IUIS-IIS-FIMSA Immunology course-2019',institutionString:"Nirma University",institution:{name:"Nirma University",country:{name:"India"}}},{id:"334383",title:"Ph.D.",name:"Simone",middleName:"Ulrich",surname:"Ulrich Picoli",slug:"simone-ulrich-picoli",fullName:"Simone Ulrich Picoli",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/334383/images/15919_n.jpg",biography:"Graduated in Pharmacy from Universidade Luterana do Brasil (1999), Master in Agricultural and Environmental Microbiology from Federal University of Rio Grande do Sul (2002), Specialization in Clinical Microbiology from Universidade de São Paulo, USP (2007) and PhD in Sciences in Gastroenterology and Hepatology (2012). She is currently an Adjunct Professor at Feevale University in Medicine and Biomedicine courses and a permanent professor of the Academic Master\\'s Degree in Virology. She has experience in the field of Microbiology, with an emphasis on Bacteriology, working mainly on the following topics: bacteriophages, bacterial resistance, clinical microbiology and food microbiology.",institutionString:null,institution:{name:"Universidade Feevale",country:{name:"Brazil"}}},{id:"229220",title:"Dr.",name:"Amjad",middleName:"Islam",surname:"Aqib",slug:"amjad-aqib",fullName:"Amjad Aqib",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/229220/images/system/229220.png",biography:"Dr. Amjad Islam Aqib obtained a DVM and MSc (Hons) from University of Agriculture Faisalabad (UAF), Pakistan, and a PhD from the University of Veterinary and Animal Sciences Lahore, Pakistan. Dr. Aqib joined the Department of Clinical Medicine and Surgery at UAF for one year as an assistant professor where he developed a research laboratory designated for pathogenic bacteria. Since 2018, he has been Assistant Professor/Officer in-charge, Department of Medicine, Manager Research Operations and Development-ORIC, and President One Health Club at Cholistan University of Veterinary and Animal Sciences, Bahawalpur, Pakistan. He has nearly 100 publications to his credit. His research interests include epidemiological patterns and molecular analysis of antimicrobial resistance and modulation and vaccine development against animal pathogens of public health concern.",institutionString:"Cholistan University of Veterinary and Animal Sciences",institution:null},{id:"62900",title:"Prof.",name:"Fethi",middleName:null,surname:"Derbel",slug:"fethi-derbel",fullName:"Fethi Derbel",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62900/images/system/62900.jpeg",biography:"Professor Fethi Derbel was born in 1960 in Tunisia. He received his medical degree from the Sousse Faculty of Medicine at Sousse, University of Sousse, Tunisia. He completed his surgical residency in General Surgery at the University Hospital Farhat Hached of Sousse and was a member of the Unit of Liver Transplantation in the University of Rennes, France. He then worked in the Department of Surgery at the Sahloul University Hospital in Sousse. Professor Derbel is presently working at the Clinique les Oliviers, Sousse, Tunisia. His hospital activities are mostly concerned with laparoscopic, colorectal, pancreatic, hepatobiliary, and gastric surgery. He is also very interested in hernia surgery and performs ventral hernia repairs and inguinal hernia repairs. He has been a member of the GREPA and Tunisian Hernia Society (THS). During his residency, he managed patients suffering from diabetic foot, and he was very interested in this pathology. For this reason, he decided to coordinate a book project dealing with the diabetic foot. Professor Derbel has published many articles in journals and collaborates intensively with IntechOpen Access Publisher as an editor.",institutionString:"Clinique les Oliviers",institution:null},{id:"300144",title:"Dr.",name:"Meriem",middleName:null,surname:"Braiki",slug:"meriem-braiki",fullName:"Meriem Braiki",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/300144/images/system/300144.jpg",biography:"Dr. Meriem Braiki is a specialist in pediatric surgeon from Tunisia. She was born in 1985. She received her medical degree from the University of Medicine at Sousse, Tunisia. She achieved her surgical residency training periods in Pediatric Surgery departments at University Hospitals in Monastir, Tunis and France.\r\nShe is currently working at the Pediatric surgery department, Sidi Bouzid Hospital, Tunisia. Her hospital activities are mostly concerned with laparoscopic, parietal, urological and digestive surgery. She has published several articles in diffrent journals.",institutionString:"Sidi Bouzid Regional Hospital",institution:null},{id:"229481",title:"Dr.",name:"Erika M.",middleName:"Martins",surname:"de Carvalho",slug:"erika-m.-de-carvalho",fullName:"Erika M. de Carvalho",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/229481/images/6397_n.jpg",biography:null,institutionString:null,institution:{name:"Oswaldo Cruz Foundation",country:{name:"Brazil"}}},{id:"186537",title:"Prof.",name:"Tonay",middleName:null,surname:"Inceboz",slug:"tonay-inceboz",fullName:"Tonay Inceboz",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/186537/images/system/186537.jfif",biography:"I was graduated from Ege University of Medical Faculty (Turkey) in 1988 and completed his Med. PhD degree in Medical Parasitology at the same university. I became an Associate Professor in 2008 and Professor in 2014. I am currently working as a Professor at the Department of Medical Parasitology at Dokuz Eylul University, Izmir, Turkey.\n\nI have given many lectures, presentations in different academic meetings. I have more than 60 articles in peer-reviewed journals, 18 book chapters, 1 book editorship.\n\nMy research interests are Echinococcus granulosus, Echinococcus multilocularis (diagnosis, life cycle, in vitro and in vivo cultivation), and Trichomonas vaginalis (diagnosis, PCR, and in vitro cultivation).",institutionString:"Dokuz Eylül University",institution:{name:"Dokuz Eylül University",country:{name:"Turkey"}}},{id:"71812",title:"Prof.",name:"Hanem Fathy",middleName:"Fathy",surname:"Khater",slug:"hanem-fathy-khater",fullName:"Hanem Fathy Khater",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/71812/images/1167_n.jpg",biography:"Prof. Khater is a Professor of Parasitology at Benha University, Egypt. 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