Applications of Fission

Abstract

This chapter is devoted to a discussion of applications of nuclear fission. It covers some aspects of the topics of nuclear reactors, nuclear safeguards and nonproliferation, reactor antineutrinos, and nuclear medicine. It is, however, limited in scope and the reader is encouraged to explore the many other exciting sub-areas of the applications of nuclear fission.

1. Introduction

The two key properties of fission, the release of several neutrons and the release of a broad distribution of fission fragments, are fundamental reasons for the huge number of applications that have come since the discovery of the fission process. The importance of neutron emission mainly lies in the uses of fission chain reactions, while the radioactive nature of most of the fission fragments underlies applications from this aspect of fission. The chain reaction nature of fission can be exploited in two ways, controlled fission chain reactions used to generate nuclear energy and uncontrolled chain reactions in explosive nuclear devices. Both of these uses of fission have been in existence since the Second World War when many of the top scientists of the time concentrated on making these applications a reality. Although today the basic and practical principles determining our ability to use fission for nuclear energy or nuclear explosions are well-understood, the initial years required a lot of ingenuity and creativity. The research was equally creative, mostly started in the 1950s, that went into harnessing the products of fission for medical isotopes. Several fission fragments have ideal decay properties to be used as diagnostics or in radiotherapy to treat some medical conditions, especially cancer. The decay properties of many fission fragments also make them ideal probes for nuclear nonproliferation and reactor safeguards. Another property of the decay of fission fragments is that their beta-decay results in the emission of antineutrinos and the antineutrino fluxes from nuclear reactors have been used in several worldwide collaborations to examine neutrino oscillations and physics beyond the Standard Model of particle physics.

The enormous range and diversity of applications of nuclear fission make it one of the most intriguing subatomic processes. In this chapter, I will attempt to discuss a selection of these applications, ranging from nuclear reactors to nuclear nonproliferation to neutrino physics. It is not possible to cover all of the applications of fission that have been invented by so many resourceful scientific teams. But it is my hope that the discussion of the applications presented here will encourage the reader to explore this rich field in more depth.

2. Nuclear reactors

This section discusses aspects of nuclear reactors that are important for understanding later discussions of nonproliferation and reactor neutrino physics. In particular, this section pays particular attention to the production of plutonium in reactors. Most modern reactors use low-enriched (∼2–5% ²³⁵U) uranium fuel and thermalized neutron flux. The shape of the neutron flux depends on the initial enrichment, and in Figure 1, examples are shown for a pressurized water reactor (PWR) with different enrichments. These fluxes were derived from MCNP/CINDER [1] simulations. With fresh fuel, the burn is initially dominated by fissions from ²³⁵U, but as the burn proceeds, ²³⁹Pu is generated by neutron capture on ²³⁸U, followed by two beta decays, Figure 2.

Figure 1.

The neutron flux of PWRs with different levels of ²³⁵U enrichment. The flux is graphed as flux (Φ(E)) per unit lethargy (Δu), that is, Φ(E)/Δu, where Δu = ln(E_I/E_I + 1).

Figure 2.

Reactor production of ²³⁹Pu and ²⁴⁰Pu starts with neutron capture on ²³⁸U. The production is complicated by the capture on and beta decay of the intermediate nuclei ²³⁹U, ²⁴⁰U, ²³⁹Np, and ²⁴⁰Np. At high neutron flux, φ ∼10¹⁴ n/cm²/sec, the 2.355 half-life of ²³⁹Np affects the ²⁴⁰Pu/²³⁹Pu ratio.

The in-growth rate of the different Pu isotopes depends on the reactor design and the initial fuel enrichment of the uranium fuel. For example, in Figure 3, we compare the percentage of fissions induced by the different isotopes in the fuel for two PWRs that only differ in the fuel enrichment, one with 2.7% and the other with 4.2% enriched uranium. The total exposure of the 4.2% enriched fuel is about twice that of the 2.7% enriched fuel and is 60 GW days per metric ton of uranium (GWd/MTU). These simulations were taken from Ref. [2] and from earlier coupled calculations with the ERPI/CELL and CINDER codes [3, 4]. Apart from the factor of two differences in total burn times, the two fission histories are very similar. Indeed, increasing the fuel enrichment induces a kind of “accordion” effect in which the x-axis is simply stretched.

Figure 3.

The fission history for fresh 2.7% enriched (97.3% ²³⁸U, 2.7% ²³⁵U) and 4.2% enriched (95.8% ²³⁸U, 4.2% ²³⁵U) reactors. As the fuels burn, the importance of ²³⁵U, in terms of the fraction of fissions taking place, decreases steadily. The fission histories are very similar for the two enrichments, apart from the clear difference in burn time.

2.1 Other reactor designs

A number of alternate reactor designs to PWRs exist or have been designed. Perhaps the most famous alternate design is the Canadian design, the CANDU reactor [5]. CANDU designs use natural uranium (0.711% ²³⁵U, 9928% ²³⁸U, and trace ²³⁴U) and are pressurized heavy-water (D₂O) designs. Unlike conventional light-water PWRs, where the core fuel is placed in a pressure vessel, the CANDU bundles of fuel are contained in pressure tubes and these pressure tubes are then contained in a larger unpressurized vessel (a calandria) that is moderated by heavy water. In addition to being capable of producing energy from natural uranium, a large advantage of the CANDU design is that refueling can be done on a continuous basis. This is because only a signal fuel tube needs to be depressurized and replaced at a time. This is in strong contrast to a normal PWR, where the entire core must be shut down in order to open the pressure vessel and refuel the core. There are 30 CANDU reactors operating around the world, in Argentina, Canada, China, India, Pakistan, Romania, and South Korea.

Another very different reactor design is the thorium-uranium fuel design [6]. Thorium is more than three times more abundant on Earth than uranium and considerable research has gone into Th-U reactor designs. ²³²Th is almost stable with a half-life of 1.405 × 10¹⁰ y, and it accounts for 99.98% of the natural thorium on Earth. The remaining 0.02% is accounted for by the very small abundance of ^230Th found in parts of the ocean. In general, ²³²Th can only be used in breeder reactors because it does not undergo thermal fission. The breeding process is analogous to the production of ²³⁹Pu in uranium reactor, in which ²³²Th absorbs a thermal neutron to make ²³³Th, and two beta decays result in ²³³U, which is fissile.

$${}^{232}\mathit{Th}+n\to {}^{233}\mathit{Th}\left(22.3min\right)\stackrel{\beta -\mathit{\text{decay}}}{\to }{}^{233}\mathit{Pa}\left(26.975\text{days}\right)\stackrel{\beta -\mathit{\text{decay}}}{\to }{}^{233}U$$E1

The thermal neutron capture cross section on ²³²Th is larger than that on ²³⁸U, which results in ²³³U being bred more efficiently in thorium reactors than plutonium in uranium reactors. To sustain criticality in a thorium reactor, it normally requires a second fissile material to be included in the core to initiate the burn and to provide a neutron flux to allow the nuclear sequence in Eq. 1 to proceed. There have been many possible fissile fuels considered for adding to thorium-dominated fuel. These have mostly been low-enriched uranium (LEU) or reactor-grade plutonium (RGPu). LEU generally refers to uranium enriched up to 20% in ²³⁵U. Higher enrichments would also work, but proliferation becomes an issue. RGPu is generally spent reactor fuel containing about 50% ²³⁹Pu, with the remaining Pu coming from ²³⁸Pu, ²⁴⁰Pu, ²⁴¹Pu, and ²⁴²Pu.

In Figure 4, we show the burn history for the case of 80%ThO₂ + 20%LEU. For this example, ²³⁵U initially dominates the fissions, until sufficient ²³³U has been bred from the ²³²Th. However, the ²³⁸U in the LEU fuel also produces 2³⁹Pu, which eventually contributes more fission than ²³⁵U.

Figure 4.

The fission fractions predicted for a Th-U reactor as a function of the burnup. The main role of the ²³²Th is to breed ²³³U, and ²³³U eventually dominates the number of fissions being produced. The LEU fuel is necessary to bring the reactor up to critical and supply enough neutrons for the breeding of ²³³U. The LEU fuel is made up of 2.56% 235 U and 97.44% ²³⁸U. The ²³⁹Pu comes from neutron capture on ²³⁸U, as summarized in Figure 2.

2.2 MOX plutonium fuels

One of the important concepts for the nuclear fuel cycle is to reuse spent reactor fuel by separating the plutonium and mixing it with depleted uranium to form a mixed oxide (MOX) fuel [7]. The plutonium is recovered through reprocessing. Depending on the nation involved in the reprocessing, the spent uranium can also be reprocessed. There are about 40 reactors in Europe (France, Germany Belgium, and Switzerland) that are licensed to use MOX, although only about 30 European reactors are currently using MOX fuel. Japan also recycles MOX fuel in its reactors. Typically, commercial thermal reactors in countries that recycle reactor fuel are loaded with one-third of MOX, although some advanced light water designs are capable of accepting 100% MOX loadings.

Another concept that has been explored is to recycle weapons-grade MOX plutonium fuel. The typical isotopic difference between weapons-grade and reactor-grade MOX pluton is summarized in Table 1.

Isotope %	235 U	238 U	238Pu	239Pu	240Pu	241Pu	242Pu
Weapons	0.679	93.62	—	5.0	3.0	—	—
Reactor	0.679	93.62	0.203	2.653	1.373	0.535	0.535

Table 1.

Initial isotopics for weapons and reactor-grade MOX fuels.

There are many MOX loadings that could be considered, but in a detailed analysis we considered [8] four possible cases:

• the entire reactor core is reactor-grade (RG) MOX fuel.

• the entire reactor core is weapons-grade (RG) MOX fuel.

• one-third of the core is RG MOX fuel; the remaining two-thirds of the fuel is assumed to be fresh 2.56% enriched LEU.

• one-third of the core is WG MOX fuel; the remaining two-thirds of the fuel is assumed to be fresh 2.56% enriched LEU.

For all four cases, the Monteburns code [1] was used, which couples the Monte Carlo neutron transport code MCNP [9] to the burn code CINDER’90 [10]; the latter uses 63 neutron energy groups and tracks up to 3400 nuclides, including 638 isomers. In all cases, we assume the same reactor configuration as the H.B. Robinson Unit 2 (HBR2) PWR, which was loaded with a fuel assembly that had 2.56% enriched fresh LEU and no MOX fuel. The simulations reproduce the reported history for the HBR2 PWR using variable concentrations of burnable boron poison rods over the four burn periods and the simulations predict spent fuel isotopic inventories for the uranium and plutonium isotopes within about 5% of measurement. The equivalent burn histories predicted for our four MOX fuel scenarios are shown in Figures 5 and 6.

Figure 5.

Fission fraction for ^235,238U, and ^239,241Pu as a function of burnup for 33.3% MOX and 66.7%LEU. Panel (a) is RG and (b) WG plutonium.

Figure 6.

Fission fraction for ^235,238U, and ^239,241Pu as a function of burnup for pure MOX fuels. Panel (a) is for RG and (b) is for WG plutonium. The two grades of Pu are distinguished by the relative importance of ²³⁹Pu and ²⁴¹Pu.

As expected, the burn histories for cores involving partial or total MOX fuel are quite distinct from fuel only containing LEU. In the cases where one-third of the core is MOX fuel, the fissions are dominated by ²³⁵U and ²³⁹Pu. The largest difference in the burn between the RG and WG plutonium fuel is the relative importance of ²⁴¹Pu. A second difference is the burnup value at which ²³⁹Pu becomes a larger fraction of the fission than ²³⁵U. As is usually the case with all uranium fuel, the relative importance of ²³⁸U remains approximately constant throughout the burn. When the fuel is 100% MOX Pu, ²³⁹Pu dominates the fissions for all burnups. Burning RG fuel differs from WG fuels in the relative importance of ²³⁹Pu versus ²⁴¹Pu.

3. Fission reactor antineutrinos

One very important application of fission is the use of the antineutrinos emitted in the beta decay of fission fragments. Since the discovery of the antineutrino at the Savannah River reactor by Reines and Cowan in 1953 [11, 12, 13], neutrino physicists have taken advantage of the intense sources of low-energy antineutrinos from nuclear reactors to study the fundamental nature of neutrinos, particularly neutrino oscillations. The concept of neutrinos oscillating [14] from one flavor (ν_e, ν_μ, ν_τ) to another is a natural outcome of gauge theories with massive neutrinos and in its simplest form, it is expressed as a unitary transformation relating the flavor eigenstates (ν_e, ν_μ, ν_τ) to mass (ν₁, ν₂, ν₂) eigenstates.

Understanding the details of antineutrino fluxes from reactor is a complex and detailed subject. All of the detectable neutrinos emitted from reactors come from the beta-decay of neutron-rich fission fragments and correspond to an antineutrino spectrum ranging from 0 to 10 MeV. The antineutrino spectrum from each fissioning actinide is different and involves thousands of beta-decay branches. The study of neutrino oscillations from reactors has become increasingly important and has now reached a precision science, wherein detailed knowledge of the antineutrino spectra is required. This is especially true since the emergence of the so-called reactor neutrino anomaly [15].

The history of reactor neutrino experiments is a very rich one that spans over 60 years. These neutrino oscillation experiments mostly involved searches for variations of the emitted spectrum with the distance from the reactor. In the early experiments, performed in the 1980s–1990s, neutrino detectors were placed within 100 meters of the reactor, but no oscillations were observed. These observations agreed with predictions based on three-neutrino oscillations models and the findings of other neutrino experiments. The first observation of the disappearance of antineutrinos from a reactor was made by the KamLAND [16] experiment in the years between 2003 and 2008. KamLAND detected antineutrinos from 56 Japanese reactors at an average distance of about 180 km. By 2012, KamLAND, together with the CHOOZ [17, 18] and Palo Verde [19] experiments, had set an upper limit on the neutrino mixing angle θ₁₃ and shown that θ₁₃ was significantly smaller than the mixing angles θ₁₂ and θ₂₃. Following these experiments, the reactor neutrino field moved to much larger detectors and employed both a near detector and a main far detector. The reactor neutrino experiment Daya Bay [20], RENO [21], and Double Chooz [22] determined the value of θ₁₃ with high accuracy. The best-fit value from Daya Bay is sin²(2θ13) = 0.084+/−0.005.

3.1 The physics determining fission antineutrino spectra

For precision studies of neutrino oscillations, accurate knowledge is needed of the fission antineutrino spectra for each actinide contributing to the reactor fuel. This issue became a focal point of reactor neutrino studies when in 2011, a reevaluation of the spectra suggested by Huber [23, 24] and Mueller [25] (HM) stated that the expected spectra from all reactors should be increased by about 5–6%. If correct, this would introduce a very serious problem for the neutrino oscillations community because it would mean a need for reassessment of all previous reactor neutrino experiments. In particular, it would imply that the short-baseline experiments were observing neutrino oscillations, but this suggestion could not be accommodated by the standard three neutrino model. New models were proposed to explain the situation, including postulating the existence of a sterile neutrino.

A related problem arose from analyses of the change in the number of antineutrinos emitted from reactors with increasing fuel burnup [26]. As summarized in Figure 3, as the burn proceeds in a reactor, the relative importance of ²³⁹Pu increases. The total number of antineutrinos emitted from the fission of ²³⁹Pu is less than that emitted from ²³⁵U, so as the fuel evolves the number of antineutrinos emitted decreases. Daya Bay [26] used the reactor fuel evolution to extract a cross-section ratio for ²³⁵U/²³⁹Pu, ${\overline{\sigma }}_{235}/{\overline{\sigma }}_{239}$ =1.445+/−0.097. Here $\overline{\sigma }$ means the average cross section for an antineutrino spectrum for the inverse beta-decay process $p+{\overline{\nu }}_e\to n+e^{+}$. However, the HM [23, 25] ratio is${\overline{\sigma }}_{235}/{\overline{\sigma }}_{239}$ =1.53+/−0.05. The combination of the reactor neutrino anomaly and the anomalous ${\overline{\sigma }}_{235}/{\overline{\sigma }}_{239}$ ratio behooved the nuclear physics community to reexamine the detailed physics determining fission antineutrino spectra.

There are two complementary ways to determine the expected antineutrino spectrum from a fissioning nucleus [27]: the ab initio summation and the electron spectrum conversion methods. In either case, the aggregate fission antineutrino spectrum is determined by summing the contributions of all β-decay branches (b_ni) of all fission fragments (Y_n(A_n, Z_n)),

$$\frac{\mathit{dN}}{d{E}_{\overline{\nu }}}=\sum _n{Y}_n\left(Z_n,A_n\right)\sum _i{b}_{\mathit{ni}}\left(E_0^i\right)S_{\overline{\nu }}\left(E_{\overline{\nu }},E_o^i,Z_n\right).$$E2

Here Y_n(A_n, Z_n) is the cumulative fission yield for fragments (A_n, Z_n). The beta-decay spectrum S for a single transition in nucleus (Z, A) with end-point energy E0 = Ee + Eν is

$$S\left(E_e,Z,A\right)=S_0\left(E_e\right)F\left(E_e,Z,A\right)C\left(E_e\right)\left(1+\delta \left(E_e,A,Z\right)\right),$$E3

where S₀ = G_F² E_e (E₀-E_e)²/2π³, E_e(p_e) is the total electron energy (momentum), $F\left(E_e,Z,A\right)$ is the Fermi function, and C(E_e) is a shape factor [28] for forbidden transitions. In the case of Gamow-Teller transitions C(E_e) = 1. The corrections to the spectrum, including in the term δ(E_e, Z, A), arise from weak magnetism, finite size effects in the Fermi function, and radiative corrections. Changes in the treatment of these corrections were a major source of the initial reactor neutrino anomaly.

In the summation method, one uses the nuclear databases to carry out the sum of over all fission fragments and end-point energies, Eq. 2. This method suffers from the problem of the databases being somewhat incomplete. There are theoretical models for some of the missing data, but overall it would be difficult to use the summation method to determine whether an anomaly exists at the 5% level or not.

The second method for determining the antineutrino spectra is to convert a measured aggregate beta-spectrum into an antineutrino spectrum. This method also comes with difficulties. Any fit to an aggregate beta-spectrum is restricted to about 25–30 (fake) endpoint energies, Eⁱ_0. This is because the measured [29, 30, 31, 32] aggregate beta spectra are very smooth over five orders of magnitude, Figure 7. Thus, a prescription is needed for the 25–30 values of “Z_eff” that enter the Fermi functions and this introduces uncertainty at the few percent levels. However, regardless of the prescription used, it can be shown [33] that the ratio ${\overline{\sigma }}_{235}/{\overline{\sigma }}_{239}$ is constrained to be close to 1.53+/−0.05, if the Schreckenbach data [29] are used for the conversion.

Figure 7.

The aggregate fission antineutrino spectra for ²³⁵U, ²³⁹Pu, and ²⁴¹Pu, deduced from the aggregate beta spectra measured by Schreckenbach et al. [29]. Conversion of these spectra to antineutrino spectra by Huber [23] and Mueller [25] led to the so-called reactor neutrino anomaly [15] and to the predicted ratio for ²³⁵U/²³⁹Pu antineutrinos inverse beta decay cross sections of 1.53+/−0.05, which is larger than that observed at Daya bay [26].

To address this problem, Kopeikin et al. [34] remeasured the ratio of the beta spectra for ²³⁵U and ²³⁹Pu at a research reactor at National Research Centre Kurchatov Institute. They found a ratio of $\frac{{\overline{\sigma }}_{235}}{{\overline{\sigma }}_{239}}=1.45+/-0.03$, which is close to the average value found by Daya Bay and RENO, but 5% lower than any reasonable analysis of the Schreckenbach ²³⁵U and ²³⁹Pu aggregate beta spectra could predict. In addition, the STEREO experiment, which was performed at a reactor with highly enriched ²³⁵U fuel, showed that the anomalous results for the change in the total antineutrino flux with fuel evolutions observed at Daya Bay and RENO could be explained entirely in terms of the Schreckenbach measurements having a ²³⁵U spectrum with a normalization that was 5% too high. This then translated into the HM normalization also being too high. It is worth noting that the predictions of the summation method, using the JEFF-3.1 cumulative fission yields [35] and the ENDF/B-VIII.0 decay data yields [36], yield a ratio $\frac{{\overline{\sigma }}_{235}}{{\overline{\sigma }}_{239}}=1.445$, in agreement with the more modern experiments.

4. Nuclear threat reduction and global security

Preventing nuclear proliferation is a worldwide problem that relies on international agreements and on our ability to detect illicit nuclear activities. Undeclared production of fissile material at all stages of any such program is of most concern. These international efforts include nuclear safeguards for reactors, detecting reprocessing of spent nuclear fuel for the production of weapons plutonium, detecting trafficking of nuclear material, and developing techniques for analyzing debris in the case of a possible terrorist nuclear explosion. The techniques that can be used often depend on the standoff distance. For example, at a compliant reactor, measurements can be made on-site, while for a reprocessing facility in an unfriendly nation, the techniques used may require detection schemes that can work many kilometers from the facility. We consider here some very different situations.

4.1 Monitoring the fuel isotopic content in a molten salt reactor

The international community is paying increasing attention to molten salt reactor (MSR) technology as a promising form of clean and reliable energy. In addition to the fuel being dissolved in the salt, many MSR designs involve fuel replacement and reprocessing on a (semi-)continuous basis. These operations render standard techniques, wherein macroscopic samples are removed from fuel rods for assaying the actinide content, useless. Thus, MSR designs raise the challenge of how the isotopic composition of the dissolved fuel content will be determined as the reactor burn progresses. Actinide and fission fragment inventories for standard light water reactors are determined by assaying the spent fuel rods. In the case of MSRs, the fuel is dissolved into the salt so that standard technique cannot be used. In this sub-section, we examine a possible method of measuring inventories in-line at the reprocessing station, where the fission gases would be released. The main concept is to replace actinides measurements with actinide inferences from the fission gases measurements, applicable to MSRs with continuous refueling and reprocessing operations. Fission gases are automatically released in any reprocessing operation and are easily collected for assay (Figure 8).

Figure 8.

An example of a molten salt reactor, taken from Wikipedia. The fuel is dissolved in the salt. The red box indicates a proposed online operation where fission gas measurements would be made, that is, next to the reprocessing plant.

In MSR, the salt is typically treated in-line to remove as many fission poisons as possible One set of fission products that are relatively easy to remove are the noble gases, xenon, and krypton. This constant separation of the Xe and Kr gases makes the on-site reprocessing plant an ideal station to monitor the isotopic composition of these gases. As the burn proceeds:

• the stable Kr and Xe isotope abundances (except for ¹³⁶Xe, discussed below) simply increase linearly with burnup,

• the unstable Kr and Xe isotopes come to an equilibrium value that is determined by the cumulative fission yield

• the reactor poison ¹³⁵Xe asymptotes to an equilibrium value determined by the neutron flux and ¹³⁵Xe capture cross-section.

Therefore, for example, the growth rate of stable^{1 34}Xe is simply,

$$\frac{{\mathit{dN}}_{134\mathit{Xe}}}{\mathit{dt}}={\mathrm{\Gamma }}_f{\overline{f}}_{134\mathit{Xe}},$$E4

where Γ_f is the fission rate and ${\overline{f}}_A$ is the burn-weighted cumulative fission yield of nucleus A. Figure 9 shows the simple linear increase in the ¹³⁴Xe/¹³⁵Xe ratio with the burnup for an MSR with thorium chloride fuel enriched with 10% ²³³U [37]. Thus, a measurement of the ¹³⁴Xe/¹³⁵Xe ratio can be inverted to determine the burnup of the fuel, and when coupled with a reactor simulation, the isotopic content.

Figure 9.

The increase in the ratio of ¹³⁴Xe/¹³⁵Xe with burnup for thorium chloride+10% ²³³U MSR. By measuring the ratio of the stable xenon isotopes to ¹³⁵Xe, the fuel burnup, and hence the fuel isotopic content can be deduced. [from Monteburns simulations [1, 37].

4.2 Deducing the grade of plutonium from volatile fission fragments

The grade of plutonium is normally defined to be the ratio ²⁴⁰Pu/²³⁹Pu, and weapons-grade and reactor-grade fuel are distinguished with the former typically having a ²⁴⁰Pu/²³⁹Pu ratio of less than 7% and the latter a ratio of about 25%. If the reactor is running under equilibrium conditions, the ²⁴⁰Pu/²³⁹Pu ratio is only dependent on the total neutron fluence, Figures 10 and 11. There is no dependence on the enrichment of the uranium fuel. However, the relationship between fluency and the ²⁴⁰Pu/²³⁹Pu ratio has a small flux dependence, especially at high flux. This is because ²³⁹Pu is produced by the decay of ²³⁹Np, which has a half-life of 2.355 days, and equilibrates at a rate that is flux-dependent, Figure 2.

Figure 10.

The ^240/239Pu ratio dependence on total neutron fluence. For high flux, the curve becomes flux dependent because of the time required for ²³⁹Np to reach equilibrium.

Figure 11.

The ^240/239Pu ratio is not dependent on the fuel enrichment. In these simulations, the half-life of 239 Np has arbitrarily been set to 1 hour to emphasize the (mostly) simple dependence on fluence.

Deducing the neutron fluence (n/cm²) that fuel has been exposed to, in order to deduce the grade of plutonium, can be translated into a problem of deducing the neutron flux (n/cm²/sec) and the total irradiation time.

4.2.1 Deducing the neutron flux from Xe and Cs fission fragments

The competition between the 9.14-hour decay of xenon-135 to cesium-135 and the thermal neutron capture on xenon-135 to xenon-136, with an abnormally large cross-section of 2.6x10⁶ barns, causes the concentration of the fission products ¹³⁶Xe and ¹³⁵Cs to be sensitive functions of the neutron flux, Figure 12.

Figure 12.

The concentrations of ¹³⁶Xe and ¹³⁵Cs relative to other fission products, such as ¹³⁴Xe, are determined by the magnitude of the thermal neutron flux. This sensitivity arises because the rate of thermal neutron capture on ¹³⁵Xe competes with rate of decay of ¹³⁵Xe to ¹³⁵Cs.

If the thermal neutron flux is low, the ¹³⁵Xe dominantly beta-decays to ¹³⁵Cs, while if the thermal flux is high, the neutron capture on ¹³⁵Xe proceeds faster than the beta-decay because the capture cross section is of the order of 10⁶ barns. In comparison, most fission products are produced directly by fission and/or by the beta-decay of other fission fragments.

¹³⁵Xe is a well-known reactor poison. Under steady-state conditions, it reaches an equilibrium value that depends on the capture rate of ¹³⁶Xe and on the concentration of ¹³⁵I. Changes in the thermal flux cause short-term fluctuations in the level of xenon-135, and after about 40 to 50 hours of steady flux, the xenon-135 level settles to a new equilibrium value that reflects the new flux. Such changes in flux, as well as shutdowns and restarts of the reactor, also affect the ¹³⁶Xe/¹³⁴Xe and ¹³⁵Cs/¹³⁷Cs ratios.

4.2.2 The dependence of ^136Xe on the reactor thermal neutron flux

In a reactor, ¹³⁶Xe is produced by three main mechanisms: as a direct fission product, from the β-decay of ¹³⁶I, and from the ¹³⁵Xe(n,γ)¹³⁶Xe reaction. The first two mechanisms determine the so-called cumulative fission yield, which is about 7% per fission for both uranium and plutonium.

Under steady-state conditions, the growth rate of 136Xe is [38],

$$\begin{array}{c}{\dot{N}}_{136}={\overline{f}}_{136}{\mathrm{\Gamma }}_f+N_{135\mathit{Xe}}^{\mathit{\text{equil}}}\mathit{\varphi \sigma }\\ {\dot{N}}_{136}={\overline{f}}_{136}{\mathrm{\Gamma }}_f\left[1+\frac{{\overline{f}}_{135\mathit{Xe}}}{{\overline{f}}_{136\mathit{Xe}}}\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135I}+\mathit{\varphi \sigma }}\right]\end{array}$$E5

where Γ_f is the fission rate, f_A is the burn-weighted cumulative fission yield of nucleus A, ϕ is the thermal neutron flux, σ the capture cross section on ¹³⁵Xe, and N^equil represents the ¹³⁵Xe equilibrium value.

The ¹³⁶Xe production rate falls between two limits,

$$\begin{array}{c}\mathit{\varphi \sigma }\gg {\mathrm{\lambda }}_{135I}:{\dot{N}}_{136}={\overline{f}}_{136}{\mathrm{\Gamma }}_f\left(1+\frac{{\overline{f}}_{135\mathit{Xe}}}{{\overline{f}}_{136\mathit{Xe}}}\right)\\ \mathit{\varphi \sigma }\gg {\mathrm{\lambda }}_{135I}:{\dot{N}}_{136}={\overline{f}}_{136}{\mathrm{\Gamma }}_f\end{array}$$E6

The ratio of xenon-136 to xenon-134 is then,

$$\frac{N_{136}}{N_{134}}=\frac{{\overline{f}}_{136\mathit{Xe}}}{{\overline{f}}_{134\mathit{Xe}}}\left(1+\left(\frac{{\overline{f}}_{135\mathit{Xe}}}{{\overline{f}}_{134\mathit{Xe}}}\right)\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135}+\mathit{\varphi \sigma }}\right)$$E7

From Eq. 7, the ¹³⁶Xe/¹³⁴Xe ratio equilibrates on a (flux-dependent) time scale of weeks. Figure 6 displays the situation for different values of the thermal flux (Figure 13).

Figure 13.

The ¹³⁶Xe/¹³⁴Xe ratio equilibrates to a value that is determined by the thermal neutron flux. Thus, this ratio can be used to deduce the flux. The residual slope of the plateaus in the curves is caused by the slow evolution of the fuel composition, and hence the cumulative fission yields, from ref. [38].

4.2.3 The relationship between thermal flux and the ¹³⁵Cs/¹³⁷Cs ratio

In this section, we derive an analytic expression relating the concentration of cesium-135 to the thermal neutron flux. Cesium-135 is produced through the decay chain 135I➔135Xe➔135Cs, which is complicated by the transmutation of xenon-135 via neutron capture. The number of cesium-135 atoms produced in a time t is given by,

$$N_{135\mathit{Cs}}\left(t\right)={\mathrm{\lambda }}_{135\mathit{Xe}}\underset{0}{\overset{t}{\int }}{\mathit{dt}}^{\prime }\left[\frac{\frac{{\overline{f}}_{135I}}{{\overline{f}}_{137\mathit{Cs}}}{\dot{N}}_{137\mathit{Cs}}-{\dot{N}}_{135I}-{\dot{N}}_{135\mathit{Xe}}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\right]$$E8

Here ${\dot{N}}_A$ is the growth rate of nuclide A.

An analytic expression for ¹³⁵Cs/¹³⁷Cs ratio can be obtained by assuming that the concentration of iodine-135 and xenon-135 are at their equilibrium values and that the thermal neutron flux is constant. Under these assumptions,

$$\begin{array}{c}{N}_{135\mathit{Cs}}=\frac{{\mathrm{\lambda }}_{135\mathit{Xe}}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\frac{{\overline{f}}_{135I}}{{\overline{f}}_{137\mathit{Cs}}}{N}_{137\mathit{Cs}}+\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\left(N_{135I}^{\mathit{\text{equil}}}+N_{135\mathit{IXe}}^{\mathit{\text{equil}}}\right)\\ N_{135\mathit{Cs}}=N_{137\mathit{Cs}}\frac{{\overline{f}}_{135I}}{{\overline{f}}_{137\mathit{Cs}}}⌊\frac{{\mathrm{\lambda }}_{135\mathit{Xe}}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}+\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\left(\frac{1}{{\mathrm{\lambda }}_{135I}{T}_{\mathit{\text{irrad}}}}\right)\left(1+\frac{{\mathrm{\lambda }}_{135I}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\right)⌋\end{array}$$E9

Here λ_135I is the decay constant for iodine-135, and T_irrad is the total irradiation time in the reactor. The form of the second term, which gives rise to the term inversely proportional to the total irradiation time, arises from the proper treatment of startup transients.

4.2.4 The effect of reactor shutdowns

After a reactor shutdown, the operators must wait long enough to ensure that all the ¹³⁵Xe and ¹³⁵I have decayed before restarting the reactor. Failure to do so was one of the errors that occurred in the Chernobyl accident. Each time the reactor is shut down, the concentration of ¹³⁵Cs is increased. For constant neutron flux operation, shutdown adds P terms identical to the second term in Eq. 9, where P is the number of shutdowns before the fuel is removed. The minimum value of P is one, and the xenon ratio becomes,

$$\frac{N_{136\mathit{Xe}}}{N_{134\mathit{Xe}}}=\frac{{\overline{f}}_{136\mathit{Xe}}}{{\overline{f}}_{134\mathit{Xe}}}⌊1+\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\left(\frac{{\overline{f}}_{135\mathit{Xe}}}{{\overline{f}}_{136\mathit{Xe}}}\right)\left(1-\frac{P}{{\mathrm{\lambda }}_{135I}{T}_{\mathit{\text{irrad}}}^{\mathit{\text{total}}}}\right)\left(1+\frac{{\mathrm{\lambda }}_{135I}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\right)⌋,$$E10

while the cesium ratio becomes,

$$N_{135\mathit{Cs}}=N_{137\mathit{Cs}}\frac{{\overline{f}}_{135I}}{{\overline{f}}_{137\mathit{Cs}}}⌊\frac{{\mathrm{\lambda }}_{135\mathit{Xe}}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}+\frac{\mathit{\varphi \sigma }}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\left(\frac{\mathrm{P}}{{\mathrm{\lambda }}_{135I}{T}_{\mathit{\text{irrad}}}^{\mathit{\text{total}}}}\right)\left(1+\frac{{\mathrm{\lambda }}_{135I}}{{\mathrm{\lambda }}_{135\mathit{Xe}}+\mathit{\varphi \sigma }}\right)⌋.$$E11

Here $T_{\mathit{\text{irrad}}}^{\mathit{\text{total}}}$ is the sum of all the irradiation times to which the fuel was exposed. The shutdown correction for the cesium ratio, but not the xenon ratio, becomes significant at high flux. The difference is that for xenon the correction is relative to the constant 1. However, a measurement of the cesium ratio in spent fuel contains information on both the flux and the number of shutdowns.

4.2.5 Comparisons between the theoretical and experimental cesium and xenon ratios

Maeck et al. measured [39] fission isotope product ratios by irradiating highly enriched uranium targets in the Advanced Test Reactor (ATR) and in the Engineering Test Reactor (ETR) at Idaho National Laboratory. By placing the targets at different distances from the reactor mid-plane, each target was exposed to a different flux, and the flux ranged between 6x10¹² and 1.5x10¹⁴ n/cm²/sec. The ATR targets were 93% ²³⁵U and were irradiated for 100 days over 335 days, with several shutdowns. The ETR targets were more than 99% pure ²³⁵U and one set of targets was irradiated for 20 days and another for 180 days over 320 days with some unspecified number of shutdowns.

Figures 14 and 15 shows the experimental data and the calculated ¹³⁵Cs/¹³⁷Cs ratios. As can be seen, the ¹³⁷Cs/¹³⁵Cs ratio scales approximately linearly with the flux, but the reactor shutdowns cause the isotopic ratio to increase with flux at a slower rate at high fluxes. Figure 15 shows the flux dependence of the ¹³⁶Xe/¹³⁴Xe ratio, which is a sensitive diagnostic at low, but not high, fluxes. The ¹³⁶Xe/¹³⁴Xe ratio is an ideal probe for low-flux graphite reactors, for example.

Figure 14.

The ¹³⁷Cs/¹³⁵Cs ratio. The measurements are the data of Maeck et al. [39]. The deviation of the data from the one-shutdown scenario shows the strong dependence of this ratio on the number of shutdowns. The different colors used to display the data points distinguish the different reactor or irritation times used. The open circles and triangles correspond to targets irradiated at the ATR reactor, while the blue circles are data from targets in the ETR reactor.

Figure 15.

The ¹³⁶Xe/¹³⁴Xe ratio. The measurements are the data of Maeck [39]. Reactor shutdowns have very little effect on this ratio. The xenon ratio is a very good diagnostic for low-flux, but not for high-flux, reactors.

4.2.6 Monitoring reactor on-off times

To use the Cs and Xe ratios to address our main problem, namely, the plutonium grade of fuel that is being reprocessed, there remains the problem of knowing the irradiation times and the number of shutdowns. There are several techniques and the usefulness of these depends on the standoff distance from the reactor. We discuss only one method here, namely, reactor neutrino monitoring.

Several neutrino experiments have shown very successfully that measurements of the total number of neutrinos emitted from a reactor can be used to monitor reactor on-off times. Two examples are shown in Figure 16.

Figure 16.

Antineutrino monitoring of reactors allows accurate measurements of the reactor on and off burn times. (left) form the SONGS detector data taken at the San Onofre reactor [40]. (right) from the PROSPECT detector data taken at the 85 MW HFIR reactor at oak ridge [41].

Thus, the grade of reactor fuel can be determined if:

1. The original unirradiated fuel is some form of uranium 238 U + 235 U but of unknown enrichment.

2. During the entire burn of the fuel antineutrino, monitoring was sufficiently accurate to determine when the reactor was on or off.

3. Fission gases produced in the fuel during the burn can be measured.

This is a nice example of combining two diagnostics to gain enhanced information for nonproliferation, namely, combining reactor fission gas data and antineutrino data.

5. Fission applications to nuclear medicine

This section is intended as a short survey of the most common nuclear medical procedures that were derived from fission. In general, uses of radioisotopes and nuclear techniques in medicine fall into two main classes: (a) imaging and diagnosing structures in the body and their functioning, and (b) treating diseases. Fission isotopes contribute to both classes and many reactor facilities around the world are involved in reprocessing spent fuel to produce medical isotopes. The advances in nuclear medicine involve highly multi-disciplinary research and biology and physiology are an important aspect of these studies because of the importance of accurately targeting the organ of interest.

5.1 Nuclear imaging

The ⁹⁹Mo-^99mTm pair are the most used medical isotope and ^99mTc is used for imaging and it can be delivered to organs or tissues when injected into the body. Nuclear imaging can detect biochemical changes in an organ (as opposed solely to changes in size), and, thus, can be used to affect decisions in treating disease. The imaging technique used is known as single photon emission computed tomography (SPECT). SPECT [42] uses gamma rays emitted in the decay of a radionuclide. The ^9mTc used in SPECT comes from the 2.75-day decay of the fission product ⁹⁹Mo. Most of the ⁹⁹M is produced in reactors that use highly enriched uranium (HEU) targets, although there is considerable research on moving to production using low-enriched uranium. The isomer of ⁹⁹Tc has a half-life of 6 hours and emits a 140 keV photon. Some fractions of the photons reach the detector after escaping the body and can be used to create a 3-D image. This is done by taking 2-D projections at different angles. The 3-D dataset can be manipulated into slices along any axis. One of the advantages of SPECT is that it can be used to study blood flow. The temporal resolution for SPECT is limited so that only averaged views in time are possible. There has been some discussion in the literature [43, 44] about the advantages or disadvantages of SPECT versus positron emission tomography (PET). However, SPECT myocardial perfusion imaging is used almost 20 times more frequently than PET in clinical practices in the United States [44].

5.2 Radionuclide therapy

In targeted radionuclide therapy (TRT) [45], radiopharmaceuticals are delivered to tumor cells by targeting specific characteristics of the tumor, such as antigens. In this way, a toxic level of the radionuclide can be delivered to the site. The radionuclide of choice emits charged particles with the required stopping range for effective destruction of malignant tissue, and includes, beta electrons, Auger electrons, and alpha particles. A commonly used fission isotope is ⁹⁰Y. As a high-energy beta-emitter,⁹⁰Y is used for the treatment of larger tumors and is a successfully targeted radiotherapy of the liver. Another application of TRT is in the treatment of bone cancers. A large fraction of breast and prostate cancer patients develop bone metastases, which can cause severe pain. Both ¹⁵³Sm and ⁸⁹Sr deliver high radiation doses to bone metastases and micrometastases in the bone marrow. The field of TRT is ever going, with fission fragments playing major role. For example, ¹³¹I, which has traditionally been used to treat thyroid cancer, is now being studied for TRT in metastatic melanoma [46] (Figure 17).

Figure 17.

A toxic level of radiation is delivered to a diseased site by attaching a radionuclide to a molecular carrier that binds to the site or tumor.

6. Concluding remarks

Nuclear fission has and continues to be applied to a very broad range of needs. Many of these applications have developed into entire subfields of their own and have their own dedicated technical journals. This chapter includes a discussion of nuclear reactors, fission neutrino oscillation studies, nuclear nonproliferation, and nuclear medicine. However, there are many more applications of nuclear fission, some of which are discussed in Ref. [47]. Nuclear fission is very important for other fields, such as nuclear astrophysics, geophysics, nuclear submarines, and nuclear propulsion through space. No doubt the fission of applied nuclear fission will continue to grow as a healthy scientific area.