The invention is in the field of nuclear waste control and is particularly directed toward the elimination of long-lived radioactive nuclides of nuclear reactor waste.

The difficulties encountered in attempting to safely dispose of radio-active wastes generated by the fission process in nuclear reactors is probably the largest single cause of public resistance to the construction of nuclear power stations. A decade ago it was liberally estimated that 200,000 megawatts of nuclear generated electricity would be available by 1980. Today this expectation is down by one half. A major argument against permitting the further spread of nuclear power involves concern over methods proposed for disposal of the nuclear waste products. Present methods of disposal of nuclear waste, which may be in the gaseous, liquid or solid state consist either of dilution and dispersion or storage. In the first approach radioactive gases or liquids are diluted with large volumes of air or water to reduce the activity per unit volume to an allegedly safe level and released into the environment. In the second use, radioactive materials are stored in the containers in the ground or under the sea. With adequate safeguards, storage for about 30 years suffices to remove the harm from relatively short-lived radioactive nuclides, but the situation is quite different for the long lived wastes. Fortunately, the majority of the fission wastes have half-lives less than one year, which means that at worst they must be stored for 33 years to be reduced to 10-¹⁰ of their original amount. However, eighteen fission waste products as well as all the actinide waste products have half-lives greater than one year, but less than 10" years, and it is these products that pose the long term storage problem. To ensure that long lived waste products are kept out of the biosphere until they become harmless-involving periods of hundreds of thousands or millions of years-present proposals involve burial in geological salt formations or other formations such as granite, quartzite, tuff (welded volcanic ash) and shale.

The burial solution to the waste problem is based on the assumption that the geological formation will remain stable for the necessary containment period. While this assumption is reasonable for plutonium, for example, it is not evident for the longer lived wastes including the fission products Pd107, T_c⁹⁹, 1¹²⁹, CS¹³⁵ and Zr⁹³, as well as the actinides.

In view of the extreme hazard that would be created if these materials were not be released into the biosphere, there is a strong and growing resistance to the "bury it and forget it" philosophy, and this opposition has now developed to the point of significantly slowing the growth of nuclear power. It is therefore most desirable if a method could be found to completely eliminate the noxious radioactive wastes from the environment.

Two methods have been suggested for such a final solution to the waste problem. Extraterrestrial disposal would permanently remove the wastes by transportation by rocket into the sun. Two major problems face this technique. First the cost, and second, but more significant, there is the possibility of vehicle failure within the atmosphere leading to a highly dangerous level of radioactive contamination.

A more attractive technique involves the direct transmutation of the dangerous waste materials by neutron bombardment into innocuous materials, or at worst short lived radioactive species. Such a transmutation can be achieved, for example, by recycling waste products back into the reactor which produced them. Such nuclear transformations have been discussed in the literature but have been found only applicable for effective elimination of the actinides produced by neutron capture e.g. "Advanced Waste Management Studies Progress Report", 8, BNWL-B-223 (1973); H. C. Claiborne, "Neutron Induced Transmutation of High-Level Radioactive Wastes", ORNL-TM-3964, 1, 24; and "High Level Radioactive Waste Management Alternatives", 4, 9, BNWL 1900 (1974). The applicability of transmuting long-lived fission products as well as the actinides by neutron capture in reactors has not been regarded as practical since such a procedure reputedly produces more long term waste than it removes._'

A more sophisticated method for processing radioactive waste was disclosed in GB-A-802,971. This method comprises the following steps:

• a) separating stable nuclides (which run the risk of being transformed to radioactive nuclides during irradiation) from the initial waste material,
• b) exposing the remaining waste material to a flux of nuclear radiation in order to transform radioactive substances to stable or short-lived radioactive isotopes,
• c) fractionating the resulting material to separate said stable and short-lived isotopes, and
• d) optionally adding the remaining radioactive residue to fresh radio-active waste or alternatively exposing it to another flux.

This method will have the same disadvantages as mentioned above: the method will consume a rather high amount of neutrons and produce more long-term waste than it removes.

It is a general object of the invention now to reduce the amount of radio-active waste and in particular the amount of fission products from nuclear reactors, so that time storage requirements may be reduced from those required for natural radio-active decay.

A more specific object of the invention is to propose an improved method for processing radio-active waste materials, whereby the rate of transmutation of the radio-active elements can be increased in excess of their natural decay rates for a more rapid conversion to stable nuclides.

The invention provides a method of decreasing the amount of long-lived fission products in radio-active waste materials, wherein these waste materials, after removal of stable and other constituents, are exposed to a neutron flux, in order to produce transmutations therein, and wherein the resulting product, after removal of stable and short-lived radio-active nuclides is re-exposed to a neutron flux. This method is characterized by the following sequence of steps:

• a) separating relatively short-lived radio-active nuclides and stable nuclides from the initial waste material and storing at least some of them,
• b) separating the remaining waste material into individual components, each component essentially comprising about one relatively long-lived radio-active nuclide or combination of nuclides, selected from the group comprising _Se79, Kr⁸⁵, _Sr90, _Zr93, _Tc99, Pd¹⁰⁷, Sb¹²⁵+Sn¹²⁶, l¹²⁹, Cs¹³⁵, Cs¹³⁷, Pm¹⁴⁷, Sm'⁵¹+Eu, and actinides,
• ^c) exposing the aforesaid components with the possible exception of Se⁷⁹, ^Sn126+Sb¹²⁵, Cs¹³⁷ and Pm¹⁴⁷, individually to a neutron flux in order to induce transmutations therein,
• d) separating relatively short-lived radio-active nuclides and stable nuclides from each of said components after exposure and storing at least some of them,
• e) separating the remaining matter of each individual component after exposure into further components, each further component comprising about one relatively long-lived radio-active nuclide or combination of nuclides selected from the above-mentioned group,
• f) combining, as far as possible, those further components that contain corresponding nuclides,
• g) repeating the exposure and separation steps at least one time with at least some of the further components,
• h) and storing the components after they have reached a reduced level of radio-activity over their natural decay.

Thus, the invented method makes use of the steps of transmuting long-lived fission products by neutron capture, together with previous separation of stable and short-lived radio-active nuclides, just like in the method of GB-A-802,971. A difference with that prior art method is, however, that the long-lived. nuclides to be exposed to a neutron flux are separated into components before the exposure to that flux and that each component is individually exposed to the flux. This brings about a better economy of neutron consumption since each component may be irradiated with an appropriate amount of neutrons. Moreover, the method will not produce more long-term waste since the exposure rates can be chosen individually.

The invented method will become clear in relation to the following specificiation taken in conjunction with the drawings wherein:

• Figure 1 is a block diagram of the overall waste transmutation method and system in accordance with the invention;
• Figure 2 is a block diagram of a preferred embodiment of the separation/irradiation treatment cycle;
• Figure 3 is an illustration of the format utilized to deposit the decay/transmutation chain in general;
• Figure 4 illustrates a protion of the decay/transmutation chain for a specific nuclide;
• Figure 5 is a chart of the fission fragment decay times as compared,to one-half the decay activity of U²³⁸;
• Figure 6 is a block diagram illustrating neutron economy in the fission reactor process;
• Figure 7 represents the decay/transmutation chain for Se⁷⁹;
• Figure 8 represents the decay/transmutation chain for Kr⁸⁵ and Sr⁹⁰;
• Figure 9 is a chart showing the removal of Kr⁸⁵ as compared to its natural decay;
• Figure 10 represents the decay/transmutation chain for Zr⁹³;
• Figure 11 is a chart showing the removal of Zr^S3 for both chemical and isotope separation;
• Figure 12 represents the decay/transmutation chain for Tc⁹⁹;
• Figure 13 represents the decay/transmutation chain for Ru¹⁰⁶ and Pd¹⁰⁷;
• Figure 14 represents the decay/transmutation chain for Sn¹²⁶ and Sb¹²⁵
• Figure 15 represents the decay/transmutation chain for Sn¹²⁶ and I¹²⁹;
• Figure 16 represents the decay/transmutation chain for the Cesium isotopes;
• Figure ₁₇ is a graph showing the amount of C_S¹³⁵ and C_S¹³³ as a function of Xenon removal time after fission;
• Figure 18 is a graph showing the amount of Cs¹³³, Cs¹³⁴ and Cs¹³⁵ as a function of time;
• Figure 19 represents the decay/transmutation chain for Pm¹⁴⁷ and Sm¹⁵¹;
• Figure 20 is a graph showing the removal of Sm¹⁵¹ as a function of time;
• Figure 21 represents the decay/transmutation chain for Eu¹⁵⁴ and Eu¹⁵⁵; and
• Figure 22 is a graph showing the time development of Eu¹⁵⁴ and E_u¹⁵⁵.

As used herein, the term transmutation may be defined as the change of one nuclide into another nuclide of the same or a different element by any nuclear process, natural or artificial, A beneficial transmutation can be defined as any transmutation which leads, or is part of a sequence of transmutation which leads, in a reasonably short time, from a long lived radioactive nuclide to a stable nuclide.

In accordance with the principle of the invention, radioactive waste materials are re-cycled in a region of a high-flux of thermal neutrons to permit neutron induced transmutation. Chemical and/or physical and/or isotope separation of the waste is performed both prior to and after neutron irradiation.

This separation has several benefits:

• 1. It minimizes the waste of neutrons which would occur in the non-beneficial transmutation of a stable nuclide into another nuclide.
• 2. It minimizes the production of long-lived radioactive nuclides from transmutation of stable nuclides.
• 3. It minimizes the amount of material that has to be handled in the exposure to the high flux.
• 4. It maximizes the beneficial use of the available neutrons in reducing the radioactive waste hazard.

A block diagram of the process in accordance with the invention is shown in Figure 1. U²³⁵ or other fissile material undergoes fission, splitting into various fission fragments and producing neutrons. Some of these neutrons are used up in maintaining the chain reaction, while others are used in transmuting the waste. The waste products, including the fission fragments and actinides produced by neutron irradiation of Uranium, Plutonium, and/or Thorium, are separated into various components, each component comprising one or more different elements of the waste nuclei. This separation is either chemical or physical or a combination of the two and may further include isotope separation. In principle, isotope separation, as for example employing a mass spectrometer, could be utilized for separation of all isotopes. Economic consideration would, however, dictate primarily a combination of chemical and physical processing. Those "good" components which include only short-lived and stable elements and which do not include long-lived hazardous radioactive substances are stored to allow the decay of short-lived substances. Those "bad" components containing long-lived radioactive substances are exposed to a high flux of neutrons in order to induce transmutation. After a certain amount of exposure, these wastes are recycled through the separation/irradiation loop.

The high neutron flux may be produced by any of a number of methods that are often referred to as flux-trapping. These methods allow the flux in some regions of the fission reactor to be significantly higher than in other parts, making use of the strong decrease of cross sections of increasing neutron energy from thermal to MeV regime neutrons. Flux-trap reactor designs are described in, for example, U.S. Patents 3,255,083; 3,341,420; 3,276,963; 3,175,955; and 2,337,475.

Alternatively, the high flux may, in the future, be produced independently of fission reactors, most notably by fusion reactors. In this case economy of reaction utilization is not critical as copious supplies of neutrons can be produced with little accompanying radioactive waste. Figure 1 illustrates the inventive method generally.

Where reaction economy is an important factor i.e. fission produced sources, the preferred chemical/physical separation techniques is to be carried out as a two-stage process as illustrated in Figure 2.

In stage 1, reactor products are separated into components designated, for the sake of illustration A, B, D and D. Each component, once separated is maintained in a separate channel isolated from other components and fed to the high flux region. After transmutation in the high flux region the output of any given channel will generally contain some smaller amount of the original component remaining together with additional elements. These additional elements may be "good" products designated G_i, G₂....G₆, or other components which are long-lived and require further processing. The original component of each channel is thus separated in stage 2 from these additional elements as illustrated in figure 2. The recycling then occurs from the output of the stage 2 separation to the high flux region. Isotope separation may be part of stage 1 and/or stage 2 separation. Further, a specific rest stage may be provided before and/or after exposure to the neutron flux to permit β decay where desired prior to further neutron exposure.

The choice of separation/irradiation strategies depends, in addition to economic and chemical considerations, on the transmutations possible. Figure 3 shows a general format utilized in describing the decay/transmutation sequence and figure 4 illustrates, as an example, a portion of a chart of some nuclides illustrating the transmutation possibilities. Natural β decay transmutations change a nuclide into another shown directly above it, while artificial neutron induced transmutations take a nuclide into another immediately to the right. a and (3+decay are not significant, and for simplicity, only one isomer of each nuclide has been considered. The values shown on the vertical lines connecting nuclides are the half-life of the transmutation in hours, while the values on the horizontal line are neutron cross-sections in barns.

Fission yields per 100 fissions are also given in the chart. The direct fission yield is almost completely to neutron rich nuclides not shown, which would occur below those shown. These neutron rich nuclides rapidly undergo a series of (3 decays, as tabulated by Rose, P. F. and Burrows, T. W., ENDF/B Fission Product Decay Data, Aug. 1976, BNL-NCS-50545 (ENDF-243), to those nuclides which are illustrated on the chart. The yield shown on the charts of Figure 3 and 4 is therefore the same yield as the direct fission products of the same atomic weight.

Sr⁹° is a long-lived radioactive nuclide which is desired to be removed. Therefore, the transmutation from Sr⁹⁰ to Sr⁹¹ is a beneficial transmutation. Sr⁹¹ naturally transmutes in a short time to stable Zr^91. On the other hand, the other neutron induced transmutations shown are not beneficial and must be minimized by choice of the separation/irradiation loop. Y⁸⁹→Y⁹⁰, for example, does not involve long-lived nuclides at all and therefore the induced neutron transformation simply wastes neutrons. Sr⁸⁹→Sr⁹⁰ not only wastes neutrons but also procudes a long-lived nuclide. As described more fully hereinafter, the Sr89 is allowed to naturally transmute to Y⁸⁹ prior to insertion of Sr into the high neutron flux region. Y is then chemically separated from the Sr to prevent its otherwise neutron usage, and the Sr is exposed to the high neutron flux to transmute to Sr⁹⁰ to Sr⁹¹.

Table 1 lists 18 long-lived radioactive fission products of concern. These "bad" nuclides are broken-up into two groups, the first group having half-lives less than 100 years, and the second group having half-lives greater than 30,000 years. In addition, there are actinide wastes notlisted. In reference to figure 2, there may be up to 18 separate separation/irradiation loops for the fission products and an appropriate number of loops for the actinides, one loop for each substance.

The "bad" nuclides considered for elimination are listed in Table 1 and are defined primarily by the amount of radio-activity they are responsible for in the waste, after the waste has been stored for a certain length of time. Their half-life is not too long, else they provide very little radioactivity. Their half-life is not too short, else they decay during the storage period. They must be present, or at least have the possibility of being present, in a sufficiently high concentration to contribute significant radioactivity.

With these qualitative criteria in mind, the following somewhat arbitrary quantitative definition of a bad fission product nuclide is utilized:

• 1. Its half life is greater than 1 year;
• 2. Its half life is less than 10¹⁰ years;
• 3. Its atomic weight is between A=72 and A=167, since these are the limits of fission product compilations, and the yields outside this range are below the part per billion level.
• 4. It is descended from neutron-rich nuclear species by either (a) β decays or (b) a combination of decays and neutron absorptions. However, (3 decay chains through nuclides of half life greater than 10⁴ years are not considered. Exceptions to this rule are present at the 10 parts per billion level in the waste.
• 5. The excited states Sn^121m, HO^166m and Cd^113m are excluded.

A conservative level of activity at which a substance can be considered nearly safe is half the activity of an equal amount of U²³⁸. This criterion is in agreement with the cutoff in half lives of 10¹⁰ years, twice the half life of U²³⁸ (and also twice the age of the Earth). The required storage time as a function of half life is shown in figure 5, with the bad nuclides indicated by dots. For our one-year cutoff in half life, this criterion requires a storage time of 33 years. The lower group of bad nuclides requires up to 3,000 years of storage, while the upper group requires at least a million years for every nuclide in that group, and up to 1/30 the age of the earth.

The transmutation process must safisfy at leasuhreecriteria; (1) it must consume less energy than was produced when the waste was created, (2) it must generate of itself less hazardous waste than that destroyed, and (3) must eliminate waste materials at a rate significantly greater than their natural decay rate. Previous studies reported in ERDA-76-43, vol: 4 indicate that only neutron absorption processed can satisfy the first criterion. The major source of neutrons at present are the fission power reactors themselves. Therefore the issue of the second criterion is whether the number of neutrons produced in the power reactor is sufficient to transmute all or a substantial amount of the long lived waste produced along with those neutrons. The employment of chemical and/or physical separation of waste contained in this invention is aimed primarily toward the satisfaction of the third criterion. In the case of the actinides, both as a consequence of their large neutron capture probabilities and because their final removal by fission is accompanied by regeneration of some of the neutrons absorbed, all three criteria can be met. However, when the fission wastes are included, earlier studies cited above, not incorporating the principles of the invention, concluded that the second and third criteria could not be met. The invention is directed toward meeting all three criteria.

With regard to the second criterion, it is convenient to perform the transmutation in the power reactors themselves. Fission of an average U-235 nucleus generates a certain amount of waste and a certain number of neutrons. The question in satisfying the second criteria reduces to whether these neutrons are sufficient to transmute the waste produced.

More specifically, one may consider the fate of the neutrons produced from 100 fissions of U²³⁵, as illustrated in figure 6. All neutrons are considered to be thermalized. Of the 244 neutrons produced, 117 are required to maintain the chain reaction, causing 100 additional fissions and 17 absorptions without fission. The remaining 127 neutrons are absorbed in various ways including being absorbed in U²³⁸, producing actinide waste and ultimately more fission waste, and being absorbed in the moderator and structure of the reactor. Those remaining are available for waste transmutation. Of the 200 fission products there are 35 long-lived radio-active nuclei (plus those from fission of Plutonium and actinide wastes). This waste requires at least 35 of the, at most, 127 neutrons in order to accomplish the transmutation. Without the principles of the invention, many more than 35, and even more than 127, neutrons will be required.

To establish whether there are sufficient neutrons to eliminate the associated waste products, it is necessary to study the transmutation-decay chain information on all nuclides which are placed in the high flux region. The most important such nuclides are the isotopes of those elements including the long-lived radioactive fission products of which the eighteen most important radioactive nuclides are listed in Table 1. The nuclide symbol and half-life are listed in the first two columns. The cross sections which determine the neutron-induced transmutation rates are listed in the third column. The approximate amounts (per 100 fissions) in the nuclear waste is given in column 4. Column 5 gives the name of the element.

A computer program, WASTE, listed in appendix A was utilized to study the chains for all eighteen fission waste products. This program constructs a solution of a large set of coupled differential equations describing the transmutations. The form of these equations is that the time rate of change of any nuclide is equated to a sum of up to four terms as follows:

• 1. The decrease of the nuclide by natural decay.
• 2. The decrease of the nuclide by neutron-induced transmutation into another nuclide.
• 3. The increase of the nuclide from neutron-induced transmutation of another nuclide.

The computer program further allows initial separation and periodic separation between exposures to a high thermal neutron flux. A strategy for each nuclide is presented which is sufficient to meet the three criteria for successful transmutation.

In utilizing fission reactors, it is possible that (1) each reactor is responsible for precessing its own waste or (2) several "power" reactors send their waste to one "transmutation" reactor. In as much as neutrons are in short supply, and the second alternative is most probably not viable since it wastes the neutrons. The first possibility, of course, allows the exchange of waste between different reactors; one, for example, might handle all the cesium while another handles all the zirconium, with appropriate design differences between the reactors. The important consideration is that neutrons not be wasted.

Any given nuclide, which we label by its atomic weight A and its atomic number Z, may undergo β decay to the nuclide (Z+1,A) or it may undergo neutron absorption to the nuclide (Z,A+1). The rate constants for these processes are α_Z,_A=In 2/T_z,A(½) and σ_ZAφ respectively, where T_ZA^(½) is the nuclides half life and _UZA is its neutron absorption cross section, while φ is the effective flux. Thus the amounts N_Z,_A of the nuclides obey the set of differential equations

The first two terms determine the loss of the nuclide due to its decay and neutron absorption while the last two terms determine its gain due to the decay or transmutation of other species.

The solution of this equation has the form0 where λ_Z',A',=α_Z',A'+σ_Z',A'φ and the C's are determined by the initial amounts and by substituting this solution into the differential equation.

In detail, the C's are given by:

• 1) for Z,A not both equal to Z',A' C_Z,_A;Z',_A'(where C's which don't obey the conditions Z'≤Z, A'?A are zero)
• 2) For Z,A=Z',A'These substitutions are carried out in order of increasing Z and increasing A. Thus the lowest nuclide in a chain, which will occasionally be a bad isotope, has its amount decreased following an exponential curve:The effective half life for removal is

These effective half lives of the bad nuclides are compared to the natural half life in Table 2. The effective flux is taken to be 10¹⁶ neutrons/cm² sec.

Another case of importance is that of a nuclide which has a lower nuclide in the chain with a smaller value of À. Let us take, for example, a nuclide (Z,A) accompanied by a lighter isotope (Z, A-1) such that λ_Z,A-1 <λ_Z,A

Then the solutionwill approach for large t so that the ratioThis constant is evaluated by substitution into the differential equation, and found to beIn the cases considered below, neutron absorption dominates λ_Z,A and σ_Z,A>>σ_Z,A―1, so this equilibrium ratio becomes the ratio of cross sectionsThis establishment of equilibrium also applies to longer chains. This effect is important for Kr⁸⁵, Zr⁹³, Pd¹⁰⁷, and Sm¹⁵¹, as is discussed below.

The transmutations of the 18 bad isotopes have been analyzed for periods of up to about 100,000 hours (about 11-1/2 years) of irradiation in a flux of 10¹⁶ neutrons/cm2 sec. From Table 2, one can see that this time period ranges from orders of magnitude more than enough time to remove a nuclide to less than one half-life. The improvements of removal rate over natural decay varies from a few percent to a factor of over 1₀₈.

Two types of ideal cases may be considered, one with perfect isotope separation being carried out frequently before and during the separation/irradiation cycles and one with perfect chemical separation being carried out periodically. Clearly, the more separation that can be accomplished, the more efficient is the transmutation. The isotope separation provides an absolute optimum situation, and provides a measure of the inefficiency of chemical separation. For the case of chemical separation, two possibilities are treated for some waste components. In the first case, it is assumed that there is control over the time between fission and chemical separation. This situation is possible in liquid fission fuel reactors where the fuel and waste may, for example, be continuously cycled without shut-down of the reactor, In the second, the time between fission and separation is assumed long, as for example, in solid fuel fission reactors. The extra control allows one to separate nuclides which would otherwise decay into another element.

Table 3 shows the results of the computer analysis for chemical separation and for isotope separation. The two cases of chemical separation are labeled a and b for separation with and without timing respectively. The table is ordered by increasing half life and divided into the first and second groups previously defined in relation to Table 1.

A very rough measure of the hazard of nuclear waste is the total amount of each of the two groups of bad nuclide. (This measure neglects differences in biological activity, in ease of storage (i.e., geochemical effects, in half life within a group, and in the nature of the radiation emitted). The waste starts with about 15 atoms per hundred fissions for the low group and 20 atoms of the high group.

With isotope separation, after the processing of each nuclide for a length of time somewhat appropriate for the nuclide, but for less than '12 years, 4 atoms of the low group and 2 atoms of the high group remain. If the processing (with isotope separation) were to continue up to 12 years, half the Cs¹³⁷ (3.1 atoms), a small amount of Sr⁹⁰ (.14 atoms) and traces of Ru¹⁰⁶, Sb¹²⁵, and Kr⁸⁵ would remain in the lower group. Other sizable numbers in the table result from the short time of processing imagined. The high group would contain a small amount of Sn¹²⁶, an amount of Sell depending on its cross section but less than .055 atoms, and a trace of Zr⁹³. All other bad nuclides would be removed. About 32 of the up to 127 neutrons would be used.

With chemical separation only there are a number of significant differences. After processing, there are in addition .0014 atoms of Sb¹²⁵, .06 atoms of Kr⁸⁵, and .013 atoms of Sm¹⁵¹ remaining in the lower group, and a considerable amount (.5 to .86 atoms) of Zr⁹³ and .035 atoms of Pd¹⁰⁷ remaining in the upper group. The neutron usage has increased from 32 up to 47 or 74 neutrons, from 12 to 20 in the lower group and from 20 to 27 or 55 in the higher group. The 8 extra neutrons in the lower group have been used about 4 for Pm¹⁴⁷, and about 1 each for Eu¹⁵⁵ , Kr⁸⁵, and Sm¹⁵¹. In the upper group the extra neutrons have been used largely by Zr⁹³, even in case a, and by Cs¹³⁵ if case b holds. Pd¹⁰⁷ has also used up an extra neutron.

It is to be noticed that case a of Cs¹³⁵ (discussed in detail below) is even superior to isotope separation, due to the tiny amount of processing time required.

With chemical separation only there is another important consideration. For a number of the elements with bad isotopes, there are stable isotopes with a smaller cross section than the bad isotope. As separation/irradiation goes on, the bad isotope is depleted while the level of stable isotopes remains high. In five cases, listed in Table 4, a significant amount of stable isotopes remain after a reasonable amount of processing. The amount of bad isotope is listed and the number of neutrons that would be wasted in completely transmuting all of the stable isotopes. This amount is most significant for Zr⁹³, even though the more favorable case was chosen (i.e., case a). The ratio of extra neutrons to bad isotope remaining is the largest in the case of Sm¹⁵¹, in which it requires over a thousand neutrons to convert the good Samarium in order to remove one atom of the bad.

If the large number of neutrons required are not available, then the remaining amounts of these elements, containing the remaining bad isotope, have to be disposed of, and the bad isotope remains a hazard. As the high neutron flux exposure goes on, different lots of these elements at different degrees of depletion of the bad isotope may be kept isolated from one another. This process may be accomplished by a spiral-type channel arrangement shown in Figure 2 by the dotted lines in reference to component A.

On the other hand, the remaining elements, most notably the large amount of Cs¹³⁷, can have the partially processed part of the element combined with the part of that element freshly separated from the recent fission waste, as indicated by the solid lines in Figure 2.

The greatest advantage of isotope separation would occur for Zr⁹³, which wastes a large number of neutrons and which has a very significant amount of Zr⁹³ left with the stable isotopes of Zirconium after a reasonable amount of processing has taken place. Isotope separation is significant for Cesium unless case a is utilized, because of the large number of neutrons needed. Isotope separation is also useful for Sr⁹⁰ and for the other elements on Table 4 if the amounts remaining are considered objectionable, and depending on the required neutron economy could be useful for those elements which require extra neutrons.

Each element was studied by computer runs utilizing the program WASTE shown in the appendix. Perfect chemical separation processing has been assigned for each channel with respect to all elements not originally in the channel.

The bad nuclides are discussed in order of increasing atomic number and increasing atomic weight. It is noted that in developing a strategy for each individual bad nuclide, there is no interdependency between the individual bad nuclides except in the case of Pr¹⁴⁷ and Sm¹⁵¹.

The decay/transmutation chain for Se⁷⁹ is shown in Figure 7. The thermal neutron absorption cross section for Se⁷⁹ is shown in Figure 7. The thermal neutron absorption cross section for Se⁷⁹ is not reported (probably owing to its low abundance) and may be assumed small. Thus one may assume that no significant reduction of this isotope is possible. If however the neutron absorption cross section is found to be significant, the separation/irradiation process may be utilized with Br and Kr removed periodically to enhance neutron economy.

Figure 8 shows the decay/transmutation chain for Kr⁸⁵. Only about 20% of the A=85 waste ends up as radio-active Kr⁸⁵. The remainder ends up as Rb⁸⁵, because the rapid β decay chain passes through an excited isomer of Kr⁸⁵ which β decays to Rb⁸⁵. As a result, there is considerably more of the stable isotopes K_r⁸³, Kr⁸⁴, and Kr⁸⁶. Kr⁸³ has by far the largest neutron absorption cross section. Kr⁸⁴ and Kr⁸⁶ each have a cross section about 1/20 of Kr⁸⁵.

When the Kr is subject to the neutron flux Kr⁸³ is converted into Kr⁸⁴. At this point the ratio of Kr⁸⁴ to Kr⁸⁵ is about 5. This ratio cannot exceed 20 (the ratio of the cross sections of Kr⁸⁵ and Kr⁸⁴). Therefore, after about 75% of the Kr⁸⁵ has been transmuted, it becomes difficult to convert any more Kr⁸⁵. For every 20 atoms of Kr⁸⁴ converted to Kr⁸⁵, only 21 are converted to Kr⁸⁶. Meanwhile about 30 Kr⁸⁶'s are transmuted. Thus it takes about 70 neutrons to gain 1 Kr⁸⁵.

The results of the actual circulation are shown in Figure 9 to 48,000 hours (somewhat over 5 years) at which time 75% of the Kr⁸⁵ is gone. At about this time, the natural decay of Kr⁸⁵ actually removes if faster than continued exposure to neutrons. Only isotope separation would improve matters. Figure 9 also shows the removal of Kr⁸⁵ as compared to its natural decay. Also shown are the average and marginal usage of neutrons showing the effects to Kr⁸³ at very small times and Kr⁸⁴ at large times. Different scales are used for amounts and neutron usage.

Thus it is reasonable to reduce Kr⁸⁵ to a level 2 or 3 times lower than natural decay would give, and no further except with isotope separation. In order to conserve neutrons it was assumed that all the decay/transmutation products, i.e., Rb and Sr were completely separated from Kr after each irradiation step was completed. The gas Kr may be readily separated from these solid products.

The decay/transmutation chain for Sr⁹⁰ is also shown in Figure 8. Sr⁹⁰ is transmuted according to the exponential law, since the only other isotope of Strontium in the waste is stable Sr⁸⁸ which transmutes to Sr⁸⁹ with a very small cross section. Sr⁸⁹ is initially present in the waste (as well as being produced from Sr⁸⁸), but it decays with a half life of 1250 hours, short compared to the relevant time scale for the transmutation of Sr⁹⁰.

The program WASTE was utilized with chemical processing every 3000 hours. No indication of undesirable effects of the build-up of Yttrium and Zirconium were noted. Clearly a much less frequent chemical processing for separation of Y and Zr from Sr would suffice. Only 1.06 neutrons are required for each transmutation of the first 96% of the Sr⁹⁰. The effective half life of Sr⁹⁰ in a flux of 10¹⁶ neutrons per square cm per second is 2-1/4 years.

More of the nuclear waste is Zirconium (15%) than any other single element. The presence of many stable isotopes of Zirconium, in addition to the bad isotope Zr⁹³, make the removal of this isotope by transmutation difficult. The stable isotopes in the waste are Zr⁹¹, Zr⁹², Zr⁹⁴, and Zr⁹⁶. Although Zr⁹³ has a larger neutron absorption cross section than any of the stable isotopes, it is not large enough to make transmutation easy. Figure 10 shows a portion of the decay/transmutation chain including Zr⁹³.

Two possibilities for the treatment of Zr⁹³ are considered. In the more favorable case, the initial chemical separation is carried out in a time short compared to two months after the fission process. Such is the case, for example, in a liquid fuel reactor with continuous processing for wastes. In this case, the Yttrium is separated from the Zirconium. The y⁹¹, with a half life of about two months, decays into stable Zr⁹¹, which therefore is isolated from the Zr⁹³. The Zr⁹², Zr⁹³, Zr⁹⁴, Zr⁹⁵ and Zr⁹⁶ are then allowed to stand, allowing the Zr⁹⁵ to decay (with a half life also of about two months).

The results presented for Zr⁹³ labelled as case a assume the ideal situation of no Zr⁹¹ in the Zirconium to be irradiated by the neutrons. In this case, the Zr⁹³ which starts at the level of 6.36 atoms per hundred fissions, is irradiated for about 6 years resulting in about 92% net removal of the Zr⁹³, at a cost of 12 neutrons, or a little worse than 2 neutrons per atom removed. Further irradiation accomplished little, because at this point the transmutation of Zr⁹³ is approaching equilibrium with the transmutation of Zr⁹² into Z_r⁹³, and there are significant amounts of Zr⁹⁴ and Zr⁹⁶, as well as Zr⁹² competing for the transmutation neutrons. The removal of Zr⁹³ is shown in Figure 11.

In the less favorable case, labelled b in the results, the Zr⁹¹ is included. After 50,000 hours (about 6 years) the Zr⁹¹ has added an extra 6% of the original Zr⁹³ by the sequential transmutation chain, Zr⁹¹→Zr⁹²→Zr⁹³ atom removed. In both cases, neutron economy is enhanced by periodically separating Zr from Nb and Mo.

It is clear that isotope separation would help greatly for Zr^93. The exponential removal curve for pure Zr⁹³ is compared to the curves for chemical separation in Figure 11. After 50,000 hours almost 99% of the Zr⁹³ is transmuted.

Tc⁹⁹, whose decay/transmutation chain is shown in Figure 12, provides one of the most favorable cases for transmutation. It has a reasonably large cross section for neutron absorption and there is only the single isotope, Tc⁹⁹, in the waste. Therefore the removal follows an exponential curve (with an effective half life of 42 days). After chemical processing, all the Tc can be combined, since it is all Tc⁹⁹. With chemical processing every 300 hours, the neutron usage is 1.03 neutrons per transmutation. The extra 3% comes from absorption in Ru¹⁰⁰ which builds up for the 300 hours.

Ru¹⁰⁶, whose decay/transmutation chain is shown in Figure 13, has a half life of 1.01 years, just above the cutoff of 1 year. It requires 33.4 years to decay to half the activity of U^238. It has a very small neutron absorption cross section, 146 barns, requiring an exposure to neutrons for 31.4 years to reduce the activity to the same level. The saving of 2 years is not deemed worth the trouble and expense of cycling and processing. Therefore Ru¹¹⁶ may be treated as a short-lived isotope, storing it for at least 33-1/2 years before allowing it to enter the environment.

The decay/transmutation chain for Pd¹⁰⁷ is shown in Figure 13. There is not much Pd¹⁰⁷ in the waste since it is on the high side of the lighter bump in the fission yield curve. Pd¹⁰⁵, with an atomic weight smaller by only 2, has 6 times the fission yield. Ru¹⁰⁶ has an intermediate yield, and decays to Pd¹⁰⁶ (in two steps) with a half life of 1 year. Ruthenium is assumed to be separated from the Palladium before a significant amount of it has been allowed to decay (if processing occurs within half a year after fission, the results are not substantially modified).

The Pd¹⁰⁵ has a cross section 40% larger than Pd¹⁰⁷, which when multiplied by the factor of 6 in yield gives a conversion rate 8.4 times that of Pd¹⁰⁷ Pd¹⁰⁷ transmuted to Pd¹⁰⁸, which, with a roughly comparable cross section, converts to Pd¹⁰⁹ which rapidly decays. Thus, in the early stages of transmutation it takes over 10 neutrons for each transmutation of a Pd¹⁰⁷ atom.

Later, the concentration of Pd¹⁰⁶ builds up, approaching an equilibrium value of about 40 times the amount of Pd¹⁰⁷, since its cross section is 40 times smaller. At equilibrium 40 atoms of Pd¹⁰⁶ convert to Pd¹⁰⁹, requiring 120 neutrons, for every net Pd¹⁰⁷ removed. The average neutron use per Pd removed approaches 4x6+2=26 for each 6 atomes of Pd¹⁰⁵ and one atom of Pd¹⁰⁷ converted to Pd¹⁰⁹.

In an actual example calculation 78% of the Pd¹⁰⁷ was removed in 9000 hours, at a cost of about 12 neutrons for each atom of Pd¹⁰⁷ removed. Since the initial amount was small, this corresponds to, for example, a level of Cs¹³⁵ after removal of 99-1/2% of the initial amount.

Neutron economy would dictate removal of Pd from Ag and Cd prior to recycling into each new irradiation step.

The decay/transmutation chain for Sn¹²⁶ and Sb¹²⁵ are shown in Figure 14. These isotopes occur at the minimum of the yield curve, and are present in very small amounts. As a result, neutron economy is not of paramount importance and the products I and Te need not generally be separated. They are treated together because exposure of tin to neutrons produces Sb¹²⁵. The cross section for Sn¹²⁶ is very small, so transmutation is very slow. After about 12 years in a flux of 10¹⁶ neutrons/cm² sec., one third of the original Sn¹²⁶ still remains. However, this corresponds to .3% of any one of the five most common bad isotopes. Sb¹²⁵ is easily removed.

1¹²⁹ (Figure 15) is removed following an exponential curve, since 1¹²⁸ is highly unstable. The effective half life of 1¹²⁹ in a flux of 10¹⁶ neutron/cm² sec., is about a month. The neutron use does not exceed 1.2 neutrons per 1¹²⁹ atom transmuted, as the 1¹²⁹ is accompanied by 1/5 as much I¹²⁷. In the early stages, the situation is even more favorable since the cross section for I¹²⁷ is smaller. After 3000 hours, the average use was 1.1 neutrons per transmutation, as only about half of the I¹²⁷ was removed.

The enrichment of I¹²⁷ relative of 1¹²⁹ probably is not significant enough, due to the small amount involved, to make it worthwhile keeping the iodine already processed separate from the iodine freshly produced from fission.

The results for a 3000 hour processing run are presented in Table 3, but it is to be understood that exponential removal continues idenfinitely.

Iodine may readily be separated from the fission waste and is thus a very favorable element for waste transmutation.

C_S¹³⁵ and Cs¹³⁷ are somewhat separate problems, and are discussed separately. Cs¹³⁴ is not a direct fission product and therefore occurs in small amounts in the waste. It has a large cross section and is easily removed in the treatment of Cs¹³⁵ and Cs¹³⁷. Figure 16 shows a portion of the decay/transmutation chain including Cesium.

The major problem with the treatment of Cs¹³⁵ is the large amount (6.75 atoms/100 fissions) of stable Cs¹³³ in the waste. Cs¹³³ has a considerably higher neutron absorption cross section than Cs¹³⁵, and must absorb 3 neutrons before again becoming a stable nuclide. The chain is Cs¹³³→nCs¹³⁵→nCs¹³⁶→Ba¹³⁶.

It is noted, however, that the cesium in the waste comes from (3 decay of the inert gas Xenon. Xe¹³³ has a half life of over 5 days, and Xe¹³⁵ has a half life of over 9 hours. Xe¹³⁵ has an extremely high neutron absorption cross section (3x10⁶ barns) and stable Xe¹³⁶ has a very small cross section (.16 barns). Stable Xe¹³⁴ also has a rather small cross section (1.73 barns).

If the Xenon is separated in a time small compared to 5 days after fission, and especially if it can be separated in a time small compared to 9 hours, Cesium may be efficiently treated. A liquid fuel reactor would clearly be desirable in achieving these short processing times, since the processing may be continuous.

As soon as Xenon is separated out, it is exposed to a high neutron flux for a short time. At 10¹⁶ neutrons/cm² sec., the optimum time is 11 minutes. In the example of Table 3, 20 minutes was used. After this irradiation the Xenon is removed from the flux and stored for, say, two months for the Xe¹³³ to cecay (this is about 30 half lives of Xe¹³³). After this, the Xenon left is not radioactive. There may be a further separation of the Cesium produced in the first two hours after fission. Thus there are three, possibly four, places in which Cesium is produced. The Cesium produced before separation consists of some or most of the Cs¹³⁷ and a small amount of Cs¹³⁵ and Cs¹³³. The amounts depend on the time before separation. The Cesium produced during the irradiation is some or most of the Cs¹³⁷, and a small amount of C_S¹³⁵ and Cs¹³³. For the first two hours after fission, Cs¹³⁷ is produced, and it might be desirable to keep it with the Cesium produced in the first two steps. After 2 hours, most of the Cs¹³³ is produced. This Cs¹³³ would not be subject to further irradiation. The amount of Cs¹³⁵ that is contained in with this Cs¹³³ is 4.4x10^―6 atoms per 100 fissions (22 parts per billion of the waste), coming from the equilibrium between Xe¹³⁴ and Xe¹³⁵.

Figure 17 shows the amount of Cs¹³³ and C_S¹³⁵ produced up to end of the time of irradiation as a function of the time of separation. If, for example, separation is accomplished in 6 minutes, there will be 0.055 atoms of Cs¹³⁵ per 100 fissions. In the first two hours after irradiation 0.08 atoms of Cs¹³³ per 100 fissions out of a total of 6.75 are produced.

The results labeled a in Table 3 correspond to no further treatment of the Cs¹³⁵, although, of course, it would be treated if the Cs¹³⁷ is treated. The results assume immediate separation of the Xenon.

In cases when the Xenon cannot be separated out rapidly (solid fuel reactors), much of the Xe¹³⁵ is not transmitted to Xe¹³⁶ but decays to Cesium which must be treated. These results are shown in Figure 18, and as case b in Table 3.

As can be seen, the time scale is long and the neutron usage is extremely large, costing 20 neutrons (per 100 fissions) to convert the stable Cs¹³³ to Ba¹³⁶. Isotope separation would clearly be highly desirable. Figure 18 shows the following sequence of events:

• 1. Cs¹³⁴ relatively rapidly builds up from the transmutation of C_S¹³³, until after about 500 hours it is in equilibrium with C_S¹³³_;
• 2. After about 100 hours enough C_S¹³⁴ has built up that the amount of C_S¹³⁵ actually increases:
• ₃. After ₂₀₀₀ hours the C_S¹³³ (and C_S¹³⁴) is mostly depleted, and the Cs¹³⁵ starts being removed following an exponential curve;
• 4. At about 2700 hours, the amount of Cs¹³⁵ is back to where it started.
• 5. The amount of C_S¹³⁵ lags 2900 hours (4 months) behind where it would be had there been no Cs¹³³ in the waste to be irradiated.

If the Cs¹³⁵ is handled by transmuting Xe135 the remainder of the Cs¹³⁵ can be removed following curves similar to case b, but about 100 times lower. The extra neutron usage will also be about 100 times smaller. If the separation time in case a is 2 to 100 hours, a situation intermediate between case a and case b results.

Cs¹³⁷ has the smallest neutron absorption cross section of any of the bad nuclides (with the possible exception of Se⁷⁹). Irradiation in a flux of 10¹⁶ neutrons/cm² sec. only brings the effective half life to 12 years, compared to 30 years for natural decay. Aside from a small amount of C_S¹³⁷ generated fromCs¹³⁷ removal follows an exponential curve (most Cs¹³⁶ decays to Ba¹³⁶).

Since the Cesium becomes essentially pure Cs¹³⁷ as the processing continues, there is no need to segregate the old and new Cesium if Cs¹³⁷ is to be treated.

The modest gain in removal rate in Cs¹³⁷ might make it not worthwhile to treat it beyond what is needed for C_S¹³⁵ removal, unless a flux even higher than 10¹⁶ neutrons/cm² sec., is utilized. Neutron economy is improved by separation of Cs from all other products, i.e. Ba, La, Ce, etc.

Pm¹⁴⁷ (figure 19) is the lightest isotope of Promethium in the waste, and the only one with a large half life. It is transmuted following an exponential curve with an effective half life of 4-1/3 days in a flux of 10¹⁶ neutrons/cm² sec.

The difficulty in removing Pm¹⁴⁷ concerns neutron economy. In any flux which gives a transmutation rate larger than the natural decay, most of the Pm¹⁴⁷ ends up as Sm¹⁵⁰, mostly by the chain Pm¹⁴⁷→Pm¹⁴⁸→Pm¹⁴⁹→Sm¹⁴⁹→Sm¹⁵⁰. Thus it costs 3 neutrons per Pm¹⁴⁷ atom transmuted.

There is also a small amount of the bad isotope Sm¹⁵¹ created from the Sm¹⁵⁰, the amount depending on the frequency of chemical separation of the Samarium from the Promethium (the Samarium is then not exposed to any more neutrons). In the example of Table 3, chemical processing was assumed to occur every 2 hours. The amount of Sm¹⁵¹ produced is comparable to the amount of Sm¹⁵¹ left after the irradiation of the Samarium waste. It is not feasible, without isotope separation, to transmute this Sm¹⁵¹.

Since Pm¹⁴⁷ with a half life of 2.6 years is rendered essentially harmless by storage of about 85 years, while the Sm¹⁵¹ produced requires 1900 years to reduce it to the same low level of activity, it may be better not to attempt to transmute the Pm¹⁴⁷. However, if higher level are considered acceptable, the decrease of 2.3 atoms of Pm¹⁴⁷ to .005 atoms of Sm¹⁵¹ is significant.

The Sm¹⁵¹ (figure 19) is accompanied by a larger amount of Sm¹⁴⁹. Sm¹⁵¹ has a large neutron absorption cross section (1.4x10⁴ barns) but Sm¹⁴⁹ has an even larger cross section by nearly a factor of five.

Therefore, a Samarium is exposed to the neutrons, the first thing to happen is the conversion of Sm¹⁴⁹. This can be seen on figure 20 by the large neutron usage in the first two hours of irradiation. The next thing to happen is the transmutation of most of the Sm¹⁵¹. The cost in neutrons rises during this period from a minimum at around 3 hours into the irradiation. This rise in neutron usage is due to the competition of neutron absorption in Sm¹⁵² and Sm¹⁵⁰, and the Sm¹⁵¹ being produced from Sm¹⁵⁰. Finally, the Sm¹⁵¹ comes into equilibrium with the Sm¹⁵⁰ at a level Sm¹⁵¹/Sm¹⁵⁰=σ¹⁵⁰/σ151|≈1/40. At this point, about 98% of the initial amount of Sm¹⁵¹ is removed. Equilibrium is nearly obtained after about 15 hours, as seen in figure 20. Further irradiation is extremely costly in neutron usage even though there is such a small amount of Sm¹⁵¹ remaining. Moreover, the Sm¹⁵¹ resulting from the treatment of Promethium'is at roughly the same level. The treatment of this other Samarium would actually cause an increase in the amount of Sm¹⁵¹, since the Sm¹⁵¹/Sm¹⁵⁰ ratio is well below 1/140. Thus, without isotope separation, (or an extremely copious supply of neutrons) a reduction of Sm¹⁵¹ to about .013 atom per 100 fissions is the best that can be achieved. Neutron economy may be enhanced primarily by separation of Eu products.

Europium (figure 19 & 21) is one of the heaviest elements in the waste, and occurs in small amounts. Eu¹⁵² and Eu¹⁵⁴ do not occur directly as fission products. What little Eu¹⁵² does occur will be rapidly transmuted while the Eu¹⁵⁵ is being removed, as will the Eu¹⁵¹ coming from the Sm¹⁵¹ that decayed before it was transmuted.

In processing the Europium, it need not be separated from the Samarium while the Samarium is being processed, as there will be small amounts of radioactive Europium produced in the treatment of Sm¹⁵¹, which should be included with the fission-produced Eu¹⁵⁵.

Transmutation of Eu¹⁵⁵ per se is very simple, as indicated by the "isotope separation" columns of table 3. However, the waste contains some Eu¹⁵³, which is converted to radioactive Eu¹⁵⁴. Therefore, in order to remove the Eu¹⁵⁵ it is necessary to convert the Eu¹⁵³ by the chainThere is 5 times as much Eu's3 as Eu¹⁵⁵, and it requires 5 neutrons for conversion to Gd¹⁵⁸ leading to neutrons per atom of Eu¹⁵⁵ removed.

If the flux were 10-30 times smaller, the Eu¹⁵⁶ would have time to decay, terminating the chain at Gd, saving up to 40% of the neutrons.

Figure 22 shows the time development of the amounts of Eu¹⁵⁴ and Eu¹⁵⁵. For the first 15 hours or so, the initial Eu¹⁵⁵ is rapidly transmuted away, while the Eu¹⁵⁴ builds up almost as fast as the Eu¹⁵⁵ is removed. After that, the Eu¹⁵⁴ continues to build up while it, in turn, transmutes to Eu¹⁵⁵. After about 60 hours the Eu¹⁵⁴ and Eu¹⁵⁵ are in equilibrium with the remaining Eu¹⁵³ and then are removed at a rate determined by the Eu¹⁵³ cross section.

In the processing, all isotopes of Europium are removed. Therefore, no harm is caused by combining the already-processed Europium with fresh Eu.

The amounts and composition of the actinides depends on the parameters of the reactor system such as the enrichment of the Uranium and the integrated flux to which it has been exposed. We consider four components of the actinides produced from U²³⁸ and U²³⁵ by neutron absorption, which may coincide with the components in the transmutation system. These components are:

• ¹. _U236
• 2. Np²³⁷
• 3. Fresh plutonium
• 4. Spent plutonium and trans-olutonium actinides.

Fifteen percent of the U²³⁵ on absorbing a neutron does not fission but produces U236. This U236 would be only moderately expensive in neutrons to transmute except that it is mixed in with all the U²³⁶ in the spent fuel. It is impossible from the point of view of neutron economy to put the U²³⁸ in the high flux region. If the U²³⁶ produced from all U²³⁵ by neutron irradiation is mixed in with the amount of U²³⁸ accompanying that much U²³¹ in natural uranium, the radioactivity is double that of U²³⁸. Therefore, U²³⁶ does not pose a serious hazard if combined with the U²³⁸.

Some of the U²³⁶ will absorb a neutron, giving the transmutation chainIf this Np²³⁷ is exposed to as high a flux as possible, it first transmutes to Np²³⁸ which then fissions if it absorbs a neutron or decays to P_U²³⁸. The fissioning is preferable on the grounds of neutron economy.

U²³⁸, if it absorbs a neutron, becomes PU239 This plutonium (as well as the Pu²³⁸ discussed above) is, on separation, used as a fissionable substance. In thermal fission, 3/4 is fissioned and 1/4 becomes Pu²⁴⁰. The Pu²⁴⁰ absorbs a neutron becoming Pu²⁴¹, Three-fourths of Pu²⁴¹' fissions and 1/4 becomes Pu²⁴².

Pu²⁴² and heavier isotopes are not fissionable with high probability and form part of the heavy actinide waste. By sequential neutron absorption, these eventually lead to fission. Fissionable isotopes include Cm²⁴⁵, Cm²⁴⁷, Bk²⁵⁰, Cf²⁴⁹, Vg²⁵¹, and Es²⁵⁴. Although the number of neutrons required per atom of Pu²⁴² is large, the very small quantities involved makes the neutron usage not have a serious effect on the total neutron economy. This is consistent with the conclusion of earlier studies that actinides can be reduced by transmutation.

The neutron economy is approximately a net loss of one neutron for each atom of Np²³⁷ (including the absorption on U²³⁶) and approximately a balance (a small net loss) for each atom of U²³⁸ transmuted. In addition, the fission wastes from Plutonium and other actinides increase the amount of fission wastes that must be processed by the excess neutrons from the fission of U²³⁵.