IRRADIATED FUEL INVENTORY
Several computer programs are commonly used to compute the changing inventory of nuclides during reactor operation and at any time after shutdown (for example, ORIGEN (Bell, 1973), FISP (Clarke, 1972; Tobias, 1978) and FISPIN (Burstall and Thornton, 1977; Burstall, 1979). Fissionproduct yields for each fissioning nuclide are used in conjunction with the effective groupaveraged fission cross sections, decay constants and mean alpha, beta and gamma energy releases to calculate decay heat. Thus, substantial quantities of data are required to determine core inventories and define their decay characteristics. The nuclides listed in Tables 1, 2 and 3 represent the fission products, structurallybased activation products and actinides (and their decaychain nuclides) respectively, that would normally be included within inventory calculations.
The resulting fission products can undergo transformation by several modes of radioactive decay, neutron absorption, or a combination of these processes. A series of linear decay chains can be defined that include a number of shortlived fission products that have not been experimentally observed or adequately characterised; theoretical data can be adopted (halflives denoted in parentheses in Appendix B. 1, which also provides a reasonable summary of the fission products associated with decayheat calculations). All such data are subject to significant modifications throughout future years.
The effective yield of fission product i (a) is given by the equation:
N
a = Z Z J°* tkNa (t) Y’a, k
a k =1
where <JFk is the effective groupaveraged fission cross section of actinide a in the kth neutron group (of N groups,), ф is the neutron flux in the kth neutron group, Na(t) is the number of atoms of fissile actinide a at time t of irradiation, and Y’ak represent
the independent yields for fission product i. A period of reactor operation may be represented as a series of time steps in which timedependent quantities are constant for an individual step, but vary between steps.
Consider a linear decay chain
N1 —— N2 —— N3 —— Ni ——
with effective fission yields a, decay constants Лі per sec, and effective neutron — capture cross sections Ji cm2. The number of atoms Ni as a function of time is given by
(N1 ) = (л + a F
where ф (n cm2 s1) is the effective neutron flux, and F is the fission rate (s1)
(Л + 02ф) N 2 + a2 F + y1 N1
and
in which y1 = (ki1)(Ai.1) or (к.1)(аі.1)ф, depending on the coupling between (i1) and i, and ki1 is the relevant branching fraction. The set of equations represented by
d (N) can be solved by either an analytical method or numerical integration.
dt
Actinide inventories can be calculated in a similar manner on the basis of the following processes:
(a) radioactive decay,
(b) total neutron absorption and production from (n, y) and (n, 2n) reactions,
(c) production from alpha and beta decay of parent nuclides.
Appendix B. 2 outlines the formation of these actinides in irradiated fuel (particularly Pu, Am and Cm radionuclides) and their decaychain products. The number of atoms NZA of nuclide of atomic number Z and mass number A is given by the equation:
X{ 0^1 (E)Ф(Е)dE X{ <An+1 (E)ф(Е)dE
where ufj (E), о(^7) (E) and оц71п) (E) are the total neutron absorption, (n, y) and (n, 2n) cross sections respectively, at neutron energy E for a nuclide of atomic number i and mass number j; , Лв. , Лв. , Л]. are the alpha, negatron, positron
and total decay constants for the nuclide of atomic number i and mass number j; ka, k and kg+ are the branching fractions for a, P" and P+ decay to nuclide Z, A; and
ф(Е) is the neutron flux at neutron energy E. The coupling of the linear system of firstorder differential equations is complex, and they are normally solved by means of numerical integration.
After reactor shutdown, the fission products and actinides formed during reactor operation will undergo radioactive decay. The number of atoms at time t following shutdown can be expressed as a series of equations:
dN = — лN +Л1 n
dt
that are coupled in a much less complex manner after shutdown than for reactor operation.
When the actinide and fissionproduct inventories have been calculated for the specified conditions of reactor operation and subsequent cooling period, the decay heat can be derived by summing the products of the nuclear activities in terms of the mean alpha, beta and gamma energy releases per disintegration of that nuclide:
M
Ha(t) = ХЛ N (t) E’a
i=l
M
Hp(t) = XЛЛ N,(t) EP
i=1
M
Hr(t) = £Л[ N(t) EY
i=l
where E’a, E’p and Elf are the mean alpha, beta and gamma energy releases
respectively per disintegration of nuclide i; Л] is the total decay constant of nuclide i, and Ha(t), Hp(t) and H(t) are the total alpha, beta and gamma decay heat respectively at time t after reactor shutdown.
The nuclear data requirements for decayheat calculations can be determined from the information given above:
_F &a, k 
— effective groupaveraged fission cross section of actinide a in the kth neutron group, 
<■ 
— total neutron absorption cross section of fission product i, 
Nf 
— (n, y) cross section of fission product i, 
_(n,2n) i, j 
— (n, 2n) cross section of fission product i, 
YU 
— independent yields for fission product i, 
U 
— decay constant(s) of fission product i, 
ka, kp~ , ke+ 
— branching fractions for a, P — and P+ decay to nuclide Z, A, 
К, E, EY 
— mean alpha, beta and gamma energy releases per disintegration of nuclide i. 

34 Se74, Se75, Se76, Se77, Se77m, Se78, Se79, Se79m, Se80, Se81, Se81m, Se82, Se83, Se83m, Se84, Se85, Se86, Se87, Se88, Se89, Se90, Se91, Se92;
35 Br77, Br77m, Br78, Br79, Br79m, Br80, Br80m, Br81, Br82, Br82m, Br83, Br 84, Br84m, Br85, Br86, Br87, Br88, Br89, Br90, Br91, Br92, Br93, Br94;
36 Kr79, Kr80, Kr81, Kr81m, Kr82, Kr83, Kr83m, Kr84, Kr85, Kr85m, Kr86, Kr — 87, Kr88, Kr89, Kr90, Kr91, Kr92, Kr93, Kr94, Kr95;
37 Rb82, Rb82m, Rb83, Rb84, Rb84m, Rb85, Rb86, Rb86m, Rb87, Rb88, Rb89, Rb90, Rb90m, Rb91, Rb92, Rb93, Rb94, Rb95, Rb96, Rb97, Rb98, Rb99, Rb100, Rb101, Rb102;
38 Sr84, Sr85, Sr85m, Sr86, Sr87, Sr87m, Sr88, Sr89, Sr90, Sr91, Sr92, Sr93, Sr — 94, Sr95, Sr96, Sr97, Sr98, Sr99, Sr100, Sr101, Sr102;
39 Y86, Y86m, Y87, Y87m, Y88, Y89, Y89m, Y90, Y90m, Y91, Y91m, Y92, Y — 93, Y93m, Y94, Y95, Y96, Y96m, Y97, Y97m, Y98, Y98m, Y99, Y100, Y100m, Y101, Y102, Y103;
40 Zr88, Zr89, Zr89m, Zr90, Zr90m, Zr91, Zr92, Zr93, Zr94, Zr95, Zr96, Zr97, Zr98, Zr99, Zr100, Zr101, Zr102, Zr103, Zr104;
41 Nb91, Nb91m, Nb92, Nb92m, Nb93, Nb93m, Nb94, Nb94m, Nb95, Nb95m, Nb — 96, Nb97, Nb97m, Nb98, Nb98m, Nb99, Nb99m, Nb100, Nb100m, Nb101, Nb102, Nb102m, Nb103, Nb104, Nb104m, Nb105, Nb106, Nb107, Nb108;
42 Mo93, Mo93m, Mo94, Mo95, Mo96, Mo97, Mo98, Mo99, Mo100, Mo101, Mo 102, Mo103, Mo104, Mo105, Mo106, Mo107, Mo108, Mo110;
43 Tc96, Tc96m, Tc97, Tc97m, Tc98, Tc99, Tc99m, Tc100, Tc101, Tc102, Tc — 102m, Tc103, Tc104, Tc105, Tc106, Tc107, Tc108, Tc109, Tc110, Tc111, Tc112;
44 Ru98, Ru99, Ru100, Ru101, Ru102, Ru103, Ru103m, Ru104, Ru105, Ru106, Ru107, Ru108, Ru109, Ru109m, Ru110, Ru111, Ru112, Ru113, Ru114;
45 Rh101, Rh101m, Rh102, Rh102m, Rh103, Rh103m, Rh104, Rh104m, Rh105, Rh — 105m, Rh106, Rh106m, Rh107, Rh108, Rh108m, Rh109, Rh110, Rh110m, Rh111, Rh112, Rh113, Rh114, Rh114m, Rh115, Rh116, Rh116m, Rh117, Rh119;
46 Pd102, Pd103, Pd104, Pd105, Pd106, Pd107, Pd107m, Pd108, Pd109, Pd109m, Pd110, Pd111, Pd111m, Pd112, Pd113, Pd113m, Pd114, Pd115, Pd116, Pd117, Pd — 118, Pd119, Pd120, Pd122;
47 Ag106, Ag106m, Ag107, Ag107m, Ag108, Ag108m, Ag109, Ag109m, Ag110, Ag
110m, Ag111, Ag111m, Ag112, Ag113, Ag113m, Ag114, Ag114m, Ag115, Ag115m, Ag116, Ag116m, Ag117, Ag117m, Ag118, Ag118m, Ag119, Ag120, Ag120m, Ag — 121, Ag122, Ag122m, Ag123, Ag124, Ag125;_____________________
48 Cd108, Cd109, Cd110, Cd111, Cd111m, Cd112, Cd113, Cd113m, Cd114, Cd
115, Cd115m, Cd116, Cd117, Cd117m, Cd118, Cd119, Cd119m, Cd120, Cd121, Cd — 121m, Cd122, Cd123, Cd124, Cd125, Cd126, Cd127, Cd128, Cd130;
49 In111, In111m, In112, In112m, In113, In113m, In114, In114m, In115, In115m, In116, In116m, In116n, In117, In117m, In118, In118m, In118n, In119, In119m, In — 120, In120m, In121, In121m, In122, In122m, In123, In123m, In124, In124m, In125, In125m, In126, In126m, In127, In127m, In128, In128m, In129, In129m, In130, In — 131, In131m, In132, In133;
50 Sn112, Sn114, Sn115, Sn116, Sn117, Sn117m, Sn118, Sn119, Sn119m, Sn120, Sn121, Sn121m, Sn122, Sn123, Sn123m, Sn124, Sn125, Sn125m, Sn126, Sn127, Sn — 127m, Sn128, Sn128m, Sn129, Sn129m, Sn130, Sn130m, Sn131, Sn131m, Sn132, Sn — 133, Sn134, Sn135, Sn136;
51 — Sb118, Sb118m, Sb119, Sb120, Sb120m, Sb121, Sb122, Sb122m, Sb123, Sb124, Sb124m, Sb124n, Sb125, Sb126, Sb126m, Sb126n, Sb127, Sb128, Sb128m, Sb129, Sb129m, Sb130, Sb130m, Sb131, Sb132, Sb132m, Sb133, Sb134, Sb134m, Sb135, Sb136, Sb137, Sb138;
52 Te118, Te119, Te119m, Te120, Te121, Te121m, Te122, Te123, Te123m, Te124, Te125, Te125m, Te126, Te127, Te127m, Te128, Te129, Te129m, Te130, Te131, Te — 131m, Te132, Te133, Te133m, Te134, Te135, Te136, Te137, Te138, Te139, Te140, Te141;
53 I121, I123, I124, I125, I126, I127, I128, I129, I130, I130m, I131, I132, I132m, I133, I133m, I134, I134m, I135, I136, I136m, I137, I138, I139, I140, I141, I142;
54 Xe126, Xe128, Xe129, Xe129m, Xe130, Xe131, Xe131m, Xe132, Xe133, Xe — 133m, Xe134, Xe134m, Xe135, Xe135m, Xe136, Xe137, Xe138, Xe139, Xe140, Xe — 141, Xe142, Xe143, Xe144, Xe145, Xe147;
55 Cs130, Cs131, Cs132, Cs133, Cs134, Cs134m, Cs135, Cs135m, Cs136, Cs136m, Cs137, Cs138, Cs138m, Cs139, Cs140, Cs141, Cs142, Cs143, Cs144, Cs145, Cs146, Cs147, Cs148;
56 Ba132, Ba133, Ba133m, Ba134, Ba135, Ba135m, Ba136, Ba136m, Ba137, Ba
137m, Ba138, Ba139, Ba140, Ba141, Ba142, Ba143, Ba144, Ba145, Ba146, Ba147, Ba148, Ba149;
57 La135, La136, La136m, La137, La138, La139, La140, La141, La142, La143, La — 144, La145, La146, La146m, La147, La148, La149, La150, La151;
58 Ce137, Ce137m, Ce138, Ce138m, Ce139, Ce139m, Ce140, Ce141, Ce142, Ce — 143, Ce144, Ce145, Ce146, Ce147, Ce148, Ce149, Ce150, Ce151, Ce152;
59 Pr139, Pr140, Pr141, Pr142, Pr142m, Pr143, Pr144, Pr144m, Pr145, Pr146, Pr — 147, Pr148, Pr148m, Pr149, Pr150, Pr151, Pr152, Pr153, Pr154, Pr155;




24 Cr50, Cr51, Cr52, Cr53, Cr54, Cr55;
25 Mn53, Mn54, Mn55, Mn56, Mn57, Mn58;
26 Fe54, Fe55, Fe56, Fe57, Fe58, Fe59, Fe60;
27 Co55, Co56, Co57, Co58, Co58m, Co59, Co60, Co60m, Co61, Co62;
28 Ni58, Ni59, Ni60, Ni61, Ni62, Ni63, Ni64, Ni65, Ni66;
29 Cu62, Cu63, Cu64, Cu65, Cu66, Cu67;
30 Zn63, Zn64, Zn65, Zn66, Zn67, Zn68, Zn69, Zn69m, Zn70, Zn71, Zn71m;
31 Ga69, Ga70, Ga71, Ga72, Ga72m;
32 Ge70, Ge71, Ge71m, Ge72, Ge73, Ge74, Ge75, Ge75m, Ge76, Ge77, Ge77m;
33 As75, As76, As77;
34 Se74, Se75, Se76, Se77, Se77m, Se78, Se79, Se79m, Se80, Se81, Se81m, Se82, Se83, Se83m;
35 Br79, Br80, Br80m, Br81, Br82, Br82m, Br83;
36 Kr78, Kr79, Kr79m, Kr80, Kr81, Kr81m, Kr82, Kr83, Kr83m, Kr84, Kr85, Kr85m, Kr86, Kr87, Kr88;
37 Rb85, Rb86, Rb86m, Rb87, Rb88, Rb89;
38 Sr84, Sr85, Sr85m, Sr86, Sr87, Sr87m, Sr88, Sr89, Sr90, Sr91, Sr93;
39 Y89, Y89m, Y90, Y90m, Y91, Y92, Y93, Y94, Y96;
40 Zr89, Zr90, Zr91, Zr92, Zr93, Zr94, Zr95, Zr96, Zr97;
41 Nb91, Nb92, Nb93, Nb93m, Nb94, Nb94m, Nb95, Nb95m, Nb96, Nb97, Nb97m, Nb98, Nb100;
42 Mo92, Mo93, Mo93m, Mo94, Mo95, Mo96, Mo97, Mo98, Mo99, Mo100, Mo101;
43 Tc97, Tc97m, Tc98, Tc99, Tc100, Tc101;
44 Ru96, Ru97, Ru98, Ru99, Ru100, Ru101, Ru102, Ru103, Ru104, Ru105, Ru106, Ru107;
45 Rh102, Rh103, Rh104, Rh104m, Rh105, Rh105m, Rh106, Rh106m, Rh107;
46 Pd102, Pd103, Pd104, Pd105, Pd106, Pd107, Pd107m, Pd108, Pd109, Pd109m, Pd110, Pd111, Pd111m;
47 Ag106, Ag107, Ag108, Ag108m, Ag109, Ag109m, Ag110, Ag110m, Ag111,
Ag111m, Ag112;
48 Cd106, Cd107, Cd108, Cd109, Cd110, Cd111, Cd111m, Cd112, Cd113, Cd113m, Cd114, Cd115, Cd115m, Cd116, Cd117, Cd117m, Cd119, Cd121;
49 In113, In113m, In114, In114m, In115, In116, In116m, In117, In117m, In118, In119, In119m, In120, In120m, In121;
50 Sn112, Sn113, Sn113m, Sn114, Sn115, Sn116, Sn117, Sn117m, Sn118, Sn119, Sn119m, Sn120, Sn121, Sn121m, Sn122, Sn123, Sn123m, Sn124, Sn125, Sn125m, Sn126;
51 Sb121, Sb122, Sb122m, Sb123, Sb124, Sb124m, Sb125, Sb126, Sb126m;
52 Te120, Te121, Te121m, Te122, Te123, Te123m, Te124, Te125, Te125m, Te126, Te127, Te127m, Te128, Te129, Te129m, Te130, Te131, Te131m;
53 I125, I126, I127, I128, I129, I130, I130m, I131, I132, I135;
54 Xe124, Xe125, Xe125m, Xe126, Xe127, Xe127m, Xe128, Xe129, Xe129m, Xe130, Xe131, Xe131m, Xe132, Xe133, Xe133m, Xe134, Xe135, Xe135m, Xe136, Xe137;
55 Cs131, Cs132, Cs133, Cs134, Cs134m, Cs135, Cs136, Cs137, Cs138;
56 Ba130, Ba131, Ba131m, Ba132, Ba133, Ba133m, Ba134, Ba135, Ba135m, Ba136, Ba136m, Ba137, Ba137m, Ba138, Ba139, Ba140, Ba141;
57 La137, La138, La139, La140, La141;
58 Ce136, Ce137, Ce137m, Ce138, Ce139, Ce139m, Ce140, Ce141, Ce142, Ce143, Ce144, Ce145;
59 Pr141, Pr142, Pr142m, Pr143, Pr144, Pr145;
60 Nd142, Nd143, Nd144, Nd145, Nd146, Nd147, Nd148, Nd149, Nd150, Nd151;
61 Pm145, Pm146, Pm147, Pm148, Pm148m, Pm149, Pm150, Pm151, Pm152;
62 Sm144, Sm145, Sm146, Sm147, Sm148, Sm149, Sm150, Sm151, Sm152,
Sm153, Sm154, Sm155, Sm156;
63 Eu151, Eu152, Eu152m, Eu153, Eu154, Eu155, Eu156, Eu157;
64 Gd152, Gd153, Gd154, Gd155, Gd155m, Gd156, Gd157, Gd158, Gd159, Gd160, Gd161, Gd162;
65 Tb157, Tb158, Tb159, Tb160, Tb161, Tb162;
66 Dy156, Dy157, Dy158, Dy159, Dy160, Dy161, Dy162, Dy163, Dy164, Dy165, Dy165m, Dy166;
67 Ho163, Ho165, Ho166, Ho166m;
68 Er162, Er163, Er164, Er165, Er166, Er167, Er167m, Er168, Er169, Er170, Er171, Er172;
69 Tm169, Tm170, Tm170m, Tm171, Tm172, Tm173;
70 Yb168, Yb169, Yb170, Yb171, Yb172, Yb173, Yb174, Yb175, Yb175m,
Yb176, Yb177;
71 Lu175, Lu176, Lu176m, Lu177, Lu177m;
72 Hf174, Hf175, Hf176, Hf177, Hf178, Hf178m, Hf179, Hf179m, Hf180, Hf180m, Hf181, Hf182;
73 Ta180, Ta181, Ta182, Ta182m, Ta183;
74 W180, W181, W182, W183, W183m, W184, W185, W185m, W186, W187, W188, W189;
75 Re185, Re186, Re187, Re188, Re188m, Re189;
76 Os184, Os185, Os186, Os187, Os188, Os189, Os190, Os190m, Os191, Os191m, Os192, Os193, Os194;
77 Ir191, Ir192, Ir192m, Ir193, Ir194, Ir194m;
78 Pt190, Pt191, Pt192, Pt193, Pt193m, Pt194, Pt195, Pt195m, Pt196, Pt197, Pt197m, Pt198, Pt199, Pt199m;
79 Au197, Au198, Au199, Au200;
80 Hg196, Hg197, Hg197m, Hg198, Hg199, Hg199m, Hg200, Hg201, Hg202, Hg203, Hg204, Hg205;
81 Tl203, Tl204, Tl205, Tl206;
82 Pb204, Pb205, Pb206, Pb207, Pb208, Pb209, Pb210;
83 Bi208, Bi209, Bi210, Bi210m, Bi211;
