Category Archives: WORKSHOP ON NUCLEAR REACTION DATA AND. NUCLEAR REACTORS:. PHYSICS, DESIGN AND SAFETY

Segment 2: LEVELS

This segment contains 110 files (one for each element) with all known level schemes available from ENSDF in 1998. These files are arranged and pre­processed into an easy-to-read format for nuclear reaction codes. During preprocessing all missing spins were inferred uniquely for each level from spin distributions extracted from the existing data. Electromagnetic and y-ray decay probabilities were estimated. Missing internal conversion coeffi­cients (ICC) were calculated using the inferred or existing spin information, in which existing multipole mixing ratios were also taken into account. Par­ticle decay modes are also given whenever measured. In all cases, the total decay probability was normalized to unity, including particle decay channels.

This segment also contains the results of constant temperature fit of nuclear level schemes. The main purpose of this file is to provide cut-off energies Umax and Uc for completeness of levels and spins in each level scheme. Furthermore, the nuclear temperature inferred from the discrete levels and intended for use in the level density estimation is provided.

Endpoint energies (Qp-values)

Accurate measurements of Qp aid considerably the determination of the energies of individual P- emissions, and in the derivation of the mean beta energies (and gamma energies) of short-lived fission products. Rapid mass-separation techniques are used to alter the isobaric composition of the ion beams after their emission from fission targets, and high-purity Ge detectors measure the P-у coincidence and P singles spectra of the resulting sample (Wtinsch et al, 1978; Przewloka et al, 1992a and 1992b; Ikuta et al, 1994).

The beta endpoints are determined from Fermi-Kurie plots of the measured P — spectrum (Fermi-Kurie plot with good statistics is shown in Fig. 30 for 92Rb (Przewloka et al, 1992a)). Equivalent data for a number of neutron-rich nuclides are listed in Table 13 (Ikuta et al, 1994), and are compared with the recommended values of Audi and Wapstra (1995). Discrepancies do occur (147La, 147,149,150Ce and 150Pr), and underline the need to refine theoretical calculations in this particular region.

1.5 —

1.0

0.5 0.0

7414

Table 13: Qp values of neutron-rich nuclei in the mass region 147<A<152 (Ikuta et al, 1994)

Nuclide

Half-life

Measured Qp (keV)

Qp (keV)

Audi and Wapstra, 1995

147La

4.015 s

5130(80)

4945(55)

147Ce

56.4 s

3426(28)

3290(40)

147Pr

13.3 m

2710(50)

2686(37)

148Ce

56 s

2140(30)

2060(75)

148Pr

2.27 m

4880(50)

4932(89)

149Ce

5.2 s

4386(27)

4190(75)

149Pr

2.26 m

3430(90)

3397(10)

150Ce

4.0 s

3470(60)

3010(90)

150Pr

6.19 s

5390(30)

5690(80)

151Pr

18.90 s

4200(40)

4101(35)

151Nd

12.44 m

2460(100)

2442(4)

152Pr

3.24 s

6340(120)

6444(300)

152Nd

11.6 m

1100(40)

1110(78)

152Pm

4.1 m

3520(60)

3504(72)

Uncertainties are given in parentheses (for example, 4945(55) means 4945 ± 55).

HIGH TEMPERATURE APPLICATIONS: FUEL SYNTHESIS

As shown in Table II, liquid metal and gas-cooled reactors can generate very high temperatures, which could be used to create new synthetic fuels for energy. This will be an innovative application of nuclear energy and can considerably expand its use. This is because the transportation sector is responsible for about a quarter of the total energy use and almost 99% of this is currently supplied by organic fuel. Nuclear power can penetrate this large market through use of electric cars and production of synthetic fuels such as methanol, ethanol and their derivatives; nuclear power can also be used for coal gasification, oil extraction and hydrogen production. All of these are being seriously considered in the 21st century. However, the infrastructure for use of these fuels needs to be created first, particularly in the case of environmentally ideal hydrogen fuel.

Coal gasification (i. e., conversion of solid coal into a gaseous fuel like the natural gas) requires very high temperatures but could be practical because the infrastructure for use of natural gas already exists, and there are vast deposits of coal in the world and this conversion can remove environmental pollutants such as particulates like sulphur-dioxide and nitrogen oxides. The efficiency of coal fire plants will also be improved by coal gasification. The process of coal gasification is, however, quite energy intensive; one unit of gasified coal may require about 1.7 units of energy in solid coal13. High temperature gas-cooled reactors can play a role here.

Another possible use of nuclear energy is for oil extraction from tar and oil sands and for enhanced oil recovery operations, particularly from depleted oil deposits. Canada and Venezuela have large resources of oil and tar sands. Steam injection is used for these extraction applications and steam can also be used for processing the oil after the extraction.

The feasibility of nuclear application for production of more organic fuel really depends on the economics. So long as fossil fuel, particularly oil and gas, are available at low prices, nuclear will not be a preferable option. Only dual use, where nuclear electricity can compete in the market, could make these applications worthwhile.

Hydrogen economy has received renewed interest because of new developments in HTGR technologies. Several paths to hydrogen production are being considered: decomposition and gasification of fossil fuel such as steam reforming of methane and carbon dioxide reforming of methane; and decomposition of water, namely, low-temperature electrolysis, and combination of electricity and heat for high temperature electrolysis. These are briefly described below.

WORKSHOP ON NUCLEAR REACTION DATA AND. NUCLEAR REACTORS:. PHYSICS, DESIGN AND SAFETY

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). Fission-product yields for each fissioning nuclide are used in conjunction with the effective group-averaged 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, structurally-based activation products and actinides (and their decay-chain 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 short-lived fission products that have not been experimentally observed or adequately characterised; theoretical data can be adopted (half-lives denoted in parentheses in Appendix B. 1, which also provides a reasonable summary of the fission products associated with decay-heat 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 group-averaged 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 time-dependent 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

Подпись:where ф (n cm-2 s-1) is the effective neutron flux, and F is the fission rate (s-1)

image120(Л + 02ф) N 2 + a2 F + y1 N1

image121

and

in which y-1 = (ki-1)(Ai.1) or (к-.1)(аі.1)ф, depending on the coupling between (i-1) and i, and ki-1 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.

image122

Appendix B. 2 outlines the formation of these actinides in irradiated fuel (particularly Pu, Am and Cm radionuclides) and their decay-chain products. The number of atoms NZA of nuclide of atomic number Z and mass number A is given by the equation:

Подпись: +N.

image124

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 first-order 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 +Л-1 n-

dt

that are coupled in a much less complex manner after shutdown than for reactor operation.

When the actinide and fission-product 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 decay-heat calculations can be determined from the information given above:

_F

&a, k

— effective group-averaged 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.

image125

Table 1: Fission products (1038 nuclides) — representative listing for inventory calculations

1-H-1, H-2, H-3;

2-He-3, He-4, He-6, He-8;

3- Li-6, Li-7, Li-8, Li-9;

4-Be-7, Be-9, Be-10, Be-11, Be-12;

5- B-11, B-12;

6- C-12, C-14, C-15;

7-N-14, N-15;

10-Ne-21;

21- Sc-50, Sc-51;

22- Ti-50, Ti-51, Ti-52, Ti-53;

23- V-51, V-52, V-53, V-54, V-55;

24- Cr-52, Cr-53, Cr-54, Cr-55, Cr-56, Cr-57;

25- Mn-55, Mn-56, Mn-57, Mn-58, Mn-58m, Mn-59, Mn-60;

26- Fe-56, Fe-57, Fe-58, Fe-59, Fe-60, Fe-61, Fe-62, Fe-63;

27- Co-59, Co-60, Co-60m, Co-61, Co-62, Co-62m, Co-63, Co-64, Co-65, Co-66;

28- Ni-60, Ni-61, Ni-62, Ni-63, Ni-64, Ni-65, Ni-66, Ni-67, Ni-68, Ni-69;

29- Cu-63, Cu-64, Cu-65, Cu-66, Cu-67, Cu-68, Cu-68m, Cu-69, Cu-70, Cu-70m, Cu-71, Cu-

72, Cu-73, Cu-74, Cu-75, Cu-76, Cu-78;

30- Zn-64, Zn-65, Zn-66, Zn-67, Zn-68, Zn-69, Zn-69m, Zn-70, Zn-71, Zn-71m, Zn-72, Zn-

73, Zn-73m, Zn-74, Zn-75, Zn-76, Zn-77, Zn-77m, Zn-78, Zn-79, Zn-80;

31- Ga-67, Ga-68, Ga-69, Ga-70, Ga-71, Ga-72, Ga-72m, Ga-73, Ga-74, Ga-74m, Ga-75, Ga — 76, Ga-77, Ga-78, Ga-79, Ga-80, Ga-81, Ga-82, Ga-83, Ga-84;

32- Ge-70, Ge-71, Ge-71m, Ge-72, Ge-73, Ge-73m, Ge-74, Ge-75, Ge-75m, Ge-76, Ge-77, Ge-77m, Ge-78, Ge-79, Ge-79m, Ge-80, Ge-81, Ge-81m, Ge-82, Ge-83, Ge-84, Ge-85, Ge — 86;

33- As-72, As-73, As-74, As-75, As-75m, As-76, As-77, As-78, As-79, As-80, As-81, As-82, As-82m, As-83, As-84, As-85, As-86, As-87, As-88;

 

34- Se-74, Se-75, Se-76, Se-77, Se-77m, Se-78, Se-79, Se-79m, Se-80, Se-81, Se-81m, Se-82, Se-83, Se-83m, Se-84, Se-85, Se-86, Se-87, Se-88, Se-89, Se-90, Se-91, Se-92;

35- Br-77, Br-77m, Br-78, Br-79, Br-79m, Br-80, Br-80m, Br-81, Br-82, Br-82m, Br-83, Br- 84, Br-84m, Br-85, Br-86, Br-87, Br-88, Br-89, Br-90, Br-91, Br-92, Br-93, Br-94;

36- Kr-79, Kr-80, Kr-81, Kr-81m, Kr-82, Kr-83, Kr-83m, Kr-84, Kr-85, Kr-85m, Kr-86, Kr — 87, Kr-88, Kr-89, Kr-90, Kr-91, Kr-92, Kr-93, Kr-94, Kr-95;

37- Rb-82, Rb-82m, Rb-83, Rb-84, Rb-84m, Rb-85, Rb-86, Rb-86m, Rb-87, Rb-88, Rb-89, Rb-90, Rb-90m, Rb-91, Rb-92, Rb-93, Rb-94, Rb-95, Rb-96, Rb-97, Rb-98, Rb-99, Rb-100, Rb-101, Rb-102;

38- Sr-84, Sr-85, Sr-85m, Sr-86, Sr-87, Sr-87m, Sr-88, Sr-89, Sr-90, Sr-91, Sr-92, Sr-93, Sr — 94, Sr-95, Sr-96, Sr-97, Sr-98, Sr-99, Sr-100, Sr-101, Sr-102;

39- Y-86, Y-86m, Y-87, Y-87m, Y-88, Y-89, Y-89m, Y-90, Y-90m, Y-91, Y-91m, Y-92, Y — 93, Y-93m, Y-94, Y-95, Y-96, Y-96m, Y-97, Y-97m, Y-98, Y-98m, Y-99, Y-100, Y-100m, Y-101, Y-102, Y-103;

40- Zr-88, Zr-89, Zr-89m, Zr-90, Zr-90m, Zr-91, Zr-92, Zr-93, Zr-94, Zr-95, Zr-96, Zr-97, Zr-98, Zr-99, Zr-100, Zr-101, Zr-102, Zr-103, Zr-104;

41- Nb-91, Nb-91m, Nb-92, Nb-92m, Nb-93, Nb-93m, Nb-94, Nb-94m, Nb-95, Nb-95m, Nb — 96, Nb-97, Nb-97m, Nb-98, Nb-98m, Nb-99, Nb-99m, Nb-100, Nb-100m, Nb-101, Nb-102, Nb-102m, Nb-103, Nb-104, Nb-104m, Nb-105, Nb-106, Nb-107, Nb-108;

42- Mo-93, Mo-93m, Mo-94, Mo-95, Mo-96, Mo-97, Mo-98, Mo-99, Mo-100, Mo-101, Mo- 102, Mo-103, Mo-104, Mo-105, Mo-106, Mo-107, Mo-108, Mo-110;

43- Tc-96, Tc-96m, Tc-97, Tc-97m, Tc-98, Tc-99, Tc-99m, Tc-100, Tc-101, Tc-102, Tc — 102m, Tc-103, Tc-104, Tc-105, Tc-106, Tc-107, Tc-108, Tc-109, Tc-110, Tc-111, Tc-112;

44- Ru-98, Ru-99, Ru-100, Ru-101, Ru-102, Ru-103, Ru-103m, Ru-104, Ru-105, Ru-106, Ru-107, Ru-108, Ru-109, Ru-109m, Ru-110, Ru-111, Ru-112, Ru-113, Ru-114;

45- Rh-101, Rh-101m, Rh-102, Rh-102m, Rh-103, Rh-103m, Rh-104, Rh-104m, Rh-105, Rh — 105m, Rh-106, Rh-106m, Rh-107, Rh-108, Rh-108m, Rh-109, Rh-110, Rh-110m, Rh-111, Rh-112, Rh-113, Rh-114, Rh-114m, Rh-115, Rh-116, Rh-116m, Rh-117, Rh-119;

46- Pd-102, Pd-103, Pd-104, Pd-105, Pd-106, Pd-107, Pd-107m, Pd-108, Pd-109, Pd-109m, Pd-110, Pd-111, Pd-111m, Pd-112, Pd-113, Pd-113m, Pd-114, Pd-115, Pd-116, Pd-117, Pd — 118, Pd-119, Pd-120, Pd-122;

47- Ag-106, Ag-106m, Ag-107, Ag-107m, Ag-108, Ag-108m, Ag-109, Ag-109m, Ag-110, Ag-

110m, Ag-111, Ag-111m, Ag-112, Ag-113, Ag-113m, Ag-114, Ag-114m, Ag-115, Ag-115m, Ag-116, Ag-116m, Ag-117, Ag-117m, Ag-118, Ag-118m, Ag-119, Ag-120, Ag-120m, Ag — 121, Ag-122, Ag-122m, Ag-123, Ag-124, Ag-125;_____________________

48- Cd-108, Cd-109, Cd-110, Cd-111, Cd-111m, Cd-112, Cd-113, Cd-113m, Cd-114, Cd-

115, Cd-115m, Cd-116, Cd-117, Cd-117m, Cd-118, Cd-119, Cd-119m, Cd-120, Cd-121, Cd — 121m, Cd-122, Cd-123, Cd-124, Cd-125, Cd-126, Cd-127, Cd-128, Cd-130;

49- In-111, In-111m, In-112, In-112m, In-113, In-113m, In-114, In-114m, In-115, In-115m, In-116, In-116m, In-116n, In-117, In-117m, In-118, In-118m, In-118n, In-119, In-119m, In — 120, In-120m, In-121, In-121m, In-122, In-122m, In-123, In-123m, In-124, In-124m, In-125, In-125m, In-126, In-126m, In-127, In-127m, In-128, In-128m, In-129, In-129m, In-130, In — 131, In-131m, In-132, In-133;

50- Sn-112, Sn-114, Sn-115, Sn-116, Sn-117, Sn-117m, Sn-118, Sn-119, Sn-119m, Sn-120, Sn-121, Sn-121m, Sn-122, Sn-123, Sn-123m, Sn-124, Sn-125, Sn-125m, Sn-126, Sn-127, Sn — 127m, Sn-128, Sn-128m, Sn-129, Sn-129m, Sn-130, Sn-130m, Sn-131, Sn-131m, Sn-132, Sn — 133, Sn-134, Sn-135, Sn-136;

51 — Sb-118, Sb-118m, Sb-119, Sb-120, Sb-120m, Sb-121, Sb-122, Sb-122m, Sb-123, Sb-124, Sb-124m, Sb-124n, Sb-125, Sb-126, Sb-126m, Sb-126n, Sb-127, Sb-128, Sb-128m, Sb-129, Sb-129m, Sb-130, Sb-130m, Sb-131, Sb-132, Sb-132m, Sb-133, Sb-134, Sb-134m, Sb-135, Sb-136, Sb-137, Sb-138;

52- Te-118, Te-119, Te-119m, Te-120, Te-121, Te-121m, Te-122, Te-123, Te-123m, Te-124, Te-125, Te-125m, Te-126, Te-127, Te-127m, Te-128, Te-129, Te-129m, Te-130, Te-131, Te — 131m, Te-132, Te-133, Te-133m, Te-134, Te-135, Te-136, Te-137, Te-138, Te-139, Te-140, Te-141;

53- I-121, I-123, I-124, I-125, I-126, I-127, I-128, I-129, I-130, I-130m, I-131, I-132, I-132m, I-133, I-133m, I-134, I-134m, I-135, I-136, I-136m, I-137, I-138, I-139, I-140, I-141, I-142;

54- Xe-126, Xe-128, Xe-129, Xe-129m, Xe-130, Xe-131, Xe-131m, Xe-132, Xe-133, Xe — 133m, Xe-134, Xe-134m, Xe-135, Xe-135m, Xe-136, Xe-137, Xe-138, Xe-139, Xe-140, Xe — 141, Xe-142, Xe-143, Xe-144, Xe-145, Xe-147;

55- Cs-130, Cs-131, Cs-132, Cs-133, Cs-134, Cs-134m, Cs-135, Cs-135m, Cs-136, Cs-136m, Cs-137, Cs-138, Cs-138m, Cs-139, Cs-140, Cs-141, Cs-142, Cs-143, Cs-144, Cs-145, Cs-146, Cs-147, Cs-148;

56- Ba-132, Ba-133, Ba-133m, Ba-134, Ba-135, Ba-135m, Ba-136, Ba-136m, Ba-137, Ba-

137m, Ba-138, Ba-139, Ba-140, Ba-141, Ba-142, Ba-143, Ba-144, Ba-145, Ba-146, Ba-147, Ba-148, Ba-149;

57- La-135, La-136, La-136m, La-137, La-138, La-139, La-140, La-141, La-142, La-143, La — 144, La-145, La-146, La-146m, La-147, La-148, La-149, La-150, La-151;

58- Ce-137, Ce-137m, Ce-138, Ce-138m, Ce-139, Ce-139m, Ce-140, Ce-141, Ce-142, Ce — 143, Ce-144, Ce-145, Ce-146, Ce-147, Ce-148, Ce-149, Ce-150, Ce-151, Ce-152;

59- Pr-139, Pr-140, Pr-141, Pr-142, Pr-142m, Pr-143, Pr-144, Pr-144m, Pr-145, Pr-146, Pr — 147, Pr-148, Pr-148m, Pr-149, Pr-150, Pr-151, Pr-152, Pr-153, Pr-154, Pr-155;

60- Nd-142, Nd-143, Nd-144, Nd-145, Nd-146, Nd-147, Nd-148, Nd-149, Nd-150, Nd-151, Nd-152, Nd-153, Nd-154, Nd-155, Nd-156;

61- Pm-144, Pm-145, Pm-146, Pm-147, Pm-148, Pm-148m, Pm-149, Pm-150, Pm-151, Pm — 152, Pm-152m, Pm-153, Pm-154, Pm-154m, Pm-155, Pm-156, Pm-157, Pm-158;

62- Sm-146, Sm-147, Sm-148, Sm-149, Sm-150, Sm-151, Sm-152, Sm-153, Sm-153m, Sm — 154, Sm-155, Sm-156, Sm-157, Sm-158, Sm-159, Sm-160;

63- Eu-149, Eu-150, Eu-150m, Eu-151, Eu-152, Eu-152m, Eu-152n, Eu-153, Eu-154, Eu — 154m, Eu-155, Eu-156, Eu-157, Eu-158, Eu-159, Eu-160, Eu-161, Eu-162;

64- Gd-150, Gd-152, Gd-153, Gd-154, Gd-155, Gd-155m, Gd-156, Gd-157, Gd-158, Gd — 159, Gd-160, Gd-161, Gd-162, Gd-163, Gd-164;

65- Tb-155, Tb-156, Tb-157, Tb-158, Tb-158m, Tb-159, Tb-160, Tb-161, Tb-162, Tb-163, Tb-164, Tb-165, Tb-166;

66- Dy-157, Dy-157m, Dy-158, Dy-159, Dy-160, Dy-161, Dy-162, Dy-163, Dy-164, Dy-165, Dy-165m, Dy-166, Dy-167, Dy-168, Dy-169, Dy-170;

67- Ho-161, Ho-161m, Ho-162, Ho-162m, Ho-163, Ho-163m, Ho-164, Ho-164m, Ho-165, Ho-166, Ho-166m, Ho-167, Ho-168, Ho-169, Ho-170, Ho-170m;

68- Er-163, Er-164, Er-165, Er-166, Er-167, Er-167m, Er-168, Er-169, Er-170, Er-171, Er — 172, Er-173;

69- Tm-167, Tm-168, Tm-169, Tm-170, Tm-171, Tm-172, Tm-173, Tm-174, Tm-175, Tm — 176;

70- Yb-169, Yb-170, Yb-171, Yb-172, Yb-173, Yb-174, Yb-175, Yb-176, Yb-176m, Yb-177, Yb-177m, Yb-178, Yb-179;

71- Lu-172, Lu-173, Lu-174, Lu-174m, Lu-175, Lu-176, Lu-176m, Lu-177, Lu-177m, Lu-178, Lu-178m, Lu-179, Lu-180, Lu-181, Lu-182, Lu-183;

72- Hf-176, Hf-177, Hf-178, Hf-179, Hf-180, Hf-180m, Hf-181, Hf-182, Hf-182m, Hf-183, Hf-184;

73- Ta-181, Ta-182, Ta-183, Ta-184, Ta-185, Ta-186;

74- W-182, W-183, W-183m, W-184, W-185, W-186, W-187;

75- Re-185, Re-187;_______________________________________________________________

 

Naturally-occurring nuclides are listed in bold type.

 

Table 2: Structural materials and decay products on irradiation (708 nuclides) — representative listing for inventory calculations

1-H-1, H-2, H-3, H-4;

2-He-3, He-4, He-6;

3- Li-6, Li-7, Li-8;

4- Be-8, Be-9, Be-10, Be-11;

5- B-10, B-11, B-12;

6- C-12, C-13, C-14, C-15;

7-N-13, N-14, N-15, N-16;

8- O-16, O-17, O-18, O-19;

9- F-19, F-20;

10-Ne-20, Ne-21, Ne-22, Ne-23;

11 — Na-22, Na-23, Na-24, Na-24m, Na-25;

12-Mg-24, Mg-25, Mg-26, Mg-27, Mg-28;

13-A1-27, Al-28, Al-29, Al-30;

14- Si-28, Si-29, Si-30, Si-31, Si-32;

15- P-31, P-32, P-33, P-34;

16- S-32, S-33, S-34, S-35, S-36, S-37;

17- Cl-35, Cl-36, Cl-37, Cl-38, Cl-38m;

18-Ar-36, Ar-37, Ar-38, Ar-39, Ar-40, Ar-41, Ar-42;

19-K-39, K-40, K-41, K-42, K-43, K-44;

20- Ca-40, Ca-41, Ca-42, Ca-43, Ca-44, Ca-45, Ca-46, Ca-47, Ca-48, Ca-49;

21- Sc-45, Sc-46, Sc-46m, Sc-47, Sc-48, Sc-49, Sc-50;

22- Ti-46, Ti-47, Ti-48, Ti-49, Ti-50, Ti-51;

23- V-49, V-50, V-51, V-52, V-53, V-54;

 

24- Cr-50, Cr-51, Cr-52, Cr-53, Cr-54, Cr-55;

25- Mn-53, Mn-54, Mn-55, Mn-56, Mn-57, Mn-58;

26- Fe-54, Fe-55, Fe-56, Fe-57, Fe-58, Fe-59, Fe-60;

27- Co-55, Co-56, Co-57, Co-58, Co-58m, Co-59, Co-60, Co-60m, Co-61, Co-62;

28- Ni-58, Ni-59, Ni-60, Ni-61, Ni-62, Ni-63, Ni-64, Ni-65, Ni-66;

29- Cu-62, Cu-63, Cu-64, Cu-65, Cu-66, Cu-67;

30- Zn-63, Zn-64, Zn-65, Zn-66, Zn-67, Zn-68, Zn-69, Zn-69m, Zn-70, Zn-71, Zn-71m;

31- Ga-69, Ga-70, Ga-71, Ga-72, Ga-72m;

32- Ge-70, Ge-71, Ge-71m, Ge-72, Ge-73, Ge-74, Ge-75, Ge-75m, Ge-76, Ge-77, Ge-77m;

33- As-75, As-76, As-77;

34- Se-74, Se-75, Se-76, Se-77, Se-77m, Se-78, Se-79, Se-79m, Se-80, Se-81, Se-81m, Se-82, Se-83, Se-83m;

35- Br-79, Br-80, Br-80m, Br-81, Br-82, Br-82m, Br-83;

36- Kr-78, Kr-79, Kr-79m, Kr-80, Kr-81, Kr-81m, Kr-82, Kr-83, Kr-83m, Kr-84, Kr-85, Kr-85m, Kr-86, Kr-87, Kr-88;

37- Rb-85, Rb-86, Rb-86m, Rb-87, Rb-88, Rb-89;

38- Sr-84, Sr-85, Sr-85m, Sr-86, Sr-87, Sr-87m, Sr-88, Sr-89, Sr-90, Sr-91, Sr-93;

39- Y-89, Y-89m, Y-90, Y-90m, Y-91, Y-92, Y-93, Y-94, Y-96;

40- Zr-89, Zr-90, Zr-91, Zr-92, Zr-93, Zr-94, Zr-95, Zr-96, Zr-97;

41- Nb-91, Nb-92, Nb-93, Nb-93m, Nb-94, Nb-94m, Nb-95, Nb-95m, Nb-96, Nb-97, Nb-97m, Nb-98, Nb-100;

42- Mo-92, Mo-93, Mo-93m, Mo-94, Mo-95, Mo-96, Mo-97, Mo-98, Mo-99, Mo-100, Mo-101;

43- Tc-97, Tc-97m, Tc-98, Tc-99, Tc-100, Tc-101;

44- Ru-96, Ru-97, Ru-98, Ru-99, Ru-100, Ru-101, Ru-102, Ru-103, Ru-104, Ru-105, Ru-106, Ru-107;

45- Rh-102, Rh-103, Rh-104, Rh-104m, Rh-105, Rh-105m, Rh-106, Rh-106m, Rh-107;

46- Pd-102, Pd-103, Pd-104, Pd-105, Pd-106, Pd-107, Pd-107m, Pd-108, Pd-109, Pd-109m, Pd-110, Pd-111, Pd-111m;

47- Ag-106, Ag-107, Ag-108, Ag-108m, Ag-109, Ag-109m, Ag-110, Ag-110m, Ag-111,

Ag-111m, Ag-112;

48- Cd-106, Cd-107, Cd-108, Cd-109, Cd-110, Cd-111, Cd-111m, Cd-112, Cd-113, Cd-113m, Cd-114, Cd-115, Cd-115m, Cd-116, Cd-117, Cd-117m, Cd-119, Cd-121;

49- In-113, In-113m, In-114, In-114m, In-115, In-116, In-116m, In-117, In-117m, In-118, In-119, In-119m, In-120, In-120m, In-121;

50- Sn-112, Sn-113, Sn-113m, Sn-114, Sn-115, Sn-116, Sn-117, Sn-117m, Sn-118, Sn-119, Sn-119m, Sn-120, Sn-121, Sn-121m, Sn-122, Sn-123, Sn-123m, Sn-124, Sn-125, Sn-125m, Sn-126;

51- Sb-121, Sb-122, Sb-122m, Sb-123, Sb-124, Sb-124m, Sb-125, Sb-126, Sb-126m;

52- Te-120, Te-121, Te-121m, Te-122, Te-123, Te-123m, Te-124, Te-125, Te-125m, Te-126, Te-127, Te-127m, Te-128, Te-129, Te-129m, Te-130, Te-131, Te-131m;

53- I-125, I-126, I-127, I-128, I-129, I-130, I-130m, I-131, I-132, I-135;

54- Xe-124, Xe-125, Xe-125m, Xe-126, Xe-127, Xe-127m, Xe-128, Xe-129, Xe-129m, Xe-130, Xe-131, Xe-131m, Xe-132, Xe-133, Xe-133m, Xe-134, Xe-135, Xe-135m, Xe-136, Xe-137;

55- Cs-131, Cs-132, Cs-133, Cs-134, Cs-134m, Cs-135, Cs-136, Cs-137, Cs-138;

56- Ba-130, Ba-131, Ba-131m, Ba-132, Ba-133, Ba-133m, Ba-134, Ba-135, Ba-135m, Ba-136, Ba-136m, Ba-137, Ba-137m, Ba-138, Ba-139, Ba-140, Ba-141;

57- La-137, La-138, La-139, La-140, La-141;

58- Ce-136, Ce-137, Ce-137m, Ce-138, Ce-139, Ce-139m, Ce-140, Ce-141, Ce-142, Ce-143, Ce-144, Ce-145;

59- Pr-141, Pr-142, Pr-142m, Pr-143, Pr-144, Pr-145;

60- Nd-142, Nd-143, Nd-144, Nd-145, Nd-146, Nd-147, Nd-148, Nd-149, Nd-150, Nd-151;

61- Pm-145, Pm-146, Pm-147, Pm-148, Pm-148m, Pm-149, Pm-150, Pm-151, Pm-152;

62- Sm-144, Sm-145, Sm-146, Sm-147, Sm-148, Sm-149, Sm-150, Sm-151, Sm-152,

Sm-153, Sm-154, Sm-155, Sm-156;

63- Eu-151, Eu-152, Eu-152m, Eu-153, Eu-154, Eu-155, Eu-156, Eu-157;

64- Gd-152, Gd-153, Gd-154, Gd-155, Gd-155m, Gd-156, Gd-157, Gd-158, Gd-159, Gd-160, Gd-161, Gd-162;

65- Tb-157, Tb-158, Tb-159, Tb-160, Tb-161, Tb-162;

66- Dy-156, Dy-157, Dy-158, Dy-159, Dy-160, Dy-161, Dy-162, Dy-163, Dy-164, Dy-165, Dy-165m, Dy-166;

67- Ho-163, Ho-165, Ho-166, Ho-166m;

68- Er-162, Er-163, Er-164, Er-165, Er-166, Er-167, Er-167m, Er-168, Er-169, Er-170, Er-171, Er-172;

69- Tm-169, Tm-170, Tm-170m, Tm-171, Tm-172, Tm-173;

70- Yb-168, Yb-169, Yb-170, Yb-171, Yb-172, Yb-173, Yb-174, Yb-175, Yb-175m,

Yb-176, Yb-177;

71- Lu-175, Lu-176, Lu-176m, Lu-177, Lu-177m;

72- Hf-174, Hf-175, Hf-176, Hf-177, Hf-178, Hf-178m, Hf-179, Hf-179m, Hf-180, Hf-180m, Hf-181, Hf-182;

73- Ta-180, Ta-181, Ta-182, Ta-182m, Ta-183;

74- W-180, W-181, W-182, W-183, W-183m, W-184, W-185, W-185m, W-186, W-187, W-188, W-189;

75- Re-185, Re-186, Re-187, Re-188, Re-188m, Re-189;

76- Os-184, Os-185, Os-186, Os-187, Os-188, Os-189, Os-190, Os-190m, Os-191, Os-191m, Os-192, Os-193, Os-194;

77- Ir-191, Ir-192, Ir-192m, Ir-193, Ir-194, Ir-194m;

78- Pt-190, Pt-191, Pt-192, Pt-193, Pt-193m, Pt-194, Pt-195, Pt-195m, Pt-196, Pt-197, Pt-197m, Pt-198, Pt-199, Pt-199m;

79- Au-197, Au-198, Au-199, Au-200;

80- Hg-196, Hg-197, Hg-197m, Hg-198, Hg-199, Hg-199m, Hg-200, Hg-201, Hg-202, Hg-203, Hg-204, Hg-205;

81- Tl-203, Tl-204, Tl-205, Tl-206;

82- Pb-204, Pb-205, Pb-206, Pb-207, Pb-208, Pb-209, Pb-210;

83- Bi-208, Bi-209, Bi-210, Bi-210m, Bi-211;

image126

image127

Naturally-occurring nuclides are listed in bold type.

 

Software to Display Nuclear Data

Some of the software described below is available on CD-ROM or floppy disk, as well as through the Internet:

2.1.1 US Nuclear Data Network

• CD-ROM version 1.0 of the 8th Edition of the Table of Isotopes (TOI), with Adobe Acrobat viewer to display the hypertext data — released in March 1996 by Richard B. Firestone (LBL), CD-ROM Editor: S. Y. Frank Chu, Editor: Virginia S. Shirley, John Wiley & Sons, Inc. (ISBN 0-471-14918-7 Volume set, ISBN 0-471-16405-5 CD-ROM). Updated in 1998:ISBN 0-471-24699-9 Volume set, ISBN 0-471-29090-4.

Five folders are available on this CD-ROM corresponding to the following: Table of Isotopes,

Table of Superdeformed Nuclear Bands and Fission Isomers,

Tables of Atoms, Atomic nuclei and Subatomic Particles,

Description of Nuclear Structure and Decay Data Bases,

ENSDF Manual.

• CD-ROM entitled: Nuclear Data and References, PC Applications for

Nuclear Science, PCNudat and Papyrus™ NSR by L. P. Ekstrom, R. R. Kinsey and E. Browne.

For further information:

a) contact in the U SA:

Edgardo Browne (email: ebrowne@lbl. gov)

contact for PCNudat:

Robert Kinsey (email: kinsey@bnl. gov)

b) US Nuclear Data Network (USNDN) Home Page via Internet: h ttp://www. nndc. bn l. gov/usn dp

• EXFOR CD-ROM, see Website: http://www-nds. iaea. or. at/

• MacNuclide project at the San Jose State University.

2.1.2 University of Lund, Sweden

Lund Nuclear Data WWW Service at: http://nucleardata. nuclear. lu. se/nucleardata/

As well as the normal data services, the Lund Website includes the Isotope Explorer 2.0 program, which can interactively access and display nuclear data and search for literature references. Developed by:

S. Y. F. Chua, H. Nordbergb, R. B. Firestone3, and L. P. Ekstromb a Isotopes Project, LBNL, Berkeley bDepartment of Physics, University of Lund

For further information on the Isotope Explorer:

http://ie. lbl. gov/isoexpl/isoexpl. htm

For further information on the Lund Nuclear Data Centre and Services:

Contact: Peter Ekstrom

Address: Department of Physics

University of Lund Box 118, Office: B201 SE-221 00 Lund Sweden

+46 46 22 27647

+46 073 995 7984

+46 46 22 24709

peter. ekstrom@nuclear. lu. se

Visiting address: Professorsgatan 1, Internal post: Hamtstalle 14

2.1.3 Atomic Mass Data Centre, Paris — Orsay

Website of the Atomic Mass Data Centre (AMDC): http://csnwww. in2p3.fr/amdc

AMDC is devoted to nuclear and mass spectroscopic data. The Centre produces a newsletter that describes on-going experimental, theoretical and evaluation work on the atomic masses, and feedback on important conferences. Furthermore, the 1995 update of the atomic mass evaluation by G. Audi and A. H. Wapstra (1995), and the NUBASE data evaluation by G. Audi et al. (1997) can be displayed by the NUCLEUS PC program or by the ‘jvNubase JAVA applet’ on the Web. NUBASE contains the main nuclear and decay properties of the known nuclides in their ground and isomeric states as derived from ENSDF, the Atomic Mass Evaluation, and a critical compilation of recent literature.

For further information, contact Georges Audi:

Address: Atomic Mass Data Centre, CSNSM (IN2P3-CNRS)

Batiment 108 91405 Orsay Campus France

Telephone: +33 1 6915 5223

Fax: +33 1 6915 5268

E-mail: audi@csnsm. in2p3.fr

Economic and financial aspects

Decommissioning is a costly activity. Therefore it is needed to calculate its cost well in advance and accumulate the funds during plant operation as an assurance for being able to close the existence cycle of the plant. Therefore both aspects of cost calculations and funding will be briefly addressed.

The total cost of decommissioning is dependent on the sequence and timing of the various stages of the program. Deferment of a stage tends to reduce its cost, due to decreasing radioactivity, but this may be offset by increased storage and surveillance costs.

Even allowing for uncertainties in cost estimates and applicable discount rates, decommissioning contributes less than 5% to total electricity generation costs. In USA many utilities have revised their cost projections downwards in the light of experience, and estimates now average 325 million dollars per reactor all-up.

The cost of decommissioning nuclear power plants is based on the following factors:

• The sequence of decommissioning stages chosen;

• The timing of each decommissioning stage;

• The decommissioning activities accomplished in each stage.

In addition, costs depend on such country — and site-specific factors as the type of reactor, waste management and disposal practices and labor rates. The importance of the last item is due to the fact that decommissioning is a labour intensive activity and, therefore, its cost is strongly connected with labour practices, working hours and, of course, labor rates.

Total decommissioning costs include all costs from the start of decommissioning until the site is released for unrestricted use.

The cost estimates are based on previous decommissioning and decontamination experience, on the cost of maintenance, surveillance and component replacements, and on the cost of similar non-nuclear work. Estimates for large NPPs. have been made by several European countries as well as Japan, Canada and the United States.

The results, which include a 25 per cent contingency factor, showed a range of costs for an immediate Stage 3 decommissioning of between 97 and 173 million U. S. dollars (1984). Costs for combining Stages 1 and 3 ranged from 117 to 181 million dollars. Only the United States estimated the costs of combining Stages 2 and 3, from 158 to 186 million dollars. While these figures cannot be absolutely precise, due to differences in the original contingency factors and definitions of decommissioning stages among countries, they nevertheless show what order of magnitude actual decommissioning costs are likely to be for large power plants.

Various methodologies are available for the calculation of decommissioning costs, which present different levels of reliability and precision and are used according to the different objectives of the evaluations. The major reasons that usually lead to the need of a cost evaluation are the following:

• To provide an input for the decommissioning funding during plant operational life

• To compare costs associated with different strategies for the decision making process

• To prepare long term budgeting and cash flow

• To provide a tool for project control

According to the above objectives, the methods include:

• Scaling up or down from similar plant evaluations or experiences according to plant power, or to the total plant activity or to the waste masses, or to other criteria

• Simple calculations based on unit costs for a number of overall parameters like mass of activated metals, mass of contaminated concrete, mass of contaminated metals. This method can be used also for a generic power plant (not site specific)

• Detailed site specific calculations based on a very detailed bottom-up approach, separating each elementary work package

In the last case a detailed database and a computer code treating a large number of information are needed.

For example, one of these computer codes (STILLKO) has been developed in Germany by NIS Company and has been extensively used not only in Germany, but also in many European countries, including Italy. The STILLKO Cost Breakdown Structure (CBS) includes all decommissioning activities that are necessary for the successful completion of the decommissioning project, beginning with the licensing procedure up to the green field status at the end. The CBS is organized into different levels in a hierarchical structure as described in fig. 3.

Allocate Cost categories to building areas

Plant, Controlled Area, BP, BA, ВТ SAT, Support Building for SBP, Storage facilities. Safe Bndosure Area, Conventional Area

Subdive the Cost Categories within the Ares into sections which allow a time and personnel о rented planning

About 209 tasks; conditioning of primary waste, packaging of primary waste, release measurements, ..

Subdivide the Tasks into sections which allow a dear cost calcuilation

Ex; work permission, preparation of working area, restauration and cleaning of working area, ….

Figure 3 — Decommissioning Cost Breakdown Structure (CBS) Organization

On the first level the division of a decommissioning project is effected according to decommissioning phases which are separated according to time and obtained or necessary permits.

On the second level, the decommissioning phases are divided into the following cost categories:

• Project management and project administration

• Planning and licensing

• Plant operation and security

• Plant technical activities for Safe Enclosure

• Preparations for Dismantling

• Dismantling activated and contaminated components

• Decontamination

• Conventional dismantling

• Waste management

• Radiological and conventional worker protection

These cost categories have been created according to functional points of view and represent the volume of the decommissioning activities. The cost categories may occur in every decommissioning phase, with suitable contents of the cost categories regarding the respective phase.

The third level is used to allocate the decommissioning activities to the buildings and areas on site. Using this level in the cost structure it is possible to assign the work directly to the place where it arises but also to determine the sequence of the activities and their schedule in relation to the specific building.

On the fourth level, individual tasks are defined which allow a room by room or system by system planning, regarding to the situation on site. The execution of the tasks may be done parallel in different buildings, building levels or rooms.

On the fifth, the lowest level, the decommissioning tasks are divided into activities. These activities are formed in a way that each of them can be individually calculated.

It is useful to mention that a standardization of cost items has been developed in the framework of OECD and European Union and that it can be a useful reference for the future.

About financing methods, several alternatives can be used depending on the circumstances of each utility and the country in which it operates. In several countries, a fund of some type has been established, or proposed, to assure the availability of financing. This is usually done by an early estimation of the cost of decommissioning at the end of the normal plant lifetime and requiring payments, either annually or on a charge per kilowatt-hour basis, to ensure that this sum is in place. This estimate is updated regularly and the charge adjusted accordingly.

The drawback to this system is that the amount estimated would not be in place if the plant were to be shut down before the end of its normal lifetime. To avoid this, a fund could be established at the start of the plant’s operation which would cover the cost of decommissioning whenever it became necessary. However, this represents a heavy burden for the utility at the moment when construction and start-up costs are already high, and thus, although it may be imposed by law, this solution is clearly not favoured by utilities.

Financing methods vary from country to country. Among the most common are:

• External sinking fund (Nuclear Power Levy): This is built up over the years from a percentage of the electricity rates charged to consumers. Proceeds are placed in a trust fund outside the utility’s control. This is the main US system, where sufficient funds are set aside during the reactor’s operating lifetime to cover the cost of decommissioning.

• Prepayment, where money is deposited in a separate account to cover decommissioning costs even before the plant begins operation. This may be done in a number of ways, but the funds cannot be withdrawn other than for decommissioning purposes.

• Surety fund, letter of credit, or insurance purchased by the utility to guarantee that decommissioning costs will be covered even if the utility defaults.

However, the uncertainties in cost calculations are among the issues in decommissioning that shall be further developed.

In Italy a fund has been established to enable the decommissioning of Italian NPPs and the closure of the nuclear fuel cycle. These special provisions are included in the Financial Statement of the SOGIN Company.

Construction of physical channels

The wave functions considered so far have a definite total spin S and a definite total orbital angular momentum L, since only reduced matrix ele­ments in spin-space and orbital space were calculated, see eq. (3.21). If one wants to describe scattering, the various clusters have to be combined to two fragments with angular momentum ji and j2. This leads to new quan­tum numbers, the relative orbital angular momentum between the fragments Lrel, the channel spin Sc = j1 + j2, and the total angular momentum J = Lrel + Sc. Hence, a physical channel is characterized by the two fragments; their internal energy if one takes excited states into account, their spin j1

and j2, ^ Lreh and J.

So far the wave functions have been characterized by the spins of the frag­ments s1 and s2, the total spin S = s1 + s2, the internal orbital angular momenta l1 and l2 and their coupling to L3 = l1 + l2, and finally the total orbital angular momentum L = L3 + Lrei. This means till now we have
worked in an LS-coupling scheme, by calculating spin and orbital matrix el­ements separately, but for scattering reactions we have to use the jj-coupling scheme. This change requires a recoupling via standard procedures. In an obvious notation we find

Подпись: [Lrel[[h Sl]jl [l2S2]j2 ]Sc]J >= £ SL3 L Д? L2 (-1)Sc-Lre-J l1 l2 L3 I J S L 1 Si S2 S  Lrel L3 L  [ [ [ l1l2]L3Lrel]L[s1S2]S ]J > j1 j2 Sc J { Sc Sc 0 J

^ ^ (4-1)

where j = л/2j + 1 and the curly bracket symbols are 9 j-symbols [20].

If a fragment contains different orbital angular momenta, like the S — and D-wave component in the deuteron, then this linear combination can also be performed in eq. (4.1) with the appropriate coefficients. This is another meaning of the index a in eq. (3.3).

The generalized eigenvalue problem is then solved on the basis of physical channels, eq. (4.1). An essential point is that during solution no states ap­pear which have norm equal to zero, be they Pauli-forbidden states or states which cannot be coupled to the required quantum numbers. This is in con­trast to the treatment of ref. [3] where the Pauli-forbidden states are used as a test for a correct calculation. Here another test can be performed: Col­lecting all diagonal overlap matrix elements (and those of the Hamiltonian), which do not have permutation across fragment boundaries (nor interaction across fragment boundaries), the calculated norm is just the product of the internal norm of the fragments times the norm of the Gaussian function on the relative coordinate, which can easily be calculated. Hence, dividing by the norm of the relative motion, the calculated internal norms have to be independent of the width used for the relative motion. A further test are the matrix elements of the Hamiltonian described above, they contain all interactions of the fragments times the relative norm. Hence dividing these matrix elements by the corresponding norm matrix elements yields the in­ternal energy of the two fragments, the threshold energy, which again has to be independent of the width parameters used for the radial motion. In most cases these two checks are a very stringent test on the correctness of the calculation.

In order to calculate the reactance matrix amn eq. (2.31), the matrix elements for regular and irregular Coulomb functions are still missing.

Isomeric fission yields

The independent fission yields of isomeric states are important in the definition of inventories for decay-heat calculations. However, these data are sparse for all fission processes apart from the thermal fission of 235U. Modelling calculations are normally used to derive values, based on the partition of the independent fission yields of nuclides among their isomeric states using the spin distributions of the fission fragments and nuclear levels as fitting parameters.

Fig. 12. Peak parameters for A'(140)

Madland and England (1977) assumed that the spin distribution of the fission fragments after prompt-neutron emission could be represented by the equation:

P(J) = C x (2J + 1)e _[(4+1/2)/Jrms ]2,

in which Jrms defines the state of the spin distribution, and C is a constant. Fragments with J nearer the spin of a particular isomer state are defined as feeding that state. This model has been developed further by Rudstam and co-workers (IAEA-CRP, 2000): the probability that the spin will decrease by one unit is proportional to the density of nuclear states of spin J-1, while the probability that the spin will increase is proportional to the density of nuclear states of spin J+1. The ratio between the number of nuclear states of spin J-1 and those of spin J+1 is given by Z(J):

Z (J ) = -(2J^l Є (4 4 +2)/^

(2J + 3)

in which Jnuc is another spin parameter (defined effectively by the above equation). This approach results in a relative probability of Z/(1+Z) to decrease the spin by one unit, and a relative probability of 1/(1+Z) to increase the spin by one unit. Erroneous results will occur when the isomeric state is at a much higher energy than the ground state.

Equations have been derived to calculate the fractional independent isomeric yields (fiiy), and they can be modified to accommodate reductions in the excitation energy caused by the gamma-ray emissions. The available experimental data have been compared with the calculated fiiy values, particularly for the thermal fission of 235U. Various combinations of Jrms and Jnuc were adopted, and the best combinations were found to be:

Jrms of 6.50, and Jnuc of 6.00 for odd-mass nuclides;

Jrms of 6.00, and Jnuc of 1.00 to 2.00 for even-mass nuclides.

A value of 6.25 has been adopted for Jrms, and values of 6.00 (odd mass) and 2.00 (even mass) for Jnuc in comparing the fiiy data for the high-spin isomers listed in Table 6. Agreement between experimental and calculated values is judged to be satisfactory, although some nuclides exhibit significant discrepancies (e. g., 82As, 99Nb, 119Cd, 128Sb and 146La).

Table 6: Experimental and calculated fractional independent yields of the high-spin isomers

of nuclides formed in the thermal-fission of 235U

Nuclide

fiiy(high)

Nuclide

fiiy(high)

experimental

calculated

experimental

calculated

79Ge

1.00 ± 0.11

0.829

127In

0.87 ± 0.06

0.814

81Ge

0.70 ± 0.06

0.835

127Sn

0.90 ± 0.11

0.626

82As

0.17 ± 0.07

0.597

128In

0.30 ± 0.07

0.190

83Se

0.89 ± 0.07

0.816

128Sn

0.11 ± 0.07

0.209

84Br

0.30 ± 0.04

0.504

128Sb

0.61 ± 0.06

0.192

84Br

0.38 ± 0.04

0.504

129In

0.76 ± 0.07

0.815

90Rb

0.58 ± 0.05

0.659

129Sn

0.43 ± 0.06

0.621

90Rb

0.90 ± 0.01

0.659

130Sn

0.13 ± 0.02

0.212

99Nb

0.06 ± 0.14

0.819

130Sb

0.45 ± 0.11

0.190

113Ag

~1.00

0.847

132Sb

0.20 ± 0.02

0.190

115Ag

~1.00

0.846

132Sb

0.19 ± 0.03

0.190

116Ag

~1.00

0.391

133Te

0.78 ± 0.04

0.590

117Ag

~1.00

0.848

133Te

0.57 ± 0.04

0.590

118Ag

0.44 ± 0.10

0.388

133Te

0.61 ± 0.08

0.590

119Cd

0.39 ± 0.20

0.724

133I

0.07 ± 0.02

0.140

120Ag

0.85 ± 0.15

0.382

133Xe

0.75 ± 0.04

0.603

121Cd

0.89 ± 0.11

0.730

134Sb

0.19 ± 0.05

0.279

123Cd

0.68 ± 0.02

0.614

134i

0.20 ± 0.02

0.183

123In

0.94 ± 0.11

0.817

135Xe

0.65 ± 0.04

0.575

123Sn

1.00 ± 0.28

0.627

136i

0.79 ± 0.14

0.391

124In

0.86 ± 0.80

0.215

138Cs

0.58 ± 0.08

0.392

125Cd

0.66 ± 0.08

0.614

146La

0.06 ± 0.03

0.391

125In

0.88 ± 0.08

0.813

148Pr

0.12 ± 0.03

0.660

126In

0.42 ± 0.17

0.215

148Pm

0.71 ± 0.06

0.388

Heavy Water Advanced Reactors

Heavy water reactors (HWRs) at the beginning of 2001 represented about 8% by number and 4.7% by capacity of all operating power reactors. With many years of operating experience Canada has developed the 700 MWe CANDU-6, which has been built in several countries outside Canada. India has also built a series of 220 MWe HWRs. Work on evolutionary HWRs is ongoing in Canada, India and Russia and is briefly described below.

The new Canadian evolutionary Heavy Water Reactor11 is the 935 MWe CANDU-9. Canada is also working on a 400 — 650 MWe Next Generation CANDU. The NG CANDU design features major improvements in economics, inherent safety characteristics and performance. It optimises the design by utilizing SEU fuel to reduce the reactor core size, which minimizes the amount of heavy water required for moderation, and allows light water to be used as the reactor coolant. It is expected that the potential for offsite releases of radioactive material in NG CANDU will be sufficiently low that a target of “no evacuation” can be achieved. In June 2002, Atomic Energy of Canada renamed the NG as Advanced Candu Reactor (ACR) and announced that the ACR-700 will be “market-ready” by 2005.

In India, a continuing process of evolution of HWR design has been carried out. In 2002 construction began on two 500 MWe units at Tarapur which incorporate feedback from several indigenously designed and built 220 MWe units. The Advanced HWR (AHWR), under development in India, is a 235 MW heavy water moderated, boiling light water cooled, vertical pressure tube reactor with its design optimised for utilization of thorium for power generation. The conceptual design and the design feasibility studies for this reactor have been completed and the detailed design is in progress. The design incorporates a number of passive systems and the overall design philosophy includes achievement of simplification to the maximum extent.

A reactor design concept for an ‘Ultimate Safe’ reactor with 1000 MW output is being developed by the Russian Institute ITEP, in conjunction with other Russian organizations12. The prototype for this conceptual design is the KS150 reactor in Bohunice in the Slovak Republic. Low temperature heavy water is used as the moderator, and the design incorporates gaseous coolant, either CO2 or a mixture of CO2 and helium, and low fissile content fuel. The entire primary system, including main gas-circulators, steam generators and intermediate heat exchangers are contained within a multi-cavity, pre-stressed concrete pressure vessel. The design is said to be super safe, for example, accidental withdrawal of all control rods will add a relatively small amount of reactivity to the system compensated by the negative reactor power coefficient.