XA9744983 _

International Atomic Energy Agency INDCCCCP1-4Q4 Distr.: L

IN DC INTERNATIONAL NUCLEAR DATA COMMITTEE

CALCULATIONS RELATED TO NUCLEAR FISSION-PRODUCT YIELDS

Three papers by E.S. Bogomolova, A.F. Grashin, A.D. Efimenko, I.B. Lukasevich Moscow Engineering Physics Institute, Moscow

Translated by the IAEA

August 1997

IAEA NUCLEAR DATA SECTION, WAGRAMERSTRASSE 5. A 1400 VIENNA Reproduced by the IAEA in Austria August 1997 INDC1CCPV404 Distr.: L

CALCULATIONS RELATED TO NUCLEAR FISSION-PRODUCT YIELDS

Three papers by E.S. Bogomolova, A.F. Grashin, A.D. Efimenko, I.B. Lukasevich Moscow Engineering Physics Institute, Moscow

Original articles in Russian published in Jadernye Konstanty (Nuclear Constants) Volumes 1-2, 1995

Translated by the IAEA

August 1997 Contents

The ASIND-MEPhI Library of Independent Actinide ...... 7 Fission Product Yields (English translation from Yad. Konst. 1-2, 1995, p. 89)

Calculation of Independent Fission Product Yields by ...... 25 the Thermodynamic Method (English translation from Yad. Konst. 1-2, 1995, p. 99)

Long-Lived Fission Product Yields and the Nuclear ...... 51 Transmutation Problem (English translation from Yad. Konst. 1-2, 1995, p. 117) XA9744984

- 7 -

96-11496 (N) Translated from Russian

UDC 539.173

THE ASIND-MEPhI LIBRARY OF INDEPENDENT ACTINIDE FISSION PRODUCT YIELDS

E.S. Bogomolova, A.F. Grashin, A.D. Efimenko, LB. Lukasevich Moscow Engineering Physics Institute, Moscow

ABSTRACT

THE ASIND-MEPhI LIBRARY OF INDEPENDENT ACTINIDE FISSION PRODUCT YIELDS. This database of independent fission product yields has been set up at the Moscow Engineering Physics Institute on the basis of theoretical calculations within the framework of the super-nonequilibrium thermodynamic model. The database consists of independent yield sets for 1163 fission products in the wide range of fissile nuclides from thorium-229 to fermium-257 with excitation energies up to 20 MeV. The use of the theoretical model made it possible to raise the accuracy of prediction for poorly explored fission reactions. The number of yield sets is larger than in the ENDF/B. For example, photofission product yields are included in the ASIND-MEPhI database as virtual sets.

Fission product yields are among the most important nuclear constants. Without them it is impossible to calculate such nuclear physics characteristics as, for example, energy generation and the activity of a fission product mixture. Modern engineering designs in the area of reactor physics require knowledge of approximately 1000 yield values for each reaction. These so-called complete sets of yield data are used in protection- and safety-related calculations in the study of radioactive waste transmutation, and there are certain applications for measurement purposes. The reliability of the calculations depends on the quality and authenticity of the data. Such calculations, carried out on a computer, require accessible databases in the form of files stored on magnetic carriers. The requirements for databases on fission product yields may be summarized as follows: 8

(1) Accessibility;

(2) Authenticity and reliability of the data;

(3) Large number of data sets covering the most important fission reactions;

(4) Completeness of those data sets.

The most authentic source of data on independent fission product yields is experiment. However, the volume of information required exceeds several times over the quantity of experimental data available, besides the fact that in many cases these data contradict each other. Thus, there is an increasingly acute awareness of the need for theoretical models and calculations which would be capable of distinguishing among experimental data and completing them in the area inaccessible to experiment and in cases where experiment is unreliable. The traditional models of nuclear processes long ago reached their limit and have been unable to cope with this task for several decades. The thermodynamic approach is the most productive and flexible one for investigations into nuclear processes. However, many nuclear processes happen very quickly, and doubts have frequently been expressed about the applicability of normal (equilibrium) thermodynamics. The most important basic features of the new thermodynamic approach are [1]:

Account is taken of non-equilibrium;

There is a new concept of temperature as a characteristic of transition

energy.

The new approach has led to a substantial change in the results of calculations, whose reliability and accuracy have increased. The calculation method that has been 9

devised is based on the most general statistical concepts and a programming language that

applies diagrammatic techniques. It is thus proving applicable to a wide range of nuclear

physics phenomena and makes it possible to use a single method for calculating low- and

high-temperature processes [2-5], ensuring precise results for certain nuclear reactions.

Two highly authoritative libraries of fission product yields currently exist: the

ENDF/B file distributed and maintained by Brookhaven National Laboratory, and the

Japanese JENDL library. Both libraries have a fundamental deficiency - the method used

for predicting yields is incomplete and unsubstantiated and produces significant systematic

errors, especially in the little-explored range.

The ASIND-MEPhI library of fission product yields was established in 1986 [6] as

an alternative to ENDF/B and JENDL, from which it differed mainly in its method of predicting yields. The ASIND-MEPhI library was the first to use a theoretical model [7] to

calculate yields, which made possible a much more comprehensive list of yield data and

more accurate values for the yields of many products, in particular those far from the

isobaric distribution peaks. In the beginning, the library contained 30 data sets covering

fission induced by thermal and reactor neutrons, by 14 MeV neutrons, and spontaneous fission. Later, the library was constantly updated through the inclusion of new data sets [8]. The ASIND-MEPhI data file has been transferred to the Russian Federation

Nuclear Data Centre (Institute of Physics and Power Engineering, Obninsk) and the IAEA for storage and distribution [9].

In contrast to the other libraries, the use of a new and original method of predicting

fission product yields enables us to offer users data on yields for photofission reactions [10] 10 -

(they may be obtained on request from MEPhI) and for high energy particle induced fission reactions [11, 12]. The latter, in particular, are of interest in studying the problems associated with the transmutation of long-lived radionuclides.

Organization of the database on fission productyields

The ASIND-MEPhI database containing independent fission product yields was set up in accordance with a fully realized conceptual approach [13]. The main organizing principle of the database is that priority is given to experimental data. However, since these are relatively scarce they have been complemented by calculated yield values obtained using a thermodynamic fission model. The completed yield sets were normalized to the condition Y(A,Z) = 200%. The THERMO software package was used to calculate A z the theoretical yields (creating one yield file takes 5 min on an IBM PC). As new experimental information is received the data sets will be regularly replaced and amended.

Besides the running version, a file will be kept containing only theoretical values (version

ASIND-MEPhl-O).

The database is organized in such a way that in addition to the real data sets physically stored on magnetic carriers, it also contains virtual sets which are generated when required by the THERMO software, which was initially installed on an ES computer, but subsequently transferred from the PL/1 operating environment of the ES to an Si PC system. This allows more economical use of the information equipment storage, thus extending considerably the list of data sets. From the technical point of view, establishing a real data set is justifiable either when experimental information is available and there is a need for renormalization and substitution of theoretical yields by experimental ones, or 11 when data have great practical value and are used frequently. In the running version of

ASIND-MEPhI 50 sets have been selected for storage in real format (see Table 1). Each set contains independent yields for fission products with mass numbers between 70 and 170. For each mass chain, the independent yields of 10 isobars are given. Including isomers, each set contains some 1150 independent yield values with error indications. The data are stored on the magnetic carriers in two ways: in the conventional ENDF/B format

(in this case the yields are normalized to 2) and in a master format.

In the latter case, each record consists of an identifier for the fission product followed by its independent yield, the error in the yield, and the isomeric ratio. There are

1010 records, each 16 bytes long. The records are arranged in order of increasing A, and where A is the same, by increasing charge of all the product. The isomeric ratios are calculated by the IZOT program and the yield errors by the YLER program. For this purpose, the parameters of the model which define fission fragment deformation at the point of disruption were determined by comparison with a large volume of experimental data on thermal neutron-induced fission of 235 U. As a result, values with an error

A — 0.1 were found for these parameters. Uranium-235 was chosen because more experimentally measured yields are available for it than for any other nuclide, allowing the model parameters to be determined with the greatest accuracy. The errors for the independent yields were obtained by a standard error transfer method. The experimental values are given in the file with the errors indicated by the authors. 12

Technical characteristics

The database and accompanying description are available from the Nuclear Data

Section of the IAEA, the Russian Federation Nuclear Data Centre, and the Moscow

Engineering Physics Institute, on magnetic tape or diskette. The volume of working

memory is 420 K, and the volume of memory on floppy disk is 1 MB for the THERMO

program and 17 MB for the database. The system runs on an IBM PC/AT using MS-DOS

3.30 and higher. The first version was installed on an IBM-360 and compatible computers

of the ES series. The system is factographic, there are 7 output options, the data source is

experimental data from the literature and the results of calculations based on our own

methods, and the data are recorded in the international format used for the ENDF/B file.

Comparison with the ENDF/B file

The main argument in favour of one file or another is its predictive accuracy. It is

thus interesting to compare data from the ENDF/B and ASIND-MEPhI files with any fairly

complete set of experimental yields obtained after the files were created. This can be done

with the set of data on thermal neutron-induced fission product yields for 239Pu [6]. The

set contains 109 independent fission product yields ranging in mass from 86 to 109 and in

charge from 33 to 45. The criterion selected for comparison was the mean-square deviation from the experimental values of the values of Zp and ctz from each of the two

files.

£ZY(A,Z) Z,(A) (1) £Y(A,Z)' 13

2(Z„-Z)2-Y(A,Z) 1/2 A ct(A) = (2) ZY

For both files, the mean deviation of the positions of the isobaric distribution peaks from the experimental values is roughly the same:

t „ \ 1/2 5;l[z ”(Ai)-Z,(A,)],j =0.11 (3)

However, the mean deviation of the isobaric distribution widths

1/2 X^[=",(Al)-c7(Ai)]' (4) for the ASIND-MEPhI file is half that for ENDF/B. The more accurate widths in our file should have a particularly strong effect far from the most probable charges, where for the time being there are no experimental data. For example, the value of the independent yield for wNb in our file is two orders of magnitude greater than in the ENDF/B file.

A convenient criterion to use in comparing the files is the quantity

S = ly s(A,Z); s(A,Z) = |lg(YASIND"MEPhl(A,Z)/YENDF/B(A,Z)| (5) Ntz 1 V n which indicates by how many times on average the yield values from one file differ from those of the other. Table 2 gives the results of such a comparison for 21 data sets, for yield values greater than 107. The ENDF/B file was made available to us by the Russian

Federation Nuclear Data Centre.

As an example, let us consider in greater detail the sets for thermal neutron-induced fission of uranium-235. In the range of yield values greater than 10 2%, the data from the two files practically coincide; above 10* 5 % they differ in 70% of cases by less than a factor 14

of 3. The greatest difference (by over a thousand times) occurs in the case of 86 Ge, for

which the independent yield value in our file is 3.99±0.94 x 10“\ whereas that in ENDF/B

is 6.29±1.00 x 101. The latter value is evidently erroneous, as it produces an unlikely jump in the independent yield curve for Z = 32 (Fig. 1). The previous version of the

ENDF/B file gave a yield value of 8.64 x 10"4 for 86 Ge, which is more likely. In the

Japanese JENDL library [14], the corresponding value is 8.27 x 10"4. The situation is

similar with 100Rb: our value is 4.22 ±1.43 x 10'5 , the value in ENDF/B is

3.48±2.22 x 10"2, and JENDL has 8.26 x 10"6 . We could continue with similar examples.

It would seem that in those cases where our data differ greatly from ENDF/B (last two

columns of the table), a mistake has probably occurred in the ENDF/B file owing to poor

testing.

The mass and charge distributions of fission products are similar for the ASIND-

MEPhl and ENDF/B files (Figs 3-17). The only exception is (n^,f) fission of 232U. In this case, the ENDF/B data demonstrate a broadening of the mass distribution which is completely out of keeping with low energy fission (Fig. 2) and in our opinion incorrect.

It should be mentioned that we owe the significant progress we have managed to achieve in predicting fission product yields to the development of the thermodynamic fission model. This model’s proven applicability to a wide range of nuclear physics phenomena has enabled us to perfect our calculation methods. 15

REFERENCES

[1] GRASHIN, A.F., EFIMENKO, A.D., LEPESHKIN, M.V., A new thermodynamic approach to nuclear fission, (Proc. Int. Conf. Nuclear Fission - 50 Years, Leningrad, 1989) St. Petersburg (1992) 318-323 (in Russian).

[2] GRASHIN, A.F., EFIMENKO, A.D., Yad. Fiz. 56 11 (1993) 114-121 (in Russian).

[3] GRASHIN, A.F., EFIMENKO, A.D., Izv. Akad. Nauk., Ser. Fiz. 57 No. 5 (1993) 67-71 (in Russian).

[4] GRASHIN, A.F., EFIMENKO, A.D., KOLOBASHKIN, V.M., Izv. Akad. Nauk., Ser. Fiz. 50 No. 5 (1986) 944-948 (in Russian)

[5] GRASHIN, A.F., EFIMENKO, A.D., Izv. Akad. Nauk., Ser. Fiz. 56 No. 1 (1992) 79-83 (in Russian).

[6] GRASHIN, A.F., EFIMENKO, A.D., in Problems of Atomic Science and Technology, Ser. Nuclear Constants No. 2 (1987) 60-62 (in Russian).

[7] GRASHIN, A.F., EFIMENKO, A.D., KOLOBASHKIN, V.M., Izv. Akad. Nauk. SSSR, Ser. Fiz. 49 No. 1 (1985) 188-193 (in Russian).

[8] EFIMENKO, A.D., GRASHIN, A.F., KUDRYAVTSEVA, E.A., The ASIND- MEPhl fission product yield database, (Proc. Nuclear Data for Science and Technology, Mito, 1988) JAERI (1988) 971-974.

[9] GRASHIN, A.F., EFIMENKO, A.D., ASIYAD, a fission product yield data library, IAEA [original illegible] Nov. 1993.

[10] GRASHIN, A.F., EFIMENKO, A.D., Yields for photofission of uranium-236 and diverse energy neutron-induced fission of uranium-235, in Experimental Methods in Nuclear Physics, Energoatomizdat, Moscow (1985) 31-36 (in Russian).

[11] STEPANOV, N.V., Statistical modelling of fission for excited atomic nuclei: formulation of the model, ITEhF preprint, 87-81 Moscow (1987) (in Russian).

[12] STEPANOV, N.V., Statistical modelling of fission for excited atomic nuclei: calculation and experimental comparison, ITEhF preprint, 88-55 Moscow (1988) (in Russian).

[13] GRASHIN, A.F., KOLOBASHKIN, V.M., TELEVINOVA, T.M., et al., (Proc. Nuclear Data for Science and Technology, Antwerp, 1982), Boston (1982) 997-998.

[14] IHAZA, H., MATOMOTO, Z., TASAKA, K., et al., JNDC FP Decay and Yield Data, Preprint JAERI-M-9715 (1981). 16

Table 1

Data on independent yields given in the running version of the ASIND-MEPhI file

Nuclide Type of - Nuclide ' Type of fission* fission Th-229 T Pu-240 F Th-232 FH Pu-241 TF U-232 TF Pu-242 F U-233 TFH Pu-243 TF U-234 F Am-241 F U-235 TFH Am-242 TF U-236 F Am-243 F U-237 TF Cm-243 T U-238 FH Cm-244 S U-239 F Cm-245 TF N p-236 F Cm-247 TF Np-237 F Cf-249 T N p-238 TF Cf-251 T Np-239 F Cf-252 S Pu-236 TF Fm-254 S Pu-238 F Fm-256 s Pu-239 TFH

T, F, H and S denote thermal, fast and high-energy (~ 14 MeV) neutron-induced fission and spontaneous fission, respectively. 17

Tabk-2

Values of the parameter S describing the deviation of data from the ASIND-MEPhI and ENDF/B** files for certain data sets

S Number of points in the range Reaction s<0,5 0,5~~3 232U(llfli,f) 0,56 296 85 93 9 0 ^Ufoth,!) 0,44 307 98 45 3 0 ^U(nuf) 0,43 338 76 44 9 0 0,40 343 80 42 7 0 ^Utoth.f) 0,43 306 77 46 9 1 0,46 .308 89 53 6 1 ^UOv.f) 0,43 327 90 50 3 0 0,43 314 96 47 6 0 ^Ufar.f) 0,47 300 129 45 6 0 ' ^NpXm.f) 0,43 339 98 . 45 3 0 0,44 333 78 59 3 0 “•Puta*,© 0,34 372 74 43 3 0 ^Putnr.f) 0,38 392 76 41 6 . 0 240Pu(nf,f) 0,40 378 82 41 6 1 241Pu(nth,f) 0,37 340 78 37 3 0 242Pu(iv,f) 9,44. 347 101 52 4 0 241 Am (nth,f) 0,53 325 86 63 18 0 243Am (nth ,f) 0.45 348 112 59 5 2 "245Cm(nth,f) 0,43 364 114 46 6 0 ^Cmfoth.f) 0,29 488 88 20 ' • 0 0 :2$2 Cf(sf) 0,55 289 141 78 1~~

** The ENDF/B file was made available by the Nuclear Data Centre (Institute of Physics and Power Engineering). 18

Fig. 1. Independent yields of germanium isotopes for thermal neutron-induced fission of 235U

----ASiND-MCPni m - ENOF/e

------ASINO-MEPhl • - ENOF/e

Fig. 2a. Mass yields of thermal neutron- Fig. 2b. Charge yields of thermal neutron- induced fission products for 232 U. induced fission products for 232 U.

U233(Nf.F) U233(Nf.O

------ASIHO-MEPN • - ENOF/e

Fig. 3a. Mass yields of fast neutron- Fig. 3b. Charge yields °£Jfast neutron- induced fission products for 3 U. induced fission products for 3 U. 19

---- AS.KO-UO-W • - EfCf/B

- ASINO-MCPM

Fig. 4a. Mass yields of fast neutron- Fig. 4b. Charge yields of fast neutron- induced fission products for 234 U. induced fission products for 2u.

------asikd -uepn • - ENOF/B

Fig. 5a. Mass yields of thermal neutron- Fig. 5b. Charge yields of thermal neutron- induced fission products for 235U. induced fission products for 235U.

U23S(Nf.F) U23S(Nf,F)

• - ENOF/B 70 80 90 \6o lio'lio 130 140 150 l6o'l>0

Fig. 6a. Mass yields of fast neutron- Fig. 6b. Charge yields of fast neutron- induced fission products for 233 U. induced fission products for 2331]. 20

U236fNf.F1

------ASMO-UEPhl • - ENOF/B 70 BO 90 lio 130 1401^0 160 170

Fig. 7a. Mass yields of fast neutron- Fig. 7b. Charge yields of fast neutron- induced fission products for 2iSU. induced fission products for 23(3U.

U237(Nf.F)

- EXOf/B

Fig. 8a. Mass yields of fast neutron- Fig. 8b. Charge yields of fast neutron- induced fission products for 23‘u. induced fission products for 13 u.

- *sKO-m*i

14-

------ASINO-MEPhl

Fig. 9a. Mass yields of fast neutron- Fig. 9b. Charge yields of fast neutron- induced fission products for 23 u. induced fission products for 23 U. 21

------AS-tiC-lCPN

- ■ — ASwD-UfPtil • - 6XDf/8

Fig. 10a. Mass yields of fast neutron- Fig. 10b. Charge yields of fast neutron induced fission products for 23'Np. induced fission products for 237Np.

Np238(Nf.n Np238(Nf.F) . ' ------AStfO-WCPtt » - ex of/e

10~*I - ASMO-WEPhl

Fig. 11a. Mass yields of fast neutron- Fig. lib. Charge yields of fast neutron- induced fission products for 238Np. induced fission products for 238Np.

Pu239(Nth.F) - ASftiO-UCPM

Fig. 12a. Mass yields of thermal neutron- Fig. 12b. Charge yields of thermal induced fission products for 239Pu. neutron-induced fission products for Pu. 22

Fig. 13a. Mass yields of fast neutron- Fig. 13b. Charge yields of fast neutron- induced fission products for 139Pu. induced fission products for 239Pu.

Pu24l(Hth.F) Pu241(Mlhf) a Sjn D —u £7*tu

- oa>r/B

70 80 SO

Fig. 14a. Mass yields of thermal neutron- Fig. 14b. Charge yields of thermal induced fission products for 241 Pu. neutron-induced fission products for 241 Pu.

Pu242(Nf.O

10" • - EMor/a

40'' 4550

Fig. 15a. Mass yields of fast neutron- Fig. 15b. Charge yields of fast neutron- induced fission products for 242 Pu. induced fission products for 242 Pu. 23

Fig. 16a. Mass yields of fast neutron- Fig. 16b. Charge yields of^fast neutron- induced fission products for 4 Am. induced fission products for Am.

• - ENOF/B

Fig. 17a. Mass yields of thermal neutron- Fig. 17b. Charge yields of thermal induced fission products for 245Ku. neutron-induced fission products for 245Ku. XA9744985

- 25 - 96-11496 (N) Translated from Russian

UDC 539.173

CALCULATION OF INDEPENDENT FISSION PRODUCT YIELDS BY THE THERMODYNAMIC METHOD

E.S. Bogomolova, A.F. Grashin, A.D. Efimenko, I.B. Lukasevich Moscow Engineering Physics Institute

ABSTRACT

A non-traditional thermodynamic approach is used to investigate fission of heavy nuclei considered as a chemical reaction. New explicit expressions for thermodynamic functions are constructed with a temperature T0 ^ 0 for ground states of the fissile nuclei. Deformation of fission fragments is taken into account by means of an empirical function fitted to the (n,f) process for uranium-235. Formulae are used to calculate product fission yields for a wide range of fissile nuclei from Th to Fm with excitation energies up to 20 MeV. The method can be extended to the case of high-energy collisions with compound nucleus excitation energies up to several GeV.

GENERAL CONSIDERATIONS

Two stages may be distinguished in the fission process: in the first, the compound nucleus is disrupted and two heavy fragments are formed, and in the second the fragments fly apart, emitting neutrons, and become "fission products". The formation of the fragments may be accompanied by the departure at the moment of disruption of k = 1, 2, ... neutrons which it is usual in the foreign literature to call "scission neutrons". If we designate the probability of these multiple fission processes by the symbol Wk (A,Z), then for the yield of fragments with mass A and charge Z we have

W(A,Z)=2 WZ), (1) 26 where the first term corresponds to a disruption into two fragments without additional neutrons. At the moment of disruption, heavier nuclei may be formed as well as neutrons, for instance helium. Such multiple fission processes make a very small contribution and will be neglected in what follows.

Considering the second stage of fission as a Poisson process [1], we obtain the following expression for the product yield:

y(A,z)=2 W(A+n,Z)-Pn(A+n,Z), (2) naO

f*(A,Z)= cxp[-v(AjZ)] > (3)

where v(A,Z) is the mean number of neutrons emitted by the fragment (A,Z). These neutrons we will call "post-scission neutrons". The yields (1) and (2) are normalized as follows: 2 y(A,Z)=2 W(A,Z)= 200% . (4) AX AX

After the emission of gamma photons the fission products may be found either in the ground state or in isomeric states. The isomer yields were calculated by the

Madland-England method [2], which involves using the following well-known formula for the level density

?(t/,0)(2/+l)expj- P(VJ)= (5)

and the moment of inertia B is considered independent of the quantum numbers of the fragment. The isomeric ratios calculated in this way depend directly on the temperature T and only indirectly, by way of the same temperature, and the quantum numbers of the 27

compound nucleus AF,ZF. This method is used in creating ENDF/B files. The method may

be improved if the dependence of B on A and Z is taken into account [3].

Interpreting the formation of fragments as chemical reactions in a gas mixture [4] and taking into account the law of mass action [5] we can write

t Wk(A,Z) V*} F(Af,ZF)-/nKZ;A2,Z2)-tfn ,0)1 (6 ) T

where the quantum numbers of the additional fragment Az = AF-A-k and Z2 = ZF-Z;

F(Af,Zf) is the free energy of the compound nucleus, F(A,Z;A2,Z2) is the free energy of the

fragments, F(l,0)=m„ is the neutron mass, and the coefficient

^=2,75-10' 3-T3/2-Af. (7) * tl

Here and in what follows the temperature and energy are measured in MeV in all formulae.

The free energy of the fragments at the point of disruption is equal to the sum of free energies F(A;,ZJ of each fragment (i=1,2) and their Coulomb interaction:

F’(A„Z,;A2,Z2)= F(A„Z,)+F(A2tZ2)+ F(A„Z,;A2,Z2) . (8)

When calculating the energy of the Coulomb interaction, the fissioning system is

considered as two rotating deformed fragments. The presence of the deformation leads to a change in the Coulomb energy by some quantity AV in comparison with the main part

/0)_ 0,85Z,Z2 (9) 28 which corresponds to two touching spherical fragments.

The free energy of a fragment also proves to have a part AF(A,Z) that is dependent on deformation [6]:

F(A,Z)= /<0)(A,Z)+AF(A,Z) , ( ) /<0)=Af^D~ <2s(T2+7^)+ WXM-Mu,) , 10

" 0=

14 MeXrl» "15 MeV1 ,

The shell correction to the free energy depends on the exact mass M, which we calculate by the Janecke formula [7], and the liquid drop mass MLD of a spherical nucleus, which we can calculate by the Weizsacker formula. The concept of temperature of the ground state was introduced by the authors in Refs [6, 8].

Combining the contributions from deformation, we get the following multiple fission probability

JXAF,ZF)-I*0\A2,Z2)-km„- V<°>1 Wi(A,Z)=■?="%) cxp[: (12) /^(A,Z)-/*^(A 2,Z2) Xexp

The coefficient a is obtained from the normalization condition (4). The part depending on deformation

=Tv-6(AZ)-£&, 0O= O)-A^CTv-To) , Tv= 1,9 MeV, (13)

where the function 5(A,Z) was selected empirically in the form

<5(A,Z)=2 arorctg b£+c&A—2Z)—gj (14) i d t 29

Here two types of deformation were taken into account: Z represents deformations for which values bj=0.56, ci=b j/2 were adopted, and N represents deformations for which C;=0.756 and b =cJ2. The numerical values of the parameters g, a and d are given in Table 1.

The mean number of post-disruption neutrons entering into formula (3) can be written in the form

v(A,Z)= fi‘ P(A,Z,7t)1 , (15)

where b=0.15 MeV"1 is the reciprocal of the mean binding energy of a neutron in the fragment. In expression (15) there is a term which is proportional to the shell energy of the fragment:

SsheU~ jy3(0n)+ Cti-Al/3-r0-^(6„)j ,

el'chen 6n Ch6r' 1 en=y-A,/3-(7 n-r0), y?(5 «)= (16) sh20m sh2d„ she„ and the remaining part is written in the form of some polynomial

P(A,Z,Tj)= A, -7t+A 2- ||^A-zj + A3+ A4A , (17)

hr(A-90)/I5MeV^, h2-12,5MeV h3-50,96MeV, h4-0,34 MeV

The fragment temperature Tn differs from T owing to the transition of the deformation energy into the internal energy

where a^= AF/7.5 MeV* 1. 30 -

Note that the emission of post-disruption neutrons involves a change in hadron excitation, and hence the spectrum of these neutrons is given not by the temperature Tn but by the mean nuclear temperature x = to Tn - TQ ~ 0.8 MeV.

The mean number of prompt neutrons per fission event consists of two terms:

v= 0,01.2 V(A,Z) • W(A,Z)+ k-Wk{A,Z) (19) AX nz 1

The main contribution is from post-disruption neutrons, whereas 2% is from disruption neutrons. The mean number of neutrons emitted in the formation of fragments with a given mass, i.e. the total number of multiple neutrons accompanying the formation of fragments with mass A and of neutrons evaporated by fragments of this mass, is written in the form

2V( a>Z)-W(A,Z)

^ W(AZ) * (20) z

Comparing theory with experiment for the function p(A) (Fig. 1) enabled us to select the parameters in formula 17.

Fission by thermal neutrons, reactor spectrum neutrons and spontaneous fission

The method described above was used to calculate the yields for fission reactions of heavy nuclei from thorium-229 to fermium-256. The empirical function 6(A,Z) parametrizing the form of the fragments in the thermodynamic model of fission is universal and does not depend on which specific fission reaction they were formed in. Aside from 31 the mass AF and the charge ZF of the compound nucleus, the only parameter which was changed in the transition from one fissioning nucleus to another was the temperature T. This we selected using the available experimental yield data, in particularthe "peak/valley" ratio.

This method gives an error AT < 0.01 MeV.

Table 2 gives the temperatures for several cases of thermal neutron-induced fission, corresponding to a compound nucleus excitation energy equal to the neutron binding energy.

For nuclei with small fission cross-sections for thermal neutrons, Table 3 gives the characteristics for fission by reactor spectrum neutrons with a mean energy equal to

$o£E)-E-n{E)dE (21) Joj(E)'n(E)dE where a/E) is the fission cross-section and n(E) is the neutron spectrum.

In this case the compound nucleus excitation energy is equal to the sum

V=Bn+Ef, (22)

where Bn is the neutron binding energy.

Tables 2-4 show, for several fission reactions, the temperatures calculated by the thermodynamic model and the positions of the light and heavy mass distribution peaks for fission fragments (A* L,A* H) and fission products (AL,AH), as well as the mean number of prompt neutrons.

In Figs 2-4 the solid line indicates the mass distributions of the fission productyields calculated by the thermodynamic model for fission induced by thermal neutrons in thorium-229 and by fast neutrons in americium-241 and for spontaneous fission of 32

fermium-254. The points indicate the experimental values. In Tables 6-13 the results of calculations of the mass and charge distributions of the fission products are given.

Fission by neutrons with an energy E„ > 6 MeV

In calculating yields for fission induced by neutrons with energies of 6-14 MeV one must take into account the contribution of (n,nf) reactions (threshold energy En — 6 MeV) and (n,2nf) reactions (threshold energy E„ ~ 12 MeV), which in the foreign literature are called "second-chance fission" and "third-chance fission". The total cross-sections and product yield are equal to

ctx\n,xnf) , (23) x—0.1.2

H-4,Z)=2 , x-0.1.2 (24)

where Y(X)(A,Z) is the yield for fission of a nucleus (AF-x,ZF) with an excitation energy

U(0) = Bn (AF,ZF)+En for x = 0 or U(x) = U(x l)-Bn(AF-x,ZF)-E(x)k for x = 1, 2 and a temperature T(x), which are related to each other by the equation of state

£(W= T%r). (25)

Tsf is the temperaturecorresponding to spontaneous fission of the nucleus; a^ is the effective level density parameter; E% is the mean kinetic energy of a neutron, equal to 3/2(T(x)-TSF).

Table 5 gives the values of A^ and TSF for several nuclei. Knowing these we can calculate the yields for fission by neutrons of any energy using equation (25) to determine the temperature. 33

The values of TSF and aefr can also be obtained by considering the link between the spontaneous fission width and the fission barrier [9]. Starting with the isotopes of plutonium and for heavier elements such a method of evaluating acfT gives good results. However, for light actinides the external barrier may even exceed the internal one [10], therefore an appropriate correction must be made to the values of aeff obtained by the method of Ref. [9].

The cross-sections a05 and o* 2) are equal to zero all the way to the corresponding threshold energies, so it is natural that a term with x = 1 or 2 should give a contribution to formula (24) only if a00 is different from zero, i.e. if U(1) and U(2) are greater than the fission thresholds for the nuclei (AF-1,ZF) and (AF-2,ZF). Figure 5 shows a comparison of our calculations with experimental data [15] for fission of 238U by 14.5 MeV neutrons.

Photofission, fission induced by high energy particles, product yields in reactions with heavy ions

Yet another class of reactions whose product yields were calculated by our model is photofission under the action of bremsstrahlung. The existence of a giant dipole resonance in the photo absorption of nuclei leads to the mean compound nucleus excitation energy initially increasing almost linearly with the cut-off energy of the bremsstrahlung spectrum and then entering a plateau and practically not changing with further growth in Ec0. The dependence of U(0) on Ec0 was taken from Refs [16, 17] or calculated. The cross-section for the giant dipole resonance was approximated by the sum of two Lorentz curves with the parameters published in the paper by Caldwell [18]. As in the case of fission by monoenergetic neutrons, the total fission cross-section and product yield can be written in the form

(26) °=

>Taz )= £!M^,(a,Z)+ ’ZLn&s'KAZ)*... . (27)

The threshold for the (y,nf) reaction is equal to the sum of the threshold for the (y,n)

reaction for a nucleus (AF,ZF) and the threshold for the (y,f) reaction for a nucleus (AF-1,ZF).

For neptunium-237, for example, the threshold of the (y,nf) reaction is 12.1 ±0.4 MeV.

Tables 14 and 15 give the mass and charge yields of products formed in the photofission of

plutonium-239by bremsstrahlung with a cut-off energy of 28 MeV. For our calculations we used experimental cross-section ratios a.^knf) results of calculations of the product o yields for photofission of uranium-235 are published in Ref. [19].

Note that the examples given here do not by a long way exhaust the sphere of application of the thermodynamic fission model. In particular, it has been used successfully to describe the fission of heavy nuclei (^Bi, 238U, ...) by protons with energies from

170 MeV to several GeV [20], and also to describe reactions with heavy ions at energies

E*, ^ 8 GeV [21]. 35

REFERENCES

[1] CROUCH, E.A.C., "The assessment of fission yields", Proc. Int. Conf. Chem. Nucl. Data Measurements and Applications, Canterbury 1971, London (1971) 1, 6.

[2] MADLAND, D.G., ENGLAND, T.R., Nucl. Sci. and Eng. 64 (1977) 859, 865.

[3] GRASHIN, A.F., EFIMENKO, A.D., "Calculation of inertia momenta and nuclear deformations using the thermodynamic method", Proc. 36th Conf. on Nuclear Spectroscopy and the Structure of the Atomic Nucleus, Leningrad, Nauka (1986) 219 [in Russian],

[4] LANDAU, L.D., LIPSHITS, E.M., Statistical Physics, Moscow, Nauka (1977) [in Russian],

[5] KITTEL’, Ch., Statistical Thermodynamics, Moscow, Nauka (1977) [in Russian].

[6] GRASHIN, A.F., EFIMENKO, A.D., KOLOBASHKIN, V.M., Izvestiya AN SSSR, Ser. fizicheskaya 49 1 (1985) 188, 193 [in Russian],

[7] JANECKE, J., At. Data and Nucl. Data Tables 17 (1976) 455, 462.

[8] GRASHIN, A.F., EFIMENKO, A.D., Yademaya fizika 43 (1986) 1330, 1331 [in Russian].

[9] GRASHIN, A.F., EFIMENKO, A.D., Izv. AN, Ser. fizicheskaya 56 1 (1992) 79, 83 [in Russian].

[10] OSTAPENKO, Yu.B., SMIRENKIN, G.N., SOLDATOV, A.S., et al., Fizika ehlementamykh chastits i atomnogo yadra 12 6 (1981) 1364, 1431 [in Russian].

[11] APALIN, V.F., GRITSYUK, Yu.N., KUTIKOV, I.E., Nucl. Phys. 713 (1965) 553, 560.

[12] GINDLER, J.E., et al., J. inorg. nucl. Chem. 43 (1981) 1433, 1437.

[13] SIGG, R.A., KANTELO, M.V., Phys. Rev. C27 (1983) 245, 252.

[14] GINDLER, J.E., FLYNN, K.F., GLENDENIN, L.E., et al., Phys. Rev. C16 4 (1977) 1483.

[15] YAMAMOTO, H., MORI, Y., WAKUTA, Y., et al., Journal of Nucl. Sci. and Techn. 16 (1979) 779, 791.

[16] DE FRENNE, D., THIERENS, H., PROOT, B., et al., Phys. Rev. C26 4 (1982) 1356, 1368. - 36

[17] THIERENS, H., DE CLERQ, A., JACOBS, E., et al., Phys. Rev. C23 5 (1981) 2104, 2113.

[18] CALDWELL, J.T., DOWDY, E.J., BERMAN, B.L., et al., Phys. Rev. C21 4 (1980) 1215, 1221.

[19] GRASHIN, A.F., EFIMENKO, A.D., "Yields for photofission of uranium-236 and fission of uranium-233 by neutrons of various energies", Experimental Methods in Nuclear Physics, Moscow, Ehnergoatomizdat (1985) 31, 36 [in Russian].

[20] STEPANOV, N.V., Statistical Modelling of Fission of Excited Atomic Nuclei: Calculations and comparison with experiment, Preprint ITEhF [Institute of Theoretical and Experimental Physics] 88-55, Moscow (1988) 1, 19 [in Russian].

[21] GRASHIN, A.F., EFIMENKO, A.D., KOLOBASHKIN, V.M., Izv. AN SSSR, Ser. fizicheskaya 50 5 (1986) 944 [in Russian]. 37

Table 1

Deformation 1 2 3 4 5 6 Parameter type £ Z 31,5 34 39,7 46,5 50.1 57,5 N 65,8 72,9 78,3 81 85 86.5 a z . 3,3 -0,4 0,8 -4 2,57 -0,4 N -0,6 3,2 -L5 2,2 -0,1 0.6 d Z 2 0,7 1,8 1,6 0,5 1,5 N 3 2,7 2 3,2 0,5 1

Table 2

Thermal neutron fission

Target T Al AJ/ Al Ah V Th-229 1,88 90,55 139,64 89,64 138,33 2.00 U-233 1.9 94.39 139,61 93,08 138,27 2,60 , U-235 1,9 96,12 139,87 94,80 138,75 2,42 Pu-239 1,95 100,47 139,53 98,74 137,99 3,19 . Pu-241 1,94 101,80 140,20 100,13 138,90 2,92 Cm-245 / 1,975 105.25 140,74 103.41 138,97 3,52 Cf-249 , 1,99 108,15 141,82 106,30 139,69 3,84 38

Table 3

Reactor neutron fission

Target T Al AP Al Ah V Th-232 1,92 93,58 139,42 92,60 138,16 2,21 U-233 1,93 94,98 139,02 93,62 137,43 2,89 U235 1,925 96,56 139,44 95,18 138,12 2,66 U-238 1,93 99,15 139,84 97,80 138,74 2,43 Pu-239 1,97 100,76 139,23 99,04 137,48 3,37 Pu-240 1,97 101,53 139,47 99,82 137,78 3,31 Pu-241 1,97 102,21 139,79 100,54 138,19 3,19 Pu-242 1,95 102,68 140,32 101,01 139,00 2,94 Am-241 1,99 102,63 139,36 100,82 137,31 3,72

Table 4

Spontaneous fission

Target T Al AP Al Ah V Cm-244 1,92 102,99 141,00 101,13 139,51 3,26 Cf-252 1,95 108,91 143,06 107,09 141,45 3,37 Fm-254 1,96 109,85 144,07 108,06 141,87 3.89 Fm-256 1,98 111,99 143,81 110,80 141,39 3,61

Table 5

Effective level density parameter and temperature for spontaneous fission of certain nuclei

Uranium-234 Uranium-239 i Compound - Thorium-233 Uranium-236 Plutonium-240 nucleus Tsp(MeV) 1,795 1,78 1,79 1,81 1,875 a.* (MeV1) 16,07 14,74 15,38 15,99 21,89 39 - Table 6

Mass yields, most probable charges and charge distribution widths Fast neutron fission of 237 Np

A Yield Zcp Width A Yield Width

70 3.73318,-04 28.72 0.58 120 2.21846,-02 47.46 0.62 71 4.81135,-04 29.07 0.61 121 2.34833,-02 47.77 0.58 72 7.23909*-04 29.53 0.66 122 2.71109^-02 48.10 0.56 73 1.13264,-03 29.91 C. 63 123 3.30651,-02 48.50 0.58 74 2.05943c-03 30.27 0.60 124 3.71998,-02 48.76 0.52 75 3.55905,-03 30.62 0.57 125 4.24829,-02 49.02 0 SO 75 5.70085,-03 30.88 0.60 126 5.40720,-02 49.36 0.60 77 9.35700,-03 31.25 0.68 127 1.07169,-01 49.79 0.62 78 1.90271,-02 31.73 0.69 128 3.14892,-01 50. 15 0.60 79 3.72954,-02 32.09 0.66 129 7.98229,-01 50.47 0.65 80 8.89161,-02 32.39 0.61 130 1.95543,-00 SO. 70 0 64 81 1.77554,-01 32.77 0.58 131 3.69438**00 50.97 0.59 82 2.88713,-Cl 33.03 0.64 132 4.74820,-00 51.23 0.65 83 4.37915,-01 33.46 0 65 133 6.12046,-00 51.63 0.67 84 7.73142,-01 33.98 0.55 134 8.00996,-00 52. 11 0.59 85 1.06425,,00 34.32 0.58 135 8.28969,-00 52.55 0.63 86 1.43873,-00 34.72 0.59 136 6.74814,-00 52.97 0.60 67 1.53048,-00 35.07 0.60 137 6.76258,-00 53.44 0.68 88 1.65624,-00 35.55 0.68 138 7.05389,-00 53.97 0.62 85 2.61941,-00 35.99 0.58 139 6.29102,-00 54.40 0.65 90 3.69411,-00 36.31 0.57 140 5.91936,-00 54.78 0.63 91 4.38155,-00 36.73 0.57 141 5.12001^*00 55. 16 0.67 92 4.31310,-00 37. Gr 0.63 142 S. 04453,-00 55.64 0.68 S3 4 44043,-00 37.53 0.67 143 4.58182,-00 56.04 0.66 94 6.12875,-00 37.99 0.56 144 3.99900,-00 56.43 0.64 95 S. 99054,-00 38.37 0.61 145 2.98808,-00 56.78 0.64 96 6.0715Se-00 38.73 0.62 146 2.27914,-00 57.19 0.70 97 5.54801,-00 39.13 0.66 147 1.76730,-00 57.61 0.70 98 5.96327,-00 39.61 0.68 148 1.4424!—00 58.03 0.67 99 6.67356^-00 39.98 0.63 149 1.11216,-00 56.39 0.65 100 7.5700=^*00 40.32 0.60 ISO 8.32724,-01 58.70 0.62 101 6.98661,-00 40.64 0.59 151 6.10133,-01 59.06 0.65 102 5.67234,-00 40.95 0.63 152 4.39273^-01 59.45 0.66 103 5.08564,-00 41.42 0.64 153 2.87447^-01 59.62 0.65 104 4.69744,-00 41.81 0.55 154 1.78558,-01 60.18 0.63 105 3.20185,-00 42.13 0.59 155 9.48083,-02 60.S3 0.61 106 1.87359,-00 42.37 0.59 156 4.65658^-02 60.90 0.65 107 8.84318,-01 42.62 0.-61 157 2.23526,-02 61.34 0.66 108 3.02112,-01 42.85 0.70 158 1.10944e-02 61.76 0.6 S 109 9.89222,-02 43.30 0.74 159 5.53224,-03 62.19 0.65 110 5.12860,-02 43.88 0.68 160 2.89934^-03 62.54 0.62 111 3.83928,-02 44.35 0.64 161 1.57499^-03 62.94 0.64 112 3.10623,-02 44.67 0.60 162 9.62192,-04 63.40 0.66 113 2.54964,-02 45.03 0.62 163 5.95685^-04 63.90 0.64 114 2.51173^-02 45. SO 0.64 164 4.03443^04 64.21 0.84 US 2.36458,-02 45.83 0.59 165 2.69459e-04 " 64.57 0.61 116 2.41589,-02 46.16 0.58 166 1.78644,-04 64.81 0.61 117 2.38982,-02 46.52 0.58 167 1.20902^-04 65.30 0.66 116 2.17807 e-C2 46.76 0.56 168 8.25246,-05 65.70 0.66 119 2.03587,-02 47.05 0.59 169 5.76574 —05 66.11 0.67 40

Table 7

Element yields, most probable masses and isotope distribution widths Fast neutron fission of 237 Np

1 Width z Yield Acp Width Z Yield Acp

24 2.76555e-15 70.02 . 0. 16 47 7.07205e-02 118.49 1.90 25 1.03820e-11 70.09 0.31 48 8.13806C-02 122.05 1.87 26 2.76284e-08 70. 14 0.41 49 2.29791e-Cl 126.52 2.39 27 3.56308e-06 70.35 0.64 50 2.62939e+00 130.29 1.49 28 2.37268e-04 70.83 1.06 51 1.0580Ge+01 131.92 1.36 29 1.36787e-03 72. 16 1.65 52 1.5810.8e+01 134.00 1.37 30 6. 33615e-03 75.18 1.88 53 1.75653e+01 135.87 1.35 31 3.07949C-02 77.86 1.80 54 1.44355e+01 138.22 1.47 32 1.96510e-01 80.77 1.45 55 1.37405c+01 " 140.25 1.58 33 7. 51091e-01 82.55 1.40 56 1.05282e*01 142.74 1.55 34 2.18096e+00 85.02 1.36 57 7.40002e+00 144.71 1.65 35 3.73762e+00 87.04 1.49 58 3.73700e+00 147.43 1.65 .36 7. 40376e+00 89.85 1.43 59 2.180056+00 149.64 1.70 37 1.05288e+01 91.79 1.47 60 7.51067e-01 152.31 1.51 38 1.37452e+01 94.47 1.45 61 1.96478e-01 154.40 1.49 39 1.44319e+01 96.60 1.64 62 3.079136-02 157.10 1.44 40' 1.75643e+01 99.39 1.60 63 6.337336-03 159.55 1.56 41 1.58056e+01 101.37 1.62 64 1.54014e-03 162.50 1.57 42 1.05801e+01 104.02 1.41 65 5.96388e-04 165.00 1.66 43 2.62927e+00 105.76 1.30 66 1.711546-04 167.65 1.46 44 2.29782e-01 108.52 1.91 67 4.68126e~05 169.04 1.08 45 8.13420e-02 112.27 ■1:81 68 1.80614e-06 169.53 0.75 46 7.07280e-02 115.62 1:80 69 6.62687e-08 169.77 0.48 41

Table 8

Mass yields, most probable charges and charge distribution widths Thermal neutron fission of 2* 5Cm

* 1 Yield Z=P Width A Yield Zcp Width

70 2. 4S4CZe-C4 28.69 0.58 120 6.12540,-02 47.45 0.67 71 3. 125346-04 29.05 0.60 121 5.75932e —02 47.81 0.57 72 4.70622e-04 29.53 0.64 122 5.98380e-02 48. 15 0.55 73 7. 16944e-04 29.89 0.59 123 6.70189^02 48.60 0.57 74 1.23124C-03 30.20 0.57 124 6.74232,-02 48.92 0.58 75 1.98432e-03 30.58 0.58 125 7.67599,-02 49.30 0.61 76 2.929S4e-03 30.85 0.61 126 1.37351,-01 49.79 0.55 77 4.43667,-03 31.22 0.66 127 2.65176^-01 50.07 0.54 78 8.65230,-03 31.72 0.65 128 5.72664,-01 50.34 0.62 79 1.55176,-02 32.05 0.62 129 1.23114,*00 50.69 0.63 BO 3.22178,-02 32.34 0.60 130 2.03428,*00 50.93 0.66 61 5.68184,-02 32.74 0.59 131 2.74224**00 51. 17 0.64 82 8.47775,-02 33.05 0.66 132 3.40679**00 51.56 0.66 83 1.21656,-01 33.50 0.65 133 4.50031**00 51.93 0.64 84 2.20545,-01 33.98 0.51 134 6.92581**00 52.23 0.57 85 2.76149,-01 34.30 0.57 135 6.83499**00 52.74 0.62 86 3.50463^01 34.70 0.61 136 5.57108**00 53.15 0.69 87 3.67924,-01 35.08 0.62 137 6.51921**00 53.64 0.68 88 4.10772,-01 35.59 0.68 138 8.34705**00 54.05 0.56 89 6.34518e-01 36.00 0.57 139 7.12077**00 54.46 0.64 90 8.44266,-01 36.30 0.58 140 6.27127**00 54.82 0.68 91 9.80025,-01 36.75 0.62 141 5.43297c* 00 55.26 0.71 92 1.03915,*00 37.13 0.70 142 5.93095, *00 55.76 0.63 93 1.22853^00 37.63 0.70 143 4.96063**00 56.09 0.62 94 1.95621^00 38.04 0.57 144 4.07885**00 56.44 0.64 95 2.25626**00 36.39 0.63 145 2.96444**00 56.82 0.69 96 2.72700**00 38.75 0.65 146 2.44748**00 57.31 0.73 97 2.98715**00 39.16 0.69 147 2.00524**00 57.71 0.67 98 3.78480**00 39.65 0.67 148 1.71035, *00 58.06 0.63 99 4.68286**00 39.99 0.61 149 1.31968^*00 58.39 0.65 100 5.68352**00 40.31 0.61 ISO 1.01073^*00 58.75 0.70 101 5.73338**00 40.65 0.62 151 8.25961^01 59.21 0.73 102 5.36010^*00 41.00 0.69 152 7.31788^-01 59.63 0.67 103 5.72676**00 41.50 0.68 153 6. 182S2e-01 69.98 0.63 104 6.80683^00 41.89 0.58 154 5.10146*-01 60.30 0.63 105 6.41686e*00 42.22 0.61 155 3.89442*-01 60.64 0.67 106 6. 18741«*O0 42.50 0.61 156 3.10338^-01 61.07 0.72 107 5.38647**00 42.63 0.62 157 2.60662^-01 61.51 0.68 108 5.04294**00 43.28 0.68 . 158 2.20679e-01 61.86 0.60 109 S.00854e*00 43.69 0.60 159 1.69224^01 62.17 0.60 110 4.85029**00 43.96 0.53 160 1.16568e-01 62.45 0.62 ill 4.06384^*00 44.33 0.59 161 7.31037*-02 62.82 0.67 112 3.05355^*00 44.57 0.59 162 4.89609^-02 63.31 r. to 113 2.08439**00 44.88 0.61 163 2.96314,-02 63.69 0.61 114 1.57389**00 45.33 0.68 164 1.75489^02 64.05 0.S8 115 9.09378,-01 45. SB 0.64 165 8.86047,-03 64.39 0 62 116 4.82021*-Ol 45.81 0.58 166 4.5O444e-03 64.76 0.68 117 1.87529^-01 46.09 0.65 187 2.S4421e-03 65.27 0.70 •16 1.02991*-01 46.44 0.64 188 1.56683^-03 65.70 0.63 lie 6.S8733*-02 46.88 0.67 169 9.46336,-04 66.07 0.62 42

Table 9

Element yields, most probable masses and isotope distribution widths Thermal neutron fission of 245 Cm

z Yield Acp Width Z Yield Acp Width i

24 2.28236e-15 70.02 0. 16 47 2.40793e-01 117.58 2.1 25 7. 35732e-12 70. 10 0.32 48 1.75711e-01 121.54 1.6E 26 2.00814e-08 70. 14 0.41 49 2.407o6e-01 125.16 2. 14 27 2.32703e-06 70.35 0.64 50 2.15087e+00 129.25 1.73 28 1.68058e-04 70.79 1.03 51 6.47644c+00 131.20 1.53 29 8.34286e-04 72.06 1.59 52 1.3941Se+01 133.63 1.50 30 3.86365e-03 74.98 1.82 53 1.38434e+01 135.63 1.46 31 1.29591e-02 77.61 1.77 54 1.825260-^01 138.05 1.48 32 7.33974e-02 80.53 1.47 55 1.34723C+01 140.03 1.58 33 2.00383e-01 82.44 1.42 56 1.34G50C+01 142.53 1.56 34 6.15115e-01 84.92 1.38 57 6. 92876e +00 144.61 1.66 35 8.46757e-01 87.00 1.49 58 5.13096e+00 147.34 1.70 .36 1.832126+00 89.80 1.48 59 2.38000e+00 149.71 1.79 37 2.38154e+00 91.94 1.57 60 1.83094e+00 152.60 1.72 38 5.13268e+00 94.76 1.57 61 8.45921e-01 154.98* 1.76 39 6.930276+00 96.91 1.69 62 6.14786C-01 157.76 1.65 40 ' 1.34665e+01 99.63 1.64 63 2.00290C-01 159.96 1.61 41 1.34712e+01 101.71 1.71 64 7.33740e-02 162.58 1.48 '42 1.82517e+01 104.60 1.65 65 1.29461e-02 164.87 1.53 43 1.38401e+01 106.86 1.71 66 3.72288e-03 167.51 1.41 44 1.394026+01 109.81 1.63 67 5.57575e-04 169.04 1.05 45 6.47606e+00 112.08 1.59 68 2.852946-05 169.54 0.73 46 2.15089e+00 114.60 1.48 69 5.213136-07 169.77 0.47 43

Table 10

Mass yields, most probable charges and charge distribution widths

Thermal neutron fission of 249Cf

Yield A Zcp Width A Z cp Width Yield 1

70 1.49332e-04 28.87 0.61 120 5.10269c-01 47.53 0.66 71 l:95520e-O4 29.28 0.65 121 2.47520C-01 47.81 0.64 72 3.28793c-04 29.75 0.60 122 1.63141C-01 48.25 0.62 73 4.B8882*-04 30.09 0.59 123 1.23372e-01 48.67 0.59 7« 8.160S2C-04 30.41 0.59 124 1.05S95C-01 49.07 0.65 75 1.2

Table 11

Element yields, most probable masses and isotope distribution widths Thermal neutron fission of2 vf

z Yield A Width Z Yield Width cp ACP !

24 2.82777e-16 70.02 0. 15 47 3.58291e+00 117.07 1.59 25 1.19084e-12 70.08 0.30 48 1.033G7e+00 119.87 1.66 26 4.22208e-09 70. 12 0.37 49 3.14124e-01 123.45 1.87 27 6. 58789e-07 70.30 0.59 50 1.03300e+00 127.75 1.83 28. 6. 35794e-05 70.66 0.93 51 3.58262e+00 130.13 1.60 29 3.98946e-04 71.71 1.47 52 9.9533Ge+00 132.66 1.55 30 1.89055e-03 74.35 1.80 53 1.17908e+01 134.79 1.49 31 6. 07848e-03 76.99 1.81 54 1.64937e+01 137.21 1.52 32 3.29475e-02 79.97 1.54 55 1.37852e+01 139.30 1.63 33 9.40086e-02 81.95 1.46 56 1.62456e+01 141.80 1.61 34 3.00664e-01 84.48 1.37 57 9.90134e+00 143.84 1.67 35 4.44590e-01 86.52 1.48 58 7.57676e+00 146.46 1.67 36 9.74055e-01 89.29 1.48 59 3.54650e+00 148.80 1.80 37 1.3099Ge+00 91.45 1.55 60 2.6869Se+00 151.69 1.76 38 2.68888e+00 94.21 1.54 61 1.30845e+00 154.10 1.78 39 3.54834e+00 96.39 1.69 62 9.73032e-01 156.92 1.72 40 7. 57846e+00 99. 19 1.70 63 4.44071e-01 159.31 1.76 41 9.90218e+00 101.31 1.76 64 3.00430e-01 162.04 1.65 42 1.62491e+01 104.07 1.64 65 9.39367e-02 164.26 1.61 43 1.37881e+01 106.32 1.73 66 3.26247e-02 166.82 1.45 44 1.64961e+01 109.35 1.71 67 4.91417e-03 168.63 1.17 45 1.17902e+01 111.80 1.74 68 3.15380e-04 169.52 0.78 46 9.96347e+00 114.78 1.63 69 6. 30581e-06 169.67 0.58 L 45

Table 12

Mass yields, most probable charges and charge distribution widths Spontaneous fission of 252Cf

Yield | Width A Z=P Width Z Yield Zcp

70 3.20313*-05 28.60 0.57 120 6.9664)e-01 47.00 0.70 71 4.16638c-OS 28.94 0.57 121 4.32331e-01 47.37 0.68 72 6. 0:3S4e-05 29.38 0.65 122 2.63145**01 47.72 0.58 73 9.51922C-05 29.77 0.61 123 9.18453e-02 47.96 0.64 74 1.84198c-04 30.10 0.55 124 4.82501**02 48.40 0.63 75 3.081OSC-O4 30.48 0.59 125 3.<2621**02 48.88 0.59 76 5.14436C-04 30.76 0.60 126 3.38246**02 49.37 0.66 77 8.27465c -04 31.09 0.63 127 5.08113**02 49.87 0.64 78 1.54017e-O3 31.57 0.70 128 1.4ES94e-01 SO. 23 0.61 79 2.84174C-03 31.95 C. 66 129 3.40572**01 50.62 0.68 80 7.72431C-03 32.23 0.58 130 6.87932**01 50.92 0.75 81 1.35364C-02 32.64 0.61 <31 1.20902**00 51.21 0.67 82 2.51137c-02 32.92 0.66 132 1.71852**00 51.69 0.69 83 3.85535c-02 33.34 0.63 133 2.35490**00 51.93 0.65 84 6,3723:c-02 33.89 0.56 134 3.94113**00 52.23 0.58 85 9.86831C-02 34.19 0.54 135 4.42028**00 52.63 0.66 86 1.24294C-01 34.55 0.62 136 5.42315**00 53.04 0.67 87 1.47122e-01 34.97 0.59 137 5.20568**00 53.45 0.68 88 1.52349e-01 35.42 0.69 138 6.53496**00 53.93 0.58 89 2.C8789C-01 35.88 0.63 139 6.45204**00 54.26 0.61 90 3.60179c -01 36.18 0.54 140 6.85701**00 54.64 0.65 91 3.99761C-01 36.61 0.62 141 6.40755**00 55.02 0.68 92 4.56630C-01 36.97 0.66 142 6.89823**00 55.52 0.69 93 5.10S28C-01 37.45 0.70 143 7.22665**00 55.83 0.61 94 7. 85189c-01 37.93 0.59 144 6.97142**00 56.23 0.60 95 9.610S1C-01 38.25 0.61 145 5.52041**00 56.57 0.64 96 1.22586c* 00 38.62 0.65 146 4.23508**00 56.96 0.72 97 1.36641**00 39.03 0.69 147 3.51545**00 57.44 0.70 98 1.65663**00 39.54 0.73 148 3.02095**00 57.83 0.62 99 2.30069**00 39.94 0.64 149 2.29934**00 58.18 0.63 100 3.15937**00 <0.25 0.61 ISO 1.70091**00 58.47 0.64 101 3.74289**00 40.59 0.62 151 1.22149**00 58.86 0.69 102 4.04125**00 40.90 0.67 152 1.06106**00 59.37 0.71 103 4.50584**00 41.33 0.70 153 8.79356*-01 59.74 0.64 104 6.27917**00 41.78 ' 0.60 154 7.71807e-Ol 60.08 0.60 105 6.68205e*00 42.09 0.59 155 6.06326**01 60.40 0.63 106 7.13046**00 42.38 0.59 "156 4.54800**01 60.72 0;67 107 6.29928**00 42.70 0.60 157 3.65063e-01 , 61.20 0.71 108 5.32280**00 43.06 0.68 159 3.26197**01 61.64 0.65 109 5.39879e*00 43.57 0.64 159 2-63275**01 61.96 0.61 110 5.84138**00 43.91 0.54 160 2.13226*-01 62.29 0.61 111 5.05539**00 44.21 0.59 161 1.55498*-01 62.64 0.64 112 4.72955**00 44.46 0.59 162 1.18640**01 63.07 0.71 113 4.04680**00 44.74 0.59 163 8.92830**02 63.53 0.65 114 3.55S11**00 45.11 0.69 164 . 8.24236e-02 63.86 6.57 115 3.29524**00 45. SI 0.64 165 6. 1815Se-02 64.18 0.58 116 3.18457**00 45.83 0.54 166 4.06474**32 64.46 0.60 117 2.36765**00 46.12 0.59 167 2.37278e-02 64.82 0.65 118 1.75527**00 46.35 0.59 168 1.53067.-02 65.34 0.68 119 1.11556* *00 46.66 0.60 169 e.47048*-03 65.71 0.59 46

Table 13

Element yields, most probable masses and isotope distribution widths Spontaneous fission of 252 Cf

z A Width Z Yield cp Yield a=p Width !

24 6.24575e-16 70.03 0. 17 47 2.73382o00 118.39 1.60 25 1.68312e-12 70.11 0.33 48 7. 39528e-01 121.00 1.52 26 4.15614e-09 70. 16 0.43 49 1.18217e-01 124.88 2.30 27 4.22653e-07 70. 39 0.68 50 7.39512o01 129.72 1.56 28 2.81603e-05 70.93 1. 12 51 2.73371o00 131.72 1.47 29 1.35109e-04 72.41 1.70 52 3.69G20C+00 134.02 .1.55 30 7.30984e-C4 75.54 1.83 53 1.09712c+01 136.08 1.53 31 3.04859e-03 78. 17 1.74 54 1.6912£c+01 138.53 1.62 32 2.16617e-02 81.04 1.40 55 1.48745001 140.76 1.64 33 6.76174e-02 82.84 1.38 56 1.85908e+01 143.29 1.57 34 2.30453e-01 85.31 1.38 57 1.04325e+01 145.30 1.62 35 3.32435e-01 87.37 1.49 58 7.761 lOoOO 147.99 1.62 36 7.85315e-01 90.20 1.47 59 3.249340-00 150.35 1.73 37 1.06512O00 92.31 1.57 60 2.3803SO-00 153.33 1.67 38 2.38145e+00 95. 12 1.57 61 1.064G6O00 155.71 ' 1.71 39 3.24984e+00 97.33 1.71 62 7.84952c-01 158.58 1.63 40 7.76046e+00 100.22 1.71 63 3.32188e-01 160.95 1.68 41 1.04899O01 102.30 1.76 64 2.30362e-01 163.73 1.58 42 1.85907e+01 105.10 1.62 65 6.74961e-02 165.90 1.51 43 1.48744e+01 107.28 1.72 66 2.02208e-02 168.26 1.21 44 1.69135e+01 110.46 1.75 67 1.36842e-03 169.43 0.84 45 1.09714e+01 113.00 1.80 68 1.79046e-05 169.66 0.62 46 8.69651e*00 116.06 1.65 69 1.56561e-07 169.84. 0.39 - 47 - Table 14

Mass yields, most probable charges and charge distribution widths Photofission of 239Pu (Eco = 28 MeV)

1 A Yield 2=P Width A Yield Zcp Width

70 2.55154.-03 28.95 0.63 120 3.23915.-01 47.97 0.56 71 3.2710S.-03 29.38 0.66 121 3.54034.-01 48.30 0.59 72 5.23249.-03 29.83 0.59 122 3.78399.-01 48.60 0.59 73 7.30927.-03 30. 16 0.60 123 3.92S96e-01 48.93 0.61 74 1.09522e-02 30.48 0.59 124 4.62971.-01 49.38 0.66 75 1.50S26e-02 30.81 0.59 125 6.76044.-01 49.80 0.58 76 2.03217.-02 31.17 0.67 126 1.02772e*00 50. 11 0.55 77 3.23064e-02 31.64 0.66 127 1.6230Se*00 50.44 0.58 76 6.23119c-02 32.01 0.58 128 2.50801c*00 50.72 0.58 79 9.880S2e-02 32.36 0.62 129 3.41582e*00 50.99 0.61 80 1.57370c -01 32.66 0.62 130 4.40388e*00 51.38 0.67 61 2.21408c-01 33.00 0.62 131 5.53915. *00 51.73 0.62 62 2.98633e-01 33.43 0.69 132 6.64138e*00 52.05 0.59 83 4.S0724C-01 33.es 0.62 133 7.21627e*00 52.44 0.64 64 6.20563e-01 34.19 0.52 134 7. 15750e*00 52.80 0.66 85 8.93247e-01 34.65 0.60 135 6.71106e*00 53.28 0.68 86 9.79656c -01 35.02 0.64 136 7. 09386c *00 53.81 0.62 87 1.06409e-00 35.50 0.68 137 6.21412e*00 54.17 0.63 88 1.61443c-* 00 35.95 0.57 138 5.59444e+00 54.60 0.67 89 1.94688c-*00 36.26 0.59 139 4.49679e*00 55.04 0.71 90 2.41438e*O0 36.64 0.62 140 4. 16784c -00 55.54 0.71 91 2.56977e-*00 37.02 0.64 141 3.984C8e *00 55.91 0.65 92 2.74SB6e*00 37.50 0.69 142 3.61150c *00 56.27 0.66 93 3.83187e*00 37.93 0.59 143 2.97600**00 56.64 0.69 94 4.3857 9c-* 00 38.25 0.60 144 2.39295c *00 57.06 0.74 95 4.59076c *00 38.68 0.64 145 2.05899e*00 57.52 0.72 96 4.35174e*00 39.07 0.70 146 1.739Sle*00 57.90 0.67 97 4 7C969c*00 39.56 0.70 147 1.39874.-00 58.25 0.67 98 5.83690e*00 39.96 0.61 148 1.07964e*00 58.59 0.70 99 6. 10135c-00 40.29 0.63 149 8.4962SC-01 59.01 0.74 100 6.3021 Sc-* 00 40.61 0:64 ISO 7. 13244C-01 59.44 0.71 101 5.92325c-*00 40.98 0.67 151 5.90549.-01 59.80 0.65 102 6. 20049c-00 41.45 0.68 152 4.71207e-01 60.11 0.63 103 6. 32659c *00 41.81 0.60 153 3.38191.-01 60.42 0.65 104 6. 12785c *00 42.13 0.57 154 2.28405.-01 60.79 0.70 105 S.2S572e*00 42.47 0.59 155 1.54633.-01 61.23 0.71 106 3.84939e*00 42.74 0.61 156 1.04241.-01 61.64 0.66 107 2.79378e*00 43.12 0.66 157 6.67260.-02 62.00 0.63 108 2.27721**00 43.58 0.63 158 4.00489.-02 62.33 0.64 109 1.30296c*00 43.84 0.61 159 2.33493c-02 62.72 0.68 110 8.13l76e-01 44.20 0.62 160 1.49255^-02 63.19 0.73 111 S.2S490C-01 44.59 0.64 161 '9.98508^-03 63.61 0.68 112 4.02680*-01 45.00 0.69 162 6.93776.-03 83.99 0.65 113 3.81340C-01 45.48 0.67 163 4.68945^03 64.35 0.66 114 3.719S4e-01 45.84 0.59 164 3.14345.-03 64.73 0.70 115 3.3S808e-01 46.18 0.61 165 2.26606.-03 65.18 0.72 116 3.05686*-01 46.50 0.61 166 1.70727.-03 65.58 0.68 117 267451.-01 46.84 0.63 167 1.28398^03 65.84 0.64 118 2.61546.-01 47.27 0.68 168 9.25731.-04 66.27 0.65 119 2.91104C-01 47.67 0.61 169 6.39982e-04 66.63 0.70 48

Table 15

Element yields, most probable masses and isotope distribution widths Photofission of 239Pu (E^ = 28 MeV)

2 Yield Acp Width 2 Yield Acp Width

24 3.2236Ge-15 70.02 0. 15 47 7. 41497e-01 117.13 1.86 25 1.58392e-ll 70.07 0.28 48 1.03S55e+00 120.43 1.83 26 5.51955e-08 70. 11 0.36 49 1.19538e+00 123.42 1.96 27 9.30934e-06 70.27 0.55 50 4.21002e+00 127.31 1.85 28 8.89674e-04 70.58 0.86 51 9. 63882e+00 129.55 1.67 29 5.64321e-03 71.48 1.37 52 1.72689e+01 132.07 1.52 30 2.30532e-02 73.89 1.76 53 1.47948e+01 134.17 1.46 31 5.83317e-02 76.48 1.81 54 1.5560Se+01 136.52 1.46 32 2.43008e-01 79.47 1.59 55 1.02635e+01 138.59 1.61 33 5.81889e-01 81.54 1.52 56 1.01604e+01 141.09 1.66 34 1.62954e+00 84. 14 1.37 57 5.95049e+00 143.19 1.74 35 2.25242e+00 85.17 1.51 58 4.66963e+00 145.80 1.74 36 4.67586e+00 88.93 1.49 59 2.24833o+00 148.11 1.84 37 5.95925e+00 91.05 1.54 60 1.62780e+00 150.85 1.75 38 1.01693e+01 93.72 1.50 61 5.81303e-01 153.11' 1.73 39 1.02702e+01 95.88 1.65 62 2.42812e-01 155.77 1.63 40 1.55618e+01 98.61 1.66 63 5. 82556e-02 158.17 1.69 41 1.47874e+01 100.74 1.72 64 2.31264e-02 160.98 1.69 -42 1.72631e+01 103.48 1.61 65 7. 44883e-03 163.48 1.77 43 9.63655e+00 105.63 1.59 66 3.98622e-03 166.22 1.71 44 4.20937e+00 108.31 1.53 67 1.12958e-03 168.19 1.44 45 1.19485e+00 111.18 1.81 68 2.19079e-04 169.28 0.97 46 1.03825e+00 114.38 1.73 69 9.59334e-06 169.57 0.68 Yield, % Mean number of neutrons Fig. thermal our experimental our experimental neutron Fig.

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XA9744986 51

96-11496 (N) Translated from Russian

UDC 539.173

LONG-LIVED FISSION PRODUCT YIELDS AND THE NUCLEAR TRANSMUTATION PROBLEM

E.S. Bogomolova, A.F. Grashin, A.D. Efimenko and I.B. Lukasevich Moscow Engineering Physics Institute

ABSTRACT

Using the ASIND-MEPhI fission product yield database it is shown that cumulative and particularly independent yields of long-lived fission products are strongly dependent on the fissile nucleus and the neutron energy. This explains why an increase in the neutron flux during irradiation of 237Np leads to an increase in the amount of long-lived strontium-90 and caesium-137. Estimations of this kind are best carried out using the updated version of the ASIND-MEPhI database.

Fission in a reactor produces a large number of radioactive fission products, some of which are long-lived. The most important of these are 79Se, "Sr, 93Zr, 93Nb m, "Tc,

107Pd, 126 Sn, 129I, 135 Cs, 137Cs and 151 Sm. Together with the 90Y, 126 Sb, 126 Sb m and 137Bam which form as a result of their decay, these nuclides are the major contributors over a period of one hundred to hundreds of thousands of years to the total fission product activity. Apart from fission, radiative capture on heavy nuclei occurs continuously in a reactor, accompanied by p -decay of the heavier isotopes which leads to the formation of nuclides with an ever increasing atomic number. Every ton of spent fuel can contain fission products in kilogram quantities (236 U, 239Pu, 240Pu, ...), gram quantities or fractions of a gram, and the list of actinides in spent fuel runs to 30 (up to 252 Cf). 52

The continually increasing volume of highly radioactive waste from the nuclear

power sector, and the unpredictability from the point of view of ecological safety of the

consequences of conventional storage and disposal in deep geological formations in

thousands of years’ time, means that alternatives have to be developed one of which is

nuclear transmutation. Existing evaluations [1] indicate that nuclear transmutation can be

effective, for example, in burning 129I or 98Tc. However, the main aim is transmutation of

the transuranic elements. Thus, there is a pressing need to create reliable libraries of the

relevant nuclear constants and, in particular, for a library of fission product yields of the

transuranic nuclei, including spontaneous fission and fission induced by neutrons at various

energies.

In addition to isotopes of uranium and plutonium, spent fuel contains an appreciable

quantity of 237Np, 241Am, 243Am, 244Cm, 245 Cm and 242Am™ in particular, as well as other

Cm isotopes and some isotopes of Th, Pa and Cf. Before selecting a specific transmutation

scheme for these actinides (specifically the energy and flux of the fissioning neutrons), a

preliminary quantitative evaluation of the composition of the fission products formed must

be carried out. Changes in the cumulative yields of long-lived fission products which occur through transition from one fissioning nucleus to another and from one mean neutron energy (for example, thermal) to another mean energy value should not be underestimated.

We will see that, by varying the flux, we can change the percentage composition of fissile nuclei. 53

Cumulative long-lived fission product yields

At least 200 years after short-lived fission products have decayed, a substantial part of the total activity comes from ^Sr and 137Cs. This is due to their half-life (~ 30 years) and the quantities in which they form as a result of fission and subsequent (3 -decays, i.e. the cumulative yield. For a number of fissile nuclei, the quantity of various specific fission products produced (cumulative yields) can vary considerably (Table 1). Figures 1 and 2 show how the cumulative yields of ^Sr and 137Cs vary for different fissile nuclei subjected to fast neutron fission. The 137Cs yield fluctuates by a factor of approximately

1.5, from 6 to 8.5%. The maximum fluctuation occurs for fission of 239Np (8.64%). The

^Sr yield changes even more sharply - from 1 to - 6%. Fission of 245 Cm, for example, produces yields six times lower than fission of 235 U.

Thus, we can see that between 10 and 200 years the total activity of the heavy actinide fission products is considerably less than for the light actinides (by a factor of 2).

Of the other long-lived fission products, the cumulative yield of 107Pd varies the most sharply (by a factor of more than 60 over a range of eight mass units). Figure 3 shows that the cumulative yield of l07Pd is much more dependent on the mass of the fissile nucleus than its charge. Thus, for example, in fission of heavy isotopes of Pu, six times more 107Pd is formed than in fission of light isotopes. The cumulative yield of "Tc, by contrast, diminishes during the transition to heavy isotopes, although the scale of the changes is much smaller than for 107Pd. The cumulative yields of 129I behave similarly, 54 - although they are much more dependent on the charge of the fissile nucleus than is the case with other long-lived fission products.

Independent yields of long-lived fission products

Independent fission product yields fluctuate over a broader range than cumulative yields. Independent yields for several long-lived fission products are given in Table 2. It should be noted that they can change much more sharply than the cumulative yields relative to the fissioning neutron energy. Thus, for example, the independent yield of 151 Sm in fast neutron fission of 232Th is almost 1000 times less than for fission by 14 MeV neutrons.

The cumulative yield of 15 ^m is roughly the same in both cases.

237Np transmutation

The importance of the above trends in the behaviour of cumulative yields when predicting the consequences of nuclear transmutation can be demonstrated by taking as an example the transmutation of 237Np. When 237Np is irradiated with neutrons, we obtain a branched chain of radioactive transformations which includes fission, radiative capture, p -decays and a-decays. The branching coefficients (relative transition probabilities) are determined by the decay constants and the product of the corresponding sections (af or ) and the neutron flux. If 237Np is irradiated with a high neutron flux

(this is under consideration), the main decay channel will be: 237Np(n,y) => 238Np(n,f). At a flux of 1016 cm"2 ■ s'1, for every 100 fission events 84.5 will occur on 239Np (compound),

11 on 240Pu (239Pu(n,f)), 3 on 242Pu and approximately 0.5 each on 246 Cm, 245 Am and 239Pu.

Thus, when 237Np is irradiated with a neutron flux of 1016 cm"2 • s'1, approximately 85% of the fission products, including the long-lived products, are formed as a result of 239Np - 55' fission. If 237Np is irradiated with a neutron flux of 1013 cm'2 ■ s'1, then the main decay channel will be 237Np(n,y) => 238Np((3) => 238Pu(n,y) => 239Pu(n,f) and for every 100 fission events 71 will occur on 240Pu(239Pu(n,f)), 17 on 242Pu, about 5 on 246 Cm, around 3 on

^Pu, approximately 0.5 each on 245 Cm and 248Cm, and even 0.2 on 250 Cf. In addition, the

241Pu( p) => 241 Am channel becomes detectable as a result of the contribution to fission from Am isotopes. However, 239Np, the actinide on which the majority of fissions occur under high neutron flux irradiation, is responsible for only 0.05% of the events in this instance.

Qualitative analysis of the curves in Figs 1 and 2 leads us to the conclusion that there is an increased yield of the long-lived isotopes 137Cs and "Sr in neptunium fission compared to plutonium fission. More rigorous calculations carried out using the data from the ASIND-MEPhI library [3] show that, in the case of high neutron flux irradiation of

237Np, the quantity of long-lived 137Cs and ^Sr radionuclides increases by a factor of 1.3 and 1.5 respectively compared to irradiation with a neutron flux of 1013-1014 cm"2 • s'1 .

Thus, when taking a decision about the transmutation of 237Np, we assume we will have to take account of the fact that increasing the neutron flux (with all its concomitant advantages), will raise by a factor of almost 1.5 the total activity of the long-lived fission products formed as a result of transmutation over a period ranging from several years to several hundreds of years following irradiation.

Similarly, it can be shown that, when 244Cm is irradiated with a neutron flux

O = 1016 cm"2 • s'1, two times less **Sr is formed than for a flux of O = 1013 cm"2 • s’1 , and the quantity of all remaining long-lived fission products formed is practically identical - 56

for the same change in flux. In this case, unlike 237Np, increasing the neutron flux leads to a reduction in fission product activity.

In our view, these evaluations demonstrate unequivocally the need to carry out similar calculations when preparing any specific project on the transmutation of long-lived actinides. Our ASIND-MEPhI data bank can supply all the information required for such yield calculations (for any fissile nucleus and any neutron energy). There are no other data files on yields which contain such comprehensive information. Even the most comprehensive and authoritative - the ENDF/B-6 file - does not contain any data on

238Np(nd],f) and 247Cm(nth,f)

REFERENCES

[1] EGOROV, N.N., et al., Atomnaya ehnergiya 72 2 (1992) 151 [in Russian],

[2] EFIMENKO, A.D., GRASHIN, A.F., KUDRYAVTSEVA, E.A., “The ASIND-MEPhI fission product yield database ”, Proc. Nuclear Data for Science and Technology (Mito, 1988), JAERI (1988) 971, 974.

[3] GRASHIN, A.F., EFIMENKO, A.D., “A fission product yield data library ”, IAEA-NDS-133 (November 1993). - 57 - Table 1.

Cumulative yields of some long-lived fission products from the ASIND-MEPhI file [2]

Reaction "^S* “sr =:c I07 Pd I37 c ,S1S-

232Th(nf.f) 9.13—02 7.13 —00 3.80-00 5.32—02 7.57 —00 1.85—01

232Th(nUMeV-n 3.08—01 5. 29c-00 4. 13—00 1.04c-00 5.27**00 1.90—01

232U(nf.f) 1.64 —01 6.34e*O0 4.96e-00 5. 83c-02 8.13**00 1.21—01

9.41—02 7.12 —00 5.32 c-00 1.71 —02 6.63**00 1.84—01

233U(r.f.r) 1.35c-01 6 . 22c-00 5.85—00 5.62 —02 7.32e*00 2. 11—01

233u;n14HeV.n 2.90-01 4.29—00 4.90—00 1.06c *00 5.60**00 1.83—01

23

23Su(nlh.n 3.89—02 5.90e-00 6.34C-O0 1.12e-01 6.27**00 4.51—01

235 U(nr.f) 5.90-02 5.69c-00 6.67 —00 1.02—01 6.61**00 4.47 —01

235u(n14MeV.n 2.04C-01 4 10-00 5.80—00 1.lle*00 5.59**00 3.26 —01

23Gu.nf.n 4.<0e-02 4.80-00 6.58—00 2.91—01 7.35 —00 6.17 —01

237u(nth.n 1.58e-Q2 3.82c-00 S. 35e-O0 4.8SC-01 7.51**00 7.69 —01

237U(nf.f) 2.92e-02 3.E2e-00 5.62 —00 7.77e-01 7.49**00 7.36 —01

23eNp(nf.f) S. 45c-02 4.26e-00 7.03 —00 4 06 —01 6 .66**00 5.07 —01

237Hp(nf.f) 4.57e-02 3.60-00 6.73 —00 8.57—01 6.80**00 6.34 —01

238Np(nth.f) 1.39e-02 3.26c-O0 6.09e-00 1.23—00 8.95**00 7.00 —01

238Wp(nflf) 2.47e-02 3 12e-00 6 .lle-OO 1.70 —00 7.83**00 6.87 —01

239Np(nf.f) 2.00-02 2.35e-00 5.77c+00 2.71**00 8.63**00 7.62 —01

^PuCn^.f) 8.33e-02 3.50-00 6.91—00 7.67 —01 6.89**00 4.85—01

23GPu(nf.f) 1.00-01 3.32e-00 6 .86 —00 1.01—00 6 . 45—00 4.76 —01

239pu("th-r» 4.20-02 2.23c-00 6.07e*00 2.81—00 6.83—00 6.64 —01

^Putiyf) 5.53C-02 2.24C-O0 6 . IS—00 2.88—00 7.10 —00 6 .66 —01

Pu,n14H»Vfl 1.20-01 1.90-00 5.13—00 3.65 —00 5.08—00 5.77 —01 2<0Pu(nf.f) 4.20-02 1.92c-00 5.84—00 3.80**00 6.76 —00 6.91—01

241Pu(nth.r) 1.80-02 1.74 —00 5.90—00 4.37**00 8. 12—00 7.47 —01

241Pu(nf.f) 3.12e-02 1.60-00 5.53—00 4.82—00 7.04**00 7.38—01

242Pu(nf.f) 1.72C-02 1.37 —00 5.46 —00 5.47 —00 8.20—00 8:47—01

243Pu(nthif) 1.00-02 9.72—01 4.91—00 5.99—00 7.97 —00 9.06—01

243Pu(nf.f) 1.70-02 1.05—00 4.49—00 6 .20—00 7.79 —00 8.94—01

2<1A»(Rf,r) 4.37c-02 1.51—00 5.49—00 4.46 —00 7.36 —00 6.83—01 242 2.54—02 1.20-00 5.49—00 4.94**00 7.20 —00 7.32 —01

2<2Aa(nf.f] 3.30-02 1.27 —00 5.17 —00 5.13—00 7.18—00 7.29—01

243Ae(nf.f) 2.64C-02 1.14—00 4.90—00 5.71 —00 6.61 —00 7.80—01

2<5 c-(nth.n l.SSc-02 6.43 —01 4.68c«00 5.39—00 6.50 —00 8.28—01

249cr(nth.n 1.0Se-02 4.78 —01 2.97—00 5.04—00 6.84—00 1.06 —00

^crisf) 3.50-03 3.57 —01 2.35—00 6 .21—00 5.19—00 1.26 —00 - 58 Table 2

Independent yields of some fission products from the ASIND-MEPhI file [2]

79s. "sr "t = ,07 Pd Reaction ,37Cb 151 s-

232Thlnf.n t.S4e-04 1.63e-02 S. B0e- C8 4.00-10 2.246-02 2.406-09

234trb,ni4K.-v,r) 9. 53c-04 3.90e-02 2.04e-06 6 .006-00 1.346-01 l.GOe-OG

4.07e-03 3.50-01 1.17e-04 5.8G«-06 1.37etOO 7.84e-05

1.9 If 03 2.30-01 2 786-05 3.lSe-07 5.80c-01 4.926-06

^UCry.f) 2.60e-03 2.20-01 4.87e-05 1.27e-06 7.33e-01 1.536-05

U(nl4HeVfl 9.35e-03 4.02e-01 7.536-04 8.21c-05 1.726-00 7.35e-04

8. 106-04 1.03e-01 1.416-05 2.79e-07 4.226-01 7. 33e-06

235 U(nth.r> 3.09e-04 5.296-02 2.80-06 9.30-09 1.306-01 2.S7c-07

ZBU(nr.f) 4.42e-04 5.826-02 4.09e-06 3.I5c-08 1.73e-01 7.206-07

• '“'"'Wir” 2.41e-03 1.33e-01 7.9V-0S 4.50c-06 6 .006-01 9.4Re-05

^tVf) 1.95e-04 2.68e-02 1.!8e-06 5. 80 -09 7.96c-02 1.74e-07

2. 10-05 9. 736-03 3.13e-07 3.026-10 2.346-02 9.50e-09

237U(nrn 3.926-05 1.046-02 3.5/6-07 9 316-10 3.84c-02 3.626-00

^HpCtyf) 5.90-04 1.026-01 1.20e 04 3.406-07 7.42c-01 2.51e-05 237 Np(nf. f) 3.98e-04 S.86e-02 6.976-05 1.09e-07 3.27e-01 4.32e-06 •>*& Hp(nth.f) 5.80-05 2.25e-02 1.506-05 2.226-08 1.36c -01 4.206-07 ^NpCiy.r) 1,04e-04 2.42c-02 2.256-05 4.72e-08 1.89c- 01 1.47c-06

239Npinf.f) 4.106-05 1.15e-02 S.G8c-06 3.81 e-00 0.256-02 2.696-07

3.14e-03 3.78e-01 S. 14c-03 2.26c -05 2.726-00 2.23e-03

23tiPu(nr f) 3.file-03 3.726-01 6 . 10-03 4.266-05 2.906-00 3. 166-03 ^Putn^.f) 4.966-04 1.076-01 4.93e-04 2. S5e-06 5.I7c-01 4.726-05

^Puc^.n 6.40-04 7.70-02 5.65c 04 3.57c-CG S.91c-01 8.27e-05

?u(n14MtV.f) 2.24e-03 1.186-01 1.546-03 2.716-05 1. 106-00 1.01e-03

3. 10-04 4.136-02 1.0Oe-O4 1.47c-06 3.07e-01 2.38c-05 S*lpU,n th,f> fi.34e-OS 1.926-02 3.60e-05 4.24e-07 1. 176-01 1.41e-06

2

243Pu(nf.f> 1.41e-05 3.76e-03 4 146-07 4.21e-0S 3.52e-02 l.Olc-07

24,A»(of.f) 5.326-04 6.506-02 I.SOc-03 1.54e-05 1.206-00 7.456-04

2<2AB(ntb.f) ‘ l.92e-04 3.43e-02 4.49e-04 4.406-06 6 .44c-01 1.48e-04

242Aatnr.f) 2.576-04 3.576-02 4.70-04 4.636-06 7.106-01 2.306-04 .243Ae(nr,f) 1.20-04 l.BCe-02 1.10c-04 1.47c-06 3.84e-01 6 .3 5c-OS

2* bcB,^h-n . 1.066-04 1.90-02 2.27c 04 4.806-00 4.006-01 1.536-04

^crin^.ri 1.326-04 2.00-02 8.576-04 5.736-05 l.OBc-OO 1,186-03

■.^crcwD 2.846-05 5.666-03 1.046-04 9.61e-0C 2.49e-01 . 1.306-05 - 59

—• Fu

w 2ie ' 2ia z4o ' 2^4 2i« ' 2i* ' a4o 2^2

Fig. 1. Cumulative yields of 90 Sr formed Fig. 2. Cumulative yields of IS7Cs via fission of various actinides by fission formed via fission of various actinides spectrum neutrons. by reactor spectrum neutrons.

Pd-107

Fig. 3. Cumulative yields of 107Pd formed via fission of various actinides by reactor spectrum neutrons. Nuclear Data Section e-mail, INTERNET: [email protected] International Atomic Energy Agency fax: (43-1)20607 P.O. Box 100 cable: INATOM VIENNA a A-1400 Vienna telex: 1-12645 atom a Austria telephone: (43-1)2060-21710 online: TELNET or FTP: IAEAND.IAEA.OR.AT username: IAEANDS for interactive Nuclear Data Information System username: ANONYMOUS for FTP file transfer username: FENDL for FTP file transfer of FENDL files For users with web-browsers: http://www-nds.iaea.or.at