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Predictions of some spontaneous fission decay modes
Pergmon
Ann. Nucl. Energy, Vol. 24, No. 17, pp. 145%1459, 1997 © 1997 Elsevier Science Ltd. All fights reserved PII: S0306-4549(97)00014-5 Printed in Great Britain 0306-4549/97 $17.00 + 0.00
TECHNICAL NOTE
PREDICTIONS OF SOME SPONTANEOUS FISSION DECAY MODES YIGAL RONEN Department of Nuclear Engineering, Ben-Gurion University, Beer-Sheva, Israel
(Received 10 January 1997) Abstract--Based on correlations of spontaneous fission isotopes with their respected 2Z-N values, we predict that the isotopes 261Md and 106262, which have not yet been discovered, have a spontaneous fission mode of decay. © 1997 Elsevier Science Ltd
INTRODUCTION There are quite a few nuclear properties which are related to the 2Z-N of the nucleus (Ronen, 1990, 1992, 1995a,b, 1996a,b, 1997; Dufflo, 1994). In this respect, Z is the atomic number and N is the number of neutrons. It was suggested (Ronen, 1990, 1995) that the 2Z-N value is related to a deuteron structure in the nuclei, and that the 2Z-N value represents the number of such deuteron clusters in the nucleus. The majority of the nuclear properties, which were found to be correlated to the 2Z-N values of the nuclei, were related to fission. As a result, we have looked to find correlations related to nuclei which decay in a spontaneous fission (s.f.) mode. Table 1 presents all isotopes which have an s.f. mode of decay. We have not included s.f. isomers. In Table 1 we also have the 2Z-N values of these isotopes. We can see from this table that there are certain 2Z-N values for which there are many s.f. isotopes. The number of s.f. isotopes in each of the 2Z-N values was counted and presented in Table 2. Here we see that the highest numbered s.f. isotopes have even numbers of deuteron clusters (2Z-N is even). In consequence, we have plotted (Fig. 1) the numbers of s.f. isotopes with respect to their 2Z-N values. Only even values of 2Z-N (which also means that the number of neutrons is even) were considered. From Fig. 1 we can see that there are two preferable zones of 2Z-N for which there are many s.f. isotopes. These zones are around 2Z-N = 42 and 56. Furthermore, there is clear dependence of the number of s.f. isotopes and the number of the deuteron clusters (2Z-N). This dependence is a systematic one.
If we consider the isotopes with 2Z-N = 42, we can see that, starting from 234U92, all the elements, besides 237Np93 up to Md, have s.f. isotopes. Even 237Np93 which has no s.f. mode of decay, does have an s.f. isomer, and it is the only Np isotope that has an s.f. 1457
1458
Technical Note Table 1. Isotopes which decay in spontaneous fission mode
Z 90 92
Isotope
2Z-N
232Th
38 42 41 40 38 46 44 43 42 40 38 44 43 42 48 46 45 44 43 42 40 38 42 57 56 54 46 45 44 42 40 38 44 42 40 58 56
234U 235U
236U 94
95 96
97 98
23sU 236Pu 23Spu 239pu 24°pu 242pu 244pu 241Am 242mAm 243Am 24°Cm 242Cm 243Cm 244Cm 245Cm 246Cm 24SCm 25°Cm 249Bk 237Cf 23sCf 24°Cf 24sCf
249Cf
99 100
25°Cf 252Cf 254Cf 256Cf 253Es 255Es 257Es 242Fm 244Fm
Z
101
102
103 104
105
106
Isotope
2Z-N
246Fm 24SFm 25°Fm 252Fm 254Fm 255Fm 256Fm 25SFm 259Fm 245Md 247Md 259Md 26°Md 25°No 252No 25SNo 26°No 262NO 251Lr 261Lr 253 254 255 256 257 258 259 260 262 255 256 257 261 262 263 260 263
54 52 50 48 46 45 44 42 41 58 56 44 43 56 54 48 46 44 50 48 59 58 57 56 55 54 53 52 50 60 59 58 54 53 52 58 55
Table 2. Number of isotopes with the same 2Z-N value which decay in spontaneous fission mode 2Z-N 38 39 40 41 42 43 44 45 46
Number of isotopes 5 0 5 2 8 3 8 3 5
2Z-N 47 48 49 50 51 52 53 54 55
Number of isotopes 0 4 0 3 0 3 2 5 2
2Z-N 56 57 58 59 60 61 62
Number of isotopes 5 1 5 2 1 0 0
Technical Note
1459
S.F. ISOTOPES ¢n uJ
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u.I m
2
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Z
0
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30
t
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35
40
45
50
2Z-N
55
60
65
Fig. 1. The dependence of the number of spontaneous fission isotopes on their 2Z-N value.
isomer. Furthermore, the only isotope of Bk with an s.f. mode of decay is 249Bk with 2Z-N = 42. The isotope of Md, with 2Z-N= 42, is 261Mdlol; this isotope has not yet been discovered. However, the correlation obtained with all the other elements suggests that 26]Md10] should also be an s.f. isotope. With respect to isotopes with 2Z-N = 56, starting from 23scf up to 104256, all even-Z and most of the odd-Z isotopes have an s.f. mode of decay. As a result, we should expect the isotope 106262, that has not yet been discovered, to have an s.f. mode of decay. The isotope 105259, also not yet discovered, also has 2Z-N= 56. However, not all odd-Z isotopes with 2Z-N = 56 have an s.f. mode of decay, like 253Lr and 241Es. So, the prediction that 105259 has an s.f. mode of decay is questionable. In summary, based on the 2Z-N correlations of isotopes with an s.f. mode of decay, we predict that 261Md and 106262 should be s.f. isotopes, namely they should have an s.f. mode of decay. REFERENCES Dufflo, J. (1994) Phenomenological calculation for nuclear masses and charge rodii. Journal of Nuclear Physics A576, 29. Ronen, Y. (1990) Some 2Z-N nuclear correlations. Journal of Physics G16, 1891. Ronen, Y. (1992) Prediction of first level isomeric half-lives of some even-even actinides. Physical Review C45, R525. Ronen, Y. (1995a) Correlations of the independent fission product yields of different isotopes. Nuclear Science and Engineering 121,485. Ronen, Y. (1995b) A Deuteron Model for N = Z Nuclei. International Conference on Exotic Nuclei and Atomic Masses, Aries, France, 19-23 June. Ronen, Y. (1996a) Correlated nuclear properties of heavy even Z nuclei with 2Z-N = 38. Kerntechnik 61, 101. Ronen, Y. (1996b) Correlations for delayed neutron yields for thermal fast and spontaneous fissions. Annals of Nuclear Energy 23, 239. Ronen, Y. (1997) Systematic behaviour in cluster radioactivity. Annals of Nuclear Energy 24, 161.
Ann. Nucl. Energy, Vol. 24, No. 17, pp. 145%1459, 1997 © 1997 Elsevier Science Ltd. All fights reserved PII: S0306-4549(97)00014-5 Printed in Great Britain 0306-4549/97 $17.00 + 0.00
TECHNICAL NOTE
PREDICTIONS OF SOME SPONTANEOUS FISSION DECAY MODES YIGAL RONEN Department of Nuclear Engineering, Ben-Gurion University, Beer-Sheva, Israel
(Received 10 January 1997) Abstract--Based on correlations of spontaneous fission isotopes with their respected 2Z-N values, we predict that the isotopes 261Md and 106262, which have not yet been discovered, have a spontaneous fission mode of decay. © 1997 Elsevier Science Ltd
INTRODUCTION There are quite a few nuclear properties which are related to the 2Z-N of the nucleus (Ronen, 1990, 1992, 1995a,b, 1996a,b, 1997; Dufflo, 1994). In this respect, Z is the atomic number and N is the number of neutrons. It was suggested (Ronen, 1990, 1995) that the 2Z-N value is related to a deuteron structure in the nuclei, and that the 2Z-N value represents the number of such deuteron clusters in the nucleus. The majority of the nuclear properties, which were found to be correlated to the 2Z-N values of the nuclei, were related to fission. As a result, we have looked to find correlations related to nuclei which decay in a spontaneous fission (s.f.) mode. Table 1 presents all isotopes which have an s.f. mode of decay. We have not included s.f. isomers. In Table 1 we also have the 2Z-N values of these isotopes. We can see from this table that there are certain 2Z-N values for which there are many s.f. isotopes. The number of s.f. isotopes in each of the 2Z-N values was counted and presented in Table 2. Here we see that the highest numbered s.f. isotopes have even numbers of deuteron clusters (2Z-N is even). In consequence, we have plotted (Fig. 1) the numbers of s.f. isotopes with respect to their 2Z-N values. Only even values of 2Z-N (which also means that the number of neutrons is even) were considered. From Fig. 1 we can see that there are two preferable zones of 2Z-N for which there are many s.f. isotopes. These zones are around 2Z-N = 42 and 56. Furthermore, there is clear dependence of the number of s.f. isotopes and the number of the deuteron clusters (2Z-N). This dependence is a systematic one.
If we consider the isotopes with 2Z-N = 42, we can see that, starting from 234U92, all the elements, besides 237Np93 up to Md, have s.f. isotopes. Even 237Np93 which has no s.f. mode of decay, does have an s.f. isomer, and it is the only Np isotope that has an s.f. 1457
1458
Technical Note Table 1. Isotopes which decay in spontaneous fission mode
Z 90 92
Isotope
2Z-N
232Th
38 42 41 40 38 46 44 43 42 40 38 44 43 42 48 46 45 44 43 42 40 38 42 57 56 54 46 45 44 42 40 38 44 42 40 58 56
234U 235U
236U 94
95 96
97 98
23sU 236Pu 23Spu 239pu 24°pu 242pu 244pu 241Am 242mAm 243Am 24°Cm 242Cm 243Cm 244Cm 245Cm 246Cm 24SCm 25°Cm 249Bk 237Cf 23sCf 24°Cf 24sCf
249Cf
99 100
25°Cf 252Cf 254Cf 256Cf 253Es 255Es 257Es 242Fm 244Fm
Z
101
102
103 104
105
106
Isotope
2Z-N
246Fm 24SFm 25°Fm 252Fm 254Fm 255Fm 256Fm 25SFm 259Fm 245Md 247Md 259Md 26°Md 25°No 252No 25SNo 26°No 262NO 251Lr 261Lr 253 254 255 256 257 258 259 260 262 255 256 257 261 262 263 260 263
54 52 50 48 46 45 44 42 41 58 56 44 43 56 54 48 46 44 50 48 59 58 57 56 55 54 53 52 50 60 59 58 54 53 52 58 55
Table 2. Number of isotopes with the same 2Z-N value which decay in spontaneous fission mode 2Z-N 38 39 40 41 42 43 44 45 46
Number of isotopes 5 0 5 2 8 3 8 3 5
2Z-N 47 48 49 50 51 52 53 54 55
Number of isotopes 0 4 0 3 0 3 2 5 2
2Z-N 56 57 58 59 60 61 62
Number of isotopes 5 1 5 2 1 0 0
Technical Note
1459
S.F. ISOTOPES ¢n uJ
o
I-
o
10
....
I ....
r ....
i ....
i ....
[ ....
, ....
8 6
¢n 14.
4
u.I m
2
o
Z
0
J
30
t
i
i
i
35
40
45
50
2Z-N
55
60
65
Fig. 1. The dependence of the number of spontaneous fission isotopes on their 2Z-N value.
isomer. Furthermore, the only isotope of Bk with an s.f. mode of decay is 249Bk with 2Z-N = 42. The isotope of Md, with 2Z-N= 42, is 261Mdlol; this isotope has not yet been discovered. However, the correlation obtained with all the other elements suggests that 26]Md10] should also be an s.f. isotope. With respect to isotopes with 2Z-N = 56, starting from 23scf up to 104256, all even-Z and most of the odd-Z isotopes have an s.f. mode of decay. As a result, we should expect the isotope 106262, that has not yet been discovered, to have an s.f. mode of decay. The isotope 105259, also not yet discovered, also has 2Z-N= 56. However, not all odd-Z isotopes with 2Z-N = 56 have an s.f. mode of decay, like 253Lr and 241Es. So, the prediction that 105259 has an s.f. mode of decay is questionable. In summary, based on the 2Z-N correlations of isotopes with an s.f. mode of decay, we predict that 261Md and 106262 should be s.f. isotopes, namely they should have an s.f. mode of decay. REFERENCES Dufflo, J. (1994) Phenomenological calculation for nuclear masses and charge rodii. Journal of Nuclear Physics A576, 29. Ronen, Y. (1990) Some 2Z-N nuclear correlations. Journal of Physics G16, 1891. Ronen, Y. (1992) Prediction of first level isomeric half-lives of some even-even actinides. Physical Review C45, R525. Ronen, Y. (1995a) Correlations of the independent fission product yields of different isotopes. Nuclear Science and Engineering 121,485. Ronen, Y. (1995b) A Deuteron Model for N = Z Nuclei. International Conference on Exotic Nuclei and Atomic Masses, Aries, France, 19-23 June. Ronen, Y. (1996a) Correlated nuclear properties of heavy even Z nuclei with 2Z-N = 38. Kerntechnik 61, 101. Ronen, Y. (1996b) Correlations for delayed neutron yields for thermal fast and spontaneous fissions. Annals of Nuclear Energy 23, 239. Ronen, Y. (1997) Systematic behaviour in cluster radioactivity. Annals of Nuclear Energy 24, 161.