Review of alpha-decay data from doubly-even nuclei i - r Y. A. AKOVALl

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37837 -6371, USA* '? I

f-3 Abstract: Alpha-decay data from doubly-even nuclei throughout the periodic table are reviewed and .w %'& -*

evaluated. From these data, nuclear radius parameters are calculated by using the Preston formula for adecay probabilities. The radius parameters for each element behave rather regularly as a function of neutron number. They show minima at the major closed shells, increase sharply for parents just above the closed shells, and decrease smoothly toward the next shell closure. The same trend is observed for a reduced widths calculated using the Rasmussen formalism. Any irregularity or large departure from this behavior indicates probable incorrect input data. This systematic behavior can also be utilized to estimate partial half-lives,

Alpha-hindrance factors, HF, defined as the ratios of experimental to theoretical partial half-lives of a transitions, are powerful tools in obtaining spectroscopic information about nuclear states. Various models have been introduced in order to understand the a-decay process and to calculate the penetrability of a particles through a bamer.

In one of the early models', a preformed a particle inside a nucleus was treated as being in a rectangular potential field with a depth of VO and an effective nuclear radius, R-ro A'", where A is that of the daughter nucleus; for distances larger than this radius, the field is a Coulomb potential between a particle and daughter nucleus. The spin- independent part of the Preston equations' is used widely2. The nuclear radius parameter R (or ro) for an even-even nuclide is determined by defining the calculated transition probability for an a transition from parent's ground state to ground state in the daughter nucleus to be equal to the experimental transition rate, that is HF=l .O for such a transition. In the calculation of hindrance factors for a transitions from odd and odd-odd nuclei, the radius parameters are chosen from the ro values for the neighboring even-even nuclei. In a later model3, nuclear-barrier penetration was calculated by using an optical-model potexdid derived from the analysis of a-particle scattering data. A centrifugal barrier was added to the nuclear potential to take I dependence into account.The a-decay rates are discussed in ternis of reduced widths, defined by a'= hhP2 where P is the penetrability factor, h is the decay constant and h is the Planck's constant. The Rasmussen formalism is used by many researchers4.

With a better understanding of the nuclear potential and with the availability of faster computing capabilities, interest in exploring the adecay process has increased recently. There are numerous excellent theoretical studies where absolute transition rates have been calculated for various nucleis. These studies will not b:: reviewed here; the reader is referred to papers given in Ref.5 and the earlier references quoted in them.

The purpose of this study is to provide a toot for estimating half-lives and a-decay branchings for not-yetdiscovered nuclei, as well as to provide evaluated a-decay data for even-even nuclei. In this study, the experimental a-transition rates and their hindrance factors for all known even-even a emitters are examined. For calculations of hindrance factors, experimental half-lives of parent nuclei, a-decay branchings, a energies and relative a intensities are needed. A11 available data6for these experimental quantities have been reviewed, evaluated and listed in Table 1. The nuclear radius parameters given in this table are calculated by using the Preston formula'. As mentioned above, for a transitions from odd and odd-odd nuclei the radius parameters obtained from these ro parameters are to be used in the computation of hindrance factors. A systematic study of hindrance factors for a transitions between various orbitals has been done previously and rules for hindrance factors were deduced'.

The calculated radius parameters for all nuclides decrease gradually with increasing neutron number between closed shells; they reach minima at the N=126, the only major closed shell for a decaying nuclei, increase sharply just above this closed shell, and decrease again with increasing neutron number toward the next major shell with a slight minimum at the N=l52 minor closed shell. A similar pattern has been observed4 for a reduced widths for these s-wave a transitions.

The submeed rnanuscnpt has bnn authored by a contractor of the U S Government wder contract No DE-

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.

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This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

lo6Te 08Te

11OTe 11OXe 1 %e 144Nd 146sm 1483, 148Gd 50Gd

15%

152Dy 152b

52Gd

154m

54Er 154yb 156yb 1 5 6 ~ 158yb 158W

60 ps 30 2.1 S I

18.6 s 8 (0.05 s) 2.7 s 8

2 . 2 9 ~ 1 0 ~ ~ y I6 10.31 x107 y 45

74.6 y 30 8x1015 y 2

1 . 7 9 ~ 1 0 ~ y 8 7.17m5

1 . 0 8 ~ 1 0 ~ ~ y 8 2.38 h 2

10.3 s I

3 . 0 ~ 1 0 ~ y 15 3.7 m 3 0.409 s 2

2 6 s 2 23 ms I

1.60 m 10

2.85 s 7

1 .o 0.49 4

(6.740 6, (0.87) 0.008

1 .o 1 .o 1 .o 1 .o 1 .o

0.36 5 1 .o

0.00108 I1 0.91 4

1 .o 0.0047 13

0.92 2 0.10 2 0.97 3

0.000021 13 0.44 3

1.70 1.632 (1.57 (1.70 1.64 1.596 1.569 (1.554 1.570 1.572 1.566 1.574 1.584 1 S67 1.54 1.551 1.5570 1.596 1.552 1.52 1.562

4 14

5 ) 6 ) 9 9 8

26) 3 12 10 7 13 4 4 24 25 19 6 6 7

4128 9 3318 4

2624 15 3745 15 3211 7

1852.3 18 2455 4

1932.3 12 3182.680 24

2734 7 4235.1 17

2146.6 15 3628 4

4804.3 I6 2870 5 4168 3

5330.9 17 4687 4 5873 4 4065 8 5267 4

\

100 100 100 100 100 100 100 100 100 100 100

100 100 100 100 100 100 100 100 100 100

The regular behavior of ro parameters (and 6's) is often utilized to calculate some unmeasured property of an observed a transition, such as its partial a half-life, or to predict some nuclear properties for yet unobserved a decays. In these cases, the ro parameter for a nucleus is obtained from the ro systematics by extrapolation or interpolation, and the desired properties are computed from this radius parameter. Examples below illustrate some of the methods used for (i) estimating the half-life of a nucleus; (ii) estimating branching ratio for adecay; (iii) choosing the best half- Me of a nucleus from various measured values.

0 A 7428-keV a group following the'66Er(36Ar,xn) reaction was observed* and identified as decaying from neutron- deficient '%. The ro systematics suggests r0=1.56N.02, which leads to T,1~(7428-keV a)=7k3 m. The partial half- life of '% for p decay was estimated as =5 seconds from gross beta calculationsg. These calculated partial half-lives predict that the a branching for '?Rn is 99.9% and the p branching is =O. 14%. The calculated half-life of 7 ms agrees well with the time difference of 5 ms measured between residues in 166Er(36Ar,rm) reaction and the a detection'.

0 In the decay of 228pU, only one a group with energy of 7810 keV has been observed"; its half-life has not been measured, and no other mode of decay has been detected. From a separate systematic study' of hindrance factors for a's to the first 2' states, the intensity ofthe 7810-keV a transition to the ground state of 224U is deduced as 75%. From the radius parameter of ro =1.525iO.015, the partial half-life for a decay is calculated to be 0.28H. 10 seconds. Together with the partial half-life of 90 seconds for p decag, the total half-life and a and f3 decay branchings of 228Pu are predicted to be Tln=0.2S+0. 10 seconds, 99.7% and 0.3%, respectively.

The ro values placed in parentheses in Table 1 are obtained from the systematics of radius parameters that are calculated in this work, and TIl2 or a branchings listed in parentheses are the values computed using the corresponding ro values. It is hoped that this table will serve as a useful tool for analyzing new results and estimating the a-decay properties for nuclei in new regions to be studied.

The author is greatfid to Mrs. Mary Ruth Lay for preparing the table and for editing the manuscript. The author wishes to thank Dr. Murray Martin for valuable discussions.

Table 1. Calculated ro parameters and the data used in calculations Parent Parent T l n a-branching ro(daughter) Eolo (kev) I a

ratio I ~ O - ' ~ cm) her 100 n I

Table 1. Calculated ro parameters and the data used in calculations Parent Parent T1/2 a-branching ro(daughter) Em &ev) Ia

ratio (10-l~ cm) (per 100 a ) 100 1 .o 1.581 36 6437 30 1 5 8 ~

160m 1 6 0 ~ 1 6 2 ~ 1 6 2 ~

1620s 164W 1640s

1660s

1680s

1700,

1720,

1 6 6 ~

166pt

168pt

170pt

172pt 174m

1740s 174pt 176pt

176Hg

178Hg

lS0Hg 8oPb

82Hg 82Pb

ls4Hg 84Pb

178pt

180pt

182pt

184pt

1860s 186pt

s6Hg 86Pb

188pt

88Hg 88Pb

0.9 ms 3 13.6 s 2 91 ms5 39.8 s 4

1.3 s I 1.7ms 7 6.0 s 3

21 m s l 18.8 s 4

220 ms 7 0.3 ms I 2.1 s 1 2.0 ms 4 8.1 s 10

14.7 ms 5 19.2 s 9 0.096 s 3

2.0~1015 4 4 4 s 4

0.90 s I 7.5 s 35

18 ms 10 21.1 s 20

266 ms 25 5 2 s 3 2.56 s 2 4 m~ +4-2

3.0 m 2 10.83 s 6 55 ms 40 17.3 m 2 30.6 s 3 0.55 s 6

2 . 0 ~ 1 0 1 5 ~ 11 2.2 h2 1.38 m 7 4.83 s 5

10.2 d 3 3.25 m 15

24 s 2

0.007 2 0.87 8

7x10 -5 I 0.46 3 0.998

0.038 12 0.990 I O

3x10 I 0.72 13

1 .o 0.44 4

1 .o 0.085 34 (0.993 3)

0.011 2 0.94 6

1 .o 0.00020 IO

0.67 6 0.40 3

(0.986 14) 0.046 31

0.95 +5-26 0.0030 15

0.48 5 1 .o

0.00031 7 0.152 8

1 .o 1.7~10 -5 7 0.0126 20

(>0.89) 1 .o

1.4~10 1 . 8 ~ 1 0 ~ 5

(0.55 17)

2 . 9 ~ 1 0 - ~ 5 4 . 0 ~ 1 0 - ~ 8

0.10 5

1.548 1.557 1.576 1.569 1.563 1.567 1.553 1.509 1.558 1.551 1.563 1.554 1.550 1.562 1.569 1.558 1.55 1.53 1.546 1.551 1.55 1.544 1.545 1.53 1.533 1.53 1.533 1.522 1.51 1.536 1.512 1.505 1.49 1.49 1.504 (1.50 1.470 1.481 1.498

20 10 13 9 33 24 13 25 16 28 11 17 37 9 20 8 2 4 11 24 3 30 10 4 8 5

26 5 6 31 11 13 3 3 27

2) 17 28 39

4780 3 5912 5 4308 8 5534 3 6618 10

5149.8 23 6321 7 4739 4 5990 6

7110 15 5676 4

6832 10 5407 4 6548 6 5105 IO 6314 4

2437.4 25 4760 I O 6038 4

575 1.2 20 6767 10 5446 3 6430 6 5140 10 6119 5 7230 40 4843 5 5866 5

6920 I O 4502 IO 5535 I5 6628 6

2761.3 17 4230 20 5094 15 6332 7 3922 5 4610 20 5983 5

100 100

(>99.5) 100 100

(>98.9) 100

P98) (>95.4)

P94)

(97 3)

(95 5) (98 2)

(99.9 I) 088.5) (>%.5)

P98)

(98 2) (92 8)

100

100

100

99.74 13

97.3 24

99.87 3 100

G-83) 98.94 I1 (>88.6) (>87.8) 99.44 IO (S2.4)

P95) ( 94 6) (94 6)

(95 5) (96 4)

98.0 18

99 I

Table 1. Calculated ro parameters and the data used in calculations Parent Parent T1,2 a-branching re(daughter) Eaa Orw I a

ratio (10-l~ cm) (per 100 a ) 190,

1 9 0 ~ ~

1 9 2 ~ ~

90Pb

92Pb

94Pb 94Po

1 9 6 ~ ~ 1 9 8 ~ ~

20%0 2 0 0 h

202PO 2 0 2 h

2WPO

1 9 8 h

202Ra

2 0 4 h 2 0 4 b

206PO

20%b 208PO

2 0 6 h

2 0 8 h

208Ra OPb

210Po 2 1 0 b

212Po 212- 2 1 2 b 21211,

2 1 4 ~ ~

ORa

2 1 4 h

214Ra 21411,

2’6PO 2 1 6 h

216Ra 21611,

6 . 5 ~ 1 0 ~ ~ y 3 1 .2mI 2.0 m~ +PI0 3.5 m I 0.034 s 3

12.0 m 5 0.392 s 4 5.8 s 2 1.76 m 3

57 ms 9

11.5 m I 1.06 s 2

44.7 m 5 9.85 s 20 0.7 ms +333 3.53 h 2 1.24 m 3

45 ms +55-21 8.8 d I 5.67 m 17 0.24 s 2 2.898 y 2

24.35 m 14 1.3 s 2

22.3 y 3 138.4 d I

2.4 h I 3.7 s 2 0.299 p 2

23.9 m I2 13.0 s 2 30 ms +20-10

1 6 4 . 3 ~ s 20 0.27 ps 2 2.46 s 3

100 ms 25 0.145 s 2

45 ps5 182 ns 10 0.028 s 2

1 .o 0.0021 7

0.9987 13

5 . 9 ~ 1 0 - ~ 6 0.995 5

7.3~10 29 0.93 7 0.94 5 0.57 2

0.994 6 0.111 3 0.86 14

0.0192 7 0.90 IO

1 .o 0.0066 I

0.73 I (0.997 3) 0.0545 5

0.63 6 (0.97 3)

0.999958 4 0.62 7

(0.95 5)

1 . 9 ~ 1 0 - ~ 8 1 .o

0.96 I (0.96 4)

1 .o 1 .o

(0.85 15) (0.997 3)

1.0 1 .o

0.99941 4 (0.999 I)

1 .o 1 .o 1 .o 1.0

1.474 1.462 1.54 1.500 1.511 1.432 1.511 1.511 1.4965 1.551 1.4803 1.516 1.4719 1.517 1.60 1.4617 1.5035 1.533 1.4550 1.492 1.527 1.4296 1.476 1.495 1.449 1.40882 1.4571 1.487 1.5212 1.4343 1.467 1.510 1.5394 1.532 1.4552 1.492 1 .5408 1.5649 1.541 1.466

10 25 4 9 8 23 6 6 34 10 26 9 31 7 +5-10 17 26 4 17 7 8 8

6 14 42 10 33 6 4 34 10 27 6 6 21 16 9 8

5 6

3180 6 5581 4

7482 20 5112 5 7167 7 4640 20 6842 6 6520 3

6182.0 22 7205 5

5861.9 18 6902.4 25 5588.1 17 6639.5 19 7860 60

5377.1 I2 6418.9 25 7488 12

5223.7 15 6260.6 25

7272 5 5114.9 14

6140.1 17 7133 5 3720 20

5304.33 7 6041 3 7019 5

8784.86 12 6264 3

6899.2 17 7802 10

7686.82 7 9036 9 7137 3 7678 10 6778.3 5 8050 10 9349 8 7921 8

(98.5 15) 99.90 2 (99.5 5) (99.8 2) (99.6 4) (99.9 I) 99.71 6

99.978 13 99.9987 3 99.93 2

100 99.986 3

100 99.9982 6

100 100 100

(99 4 100

(99.96 4) (99.2 8)

99.99976 7 99.953 4 (99.5 5)

1 00 99.99879 4 99.9944 3 (99.7 3)

100 99.950 5

(99.85 15) (98.8 12) 99.9895 6 (99.95 5)

(99.5 5 ) (99.81 19)

99.9981 3 (99.6 4) (99.97 3) (99.5 5 )

Table 1. Calculated rn narameters and the data used in calculations Parent Parent T1a a-branching ro(daughter) E* WV) I a

ratio (10-l~ cmb fner 100

2 1 8 h

8Ra 21811, 2 1 8 ~ 2 2 0 h 2 2 0 h 22011, 2 2 2 h

222R, 22211,

224Ra 22411, 2 2 4 ~

226Ra 22611, 226u 22811, 228u

23% 230u 23211, 232u 234u 234pu 236u 236pu 238u 238pu 240pu

240cm 2 4 2 h

242cm

2*ClTl 244Cf 2 4 6 ~ m 246Cf 248cm 248Cf

2 4 4 b

35 ms 5 25.6 ps 11

109 ns I1 1.5 m~ +73-7

55.6 s 1 17ms2 9.7 ps 6

3.8235 d 3 38.0 s 5 2.8 ms 3

3.66 d 4 1.05 s 2 0.7 m~ +5-2

1600 y 7 30.57 m IO 0.30 s 10 1.912 y 2 9.1 m 2

7 . 5 3 8 ~ 1 0 ~ y 30

1 . 4 0 ~ 1 0 ~ ~ y I

2 . 4 5 5 ~ 1 0 ~ y 6 8.8 h 1

2 . 3 4 2 ~ 1 0 ~ y 3 2.858 y 8

4 . 4 6 8 ~ 1 0 ~ y 3

20.8 d 21

68.9 y 4

87.7 y I 6563 y 7

27d I

3 . 7 5 ~ 1 0 ~ y 2

8 . 0 0 ~ 1 0 ~ y 9

162.8 d 2

18.1 y I

4 . 7 6 ~ 1 0 ~ y 4

3 . 4 8 ~ 1 0 ~ y 6

19.4m 6

35.7h 5

333.5d 28

0.99980 2 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1.0

0.975 25 1 .o 1.0 1 .o 1 .o 1 .o

0.06 3 1 .o 1 .o 1 .o 1 .o 1 .o

0.997 3 1 .o 1 .o

0.99879 4 1 .o 1 .o

0.999737 4 0.999996 2 0.9161 I6

0.999971 3

1.5379 1.559 1.563 1.554 1.46 1.5555 1.556 1.566 1.5487 1.5423 1.539 1.5419 1.536 1.527 1.5397 1.5385 1.529 1.5332 1.524 1.5331 1.531 1.5361 1.5288 1.5216 1.518 1.527 1.5103 1.536 1 SO75 1.5168 1.4949 1.5143 1.5013 1.5062 1.4979 1.5103 1.4946 1.4953 1.4963 1.4851

7 8 4 9 +4-9 2 8 9 2 23 8 6 5 30 4 8 18 8 9 13 5 22 6

5 39 3 3 3 2 3 18 9 10 10 7 25 10 9 8 24

6002.35 9 7129.2 12

8389 6

9666 10 8625 25

6288.08 10 7457 7 8790 20

5489.52 30 6559 5 7982 8

5685.37 15 7170 10 8466 I2

4784.34 25 6336.8 I O 7570 20

5423.15 22 6680 10 4687.0 15 5888.4 7

4012.3 14 5319.23 14

4774.6 14 6202

4493.5 21 5767.53 8

4198 3 5499.03 20 5168.13 15 6290.5 5 4902.3 14 6112.72 8

4589 1 5804.77 5 7209 4 5385.7 9

6750.0 10 5078.41 25

6258 5

99.9989 ii 99.87 I (99.5 5)

100 (99.1 9) 99.89 2 99.0 4

(99.3 7> 99.92 I 96.9 1 97 1

94.91 7 79 2

(96 4 ) 94.45 5 75.5 3 85 5

72.2 I1 70 5

76.3 3 67.4 4 78.2 13 68.0 4

71.38 16 68

74 4 69.14 33 79.0 27 70.91 IO 73.51 36 71.1 5

76.45 17 74.1 17 80.6 8 76.4 12

75 3 80.7 I1 79.3 IO 81.9 4 80.0 10

Table 1. Calculated ro parameters and the data used in calculations Parent Parent T1,2 a-branching ro(daughter) Eao 0 Ia

248Fm 36s 3 0.93 7 1.490 13 7870 20 80 20 25OCf 1 3 . 0 8 ~ 9 0.99923 3 1.4836 5 6030.22 20 84.7 6

ratio ( 1P ern) (per 100 a )

252Cf

2 5 2 ~ ~ 254Cf 2 5 4 F ~ 254No

2 5 2 F ~

2 . 6 4 5 ~ 8 25.39 h 5 2.27s 18

60.5 d 2 3.240 h 2

54 s 6 2 5 6 ~ ~ 157.6111 13

0.96908 8 0.999977 2

0.731 19 0.00310 I6 0.999408 2

0.90 4

0.081 3

1.50126 1.4670 1.490 1.517 1.4888 1.465 1.500

20 8 5 4 8 7 3

6118.10 4 7039 2 8415 6 5833 5

7192.1 17 8093 14 6917 5

84.3 3 84.0 5 83.6 20

83 I 85.0 5 86 2

87.6 12 25%0 2.91 s 5 0.9950 6 1.4765 19 8448 6 87 2

* Research sponsored by the Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corporation for the U. S. Department of Energy under contract number DE-ACO5-96OR22564. ’ M. A. Preston, Phys. Rev. 71 (1 947) 865.

See, for example, “General Policies” in Nuclear Data Sheets, first issue of every volume, p.vii J. 0. Rasmussen, Phys. Rev. 113 (1959) 1593.

4See, for example, K.Toth, et al., Phys. Rev. Lett. 53 (1984) 1623 for calculated reduced widths of s-wave CL transitions; J. Wauters, et al., Phys. Rev. Lett. 72 (1994) 1329 and R. D. Page, et al., Phys. Rev. C53 (1996) 660 for reduced widths relative to ground-state to ground-state transitions in eveneven nuclei

See, for example, the following references and the references therein: A. Insolia, R. J. Liotta and E. Maglione, Europhysics Lett. 7 (1988) 209; A. Raduta, et al., Phys. Rev. C44 (1991) 1929; D. S. Delion, A. Insolia, R. J. Liotta, Phys. Rev. C46 (1992) 1346; S. M. Lenzi, et al., Phys. Rev. C48 (1993) 1463; F. Hoyler, P. Mohr and G. Staudt, Phys. Rev. C50 (1994) 2631; B. Buck, Phys. Rev. C51(1995) 559; A. Florescu and A. Insolia, Phys. Rev. C52 (1 995) 726.

6References for experimental data are obtained from recent references maintained by the National Nuclear Data Center at the Brookhaven National Laboratory. See S. Ramavataram, Nuclear Data Sheets 76, Number 4 (1 995) p. iv for instructions on on- line access to the Nuclear Structure References (NSR) file which contains accumulated up-to-date references and on access to the Evaluated Nuclear Structure Data File (ENSDF), and see p.489-702 of the same issue for references scanned during 1995

* K. Morita, ef al., 2. Phys. A352 (1 995) 7.

lo A. N. Andreyev, et al., 2. Phys. A347 (1994) 225.

Y. A. Ellis and M. R. Schmorak, Nucl. Data Sheets B8 (1972) 345.

K. Takahashi, M. Yamada, T. Kondoh, At. DataNucl. Data Tables 12 (1973) 101. 9