UCRL 3176
UNIVERSITY OF CALIFORNIA
SEMI-EMPIRICAl CORRElATIONS OF AlPHA DECAY RATES AND ENERGIES
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SEMI-EMPIRICAL CORRELATIONS OF ALPHA DECAY RATES AND ENERGIES Charles J. Gallagher, Jr. and John 0. Rasmussen October 26, 1955
Printed for the U. S. Atomic Energy Commission -2- UCRL:-3176
SEMI-EMPIRICAL CORRELATIONS OF ALPHA DECAY RATES MiTI ENERGIES
Charles J. Gallagher, Jr. and John 0. Rasmussen Radiation Laboratory and Department of Chemistry University of California, Berkeley, California October 26, 1955
INTRODUCTION
Theoretical expressions relating alpha d.ecay rate and energy 1 2 were first derived by Gamow and Gurney and Condon. The relationships
hold best for even-even alpha emitters. Perlman, Seaborg, and Ghiorso3
in their alpha systematics have pointed out large and erratic hindrance 4 in odd types. Nordstrom has plotted distributions of hindrance factors
in an attempt to compare "forbiddenness" in alpha decay in a manner
similar to log ft values in beta decay. We have made hindrance facto'r plots for all observed alpha groups emitted from nuclei with greater
than:_l28 neutrons in an attempt to establish correlations.
BASIS OF CALCULATIONS
Even-Even Nuclei - Ground State Transitions l Decay rates to ground states of even-even nuclei are correlated
remarkably well by simple barrier penetration formulas with smoothly 5 varying radius formulas. However, there are significant trends as
shown in a plot of "effective nuclear radius" for even-even alpha
emitters. Thus, for our semi-empirical correlations of alpha decay
rates we have chosen to plot decay ra,.te trends of even-even nuclei on a type of plot which from barrier penetration theory should lead to
nearly straight line plots for isotopes of a given element. The type -3- UCRL-3176 of plot chosen sets the logarithm of the half-life against the reciprocal of the square,root of the total alpha decay energy. (We have included recoil energy and the electron screening correction.) . -l/2 From this ~elationship between log t ; , and E the "hindrance" 1 2 of an alpha particle is seen as the deviation from the curves. The alpha decay energy is then taken as the independent variable, and the hindrance factor is defined as the ratio of the experimental partial alpha half-life to that predicted from the curves.
The primary problem in this correlation, therefore, was to determine the lines which would serve as the basis for the calculations. This was done by the method of weighted least squares analyses on the ground state to ground state decay of even-even nuclei. The solid lines in
Fig. l are the result of these analyses.
The weighting consisted of giving spectroscopically determined alpha energies double weight as compared to ion chamber energy measure- ments. The solid triangles in Fig. l indicate the isotopes used in fitting the line. Solid circles indicate isotopes for which the half 216 lives had been estimated from previous alpha systematics3 (i.e. Em , 220 224 Ra , Th , etc.) or which appeared to deviate markedly from systematic 212 228 2 8 behavior (Po , u , u 3 ) and these were not used in the least squares analyses, For the elements up to curium there was no problem in fitting the lines. For curium and higher elements the scarcity of 242 244 data made the fitting somewhat arbitrary. Cm and Cm were used exclusively to set the curium line because of their well determined decay schemes, as .compared with the lighter curium isotopes about which insufficient experimental data is available. -4- UCRL-3176
250 252 ' . Cf and Cf were reJected in the determination of the californium line slopet because of their proximity to the closed subshell at 152 neutrons.·6 The slope for fermium was obtained by extrapolation as indicated in Fig. 2.
Alpha particle energies were obtained from the compilation of 5 Perlman and Asaro with the exception of the isotopes listed below.
All partial alpha half-lives were obtained using half-lives, alpha branching ratios, and alpha particle abundances listed in the Table 7 2o4 2o6 of Isotopes .· .except for the following: Ern , Ern , Reference 8; 230 ' 232 Ra 222 , a , Re f erence U , a , Reference lQ; U , 1 .. 9; 2 ay 23 238 Reference ll· Np 7 all states, Reference 12; Pu , a , a4, ' ' 3 24 242 Reference :1-3; Am 3, a , a , Reference l4; Cm , a , a , a , 3 4 3 4 5 24 245 Reference JL5; Cm 3, a , Reference JL9; Cm , a , Reference l1; 1 0 246 249 ' 250 Cf , a , a , Reference:.1§3; Cf , a , ~' Reference a9; Cf , 2 3 0 253-- a , a , Re f erence :2·o·_ , Cf252 , ao, a , Reference 21,; E , a , a , 0 1 1 0 1 254 Reference .23; Fm , a , a , a , 0 1 2 Reference 2!+.
tSince this paper was prepared, new data have been obtained on the lighter californium isotopes which reassign the alpha decay energy and 244 24 half-life of Cf to Cf 5 and which give the actual half-life and alpha particle energy of Cf 244 ~ 25~ince these new data have been found to alter the slope of the Cf line only slightly due to the anomalous be 24 havior of Cf 5, we have not recalculated the hindrance factors for the isotopes of berkelium, californium, einsteinium, and fermium which would be affected if the change were large. -5- UCRL-3176
It is easy to justify the above-mentioned type of plot from WKB
barrier penetration formulas (the form for S-wave emission). The most
important factor in these formulas is the exponential expression
2 2Ze - 2 p = exp[- ~ jE[2M(2Ze - E)]l/2dr] tl R r (1) which is expressible in analytical form as
2 2 where x = ER/2Ze , a dimensionles~ parameter; and B,= 2Ze /R, the barrier height. If we make a Taylor series expansion of this function about x = 0, we obtain
2 E 3 E 4 + ~- 4 ;2 + ... ]} (3)
If one retains only the dominant first two terms, as has Gamow 1 , then one sees that the logarithm of the penetration function is a linear function of E-l/2 .
An interesting check on simple barrier penetration theory is provided by examination of the slopes of the least SQUares lines of
Fig. 1. The form of the first term of EQuation (3) shows that the slopes of the lines of Fig. 1 should be proportional to the atomic number, z, of the daughter nucleus to accord with simple theory. In Fig. 2 these
slopes are plott~d a§ainst Z. The theoretically expected behavior is well shown by the lower elements in the series, but there is a striking break beginning at the plutonium alpha emitters and then a reversal of {I the expected trend. -6- UCRL-3176
It is beyond the scope of this paper to attempt any detailed
theoretical explanation of the deviations from simple theory. It should be pointed out that abnormal slopes in Fig. l do not necessarily mean a
changed dependence of decay rate on energy, but since energy is (above
128 neutrons) amonotonic function of the neutron number for an isotopic
series, an abnormal slope may reflect a change in the alpha decay rate
dependent on the addition of neutron pairs. Some isotopic series pass 26 through the region of the onset of validity of the Bohr-Mottelson
spheroidally deformed model and some pass through rapidly changing
spheroidal deformation. Such changes must certainly influence barrier penetration, yet, interestingly enough, the elements where these changes
are greatest, i.e. radium, thorium, and uranium, have the best-behaved
slopes. The slopes should also be influenced by variations in the alpha
formation probability entirely apart from the external barrier penetration
factor.
Even-Even Nuclei -Excited State Transitions
In contrast to the regularly behaving ground state transition
rates, the transitions to excited states show striking trends in rate for different nuclei.
For the elements thorium and above, alpha decay is often observed
to at least three levels (0+, 2+, and 4+), identifiable as a rotational band sequence. Alpha decay to states of odd parity has been observed/
To exhibit this behavior we have calculated hindrance factors to all observed states. The distribution of hindrance factors is shown in
the histograms of figures 3, 4, 5, and 6. The three lines of numbers·ort -7- UCRL-3176 each histogram block represents (l) element/mass number/ground state, indicated by zero if this is the ground state, (2) assigned number of excited state and energy of this state in klio~lectron volts, and (3) the value of the departure factor for this transition. Because of the increasing interest in the correlations achieved by the Bohr-Mottelson large-deformation model, we have segregated the cases in the region of 208 nuclear rotational bands from those cases nearer the Pb closed con- figuration. The bold line on each histogram divides these regions, ' the cases below the bold line coming from the rotational band region.
For the even-even nuclides the generally increasing nature of hindrance to the higher groups is evident, and the hindrance to the 4+,
6+, and 8+ groups generally far exceeds hindrance accountable for by the addition to the barrier of the centrifugal potential associated with angular momentum of the alpha decay system.
Asarc}7 has plotted hindrance factors* against atomic number for the even parity excited state transitions. In somewhat similar manner we have plotted hindrance factors against neutron number in Fig. 7.
*The hindrance factors of. Asaro for transitions to excited states of even-even nuclei are defined slightly differently from ours. Asaro has taken as unhindered the ground state to ground state even-even alpha transitions. We have, however, calculated hindrance factors in relation to the leas~ s~uare curves in Fig. 1. Conse~uently, we may have hindrance factors for ground state transitions, whereas Asaro will not. The 0+ hindrance factors shown in Fig. 7 illustrate this and can be used to obtain Asaro type hindrance factors from the present data. -8- UCRL-3176
We do not expect to illustrate any trends with the 0+ hindrances, but the high hindrances of the lightest isotopes of polonium, emanation, and plutonium and the slight depression at 142 neutrons are of interest. I The variation observed for the curium and californium isotopes is explained by the manner, previously mentioned, in which the lines for.tpese elements in Fig. l were determined.
The dependence upon neutron number of decay to the first excited state (2+) reflects the ground state transition probability and appears relatively unhindered, although there is some increase among the heaviest isotopes.
Of very great interest is the dependence of decay to the second excited state (4+) upon Nand z. It can easily be seen from Fig. 7(c),thatthe hindrance factors for the second state vary with Z and pass through a maximum at Z = 96. However, also notable is the apparent neutron dependence of isotopes, as manifested by the apparent maxima in the 4+ curves of thorium and uranium. The 1- states apparently follow the behavior of the 4+ states.
The relative intensities of decay groups to the even parity states have been considered by a number of authors in connection with spheroidal alpha decay theorl~, but will not be discussed here.
Odd-Nucleon Alpha Emitters
In contrast to the regular behavior of even-even alpha decay rates, nuclei with odd nucleon numbers often exhibit erratic alpha decay rates, tending generally to be slower than comparable even-even alpha emitters.
Perlman, Ghiorso, and SeaborJ have clearly pointed out that the hindrance must be associated with a lowered alpha formation probability rather than with the higher external barrier resulting from non-zero angular momentum. -9- UCRL-3176
29 The details regarding this hindrance an~ not well understood. _Rasmussen-
and Bohr, Frtlman, and Mottelson3Q have,selected and discussed a few
special cases exhibiting little or no hindrance.
To obtain the bases for calculation of these hindrance factors for
odd Z nuclei the slopes shown in Fig. 1 were interpolated to yield the intermediate
odd Z slopes. For instance, the average of the slopes for elements 84
and 86 was employed as the slope for Z = 85. Since it was impossible
to interpolate slopes for Z = 83 and 99, these slopes were obtained by
extrapolation, as indicated by the dashed line in Fig. 2. Similarly
the intercepts at Ea = oo were interpolated to, yield the intercepts for these nuclei.
The distributions of these hindrance factors for the various
nuclear types are shown in Fig, 8 (odd-even), Fig. 9 (even-odd), and
Fig. 10 (odd-odd). The histograms for odd-even and even-odd types
exhibit broad distributions.with the suggestion of a breakup into two
groups. The main group peaks around hindrance factors of order 3,
and the second and small group, around 500.
For the odd-even types in the rotational band region, most of the
cases in the highest hindered group probably involve a change in parity
in alpha decay. This fact is inferred from the apparent "favored" nature
of some of the transitiomin the same nuclei, with the levels showing the
high hindrance connected to the favored levels by El gamma transitions,
which signify a ,parity difference, Thus we suggest the possibility that
parity change is a major hindering factor in alpha decay of odd mass nuclei. Examination of other odd-even alpha transitions possibly involving a parity change indicates that the alpha transition may generally be hindered in such cases but that the hindrance associated with ,the parity change becomes less at atomic numbers below 95. -10- UCRL-3176
For the even-odd types in the rotational band region one again observed a separate group of hindered cases for log hindrance factor from
2,0 to 3.5. Here, however, we may infer that at least two cases (in the decay of Cm243 ) probably involve no parity change. This inference may be 24 drawn from the probable presence of a "favored" alpha transition in Cm 3 and the connection between favored and hindered states by Ml gamma transitions.
CONCLUSION
The data presented here represent all that are available at present on alpha decay rates. We have attempted, by presenting them in the form of hindrance factor histograms, to illustrate the distribution of the deviations from simple. theory. We hope that the presentation of the data in this form can serve as a useful reference for further studies;
ACKNOWLEDGMENTS
We are indebted to Dr. Frank Asaro and Dr. Frank Stephens and to
John Hummel, Albert Ghiorso, and others for valuable data in advance of publication. This study was carried out under the auspices of the U.S.
Atomic Energy Commission. -11- UCRL-3176
REFERENCES
l. G. Gamow, z. Physik 51, 204 (1928); G. Gamow and C. L. Critchfield,
Theory of Atomic Nucleus and Nuclear Energy Sources (Clarendon Press,
Oxford, 1949), _Chaj;l_ter VI.
2. E. U. Condon and R. W. Gurney, Phys. Rev. 33, 127 (1929); Nature 122,
439 (1928).
3. I. Perlman, G. T. Seaborg, and A. Ghiorso, Phys. Rev. 77, 26 (1950).
4. S. G. Nordstrom, Manne Siegbahn (Almq_uist and Wiksells Botryckeri Ab,
Uppsala, 1951), p. 587.
5. I. Perlman and F. Asaro, Ann. Rev. Nuclear Sci. ~ (1954); F. S. Stephens,
Jr., private communication.
6. A. Ghiorso, S. G. Thompson, G. H. Higgins, B. G. Harvey, and G. T. Seaborg,
Phys. Rev. 95, 293 (1954).
7. J. M. Hollander, I. Perlman, and G. T. Seaborg, Revs. Modern Phys.
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8. F. Asaro and I. Perlman, Revs. Modern Phys. 26, 456 (1954); A. Stoner
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9. J. M. Hollander,-w. G. Smith, and F. Asaro, private communications.
10. F. S. Stephens, Jr., F. Asaro, and I. Perlman, Phys. Rev. 96, 1568
(1954); F. Asaro and F. S. Stephens, Jr., private communications. ll. F. Asaro and L Perlman, Phys. Rev. 99, 37 (1955); G. Scliarff-Goldhaber,
E. der Mateosian, G. Harbottle, and M. McKeown, Phys. Rev. 99, 180
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12. D. Engelkemeir and L. B. Magnusson, private communication from T. Novey.
13. F. Asaro and I. Perlman, Phys. Rev. 94, 381 (1954); F. Asaro, private
communication. -12- UCRL-3176
14. F. S. Stephens, Jr., J. Hummel, F. Asaro, andi. Perlman, Phys.
Rev. 98, 261 (1955).
15. F. Asaro, S. G. Thompson, and I. Perlman, Phys. Rev; 92, 694 (1953);
F. Asaro, private communication.
16. F. Asaro ar.d I. Perlman, unpublished data (1954).
17. J. P. Htlimel, F. Asaro, and I. Perlman, unpublished data (1955).
18. J. P. Hummel, F. s. Stephens, Jr., F. Asaro, A. Chetham-Strode, Jr.,
and I. Perlman, Phys. Rev. 98, 22 (1953); F. Asaro, private communication.
19. A. Ghior:3o, G. R. Choppin, and B. G. Harvey, private communication.
20. F. Asaro, F. ,S. Stephens, Jr., B. G. Harvey, and I .. Perlman, private
communic<:' tion.
21, F.· Asaro, F. S. Stephens, Jr., B. G. Harvey, and I. Perlman, "Complex 252 Alpha 8ilci Gamma Spectra of Cf ," Phys. Rev. (to be published).
22. F. S. Stephens, Jr., J. Hummel, F. Asaro, G. R. Choppin, and I. Perlman,
prj_vate. communication.
23. B. G. Harvey, S. G. Thompson, G. R. Choppin, and A. Ghiorso, Phys. Rev.
29, 337 (1955).
24. F. Asaro, F. S. Stephens, Jr., S. G. Thompson, and I. Perlman, Phys.
Rev. 98, 19·(1955).
25. A. Chctham-Strode, G. R. Choppin, and B. G. Harvey, "Mass Assignment . 245 244 of' the 44-Mlnute Cf and the New Isotope Cf '·" Phys. Rev. (to be
plcblished).
26. A. Bohr and B. R. Mottelson, Kgl. Danske Vedenskab.Selskab, Mat.-fys.
Medd. 27, No. 16 (1953).
27. F. S. Stephens, Jr., Ph.D. Thesis, University of California Radiation
LaDoratory Unclassified Report UCRL-2970 (1955). 28. J. 0. Rasmussen, Universi·ty of California Radiation Laboratory
Unclassified Report UCRL-2431 (1953); L. Dresner, Ph.D. Thesis,
Princeton University {1955); R. F. Christy, Phys. Rev. 98, ZA7,
1205 (1955); J. 0. Rasmussen and B. Segall, University of Calif
ornia Radiation Laboratory Unclassified Report UCRL-3040 (1955),
"Alpha Decay of Spheroidal Nuclei," Phys. Rev. (to be published).
29. J. 0. Rasmussen, Arkiv Fysik 1, 185 (1953).
30. A. Bohr, P. 0.' Fr8man, and B. R. Mottelson, K:gl. Danske Vedenskab.
Selskab, Mat.-fys. Medd. 29, No~ 10 (1955). -14- UCRL-3176
w ~ 0 I ~ I month
Fig. l Graph of log partial alpha half -life vs. . the reciprocal of the total alpha decay energy (alpha particle energy plus recoil and screening corrections). Solid lines represent least sq_uare fit's to data represented by solid triangles, for Z between 84 and 98. These least sq_uare fits were used to calculate hindrance factors. Solid circles represent .data that were not used in the least sq_uares analyses. -15- UCRL-3176
• ' ' ' ' ' ' • '- ' '
I I N 135 I '::::- Iw I I I ~ I ~ I -g 130 I I "0 I I ' I I 125
82 86 90 94 98 z MU-10425
d log t 1; 2 Fig. 2 as a function of Graph of dE-l/2 z. Dotted lines indicate method used to obtain slopes for elements 83, 99, and 100. Irregularities after uranium probably indicate inadeq_uacy of simple theory. -16- UCRL-3176
86/218 I 600 .07 15 86/220 I 545 .39 88/224 I 240 .03 88/226 I 189 .05 90/226 I 110 .06 90/228 I 84 .06 10 90/230 I 65 .06 92/230 I 70 .01 92!232 I 58 .02 92/234 I 50 .07 92/236 I 50 .09 5 94/236 94/234 I 41 I "'-50 .27 .52 94/238 98/246 I 44 I 43 .24 .54 94/240 98/250 I 45 I 45 .22 .86 90/232 96/242 98/252 I 70 I 44 I 45 -.14 .16 .62 921238 96/244 100/254 I 48 I 44 I 42 -.12 .29 .64 0 -0.5 0 0.5 1.0 LOG HINDRANCE FACTOR MU-10429
Fig. 3 Distribution of hindrance factors for alpha decay to 2+ states of even-even nuclei. Heavy line in all histograms separates rotational region from region near closed shells, where rotational model is not applicable. First line of numbers indicates element and mass assignment; second, present order of state and energy of state; third, value of log of hindrance factor. -17- UCRL-3176
90/228 3 256 1.14 90/230 94/238 2 250 2 146 1.10 2.12 92/230 94/240 3 230 2 151 1.07 2.01 92/232 98/246 96/242 2 189 2 145 2 146 1.26 2.26 2.55 90/226 92/234 100/254 96/244 3 305 2 176 2 136 2 144 .72 1.13 2.15 2.99 0.5 1.0 1.5 2.0 2.5 3.0 LOG HINDRANCE FACTOR
MU-10427 .. Fig. 4 Distribution of hindrance factors for alpha decay to 4+ states in even-even nuclei. -18- UCRL -3176
6+ 94/238 3 296 2.68 96/244 3 293 2.55 8+ 96/242 98/246 96/242 94/238 3 303 3 293 4 513 4 499 2.28 2.69 3.75 4.20 2.0 2.5 3.0 3.5 4.0 4.5 LOG HINDRANCE FACTOR MU-10428
Fig. 5 Distribution of hindrance factors for alpha decay to 6+ and 8+ states in even even nuclei. -19- UCRL-.3176
90/228 2 217 1.03 90/230 3 250 1.32 90/226 92/230 92/232 96/242 2 241 2 230 3 227 5 605 .53 I. 20 1.69 2.75 0.5 1.0 1.5 2.0 2.5 3.0 LOG HINDRANCE FACTOR MU-10426
Fig. 6 Distribution of hindrance factors for alpha decay to l- states in even-even nuclei. -20- UCRL-3176
3.0 I
2.0
1- 1.0 I J( 4.0 8+ " "! 6+ 2.0 0:: 3.0 0 1- 0 I .#' Lt ~ w 0 '""' z 4+ 0+ 128 136 144 152 160 NEUTRON NUMBER MU-10433 Fig. 7 Hindrance as a function of neutron number for decay to excited states in even-even nuclei. Lines connect isotopes. 0+ is included as a basis for comparison with hindrance factors of Asaro. -21- UCRL-3176 - 85/219/0 .32 87/219/0 85/215/0 .10 .64 87/221/0 89/227/0 .44 .56 10 .89/223/C 91/229/0 .43 .76 e9t225tc 91/231 6 386 .50 .67 91/231 91/231 5 328 7 476 .24 .77 91/227/0 93/237 85/213/0 4 228 .14 .53 1.30 93/235/0 93/237 91/231 911231 83/~11/0 3 197 3 110 I 28 .28 .88 1.27 1.83 2.82 r-- 93/237 95/237/0 93/237 91/231 83/213/0 I 86 5 280 2 46 .45 .62 1.30 1.64 2.75 1 85/217/0 95/241 95/2391( 95/241 91/231 95/241/0 2 60 4 159 4 212 -.25 .16 .51 1.40 1.87 2.90 87/221 95/243 95/241 95/243 93/237 83/211 95/241 I 250 2 75 3 103 4 172 2 155 I 279 I 33 -.20 .12 .68 1.00 1.86 2.31 2.90 931233/0 97/249/0 95/243 99/253 97/243 91/231/0 971243/0 95/243/0 3 118 I 43 I 173 -.49 <,30 .68 1.23 1.87 2.43 2.61 3.18 r91247/0 97/245 99/253/( 97/243 99/253 97/245 93/237/0 971245/0 95/243 2 438 2 530 2 96 I 184 I 31 -.77 -.49 .43 .83 1.27 1.56 2.23 2.80 3.00 0 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 LOG HINDRANCE FACTOR MU-10432 Fig. 8 Distribution of hindrance factors for alpha decay for ail observed cases to states in even-odd nuclei. -22- UCRL-3176 ;--- 84/213/0 .06 84/215/0 86/217/0 .06 .82 15 86/215/0 86/219 I 270 .33 .92 86/219 88/223 2 397 2 159 .49 .84 86/219 88/223 3 622 3 269 .02 .11 88/219/0 88/223 4. 339 .41 .72 88/221/0 88/223 6 450 .49 .62 10 90/223/C 90/227 1 261 .21 .78 90/225/C 90/227 86/219/0 9 332 .32 .61 I. II 90/229 92/233 88/223 2 173 I 44 5 380 .16 .60 1.16 92/229/( 92/235 90/227 2 183 10 397 .36 .10 1.21 92/233/C 94/239/( 90/229 88/223 I 82 I 132 .15 .53 1.28 1.13 5 f- ,...--- 92/235 94/239 92/231/0 90/227 90/227 3 387 I 13 2 59 I 30 .40 .98 1.09 1.80 2.57 94/23510 94/241/0 92/233 90/227 ~ 2 94 3 19 4 110 .24 .61 1.13 1.91 2.58 96/243 94/241 94/239 90/227 90/227/0 92/235/0 3 277 I 46 2 51 5 113 .15 .81 1.01 1.98 2.13 2.99 96/245/0 96/243 96/241/0 90/227 90/229/0 92/235 4 321 6 239 I 112 >.23 .69 1.06 1.95 2.08 2.68 ~92/227/0 100/25510 98/249 96/243 90/227 96/243 98/249 96/2431 2 392 5 387 8 308 2 67 I 236 I 49 -.37 .29 .96 1.02 1.91 2.31 2.70 3.18 1 0 r:J -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 LOG HINDRANCE FACTOR MU-10431 Fig. 9 Distribution of hindrance factors for alpha decay for all observed cases to states in odd-even nuclei. -23- UCRL-3176 85/214/0 1.07 85/216/0 87/218/0 83/212 I c-40 .49 1.25 2.58 85/218/0 87/220/0 89/224/0 83/212 83/212 83/212/0 4 492 2 327 .34 .92 1.31 2.42. 2.98 3.17 91/226/0 89/220/0 ~9/254/0 91 /228 91/228/0 83/214 83/214/0 83/212 83/212 I 245 ' I. 62 3 473 5 617 -.29 .28 .82 1.06 1.-72 2.41 2.80 3.41 3.69 -0.5 0 0.5 1.0 1.5 ' 2.0 2.5 3.0 3.5 4.0 LOG HINDRANCE FACTOR MU-10430 Fig. 10 Distribution of hindrance factors for alpha decay for all observed cases to states in odd-odd nuclei. II I. \ 'I