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Relation Between Half-Life and Energy in Alpha-Decay

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Relation Between Half-Life and Energy in Alpha-Decay PHYSICAL REVIEW VOLUME 75, NUMBER 7 A P R I L 1, 1949 Relation Between Half-Life and Energy in Alpha-Decay I. PERLMAN) A. GHIQRso, AND G. T. SEAB0RG Department of Chemistry and. Radiation Laboratory, University of Cahfornm, Berkeley, California I,'Received February 21, 1949) ~ 'HE great number of new alpha-particle even isotopes it is possible to observe some definite emitters has recently made possible the ob- departures for the other nuclear types. servation of new and interesting systematics in the Even-odd nuclei (even protons, odd neutrons) alpha-decay process. For example, a plot of alpha- of an element lie above the curves for the even-even energy versus mass number for about 90 alpha- isotopes of that element signifying abnormally emitters has led to interesting conclusions as to long half-life. As an example Pu"' with its 5.15-Mev the nature of the energy surface in the region of the alpha-particle would cut the line joining Pu" and heavy elements. ' The present note contains some Pu"' at a half-life of 3000 years whereas its actual correlations between alpha-energy and half-life half-life is 24,000 vears. On the average the even- which have resulted in some new conclusions re- odd nuclei have longer half-lives by a factor of garding the eEect of nuclear type on this relation- about five over what might be predicted on the ship. basis of the even-even nuclei. The greatest devia- Figure 1 shows a plot of the logarithm of the tion noted was a factor of 10, the least was a factor half-fife versus the alpha-energy for the nuclear Qf 2. species of the even-even type. Berthelot' had pre- If one draws lines midway between each pair of viously treated a more limited amount of alpha- lines in Fig. 1 to signify hypothetical half-life- decay data in this manner and reached some of the energy curves for the odd Z elements, it is found same deductions that will be noted here. It is not that the odd-even isotopes have longer half-lives possible to give references for the many recently than would be predicted. The half-life deviation prepared isotopes which are shown here but, with a from prediction for the 15 odd-even isotopes is few exceptions, the information which is used here about fivefold on the average. may be found in a review article covering all of the In examining the odd-odd species of which six isotopes. ' All of the even-even alpha-emitters for are known, it is found that the deviations are much which both the alpha-half-life and the energy are greater than for the even-odd or odd-even types. known are included in Fig. 1 while those species On the average these isotopes have longer half- which exhibit branching decay with an unknown lives by a factor of some 10 to 20 than indicated by proportion of orbital electron capture are excluded. predictions from the hypothetical curves. It will be seen that all of the even-even species In all of these correlations, in the cases. of iso- as reported in Fig. 1 fall on seven nearly parallel topes with more than one alpha-group, partial lines corresponding to the seven elements polonium, alpha-half-lives have been calculated and the emanation, radium, thorium, uranium, plutonium, deviations noted are for the least forbidden group. and curium. (The three exceptions, Po"', Po'". As an example the short-range alpha-group of Pa"' and Po"', will be discussed below. ) The positions has a half-life three times too long while the long of these lines are such as to indicate an average range group is thirty times too long. decrease of about a factor of ten in the probability The above correlations do not include At"', for alpha-emission with an increase of two in polonium isotopes below 212, and all naturally atomic number. This displacement is in agreement occurring bismuth alpha-emitters. In all of these with the effect attributed to Z in the Gamow cases half-lives are abnormally long and this in- formula. 4 cludes the even-even nuclei. Since these are just Other nuclear types, even-odd, odd-even, and the nuclei whose alpha-energies are explained by a odd-odd have not been entered in Fig. 1 because the depression in the energy surface' it is suggested large number of points would obscure the regu- that the decreased probability of alpha-emission larities of the even-even isotopes. However, keeping is due to the attendant shrunken nuclear radius. as reference the positions of the lines for the even- If we attempt to dissociate the effect of decrease in radius from the eGects due to odd protons and neu- ' I. Perlman, A. Ghiorso, and G. T. Seaborg, Phys. Rev. 7'4, trons for bismuth isotopes by making corrections 1740' {1948). based on regularities observed in the other elements, A. Berthelot, J. de Physique (Ser. VIII) 3, 52 {1942). it is found that a discontinuity in radius of about 3G. T. Seaborg and I. Perlman, Rev. Mod. Phys. 20, 585 10 percent is required for bismuth |',1948). these isotopes. 4 G. A. Gamow, Structure of Atomic Nuclei and nuclear It is remarkable that all nuclei with odd protons 'rransformations (Clarendon Press, Oxford, 1937). or odd neutrons have abnormally long half-lives 1096 RELATION BET%'EEN HALF —L I F E AN 0 ENERGY I N ALPHA —DECAY 1097 l2 l2 -10 y 232 Th lO )II 4 w 2 0 LLI LL 2 FrG. 1. Plot of log of alpha- half-life versus alpha-energy for even-even nuclei. «K -6 t -8 CL -l0 «f, Q - l2 O -l4 —O. I ps I I I I I I I I 4.50 5.00 550 6 00 6 50 700 750 800 8 50 900 ALPHA-ENERGY MEV with the apparent exceptions At Po gIld state transition would require a spin change of the Po'". lt is perhaps noteworthy that all of these have order of some 10 units according to Gamow's rela- high decay energies, 7 Mev or greater. In addition tionship' while the measured values~' for U"' the "normal" for comparison is the line connecting and Pa"' are 5/2 (or 7/2) and 3/2, respectively, Po'" Po'" and Po"-' and it cannot be known for corresponding to a change of only 1 unit (or 2 sure that these nuclei are not already beginning units). To explain the apparent forbidden nature to show the effect which becomes so pronounced for of all alpha-decay processes in which there is an Po" and thus are themselves abnormally long- odd neutron, odd proton, or both it may be neces- lived. sary to turn to the coefficient of the exponential The generally lengthened half-life for any isotope term and connect the prohibition with a greater with odd neutron, odd proton, or both is probably difficulty in assembling the components of the not explicitly explained by existing alpha-decay alpha-particle in these cases. In this sense one may theory. The occurrence of abnormally long half- consider that the existence of one or more unpaired lives has been generally attributed to an actual nucleons presumably in the highest quantum states abnormal decrease in nuclear radius (as is no doubt will hinder the formation and emission with full the important factor for At"', the light polonium energy of an alpha particle since it must be made up isotopes, and the bismuth isotopes as mentioned of two neutrons and two protons each pair having above) and to changes in spin between parent and an tiparallel spins. product nuclei in which the alpha-particle is All of the data on alpha-emitters will be pre- emitted with angular momentum. Although spin sented in a forthcoming paper in which will be changes of this kind may contribute in some cases included further discussion of the regularities. it is probably impossible to explain all of the for- This work was performed under the auspices of bidden transitions in this way. In the 6rst place the AEC. this would demand regular alternation of large and 50. E. Anderson and H. E. KVhite, Phys. Rev. 71, 911 small spin numbers down a decay series. Further- (1947). more in a case like U"' alpha-decay, the ground ' H. Sch01er and H. Gollnow, Naturwiss. 22, 511 (1934)..
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