Nonlocal Potential and Alpha-Decay Barrier Penetrability

Abstract

The transition probabilities W{E2,y) are known only for the 2 +/ -* 0 transitions; therefore, it is necessary to use the theoretical ratio (1) to deter mine the relative transition probabilities for use in (2). The relation M(2 ;2 -2 )EE ^ » ' ^= a " a2> W(£2,y;2 -2 ) where a 2 is the theoretical E2 conversion coefficient, gives the desired ratio of transition probabilities. The monopole transition probability W(E0, e"; 2+' -2 + ) was determined in turn from (1) and the experimental B(E2;2+' -+0) d values. The nuclear monopole strength parameter, p, is defined by W(E0,e')=Qp 2 ,where £2, the electronic factor, is given graphically. 2 Reiner 3 has treated the problem of monopole enhancement for deformed nuclei and has derived a formula for the ratio of the EO to E2 transition probabilities from )3 -vibrational states. For Th 232 his formula leads to M(2 + '; 2 + ' -2 + ) = 3.8, a value which is intermediate between the experimental values obtained by Methods A and B. For U 238 , however, Reiner's formula gives ju(2 + ';2 + -*2 + ) = 1.4 which is a factor of ten larger than the value obtained experimentally. The explanation of the Since the early works on the alpha disintegration problem, the barrier for the alpha emission has traditionally been taken to be purely Coulomb-Ian with an abrupt cutoff at the nuclear boundary defined by some appropriate A ys law. Alpha decay was first considered 1 by the present author by assuming that the potential barrier is not purely Coulombian and should be taken as 2(Z -2)e 2 /r -V, where V is defined as the short-range interaction between the emitted alpha particle and the residual nucleus. Subsequently, the form of the interaction, V, which is superposed on the discrepancy is not apparent in terms of the simple vibrational model used by Reiner, since Th 232 and U 238 have similar atomic numbers, equilibrium deformations, and vibrational energies which are the only parameters entering into the calculation. The values obtained for the nuclear strength parameter p are close to the approximate value of £ predicted by Church and Weneser for 0 + -0 + transitions from vibrational states in spheroidal nuclei, 2 Again, however, it is not clear why the value of p should differ by a factor of two between Th 232 and U 238 . Perhaps one sees in these discrepancies the influence of the different ground-state configurations. tThis work was supported in part by the U. S. Atomic Energy Commission, (private communcation, 1960), and to be published. 5 F. E. Durham, D. H. Rester, and C. M. Class, Bull. Am. Phys. Soc. j5, 110 (1960). 6 De-excitation of the 788-kev state through the 4 + rotational state was ignored, in line with the interpretation of the 788-kev state as y-vibrational. 7 F. K. McGowan and P. H. Stelson, report to International Congress of Nuclear Physics, Paris, 1958 (unpublished).Coulomb field, has been taken differently by different authors 2 " 5 in their calculations of the barrier penetrability.It is, however, worth while to note that in the above calculations of the penetrabilit...

Assessment of nonlocal nuclear potentials in α decay

“…Though the calculation in Ref. [31] involves a different nonlocal framework as compared to the models considered in the present work, the 40% decrease in the value of the half-life of 254 Fm [31] (evaluated without the exchange term in the nonlocal kernel), is similar to the Perey-Buck model result in Table II, without the inclusion of the knock-on exchange term. (33), in alpha decay half-lives of nuclei using three different models of nonlocality.…”

“…The investigation in Ref. [31] was extended to several even-even nuclei and the author once again found a large increase (∼ 50 %) [32] in the penetration factors due to nonlocality. The author further studied the effects of nonlocality in deformed and rare earth nuclei [33,34] with the inclusion of an exchange term in the nonlocal kernel.…”

“…Investigating for the alpha decay of 254 Fm in Ref. [31], the penetration factor was found to increase by a factor of 1.7 due to nonlocality. This amounts to a decrease of about 40 % in the half-life.…”

“…Using an integro-differential equation similar to that of Frahn and Lemmer [35], in Ref. [31], the author calculated the transmission coefficient (or penetration factor) for alpha tunneling within the WKB approximation. The point-like Coulomb field was superimposed by a nonlocal alpha-nucleus interaction based on the Igo potential [36] and a Gaussian form was used for the nonlocal function with a nonlocality parameter of β = 0.9 fm.…”

“…Before closing the discussions, some comments about one of the earliest investigations of nonlocalities in alpha decay are in order here. In a series of works [31][32][33][34], M. L. Chaudhury studied the effects of nonlocalities in alpha decay of different nuclei. Using an integro-differential equation similar to that of Frahn and Lemmer [35], in Ref.…”