Gross Theory of First Forbidden β-Decay

Abstract

The gross theory of nuclear /3-decay developed by Yamada, Takahashi and Koyama for allowed transitions is extended to include the first forbidden transitions. The effect of the giant-resonance is taken into consideration by using sum rules. The /3-strength functions of both allowed and first forbidden transitions and the /3-decay half-lives are calculated. It is shown that the theory can explain the gross properties of the first ·forbidden transitions as well as the allowed ones. In particular, the theoretical /3-strength functions of neutrondeficient heavy nuclei are compatible with experimental data recently obtained by Hansen et al. It is also shown that the first forbidden transitions often predominate over the allowed transitions in heavy nuclei. § 1. IntroductionIt is customary to classify {9-transitions into allowed transitions, first forbidden transitions, Second forbidden transitions, etc., according to spin-parity selection rules. The ft-value is, in fact, a measure of forbiddenness. However, classification of diff~rent orders of forbiddenness by means of ft-values is, in general, obscured by hindrance phenomena. For example, many allowed transitions have ft-values comparable to those of first forbidden transitions/) and even the latter ft-values are generally much larger than the values expected from simple arguments.2) As in the case of allowed transitions, many attempts have been made to calculate absolute ft-values of first forbidden transitions, e.g., calculations based on configuration mixing, 3 )' 4 ) the Nilsson ( + superfluid correction) model 5 ),e) and the deformed Woods-Saxon model. 7 ),s)In spite of these efforts, the results have been unsatisfactory or inconclusive quantitatively, except for several of the strongest transitions in the lead region. 9 )-n)Recently, the Migdal theory was successfully applied to the evaluation of ft-values for some transitions in the lighter spherical region. 12 ) From a considerably different point of view, Ejiri, Ikeda and Fujita 13 ) investigated the giant resonance effect in the first forbidden transition microscopically by extending the Brown-Bolsterli model. . They found that a hindrance factor of about 4 is ascribable to the off-giant-resonance effect. This situation is similar to those of the allowed transitions; hindrance phenomena in heavy nuclei are due to the isospin-multiplet structure for the Fermi transition 14 ) and probably due at

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