Approximation Method Based on Identities for Calculating Nuclear Matrix Elements. I

Abstract

523The approximation method using projection operators, which was previously proposed and applied to calculations of hindered beta matrix elements, is reexamined from a more general viewpoint and extended to a method suitable to include both backward and forward correlations. The present method is compared with the previous methods, especially the RPA in the pairing model. New formulae are applicable not only to the hindered matrix elements but also to unhindered matrix elements. . The merit of the present method is that the coherent effect of small admixtures in wave functions is expressed as sum rules, which can also be regarded as semi-phenomenological parameters, and the way to estimate neglected terms is clearly seen because the method is based on identities. §I. IntroductionIt is well known 1 > that small admixtures in nuclear wave functions frequently change the magnitude of nuclear matrix elements drastically. A coherent effect of small admixtures is sometimes referred to as the core polarization effect.Previously an approximation method treating the commutator [H, m] instead of the original transition operator m was proposed 2 ) and the physical meaning of the method was discussed from various viewpoints.s), 4 )' >The method is useful if the important part of the nuclear Hamiltonian H commutes with the operator m, and using it the hindered beta matrix elements have been analysed. 2 >' 4 )~s) For the Gamow-Teller (GT) matrix elements f rr many examples were found for which experimental ft-values can be successfully explained.However, this method treats the initial and final wave functions asymmetrically, so that it is not very convenient for treating the forward and backward correlations on the same footing. On the other hand, the so called Random Phase Approximation 9 ),lo) (RPA) is suitable for including the backward correlations for simplified model interactions. In the case of the first or higher forbidden beta transitions, it is clear 11 )' 12 ) that the backward correlations play an important role.The purpose of this paper is to reexamine the commutator method from a more general viewpoint: Possible theoretical errors for calculating nuclear matrix elements are kept properly in mind. The present method is applicable to the diagonal as well as non-diagonal, unhindered as well as hindered matrix elements, at University of Ulster at Coleraine on April 14, 2015 http://ptp.oxfordjournals.org/ Downloaded from