Structure studies of direct α-transfer reactions: A general formulation for α-particle spectroscopic amplitudes in the cluster model

Abstract

Applications of recently published methods for calculating α spectroscopic amplitudes are restricted to ground state configurations or to an extremely limited number of nuclei (i.e. closed-shell nuclei). The formulations for α spectroscopic amplitudes developed presently are applicable to closed, as well as partly filled shell nuclei for which one set or more of residual models has been identified in terms of L- S or j- j coupling schemes. It has been known that the task of formulating α spectroscopic amplitudes is reduced to that of formulating the (α+core) cluster normalization factor N [ uλ] J identified with the Wildermuth type of model states. In this paper, two general methods for calculating N [ uλ] J −1 are developed, which are applicable to a wide range of structural models associated with α-clustering phenomena. The first method includes a sequence calculation for eliminating spurious state admixtures ordinarily associated with excited shell model configurations. The second method requires prior determination of these spurious admixtures by a method other than the first, and offers the advantage of enabling the calculation of N [ uλ] J −1 for all excited configurations without having to be concerned with the α-overlap factor or the four-body coefficient of fractional parentage of any of these configurations.