Tensor correlation in 4He and its Effect on the doublet splitting in 5He

Abstract

We investigate the role of tensor correlation on the structures of \nuc{4}{He} and its effect on the doublet splitting in \nuc{5}{He}. We perform a configuration mixing calculation in the shell model type bases to represent the tensor correlation for ${}^4$He. It is found that our model describes the characteristics of the tensor correlation, which is represented by an admixture of the $0s_{1/2}$ configuration with a spatially modified $0p_{1/2}$ orbit. For ${}^5$He, we solve a coupled OCM equation for an extended ${}^4$He+$n$ model, while taking into account the tensor correlation in the ${}^4$He cluster. It is shown that the tensor correlation produces the Pauli blocking, in particular, for the $J^{\pi }={1/2}^{-}$ state, and its effect causes about half of the p-wave doublet splitting in ${}^5$He. This indicates that the strength of the effective spin-orbit interaction should be reduced by about half from the conventional one. We obtain a reliable ${}^4$He-$n$ interaction, including the tensor correlation, which further improves the behavior of the $d$- and $f$-wave phase shifts in the ${}^4$He+$n$ system.

Comments: 21 pages, 9 figures, To be published in Progress of Theoretical Physics