Relation between shrinkage effect and compression of rotational spectrum in ${}_{\hat{I}}^7›$Li hypernucleus

Abstract

It has been shown experimentally that the ${}^6$Li nucleus shrinks by adding a $\hat{I}›$ particle while its spectrum is also compressed. We discuss the compatibility of these two effects, contrasting also with a relation between the shrinkage effect and the stability of the spectrum in the ${}_{\hat{I}}^9›$Be hypernucleus. To this end, we employ two-body $d$-${}_{\hat{I}}^5›$He and $\hat{I}\pm$-${}_{\hat{I}}^5›$He cluster models for the ${}_{\hat{I}}^7›$Li and ${}_{\hat{I}}^9›$Be hypernuclei, respectively. We first argue that a Gaussian-like interaction between two clusters leads to a stabilization of the spectrum against an addition of a $\hat{I}›$ particle, even though the intercluster distance is reduced. In the case of ${}_{\hat{I}}^7›$Li, the spin-orbit interaction between the intercluster motion and the deuteron spin has to be considered also. We show that the shrinkage effect makes the expectation value of the spin-orbit potential larger, lowering the excitation energy for the ${}^6$Li($3^{+})\otimes \hat{I}›(1/2^{+})$ level.

8 pages, 8 eps figures