Neutron--proton spin--spin correlations in the ground states of N=Z nuclei

TL;DR

This paper develops expressions for neutron-proton spin-spin matrix elements and uses a schematic model to analyze their expectation values in N=Z nuclei, revealing negative correlations contrary to experimental observations.

Contribution

It introduces a method to calculate neutron-proton spin correlations in a simplified shell model framework, highlighting discrepancies with experimental data.

Findings

Negative spin-spin expectation values in all studied N=Z nuclei ground states.

Contradiction with experimental inelastic scattering results.

Insights into the influence of isovector and isoscalar interactions.

Abstract

We present expressions for the matrix elements of the spin--spin operator $\vec S_{\rm n}\cdot\vec S_{\rm p}$ in a variety of coupling schemes. These results are then applied to calculate the expectation value $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ in eigenstates of a schematic Hamiltonian describing neutrons and protons interacting in a single-$l$ shell through a Surface Delta Interaction. The model allows us to trace $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ as a function of the competition between the isovector and isoscalar interaction strengths and the spin--orbit splitting of the $j=l\pm \frac{1}{2}$ shells. We find negative $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ values in the ground state of all even--even $N=Z$ nuclei, contrary to what has been observed in hadronic inelastic scattering at medium energies. We discuss the possible origin of this discrepancy and indicate directions for future theoretical and experimental studies related to neutron--proton spin--spin correlations.