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

Abstract

We present expressions for the matrix elements of the spin--spin operator ${\vec{S}}_{\mathrm{n}}\cdot {\vec{S}}_{\mathrm{p}}$ in a variety of coupling schemes. These results are then applied to calculate the expectation value $⟨{\vec{S}}_{\mathrm{n}}\cdot {\vec{S}}_{\mathrm{p}}⟩$ 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 $⟨{\vec{S}}_{\mathrm{n}}\cdot {\vec{S}}_{\mathrm{p}}⟩$ 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 $⟨{\vec{S}}_{\mathrm{n}}\cdot {\vec{S}}_{\mathrm{p}}⟩$ 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.

Comments: 11 pages, 7 figures. Accepted for publication in the European Physical Journal A