Competition of isoscalar and isovector proton-neutron pairing in nuclei
Abstract We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus 46 V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in 46 V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.
Proton-neutron pairing in the deformed BCS approach
We examine isovector and isoscalar proton-neutron-pairing correlations for the ground state of even-even Ge isotopes with mass number $A=64\char21{}76$ within the deformed BCS approach. For $N=Z$ $_{32}^{64}\mathrm{Ge}$ the BCS solution with only $T=0$ proton-neutron pairs is found. For other nuclear systems $(NgZ)$ a coexistence of $T=0$ and $T=1$ pairs in the BCS wave function is observed. The problem of fixing of strengths of isoscalar and isovector pairing interactions is addressed. The dependence of number of like and unlike pairs in the BCS ground state on the difference between number of neutrons and protons is discussed. We found that for nuclei with $N$ much bigger than $Z$ the effect of proton-neutron pairing is small but not negligible.
Shell model Monte Carlo studies of N = Zpf-shell nuclei with pairing-plus-quadrupole Hamiltonian
Abstract We perform shell model Monte Carlo calculations of selected N = Z pf-shell nuclei with a schematic Hamiltonian containing isovector pairing and quadrupole-quadrupole interactions. Compared to realistic interactions, this Hamiltonian does not give rise to the SMMC “sign problem”, while at the same time resembles essential features of the realistic interactions. We study pairing correlations in the ground states of N = Z nuclei and investigate the thermal dependence of selected observables for the odd-odd nucleus 54Co and the even-even nuclei 60Zn and 60Ni. Comparison of the present results to those with the realistic KB3 interaction indicates a transition with increasing temperature from a phase of isovector pairing dominance to one where isoscalar pairing correlations dominate. In addition, our results confirm the qualitative reliability of the procedure used to cure the sign problem in the SMMC calculations with realistic forces.