TY - JOUR

T1 - Competition between T=1 and T=0 pairing in pf-shell nuclei with N=Z

AU - Sagawa, H.

AU - Tanimura, Y.

AU - Hagino, K.

PY - 2013/3/7

Y1 - 2013/3/7

N2 - The pairing correlation energy for two-nucleon configurations with the spin-parity and isospin of Jπ=0+, T=1 and Jπ=1+, T=0 are calculated with T=1 and T=0 pairing interactions, respectively. To this end, we consider the (1f2p)-shell-model space, including single-particle angular momenta of l=3 and l=1. It is pointed out that a two-body matrix element of the spin-triplet T=0 pairing is weakened substantially for the 1f orbits, even though the pairing strength is much larger than that for the spin-singlet T=1 pairing interaction. In contrast, the spin-triplet pairing correlations overcome the spin-singlet pairing correlations for the 2p configuration, for which the spin-orbit splitting is smaller than that for the 1f configurations, if the strength for the T=0 pairing is larger than that for the T=1 pairing by 50% or more. Using the Hartree-Fock wave functions, it is also pointed out that the mismatch of proton and neutron radial wave functions is at most a few percent level, even if the Fermi energies are largely different in the proton and neutron mean-field potentials. These results imply that the configuration with Jπ=0+, T=1 is likely in the ground state of odd-odd pf-shell nuclei even under the influence of the strong spin-triplet T=0 pairing, except at the middle of the pf shell, in which the odd proton and neutron may occupy the 2p orbits. These results are consistent with the observed spin-parity Jπ=0+ for all odd-odd N=Z pf-shell nuclei except for 2958Cu, which has Jπ=1+. The magnetic moment of a (Jπ,T)=(1+,0) state is also discussed in order to show a manifestation of the change of the shell-model scheme from jj coupling to LS coupling.

AB - The pairing correlation energy for two-nucleon configurations with the spin-parity and isospin of Jπ=0+, T=1 and Jπ=1+, T=0 are calculated with T=1 and T=0 pairing interactions, respectively. To this end, we consider the (1f2p)-shell-model space, including single-particle angular momenta of l=3 and l=1. It is pointed out that a two-body matrix element of the spin-triplet T=0 pairing is weakened substantially for the 1f orbits, even though the pairing strength is much larger than that for the spin-singlet T=1 pairing interaction. In contrast, the spin-triplet pairing correlations overcome the spin-singlet pairing correlations for the 2p configuration, for which the spin-orbit splitting is smaller than that for the 1f configurations, if the strength for the T=0 pairing is larger than that for the T=1 pairing by 50% or more. Using the Hartree-Fock wave functions, it is also pointed out that the mismatch of proton and neutron radial wave functions is at most a few percent level, even if the Fermi energies are largely different in the proton and neutron mean-field potentials. These results imply that the configuration with Jπ=0+, T=1 is likely in the ground state of odd-odd pf-shell nuclei even under the influence of the strong spin-triplet T=0 pairing, except at the middle of the pf shell, in which the odd proton and neutron may occupy the 2p orbits. These results are consistent with the observed spin-parity Jπ=0+ for all odd-odd N=Z pf-shell nuclei except for 2958Cu, which has Jπ=1+. The magnetic moment of a (Jπ,T)=(1+,0) state is also discussed in order to show a manifestation of the change of the shell-model scheme from jj coupling to LS coupling.

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U2 - 10.1103/PhysRevC.87.034310

DO - 10.1103/PhysRevC.87.034310

M3 - Article

AN - SCOPUS:84875208296

VL - 87

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 3

M1 - 034310

ER -