Proton-neutron pairing in the deformed BCS approach

Abstract

We examine isovector and isoscalar proton-neutron pairing correlations for the ground state of even-even Ge isotopes with mass number A=64-76 within the deformed BCS approach. For N=Z 64Ge the BCS solution with only T=0 proton-neutron pairs is found. For other nuclear systems (N>Z) a coexistence of a T=0 and T=1 pairs in the BCS wave function is observed. A problem of fixing of strengths of isoscalar and isovector pairing interactions is addressed. A 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.Comment: 24 pages, 6 figure

Particle-number conservation in charge-radii of odd-mass proton-rich nuclei in the isovector neutron-proton pairing case

“…The latter are deduced from the odd-even mass differences [5]. The pairing-strengths are chosen such as to reproduce these values.…”

Neutron-proton pairing correlations in odd mass systems

“…In the second quantization and isospin formalism, a system of N neutrons and Z protons is described, in the isovector case by the following Hamiltonian, if one assumes that the protons and the neutrons occupy the same energy levels [1]: where the particle-number operators are defined by:…”

“…However, it is well established that in N Z nuclei, the neutron and proton Fermi levels are close to each other and neutron-proton (np) pairing is expected to play an important role in their structure. Isovector np pairing correlations may be treated within the BCS approach [1], or using a particle-number projection method [2]. However, the usual BCS wave-function can only describe eveneven systems.…”

Effects of the particle-number projection on the isovector pairing energy

“…Renewed interest in the study of the neutron-proton (np) pairing correlations occurred recently (cf., e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]) due to the development of the radioactive beam facilities that made possible the experimental study of medium mass nuclei such as N Z. The study of these proton-rich nuclei is not only interesting from the nuclear structure point of view, but it is also important in the astrophysical context.…”