Neutron-Proton Isovector Pairing Effect on the Nuclear Moment of Inertia

Abstract

The neutron-proton (n-p) isovector pairing effect on the nuclear moment of inertia has been studied within the framework of the BCS approximation. An analytical expression of the moment of inertia, that explicitly depends upon the n-p pairing, has been established using the Inglis cranking model. The model was first tested numerically for nuclei such as N = Z and whose experimental values of the moment of inertia are known (i.e. such as 16 ≤ Z ≤ 40). It has been shown that the n-p pairing effect is non-negligible and clearly improves the theoretical predictions when compared to those of the pairing between like particles. Secondly, predictions have been established for even-even proton-rich rare-earth nuclei. It has been shown that the n-p pairing effect is non-negligible when N = Z and rapidly decreases with increasing values of (N-Z).

Particle-number projected electric quadrupole moment of even-even proton-rich nuclei in the isovector pairing case

“…The neutrons and the protons are assumed to occupy the same energy levels. The total Hamiltonian of the system is given, in the isovector case, by [7][8][9][10]: …”

“…It is thus projected using the method described in Refs. [7][8][9][10]. The corresponding wave-function is given by:…”

The neutron-proton pairing and the moments of inertia of the rare earth even-even nuclei

“…So far, efforts to balance theoretical and experimental values have not been successful completely . Up to now, the studies about the moments of inertia do not include the np-pairing interaction, except [39][40][41][42].…”

Number projected isovector neutron–proton pairing effect in odd-mass nuclei

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Indeed, the region of N^Z medium mass nuclei is now accessible to experiments and this fact led to renewed interest of theoreticians for this kind of nuclei.…”

“…In the latter, one expects that neutrons and protons occupy the same levels and thus that the np pairing effect would be important. This effect is often treated within the BCS approximation [1][2][3][4][5][6][7][8]. However, it is well known that the major defect of the BCS theory is its violation of the particle-number conservation symmetry, in the pairing between like-particles case [18][19][20][21][22] as well as in the np pairing case.…”