Ground-state properties of rare-earth nuclei in the Nilsson mean-field plus extended-pairing model

Abstract

The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, energies of the first pairing excitation states, moments of inertia for the ground-state band of 152−164 Er, 154−166 Yb, and 156−168 Hf are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. The pairing interaction strengths are determined as a function of the mass number in the isotopic chains. In comparison with the corresponding experimental data, it is shown that pairing interaction is crucial in elucidating the properties of both the ground state and the first pairing excitation state of these rare-earth nuclei. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J = 0, 1, · · · , 12 for even-even 156−162 Yb are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.

Resolution of the spin paradox in the Nilsson model

“…The use of asymptotic quantum numbers for deformed nuclei is just an example of choosing a basis as close as possible to the dynamics of the physical system under study [32,33]. It should be noted that the Nilsson model is still in wide use, 65 years after its introduction [11], either in the framework of Nilsson mean-field plus pairing calculations [34,35], cranking shell model calculations based on the Nilsson potential with pairing correlations [36], or in relation to approximate SU(3) symmetries [37] like the pseudo-SU(3) symmetry [38][39][40][41][42][43][44][45][46][47], the quasi-SU(3) symmetry [48,49], the proxy-SU(3) symmetry [50][51][52][53][54][55][56][57], and the recovery of SU(3) symmetry at superdeformation [58].…”

Effects of high-$j$ orbitals, pairing and deformed neutron shells on upbendings of ground-state bands in neutron-rich even-even isotopes $^{170-184}$Hf

“…Nuclear pairing correlations in 170−182 Hf were investigated by PNC-CSM [22]. Ground-state properties of 156−168 Hf were studied by the Nilsson mean-field plus extended-pairing model [23]. Band-crossing frequencies at high rotational frequencies were investigated in the rare-earth nuclei around hafnium [24].…”

Ground state phase transition in the Nilsson mean-field plus standard pairing model

“…Particularly, the pairing interaction in the nuclear shell model plays a key role to reproduce ground-state properties of nuclei, such as binding energies, two-neutron (proton) separation energies, odd-even effects, and excitation spectra, etc. [18][19][20][21][22][23][24].…”