Deformed-quasiparticle basis for calculating potential energy surfaces and nuclear spectra

Abstract

The Nilsson model is combined with the Hill-Wheeler definition of nuclear deformations and with the stationarity condition of Yariv et al. to calculate a new deformed basis. The wave functions of this basis are the same for neutrons and for protons, and for all mass numbers. The energy levels depend on $Z$, $A$ via an isospin-$A$-dependent scaling factor. This basis is combined with an improved theory of pairing to calculate a new deformed-quasiparticle basis. It is shown that without any adjustment of the model parameters from one nucleus to another, this basis leads to reasonable potential energy surgaces for many even-even nuclei (Mg,Zr,Sm,Er,Os,Hg), and reasonable low energy spectra of $_{12}^{24}\mathrm{Mg}$, $_{40}^{102}\mathrm{Zr}$, and $_{68}^{168}\mathrm{Er}$. The Strutinsky method is used to calculate the potential energy surfaces. A modified Kumar-Baranger method is used to calculate the moments of inertia and the mass parameters, and to solve the collective Schr\"odinger equation.NUCLEAR STRUCTURE $^{148,150,152,154}\mathrm{Sm}$, $^{186,188,190,192,194}\mathrm{Os}$, $^{184,186,188,190}\mathrm{Hg}$; calculated deformation energy curves. $^{24}\mathrm{Mg}$, $^{102}\mathrm{Zr}$, $^{168}\mathrm{Er}$; calculated deformation energy curves and collective spectra. Modified Nilsson method. Modified BCS method. Combined Strutinsky method with Kumar-Baranger method.