Theoretical Calculation of the IBM1 Parameters and Band Crossing in Even Cerium Isotopes
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CLEI Theory
Theoretical Calculation of the IBM1 Parameters and Band Crossing in Even Cerium Isotopes A. D. Efimov1), 2)* Received April 14, 2020; revised April 14, 2020; accepted April 14, 2020
Abstract—An extended microscopic version of the interacting-boson model is developed. The properties of yrast-band states in even cerium isotopes up to the spin–parity of I π = 18+ are calculated on the basis of this model. These spin values include those at which band crossing occurs. The model parameters are calculated on the basis of employing an average spherical potential and residual multipole forces. An extension of the model is accomplished via taking into account high-spin quasiparticle pairs, whereby a satisfactory description of energies and B(E2) values was obtained without introducing effective charges. The present investigation is a continuation of a similar analysis of the properties of low-lying collective states in even xenon and barium isotopes. DOI: 10.1134/S1063778820050105
1. INTRODUCTION About seventy years ago, the geometric Bohr– Mottelson model employing five quadrupole-deformation variables [1] came to play a significant role in describing low-energy quadrupole collectivity. Further developments involved taking into account nonaxiality in accordance with Davydov’s model [2, 3]. The calculation of the deformation energy in terms of Strutinsky’s shell correction [4] and the evaluation of the moments of inertia according to the Inglis method [5] gave impetus to microscopically validating [6] these model versions, first viewed as a phenomenological means. The next step in describing collective states consisted in the bosonic representation of pair fermion operators. The articles of Beliaev and Zelevinsky [7], who imposed the condition of equality of fermionpair commutators to the respective boson series were among those that pioneered studies along these lines. A series of studies performed by Sorensen [8] and aimed at constructing a bosonic representation of fermion operators and at obtaining thereby an approximate solution to the multipaticle nuclear problem relied on this idea. However, the convergence of the expansion of fermion operators in a series in terms of boson ones proved to be slow. The next step was associated with the studies of Kishimoto 1)
Admiral Makarov State University of Maritime and Inland Shipping, St. Petersburg, Russia. 2) Ioffe Physical-Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia. * E-mail: [email protected]
and Tamura [9–12]. Their studies resulted in formulating a number of requirements for the theory that are necessary for correctly describing the states being considered. First of all, this is a mapping of precisely phonons to bosons rather than of quasiparticle pairs; furthermore, it is necessary to take into account the coupling of collective and noncollective excitation modes. Here, one means by collective modes the lowest quadrupole D modes or phonons and by noncollective modes all other BJ modes of angular momentum J, including giant reso
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