Influence of monopole pairing on the energies of single-nucleon states in the problem of superconducting pairing correla
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EI Theory
Influence of Monopole Pairing on the Energies of Single-Nucleon States in the Problem of Superconducting Pairing Correlations V. A. Kuz’min1)* and T. V. Tetereva2)** Received September 23, 2011
Abstract—A correlation function, the chemical potential, coefficients in a special Bogolyubov transformation, and single-quasiparticle energies were calculated with allowance for the effect of the monopole-pairing potential on the energies of single-particle nucleon states in the mean nuclear field. DOI: 10.1134/S1063778812040096
1. INTRODUCTION The hypothesis that pairing correlations of the superconducting type exist in nuclei was formulated more than 50 ago [1]. By analogy with microscopic superconductivity theory [2], it was assumed that, between nucleons moving in the mean nuclear field, there is a weak attraction under the effect of which two nucleons may be bound into a pair of zero total angular momentum. Such pairs behave as bosons and may form a condensate that possesses superfluid properties. The method usually used to describe fermion systems in which there is a weak attraction relies on a canonical transformation from nucleon creation and annihilation operators to quasiparticle creation and annihilation operators [3, 4]. The state in which there are no quasiparticles (quasiparticle vacuum) is treated as an approximate ground state of the system being considered, which is assumed to consist of an even number of nucleons belonging to a single type (protons or neutrons) [5]. The accuracy of the canonical-transformation method was explored in a large number of studies. As a rule, the attention in them was given primarily to the fact that the quasiparticle vacuum, which is a condensate of nucleon pairs, is not an exact particlenumber eigenstate. Accordingly, methods for projecting wave functions obtained by the canonicaltransformation method onto particle-number eigenfunctions were developed, and the accuracy of these 1)
Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. 2) Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia. * E-mail: [email protected] ** E-mail: [email protected]
methods was studied (see, for example, [5–7] and references therein). However, the fact that yet another approximation was made in solving the equations of the canonicaltransformation method was frequently overlooked. Specifically, the effect of the interaction leading to pairing correlations of the superconducting type on the energies of single-quasiparticle states was not taken into consideration. In other words, terms of the G s vs4 type in the expression for the quasiparticlevacuum energy [see Eq. (3) below] were disregarded in order to simplify respective calculations and to obtain solutions in a closed form. This was sometimes explained in terms of a transition to approximate equations of the canonical-transformation method or in terms of a renormalization of energies of singlenucleon states [5]. disregard of terms be The 4 longing to the G s vs type is physical
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