Effective pairing interaction for the Argonne nucleon-nucleon potential v 18
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CLEI Theory
Effective Pairing Interaction for the Argonne Nucleon–Nucleon Potential v18 S. S. Pankratov1) , M. Baldo2) , U. Lombardo2), 3) , E. E. Saperstein1)* , and M. V. Zverev1) Received May 17, 2006
Abstract—The effective pairing interaction corresponding to the Argonne nucleon–nucleon potential v18 is found within the local potential approximation for several values of the boundary energy E0 that specifies the model subspace S0 . A detailed comparison with the analogous effective interaction calculated previously for the Paris nucleon–nucleon potential is performed. It is shown that the effective interactions obtained for the two different nucleon–nucleon potentials at the same value of E0 are very close to each other. In the case of the Paris potential, a very wide subspace S complementary to S0 was required in calculating the effective interaction (the corresponding cutoff momentum being kmax = 160−180 fm−1 ), whereas a much narrower subspace S corresponding to kmax = 10−12 fm−1 could be used in the case of the Argonne potential. PACS numbers: 21.30.-x; 21.60.-n; 21.65.+f DOI: 10.1134/S1063778807040060
1. INTRODUCTION In recent years, some advances have been made in the microscopic theory of pairing in finite nuclei. In this connection, we would like to mention studies of the Milan group [1, 2], where the equation for the pairing gap within the Bardeen–Cooper–Schrieffer (BCS) approach implemented for the case of the Argonne nucleon–nucleon interaction v14 , which is quite realistic, was solved directly for a specific nucleus 120 Sn by using a basis of states whose energies are bounded by a fixed energy Emax . The application of this direct method for solving the nuclear-pairing problem is complicated by a slow convergence of the sums over intermediate states λ in the equation for the gap ∆. These sums are analogs of the integral with respect to momenta in the equation for the gap in infinite nuclear matter, a slow convergence of this integral being due to a short-range character of nucleon–nucleon forces. Even the use in [2] of an Emax value as large as 800 MeV does not seem sufficient. This is suggested by the calculations for infinite matter with the v14 interaction and the effective mass of m∗ = 0.7m, which were used in [2]. Moreover, the analysis performed in [3] revealed that convergence in 1)
Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia. 2) Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Catania, Italy. 3) Dipartimento di Fisica, Universita` di Catania, Via S. Sofia 64, I-95123 Catania, Italy. * E-mail: [email protected]
the equation for ∆ is slower in a finite system than in its infinite counterpart. Simultaneously, a two-step method for solving the problem of pairing in finite systems was developed in a series of studies that were generalized in the review article of Baldo et al. [4]. In this method, which is based on the effective-interaction concept, the full Hilbert space S of the problem is broken down into a model subspace S0 and the complementary subspace
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