Universality of many-body two-nucleon momentum distributions: Correlated nucleon spectral function of complex nuclei

摘要

Background: The nuclear spectral function is a fundamental quantity that describes the mean-field and shortrange correlation dynamics of nucleons embedded in the nuclear medium; its knowledge is a prerequisite for the interpretation of various electroweak scattering processes off nuclear targets aimed at providing fundamental information on strong and weak interactions.Whereas in the case of the three-nucleon and, partly, the four-nucleon systems, the spectral function can be calculated ab initio within a nonrelativistic many-body Schroedinger approach, in the case of complex nuclei only models of the correlated, high-momentum part of the spectral function are available so far. Purpose: The purpose of this paper is to present a new approach such that the spectral function for a specific nucleus can be obtained from a reliablemany-body calculation based upon realistic nucleon-nucleon interactions, thus avoiding approximations leading to adjustable parameters. Methods: The expectation value of the nuclear many-body Hamiltonian, containing realistic nucleon-nucleon interaction of the Argonne family, is evaluated variationally by a normalization- conserving linked-cluster expansion and the resulting many-body correlated wave functions are used to calculate the one-nucleon and the two-nucleon momentum distributions; by analyzing the high-momentum behavior of the latter, the spectral function can be expressed in terms of a transparent convolution formula involving the relative and center-of-mass (c.m.) momentum distributions in specific regions of removal energy E and momentum k. Results: It is found that as a consequence of the factorization of the many-body wave functions at short internucleon separations, the high-momentum behavior of the two-nucleon momentum distributions in A = 3,4,12,16,40 nuclei factorizes, at proper values of the relative and c.m. momenta, into the c.m. and relative momentum distributions, with the latter exhibiting a universal A-independent character. By exploiting the factorization property, it is found that the correlated part of the spectral function can be expressed in terms of a convolution formula depending upon the many-body relative and c.m. momentum distributions of a nucleon pair. Conclusions: The obtained convolution spectral function of the three-nucleon systems, featuring both two-and three-nucleon short-range correlations, perfectly agrees in a wide range of momentum and removal energy with the ab initio spectral function, whereas in the case of complex nuclei the integral of the obtained spectral functions (the momentum sum rule) reproduces with high accuracy the high-momentum part of the one-nucleon momentum distribution, obtained independently from the Fourier transform of the nondiagonal one-body density matrix. Thus, the convolution spectral function we have obtained appears to indeed be a realistic microscopic, parameter-free quantity governed by the features of the underlying two-nucleon interactions.