Stylized features of single-nucleon momentum distributions Maarten Vanhalst, ∗ Wim Cosyn, † and Jan Ryckebusch ‡ Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium (Dated: September 10, 2014) Background: Nuclear short-range correlations (SRC) typically manifest themselves in the tail parts of the single- nucleon momentum distributions. Purpose: To develop an approximate flexible method for computing the single-nucleon momentum distributions throughout the whole mass table, thereby including the majority of the effects of SRC. To use this method to study the mass and isospin dependence of SRC. Method: The framework adopted in this work, corrects mean-field models for central, spin-isospin and tensor correlations by shifting the complexity induced by the SRC from the wave functions to the operators. It is argued that the expansion of these modified operators can be truncated to a low order. Results: The proposed model can generate the SRC-related high-momentum tail of the single-nucleon momentum distribution. These are dominated by correlations operating on mean-field pairs with vanishing relative radial and angular-momentum quantum numbers. In asymmetric nuclei, the correlations make the average kinetic energy for the minority nucleons larger than for the majority nucleons. Conclusions: The proposed method explains the dominant role of proton-neutron pairs in generating the SRC and accounts for the magnitude and mass dependence of SRC as probed in inclusive electron scattering. It also provides predictions for the ratio of the amount of correlated proton-proton to proton-neutron pairs which are in line with the observations. PACS numbers: 25.30.Fj, 24.10.i, 13.60.Hb, 21.30.x I. INTRODUCTION One of the most elusive properties of nuclei is that nu- cleons forcefully repel each other as they get close. Since the early days of nuclear physics, it has been recognized that this repulsion is an important ingredient of the dy- namics of nuclei, and induces pair, triple, ... correlations in the wave functions for atomic nuclei. This calls for a more sophisticated approach to the quantum mechanical structure of nuclei and the nuclear response to external probes. Momentum distributions contain all the information about the momentum decomposition of the nuclear mo- tion. The computation of single-nucleon momentum dis- tributions has reached a very high level of sophistication. Ab-initio methods with variational wave functions can be used to compute the momentum distributions for nu- clei up to A = 12 [1–5]. Also for atomic mass number infinity, or nuclear matter, exact calculations with realis- tic nucleon-nucleon interactions can be performed [6, 7]. Momentum distributions for mid-heavy and heavy nu- clei cannot be computed with exact methods to date. Advanced approximate schemes like cluster expansions [5, 8, 9] and correlated basis function theory [10, 11] are able to provide momentum distributions for heavier nu- clei. * Maarten.Vanhalst@UGent.be † Wim.Cosyn@UGent.be ‡ Jan.Ryckebusch@UGent.be We wish to develop an approximate practical way of computing the short-range contributions to momen- tum distributions for stable nuclei over the entire mass range. Thereby, we start from wave functions that can be written as correlation operators acting on a single Slater determinant. The computation of expectation val- ues of one-body and two-body operators for those wave functions involves multi-body effective operators and a truncation scheme is in order. We propose a low-order correlation operator approximation, dubbed LCA, that truncates the modified correlated operator corresponding with an one-body operator to the level of two-body opera- tors. For the computation of the single-nucleon momen- tum distribution, the LCA model developed in Sec. II, preserves some fundamental properties like the normal- ization conditions. In Sec. III, we illustrate that the LCA method is a prac- tical approximate way of computing the effect of SRC on single-nucleon momentum distributions for nuclei over the entire mass range. It will be shown that after in- clusion of central, spin-isospin and tensor correlations, it can capture some stylized features of nuclear momentum distributions. Due to its wide range of applicability, the LCA framework allows one to study the mass and isospin dependence of SRC and to arrive at a comprehensive pic- ture of the impact of SRC throughout the mass table. To assess how realistic the LCA method is, we compare its one-body momentum distributions for 4 He, 9 Be and 12 C with those from ab-initio calculations. Of course, the LCA approximate method is only jus- tified if the resulting physical quantities like radii and kinetic energies are in reasonable agreement with data arXiv:1405.3814v2 [nucl-th] 5 Sep 2014