# A microscopic nucleon spectral function for finite nuclei featuring two- and trhee-nucleon short-range correlations: I. The model vs. ab-initio calculations for the three-nucleon systems

## TL;DR

This paper develops a convolution model for the nucleon spectral function in finite nuclei, incorporating two- and three-nucleon short-range correlations, and validates it against ab-initio calculations for three-nucleon systems.

## Contribution

It introduces a convolution model based on the factorization property of nuclear wave functions, accurately describing spectral functions and momentum distributions in the presence of SRCs, validated against ab-initio results.

## Key findings

- The convolution model agrees well with ab-initio spectral functions near the peak.
- Two-nucleon SRC dominate the spectral function at high removal energies.
- Three-nucleon SRC effects are small on the momentum distribution.

## Abstract

The main features of the convolution model which, in the region of two-nucleon (2N) and three-nucleon (3N) short-range correlations (SRC), describes the one-nucleon momentum distribution n(k_1) and the spectral function P(k_1,E) in terms of a convolution integral involving the relative n_{rel}(k_{rel}) and the center-of-mass n_{c.m.}(K_{c.m.}) momentum distributions of a nucleon-nucleon pair, are illustrated in detail. It is stressed that the model, which stems from the universal property of factorization exhibited by the nuclear wave function at short inter-nucleon distances, is only applicable in a well-defined region of k_{rel} and K_{c.m.}; it is shown, in particular, that the requirement of factorization introduces a severe constraint on the values of k_{rel} and K_{c.m.} that appear in the convolution integral. Using ab-initio relative and c.m. momentum distributions for ^3He, the validity of the convolution model is investigated by comparing the model spectral function and momentum distributions with the ones resulting from ab-initio calculations performed with realistic local NN interaction of the Argonne family. It is shown that when the constraint on the value of k_{rel} and K_{c.m.} are correctly taken into account and only 2N SRC are taken into account, the convolution model is in good agreement with the ab-initio spectral function in the region of the peak exhibited by the latter, whereas far from the peak, particularly at high values of the removal energy, the model spectral function can be qualitatively reconciled with the ab-initio spectral function only by considering the effects of 3N SRC. As for the nucleon momentum distribution, the effects of 3N SRC appears to be very small.