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

摘要

The main features of the convolution model which, in the region oftwo-nucleon (2N) and three-nucleon (3N) short-range correlations (SRC),describes the one-nucleon momentum distribution n(k_1) and the spectralfunction P(k_1,E) in terms of a convolution integral involving the relativen_{rel}(k_{rel}) and the center-of-mass n_{c.m.}(K_{c.m.}) momentumdistributions of a nucleon-nucleon pair, are illustrated in detail. It isstressed that the model, which stems from the universal property offactorization exhibited by the nuclear wave function at short inter-nucleondistances, 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 asevere constraint on the values of k_{rel} and K_{c.m.} that appear in theconvolution integral. Using ab-initio relative and c.m. momentum distributionsfor ^3He, the validity of the convolution model is investigated by comparingthe model spectral function and momentum distributions with the ones resultingfrom ab-initio calculations performed with realistic local NN interaction ofthe Argonne family. It is shown that when the constraint on the value ofk_{rel} and K_{c.m.} are correctly taken into account and only 2N SRC are takeninto account, the convolution model is in good agreement with the ab-initiospectral function in the region of the peak exhibited by the latter, whereasfar from the peak, particularly at high values of the removal energy, the modelspectral function can be qualitatively reconciled with the ab-initio spectralfunction only by considering the effects of 3N SRC. As for the nucleon momentumdistribution, the effects of 3N SRC appears to be very small.