The Effect of the Short-Range Correlations on the Generalized Momentum Distribution in Finite Nuclei

Abstract

The effect of dynamical short-range correlations on the generalized momentum distribution $n(\vec{p},\vec{Q})$ in the case of $Z=N$, $\ell$-closed shell nuclei is investigated by introducing Jastrow-type correlations in the harmonic-oscillator model. First, a low order approximation is considered and applied to the nucleus $^4$He. Compact analytical expressions are derived and numerical results are presented and the effect of center-of-mass corrections is estimated. Next, an approximation is proposed for $n(\vec{p}, \vec{Q})$ of heavier nuclei, that uses the above correlated $n(\vec{p},\vec{Q})$ of $^4$He. Results are presented for the nucleus $^{16}$O. It is found that the effect of short-range correlations is significant for rather large values of the momenta $p$ and/or $Q$ and should be included, along with center of mass corrections for light nuclei, in a reliable evaluation of $n(\vec{p},\vec{Q})$ in the whole domain of $p$ and $Q$.