Mass dependence and isospin dependence of short-range correlated pairs

The target-mass number dependence of nucleon-nucleon pairs with short-range correlations is explored in a physically transparent geometrical model within a zero-range approximation. The observed $A$ dependence of 2-nucleon ejection cross sections in $(e,e^{\prime })$ reactions is found to reflect the mass dependence of nuclear density distributions. A parametrization of this $A$ dependence is given. The $A$ dependence of proton-proton vs proton-neutron pairs relative to ${}^{12}\mathrm{C}$ is also analyzed in this model. It can be understood using simple combinatorics without any additional isospin dependence.

Figure 1

Average density per nucleon $\langle \rho \rangle$ of Eq. (2) as a function of mass number $A$ (solid curve). The points are taken from Table 1 in Ref. [5]. For a shape comparison they were approximately scaled to the values of $\langle \rho \rangle$.

Figure 2

Number of $pp$ src pairs relative to ${}^{12}\mathrm{C}$. Solid line: $A$ times average density $A\langle \rho \rangle$ of Eq. (3) as a function of mass number $A$. Dashed line: mass dependence fitted to results from Ref. [5]. Both curves are normalized to 1 for ${}^{12}\mathrm{C}$. ZRA points (triangles) and data from Ref. [1]. Open circles: simple pair count (see text).

Figure 3

Same as Fig. 2 for $pn$ pairs.