Forging the Link between Nuclear Reactions and Nuclear Structure

A comprehensive description of all single-particle properties associated with the nucleus ${}^{40}\mathrm{Ca}$ is generated by employing a nonlocal dispersive optical potential capable of simultaneously reproducing all relevant data above and below the Fermi energy. The introduction of nonlocality in the absorptive potentials yields equivalent elastic differential cross sections as compared to local versions but changes the absorption profile as a function of angular momentum suggesting important consequences for the analysis of nuclear reactions. Below the Fermi energy, nonlocality is essential to allow for an accurate representation of particle number and the nuclear charge density. Spectral properties implied by ($e$, $e^{\prime }p$) and ($p$, $2p$) reactions are correctly incorporated, including the energy distribution of about 10% high-momentum nucleons, as experimentally determined by data from Jefferson Lab. These high-momentum nucleons provide a substantial contribution to the energy of the ground state, indicating a residual attractive contribution from higher-body interactions for ${}^{40}\mathrm{Ca}$ of about $0.64\mathrm{MeV}/\mathrm{A}$.

Figure 1

Calculated and experimental elastic-scattering angular distributions of the differential cross section $d\sigma /d\mathrm{\Omega }$. Panels shows results for $n+{}^{40}\mathrm{Ca}$ and $p+{}^{40}\mathrm{Ca}$. Data for each energy are offset for clarity with the lowest energy at the bottom and highest at the top of each frame. References to the data are given in Ref. [15].

Figure 2

Total reaction cross sections are displayed as a function of proton energy while both total and reaction cross sections are shown for neutrons.

Figure 3

Spectral strength for protons in the $\ell j$ orbits which are fully occupied in the independent-particle model as well as the $f_{7/2}$ strength associated with the first empty orbit in this description. The arrows indicate the experimental location of the valence states as well as the peak energies for the distributions of deeply bound ones.

Figure 4

Comparison of experimental charge density [22] (thick line) with the DOM fit (thin line).

Figure 5

Spectral strength as a function of missing energy for different missing momenta as indicated in the figure. The data are the average of the ${}^{27}\mathrm{Al}$ and ${}^{56}\mathrm{Fe}$ measurements from [24].