The full weak charge density distribution of 48Ca from parity violating electron scattering

TL;DR

This paper demonstrates that parity violating elastic electron scattering can be used to determine the full weak charge density distribution of medium mass nuclei like 48Ca in a model independent manner, revealing detailed nuclear structure information.

Contribution

It introduces a Fourier Bessel series expansion method to extract the weak charge density from scattering data, showing feasibility for 48Ca but challenges for heavier nuclei.

Findings

Feasible to determine about six Fourier Bessel coefficients of 48Ca's weak charge density.

Full weak density measurement is difficult for heavier nuclei like 208Pb.

Provides detailed nuclear structure information such as size, surface thickness, and shell oscillations.

Abstract

Background: The ground state neutron density of a medium mass nucleus contains fundamental nuclear structure information and is at present relatively poorly known. Purpose: We explore if parity violating elastic electron scattering can provide a feasible and model independent way to determine not just the neutron radius but the full radial shape of the neutron density $\rho_n(r)$ and the weak charge density $\rho_W(r)$ of a nucleus. Methods: We expand the weak charge density of $^{48}$Ca in a model independent Fourier Bessel series and calculate the statistical errors in the individual coefficients that might be obtainable in a model parity violating electron scattering experiment. Results: We find that it is feasible to determine roughly six Fourier Bessel coefficients of the weak charge density of 48Ca within a reasonable amount of beam time. However, it would likely be much harder to determine the full weak density of a significantly heavier nucleus such as 208Pb. Conclusions: Parity violating elastic electron scattering can determine the full weak charge density of a medium mass nucleus in a model independent way. This weak density contains fundamental information on the size, surface thickness, shell oscillations, and saturation density of the neutron distribution in a nucleus. The measured $\rho_W(r)$, combined with the previously known charge density $\rho_{ch}(r)$, will literally provide a detailed textbook picture of where the neutrons and protons are located in an atomic nucleus.