Parity Violating Electron Scattering Measurements of Neutron Densities

TL;DR

This paper evaluates the statistical errors in measuring neutron densities via parity violating electron scattering across various nuclei, highlighting the advantages of smaller and neutron-rich nuclei like calcium-48 for precise measurements.

Contribution

It provides detailed error estimates for neutron radius and surface thickness measurements in multiple nuclei, emphasizing the potential of calcium-48 for future experiments.

Findings

Smaller nuclei yield more accurate neutron density measurements.

Neutron-rich isotopes have larger asymmetries, facilitating easier detection.

Calcium-48 offers a promising target for neutron density studies.

Abstract

Parity violating electron scattering allows model independent measurements of neutron densities that are free from most strong interaction uncertainties. In this paper we present statistical error estimates for a variety of experiments. The neutron radius $R_n$ can be measured in several nuclei, as long as the nuclear excited states are not too low in energy. We present error estimates for $R_n$ measurements in $^{40}$Ca, $^{48}$Ca, $^{112}$Sn, $^{120}$Sn, $^{124}$Sn, and $^{208}$Pb. In general, we find that the smaller the nucleus, the easier the measurement. This is because smaller nuclei can be measured at higher momentum transfers where the parity violating asymmetry $A_{pv}$ is larger. Also in general, the more neutron rich the isotope, the easier the measurement, because neutron rich isotopes have larger weak charges and larger $A_{pv}$. Measuring $R_n$ in $^{48}$Ca appears very promising because it has a higher figure of merit than $^{208}$Pb. In addition, $R_n(^{48}$Ca) may be more easily related to two nucleon and three nucleon interactions, including very interesting three neutron forces, than $R_n(^{208}$Pb). After measuring $R_n$, one can constrain the surface thickness of the neutron density $a_n$ with a second measurement at somewhat higher momentum transfers. We present statistical error estimates for measuring $a_n$ in $^{48}$Ca, $^{120}$Sn, and $^{208}$Pb. Again, we find that $a_n$ is easier to measure in smaller nuclei.