Parity Violating Electron Scattering Measurements of Neutron Densities

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.

10 pages, 7 fig., minor changes, J. Phys. G in press

References in corpus (4)

• Shapiro delay measurement of a two solar mass neutron star
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Neutron-Rich Nuclei in Heaven and Earth
• Dispelling the curse of the neutron skin in atomic parity violation

Cited by in corpus (13)

• Constraints on the symmetry energy and neutron skins from experiments and theory
• Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering
• Electric dipole polarizability and the neutron skin
• Weak charge form factor and radius of 208Pb through parity violation in electron scattering
• Electric Dipole Polarizability in ${}^{208}$Pb: insights from the Droplet Model
• Density dependence of the symmetry energy from neutron skin thickness in finite nuclei
• Electroweak Measurements of Neutron Densities in CREX and PREX at JLab, USA
• Generic Constraints on the Relativistic Mean-Field and Skyrme-Hartree-Fock Models from the Pure Neutron Matter Equation of State
• Elastic and quasi-elastic electron scattering off nuclei with neutron excess
• Parity violating elastic electron scattering from 27Al and the Qweak measurement
• The full weak charge density distribution of 48Ca from parity violating electron scattering
• QED corrections to the parity-violating asymmetry in high-energy electron-nucleus collisions
• Neutron density distribution and neutron skin thickness of ${}^{208}$Pb