The power of two: Assessing the impact of a second measurement of the weak-charge form factor of 208Pb

Abstract

[Background] Besides its intrinsic value as a fundamental nuclear-structure observable, the weak-charge density of 208Pb - a quantity that is closely related to its neutron distribution - is of fundamental importance in constraining the equation of state of neutron-rich matter. [Purpose] To assess the impact that a second electroweak measurement of the weak-charge form factor of 208Pb may have on the determination of its overall weak-charge density. [Methods] Using the two putative experimental values of the form factor, together with a simple implementation of Bayes' theorem, we calibrate a theoretically sound - yet surprisingly little known - symmetrized Fermi function, that is characterized by a density and form factor that are both known exactly in closed form. [Results] Using the charge form factor of 208Pb as a proxy for its weak-charge form factor, we demonstrate that using only two experimental points to calibrate the symmetrized Fermi function is sufficient to accurately reproduce the experimental charge form factor over a significant range of momentum transfers. [Conclusions] It is demonstrated that a second measurement of the weak-charge form factor of 208Pb supplemented by a robust theoretical input in the form of the symmetrized Fermi function, would place significant constraints on the neutron distribution of 208Pb and, ultimately, on the equation of state of neutron-rich matter.

14 pages, 3 tables, and 6 figures

References in corpus (12)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Nuclear symmetry energy probed by neutron skin thickness of nuclei
• Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment
• Astrophysical Measurement of the Equation of State of Neutron Star Matter
• Relativistic effective interaction for nuclei, giant resonances, and neutron stars
• Building relativistic mean field models for finite nuclei and neutron stars
• Reconstructing the neutron-star equation of state with gravitational-wave detectors from a realistic population of inspiralling binary neutron stars
• Improved Mass and Radius Constraints for Quiescent Neutron Stars in Omega Cen and NGC 6397
• Rejecting proposed dense-matter equations of state with quiescent low-mass X-ray binaries
• Isospin Diffusion in Heavy-Ion Collisions and the Neutron Skin Thickness of Lead
• Hindrance in the fusion of ${}^{48}$Ca+${}^{48}$Ca

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