Bayesian Inference of the Landau Parameter $G_0^{\mathrm{\prime }}$ from Joint Gamow-Teller Measurements

The Landau-Migdal parameter $G_0^{\mathrm{\prime }}$ characterizes the main part of the spin-isospin dependent nucleon-nucleon interaction. Consequently, the $G_0^{\mathrm{\prime }}$ is closely related to the Gamow-Teller resonance (GTR), the beta and double-beta decay rates of finite nuclei, the response of hot and dense nucleonic matter that modifies the neutrino-nucleon absorption rates in core-collapse supernovae (CCSNe) and binary neutron star (BNS) mergers, and finally the critical density for pion condensation in neutron stars. In this letter, for the first time, we report the $G_0^{\mathrm{\prime }}$ with quantified uncertainty in the framework of Bayesian inference, using a self-consistent standard Skyrme Random Phase Approximation (RPA) model and joint constraints from experimental GTR measurements on ${}^{208}\mathrm{P}\mathrm{b}$, ${}^{132}\mathrm{S}\mathrm{n}$, ${}^{90}\mathrm{Z}\mathrm{r}$. Our extracted $G_0^{\mathrm{\prime }}$ is $0.48\pm 0.034$, which is close to the prediction of a few existing Skyrme models that consider spin-isospin observables but smaller than the traditional ones extracted from pion-exchange models. We hint to possible reasons for this deviation, like the value of the nucleon effective mass $\frac{m^{\ast }}{m}$. The $G_0^{\mathrm{\prime }}$ values extracted in this work may guide the construction of new energy density functionals that aims to self-consistently describe the dense matter properties in the spin-isospin channel.