Empirical neutron star mass formula based on experimental observables

We derive the empirical formulae expressing the mass and gravitational redshift of a neutron star, whose central density is less than threefold the nuclear saturation density, as a function of the neutron-skin thickness or the dipole polarizability of ${}^{208} \mathrm{Pb}$ or ${}^{132} \mathrm{Sn}$, especially focusing on the 8 Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within $\approx 10 \, \%$ errors with our formulae, while the neutron star radius is also expected within a few $\%$ errors by combining the derived formulae. Owing to the resultant empirical formulae, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of ${}^{208} \mathrm{Pb}$ than the dipole polarizability of ${}^{208} \mathrm{Pb}$ or ${}^{132} \mathrm{Sn}$.Comment: Accepted for publication in RP

Coulomb exchange functional with generalized gradient approximation for self-consistent Skyrme Hartree-Fock calculations

We perform the self-consistent Skyrme Hartree-Fock calculation with the Coulomb exchange functional in the form of generalized gradient approximation (GGA). It is found that the Perdew-Burke-Ernzerhof GGA (PBE-GGA) Coulomb exchange functional is able to reproduce the exact-Fock energy for the nuclei in a large region of the nuclear chart with one adjustable parameter. The remaining error of Coulomb exchange energy by the GGA with respect to the exact-Fock energy dominantly comes from the functional-driven error.Comment: 22 pages, 6 figures, 3 table

Theoretical study of Nb \rm{Nb} isotope productions by muon capture reaction on 100Mo {}^{100} \rm{Mo}

The isotope ${}^{99} \rm{Mo}$, the generator of ${}^{99m} \rm{Tc}$ used for diagnostic imaging, is supplied by extracting from fission fragments of highly enriched uranium in reactors. However, a reactor-free production method of ${}^{99} \rm{Mo}$ is searched over the world from the point of view of nuclear proliferation. Recently, ${}^{99} \rm{Mo}$ production through a muon capture reaction was proposed and it was found that about $50 \, \%$ of ${}^{100} \rm{Mo}$ turned into ${}^{99} \rm{Mo}$ through ${}^{100} \rm{Mo} \left( \mu^-, n \right)$ reaction [arXiv:1908.08166]. However, the detailed physical process of the muon capture reaction is not completely understood. We, therefore, study the muon capture reaction of $^{100} \rm{Mo}$ by a theoretical approach. We used the proton-neutron QRPA to calculate the muon capture rate. The muon wave function is calculated with considering the electronic distribution of the atom and the nuclear charge distribution. The particle evaporation process from the daughter nucleus is calculated by a statistical model. From the model calculation, about $38 \, \%$ of ${}^{100} \rm{Mo}$ is converted to ${}^{99} \rm{Mo}$ through the muon capture reaction, which is in a reasonable agreement with the experimental data. It is revealed that negative parity states, especially $1^-$ state, play an important role in ${}^{100} \rm{Mo} \left( \mu^-, n \right) {}^{99} \rm{Nb}$. The feasibility of ${}^{99} \rm{Mo}$ production by the muon capture reaction is also discussed. Isotope production by the muon capture reaction strongly depends on the nuclear structure.Comment: 9 pages, 4 figures, 4 tables, RIKEN-QHP-426, RIKEN-iTHEMS-Report-1