We investigate the effect of a strong magnetic field on the structure of neutron stars in a model with perturbative $f(R)$ gravity. The effect of an interior strong magnetic field of about $10^{17 sim 18}$ G on the equation of state is derived in the
context of a quantum hadrodynamics (QHD) model. We solve the modified spherically symmetric hydrostatic equilibrium equations derived for a gravity model with $f(R)=R+alpha R^2$. Effects of both the finite magnetic field and the modified gravity are detailed for various values of the magnetic field and the perturbation parameter $alpha$ along with a discussion of their physical implications. We show that there exists a parameter space of the modified gravity and the magnetic field strength, in which even a soft equation of state can accommodate a large ($> 2$ M$_odot$) maximum neutron star mass through the modified mass-radius relation.
The nucleon form factors in free space are usually thought to be modified when a nucleon is bound in a nucleus or immersed in a nuclear medium. We investigate effects of the density-dependent axial and weak-vector form factors on the electro-neutrino
($ u_e$) and anti-electro-neutrino $({bar u_e})$ reactions via neutral current (NC) for a nucleon in nuclear medium or $^{12}$C. For the density-dependent form factors, we exploit the quark-meson-coupling (QMC) model, and apply them to the $ u_e$ and ${bar u_e}$ induced reactions by NC. About 12% decrease of the total cross section by $ u_e$ reaction on the nucleon is obtained at normal density, $rho = rho_0 sim 0.15 {fm}^{-3} $, as well as about 18% reduction of total ${ u}_e$ cross section on $^{12}$C, by the modification of the weak form factors of the bound nucleon. However, similarly to the charged current reaction, effects of the nucleon property change in the ${bar u}_e$ reaction reduce significantly the cross sections about 30% for the nucleon in matter and $^{12}$C cases. Such a large asymmetry in the ${bar u}_e$ cross sections is addressed to originate from the different helicities of ${bar u}_e$ and ${ u}_e$.
We study the effect of the density-dependent axial and vector form factors on the electro-neutrino ($ u_e$) and anti-neutrino $({bar u}_e)$ reactions for a nucleon in nuclear matter or in $^{12}$C. The nucleon form factors in free space are presumed
to be modified for a bound nucleon in a nuclear medium. We adopt the density-dependent form factors calculated by the quark-meson coupling (QMC) model, and apply them to the $ u_e$ and ${bar u}_e$ induced reactions with the initial energy $E = $ 8 $sim$ 80 MeV. We find that the total ${ u}_e$ cross sections on $^{12}$C as well as a nucleon in nuclear matter are reduced by about 5% at the nuclear saturation density, $rho_0$. This reduction is caused by the modification of the nucleon structure in matter. Although the density effect for both cases is relatively small, it is comparable with the effect of Coulomb distortion on the outgoing lepton in the $ u$-reaction. In contrast, the density effect on the ${bar u}_e$ reaction reduces the cross section significantly in both nuclear matter and $^{12}$C cases, and the amount maximally becomes of about 35% around $rho_0$. Such large asymmetry in the $ u_e$ and ${bar u}_e$ cross sections, which seems to be nearly independent of the target, is originated from the difference in the helicities of ${bar u}_e$ and ${ u}_e$. It is expected that the asymmetry influences the r-process and also the neutrino-process nucleosynthesis in core-collapse supernovae.
Strange quark contributions to the neutral current reaction in the neutrino scattering are investigated on the nucleon level and extended to the $^{12}$C target nucleus through the neutrino-induced knocked-out nucleon process in the quasi-elastic reg
ion within the framework of a relativistic single particle model. The incident energy range between 500 MeV and 1.0 GeV is used for the neutrino(antineutrino) scattering. Effects of the final state interaction for the knocked-out nucleon are included by a relativistic optical potential. We found that the sensitivity of the strange quark contents could be salient on the asymmetry between neutrino and antineutrino scattering cross sections. In specific, $A ( u ({bar u}), u^{} ({bar u}^{}) N)$ reaction is shown to be very sensitive test in the searches of the strangeness.
