Longitudinal collective modes in relativistic asymmetric magnetized nuclear matter within the covariant Vlasov approach

Abstract

The neutron-proton-electron (npe) matter under strong magnetic field is studied in the context of the covariant Vlasov approach. A covariant relativistic approach based on the Vlasov equation is applied to the study of infinite asymmetric magnetized nuclear matter. We use several relativistic mean-field nuclear models with non-linear terms. The dispersion relations for the longitudinal modes are obtained, and the isovector and isoscalar collective modes are determined in a wide range of densities as a function of the isospin asymmetry, momentum transfer, and magnetic field. A strong magnetic field gives rise to the appearance of low-lying isovector modes that propagate in nuclear matter, not present in non-magnetized matter. Neutron-like modes are essentially not affected by the presence of a strong magnetic field. In the presence of a strong magnetic field, Landau quantization modifies the proton-like collective modes, leading to the emergence of new branches associated with distinct Landau levels. These new modes can propagate even at high densities and exhibit isoscalar or isovector character.

Figures (5)

• Figure 1: Symmetry energy and energy density (top panels), symmetry energy slope and beta-equilibrium pressure.
• Figure 2: (Color online) Nuclear collective modes $\omega$(MeV) as function of the baryon density for NL3 model (top quartets), NL3$\omega\rho$ (bottom left quartet) and FSU (bottom right quartet), for $y_p=0.5$ (top panels in each quartet, a) and b)) $y_p=0.1$ (bottom panels in each quartet, c) and d)), for $q=10$MeV (left panels in each quartet, a) and c)), and $q=100$MeV (right panels in each quartet, b) and d)). For $B=0$ G (black color for isovector mode, orange color isoscalar mode), $10^{17}$ G (red color for isovector mode and gray for isoscalar mode), $5\times10^{17}$ G (green color for isovector mode and dark green for isoscalar mode), $10^{18}$ G (blue color for isovector mode and cyan color for isoscalar mode). The results are for np matter and do not include the Coulomb interaction.
• Figure 3: (Color online) Nuclear collective modes, $\omega$ (MeV), as a function of density for NL3, NL3$\omega\rho$ and FSU models, with proton fraction $y_p = 0.4$ and for a momentum transfer of $q = 100$ MeV, and magnetic field strengths $B = 0$ and $5 \times 10^{17}$ G. The middle panels of each column show the nuclear collective modes $\omega$ divided by $\omega_{0n}=q V_{F_n}$ versus density, and the bottom panels the amplitude ratio $\delta \rho_p/\delta\rho_n$ as a function of the baryon density. For $B = 0$ G, isoscalar and isovector modes are shown in black and orange, respectively. For $B = 5 \times 10^{17}$ G, the isoscalar mode is shown in green and the isovector mode in red. Results correspond to neutron-proton (np) matter. For reference we show also the nucleons Fermi modes $\omega_{0i}=qV_{Fi}$$\omega^{n}_{0p}=q \frac{P^p_{F}(n)}{E^p_{F}(n)}$are also indicated by gray lines.
• Figure 4: (Color online) Nuclear collective modes $\omega$(MeV) as function of the density for NL3 model (top quartets), NL3$\omega\rho$ (bottom left quartet) and FSU (bottom right quartet), for $y_p=0.5$ (top panels in each quartet, a) and b)) $y_p=0.1$ (bottom panels in each quartet, c) and d)), for $q=10$MeV (left panels in each quartet, a) and c)), and $q=100$MeV (right panels in each quartet, b) and d)). For $B=0$ G (black color for isovector mode, orange color isoscalar mode), $10^{17}$ G (red color for isovector mode and gray for isoscalar mode), $5\times10^{17}$ G (green color for isovector mode and dark green for isoscalar mode), $10^{18}$ G (blue color for isovector mode and cyan color for isoscalar mode). The results are for np matter and including Coulomb effect.
• Figure 5: (Color online) Collective modes, $\omega$ (MeV), as a function of the baryon density for NL3 (left), NL3$\omega\rho$ (middle), and FSU (right) models at fixed proton fractions $y_p = 0.1$ and momentum transfer $q=10$ MeV. Two magnetic field strengths are considered: $B = 0$ and $5 \times 10^{17}$ G. The top panels display the results for $B=0$G, where the solid black lines correspond to npe matter, and the solid magenta lines represent the collective modes of a relativistic free electron gas. The nucleons Fermi modes $\omega_{0i}=qV_{Fi}$ are also indicated by magenta dashed lines. The bottom panels compare the collective modes in npe matter for $B = 0$ G (black lines) and $B = 5 \times 10^{17}$ G (red lines). For reference, the collective modes of a relativistic gas of free electrons for $B = 5 \times 10^{17}$ G are shown in green solid lines.