The Study of Magnetically Deformed Atoms in the Outer Crust of Neutron Stars in Presence of Strong Quantizing Magnetic Field

We have studied the various properties of magnetically deformed atoms, replaced by deformed Wigner-Seitz cells, at the outer crust region of strongly magnetized neutron stars (magnetars) using a relativistic version of Thomas-Fermi model in cylindrical coordinates.

💡 Research Summary

The paper presents a comprehensive theoretical investigation of how atoms in the outer crust of strongly magnetized neutron stars (magnetars) are deformed by ultra‑strong, quantizing magnetic fields. Instead of the conventional spherical Wigner‑Seitz (WS) cells, the authors model each atom as a cylindrical WS cell whose axis is aligned with the magnetic field. This choice reflects the fact that, when the magnetic field strength exceeds the quantum critical value (B ≈ 4.4 × 10¹³ G), the motion of electrons perpendicular to the field is quantized into Landau levels, effectively freezing the radial degrees of freedom while allowing free motion only along the field direction.

The authors adopt a relativistic Thomas‑Fermi (TF) framework. The electron number density n_e(r,z) is expressed as

n_e = (e B / 2π²) p_F,

where p_F is the Fermi momentum along the field, which itself depends on the local electrostatic potential ψ(r,z). The potential satisfies Poisson’s equation

∇²ψ = 4πe