Hydrogen and Helium Atoms in Intense Magnetic Fields Coupled with High Pressure in Neutron Star Atmospheres

In addition to harboring intense global magnetic fields, neutron stars also have outer envelopes that are subjected to high pressures. The outermost layer of a neutron star's envelope consists of a thin atmosphere, which in turn sits atop an ocean layer of condensed matter. The pressure at the topmost layer of the ocean is generally estimated to be around P ≳ 10³ GPa. The envelope is thought to be dynamic, with mixing between the layers, and this investigation seeks to delineate the energy landscape of neutral atoms from the atmosphere, which can get trapped inside denser surrounding material of the ocean layer below during mixing. The high-pressure environment is modeled as a quantum confined model by means of a spherical cavity using a piecewise potential (V_p) and a confining radius (R_C). A range of pressures and magnetic field strengths ($$ T) are considered, and the two most astrophysically relevant atoms (hydrogen and helium) are studied herein, and, to the best of the author's knowledge, this is the first study to investigate the combination of the two effects in neutron star atmospheres. The energies of the first few low-lying states of each of hydrogen and helium atoms are computed (at the Hartree-Fock level of the theory for the latter), and the findings indicate that the binding energies of the states are considerably altered in such an environment. At the pressures relevant to the ocean layer (P ≳ 10³ GPa), it was found that the negative parity states of both hydrogen and helium do not survive as the energy shift introduced by the confinement is large enough to render them unbound. The positive parity states of these atoms do, however, survive at such pressures (albeit with somewhat lesser binding energies, for the case of helium) in neutron star envelopes. At lower pressures P ∼ 10² GPa, representing material in the lower reaches of the atmosphere though not at ocean layer depths, the energy landscape is still found to be appreciably altered for both the positive and the negative parity states of hydrogen and helium. Higher in the atmosphere, the energy shifts were found to diminish to negligible amounts for pressures relevant to the photosphere of the neutron star (P ∼ 10^-1 GPa). Overall, the study reveals that incorporating the effect of high pressure is important when studying the structure of atoms in the intense magnetic fields present in neutron star envelopes, as significant shifts in the computed energies will have bearing on any subsequent computations of oscillator strengths, transition wavelengths, as well as calculations of relative abundance of atoms and ions in atmosphere models. Thus, the results are relevant to understanding the spectra of neutron stars.