Atoms in Superstrong Magnetic Fields

Abstract

In magnetic fields B ~ 10 12 G, characteristic of neutron-star models for pulsars, the ionization energy of atoms is a few hundred electron volts and is a slowly increasing function of Z. This may greatly affect the nuclear abundances of matter lifted off the stellar surface by electric fields.Magnetic fields of enormous strength probably exist within neutron stars. Models for the slowing up of rapidly spinning neutron stars need a field J3~ 10 12 G to fit observed increases in pulsar periods. 1,2 Such huge fields are also characteristic of the amplification expected if a mainsequence star evolves to a neutron star while conserving the magnetic flux which it initially contains. The presence of immense magnetic fields can qualitatively affect the nature of the stellar surface in a variety of ways because of the very strong tendency of electrons to move only along field lines. The transparency of the surface is greatly increased in certain directions for radiation whose frequency is much less than the electron-cyclotron frequency. Since, for B ~ 10 12 G, this includes even soft x rays, the star may rapidly cool to much less than the 10 6 K estimated surface temperature for cooling neutron stars without such fields. 8 On stellar surfaces near and especially below a million degrees such a magnetic field will also so greatly raise the ionization energy of atoms that atoms can remain un-ionized.For B > 10 9 G, the quantum mechanical zeropoint motion of an otherwise free electron perpendicular to a field line is less than the Bohr radius of a normal hydrogen atom: Magnetic confinement perpendicular to the field dominates the binding attraction to a proton. A superstrong magnetic field ties the electrons to the field lines so that their response to a Coulomb attraction is essentially restricted to a one-dimensional motion parallel to the field. An immediate effect is a great increase in binding energy of atoms because the electron is much more likely to be found near its binding nucleus. The usual shell structure of heavier atoms disappears. The minimum ionization energy of the neutral atom in a superstrong B does not fluctuate with Z but increases slowly and monotonically.In cylindrical coordinates (p, cp, z) the energy eigenfunctions of a spinless nonrelativistic electron in a uniform magnetic field in the z direction are where w(£) is the appropriate normalized confluent hypergeometric function F(-n p , \m\ +1, £), n p is a positive integer, and 2Hct > -eBp 2 . The associated energy eigenvalues areThe set of degenerate eigenstates with minimum E x have n p = 0 with m all non-negative integers. The next set of states with higher E ± differ by AE = eBH/m e c ~ 10 keV for B ~ 10 12 G. This is seen below to be very much less than the additional Coulomb-field-associated energies of the outer electrons of atoms in such a magnetic field and we shall assume that the electron wave functions contain only n p =0 states. The energy to change an electron spin from antiparallel to parallel is also eBH/m e c; so we presume all elect...

Atmospheres and radiating surfaces of neutron stars

“…As first noticed in [270], atoms with bound states should be much more abundant at γ ≫ 1 than at γ 1 in a neutron-star atmosphere at the same temperature. This difference is caused by the magnetically-induced increase of binding energies and decrease of sizes of atoms in socalled tightly-bound states, which are characterized by electron-charge concentration at short distances to the nucleus.…”

A classical treatment of the quadratic zeeman effect in atomic hydrogen

“…Thus when the Coulomb potential is dom inant, the bound state problem can be solved by perturbation theory and the energy eigenvalues are the usual Coulomb levels with param agnetic and diam agnetic perturbations. The quadratic term can become very im portant if the magnetic field is very intense; it is believed th a t fields as large as 10® kC may exist on the surface of neutron stars, and this would radically alter the structure of atom s (Cohen et al, 1970). The quadratic term will also be im portant when we consider the macroscopic motion of an electron in an external field.…”

Matter in Superstrong Magnetic Fields

“…For the light atoms in the Hartree approximation each electron has its own pure Landau orbital. A variational calculation with such wave functions in a 2x 10 12 G magnetic field gives atoms whose shape and size is modeled in Figure 5 (Cohen et al, 1970). The length of the cylindrical atoms is not sensitive to Z while the radii increase roughly as (2Z+1) 1/2 .…”

“…Haines and Roberts, 1969). In the limit of huge fields a 0 >l>Q and the binding energy E grows like ln 2 B.…”