Hartree-Fock studies of atoms in strong magnetic fields

Abstract

We present comprehensive calculations of the electronic structure of selected first-row atoms in uniform magnetic fields of strength р10 10 G, within a flexible implementation of the Hartree-Fock formalism. Groundstate and low-lying excited state properties are presented for first-row atoms He, Li, C, and ion H Ϫ . We predict and describe a series of ground-state quantum transitions as a function of magnetic field strength. Due to its astrophysical importance, highly excited states of neutral He are also computed. Comparisons are made with previous works, where available.

Spectrum of neutral helium in strong magnetic fields

“…The ETG basis elements are much better, however, at reproducing the highly anisotropic behavior at high magnetic fields. This improved accuracy is reflected in the fact that the higher excited states are much superior to those published previously [12].…”

“…Our method, apart from the introduction of a different basis set, is essentially the same as that of our previous paper [12]. Here we recapitulate only the essential formulae.…”

“…Several recent attempts have been made to solve the HF self-consistent field (SCF) equations for the spectrum of magnetized helium. Thurner et al [11] used numerical quadrature of the HF SCF equations to obtain results for several excited states of helium atoms and helium-like ions over a range of magnetic fields up to 10 12 G. The errors in this method, however, were best illustrated by later calculations of Jones et al [12] who applied a basis set of Slater-type orbitals (STO) in solving the same equations, and were able to obtain lower energies for two excited states over many symmetries, but only up to magnetic field strengths of 10 10 G. Later quantum Monte Carlo (QMC) calculations [13], using these same STO wave-functions as a starting point, found that the residual basis set truncation errors were still significant over much of the range of magnetic field strengths studied, and emphasized the need for more accurate HF wave-functions. The helium spectrum in strong magnetic fields is the primary focus of this work.…”

Beryllium in strong magnetic fields

“…Thereby our knowledge on the electronic structure of the lithium atom in a strong magnetic field has been advanced significantly (for the state-of-the-art before this work see Refs. [24,25,26,27,28,29,30,31]). …”

Theory and application of explicitly correlated Gaussians

“…Various approaches have been used to calculate the energies of atoms in magnetic fields including variational (Vincke and Baye, 1989;Nakashima and Nakatsuji, 2010), HF (Proschel et al, 1982;Jones, Ortiz, and Ceperley, 1996), QMC (Jones, Ortiz, and Ceperley, 1997), and CI (Al-Hujaj and Schmelcher, 2003) calculations.…”