Variational Monte Carlo calculations of lithium atom in strong magnetic field
- PDF / 438,810 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 29 Downloads / 169 Views
, MOLECULES, OPTICS
Variational Monte Carlo Calculations of Lithium Atom in Strong Magnetic Field1 S. B. Domaa*, M. O. Shakerb, A. M. Faragb, and F. N. El-Gammalc** a Mathematics
Department, Faculty of Science, Alexandria University, 21526 Egypt Mathematics Department, Faculty of Science, Tanta University, Tanta, 31527 Egypt c Mathematics Department, Faculty of Science, Menofia University, Shebin El-Kom, 32511 Egypt *e-mail: [email protected] **e-mail: [email protected] b
Received April 26, 2016
Abstract—The variational Monte Carlo method is applied to investigate the ground state and some excited states of the lithium atom and its ions up to Z = 10 in the presence of an external magnetic field regime with γ = 0–100 arb. units. The effect of increasing field strength on the ground state energy is studied and precise values for the crossover field strengths were obtained. Our calculations are based on using accurate forms of trial wave functions, which were put forward in calculating energies in the absence of magnetic field. Furthermore, the value of Y at which ground-state energy of the lithium atom approaches to zero was calculated. The obtained results are in good agreement with the most recent values and also with the exact values. DOI: 10.1134/S1063776117010034
1. INTRODUCTION Over the last decade continuing effort has gone into calculating, with ever increasing accuracy and with various methods, the energies of atoms and ions in neutron star magnetic fields. The motivation comes largely from the fact that features discovered [1–3] in the thermal emission spectra of isolated neutron stars may be due to absorption of photons by heavy atoms in the hot, thin atmospheres of these strongly magnetized cosmic objects [4]. Also, features of heavier elements may be present in the spectra of magnetic white dwarf stars [5, 6]. While comprehensive and precise data for hydrogen in strong magnetic fields have been available for some time (cf. [7–10]), this is less the case for atoms and ions with more than one electron. Recently, significant progress has been achieved with respect to the interpretation of its rich spectrum. The detailed calculations of the hydrogen energy levels carried out by Rosner et al. [11] also retain the separation of the magnetic field strength domains due to decomposing the electronic wave function in terms of either spherical (for weak fields) or cylindrical harmonics (for strong fields). A powerful method to obtain comprehensive results on low-lying energy levels in the intermediate regime, in particular, for the hydrogen atom was provided by mesh methods [12]. On the other hand, in case of atoms with several electrons
the problem of the mixed symmetries is even more intricate than for hydrogen because different electrons feel very different Coulomb forces, i.e. possess different single-particle energies, and the domain of the intermediate fields, therefore, appears to be the sum of the intermediate domains for the separate electrons. The comparison of the stationary transitions of
Data Loading...
