Fixed-phase correlation-function quantum Monte Carlo calculations for ground and excited states of helium in neutron-star magnetic fields

摘要

We apply the correlation-function quantum Monte Carlo (CFQMC) method to the calculation of the energies of ground and excited states for helium in neutron-star magnetic fields. The method has been successfully applied by Jones, Ortiz, and Ceperley to the calculation of helium in white dwarf magnetic fields. We extend the accessible range of magnetic field strengths by introducing a fixed-phase variant of the CFQMC method. We find that with growing magnetic field strength the variances increase significantly and put a limit to the applicability of the method for atoms in strong magnetic fields. The behavior of the variances is traced back to the logarithmic divergence of the energy of the bosonic ground state with increasing magnetic field strength. We use basis sets, which account for the growing dominance of the cylindrical symmetry as the magnetic field is increased and incorporate them into the CFQMC algorithm. These basis sets are taken from Hartree-Fock calculations, performed using a B-Spline and Landau expansion beyond the adiabatic approximation.