Helium atom in an external electric field: Exact diagonalization

Abstract

An exact diagonalization method is applied to solve the quantum-mechanical problem of spinless helium atom in an external electric field of arbitrary magnitude. The basis set for two-electron problem is built from different pair combinations ψnalama(αra)ψnblbmb(αrb) of orthonormalized single-particle hydrogen-like wave functions ψnml(r) belonging to any possibly bound states of the individual a- and b-electrons in the Coulomb central field renormalized by the scale parameter α > 0. Within the selected basis the matrix elements of the total Hamiltonian allows an exact analytical representation in the form of finite numerical sums. The diagonalization procedure is performed by Jacobi algorithm for N×N square Hermitian matrix built on the basis of dimension N = 25. The systematics and the numerical values of the low-lying energy levels at zero field are in good agreement with known experimental data. The field dependences of low-lying levels (Stark effect) and polarizability in the ground state of helium atom are presented. It is shown that even extremely high external fields lead only to shifting or splitting of existing low levels, without disturbance of their systematics. Typically, no new lowenergy excitation can be created under external electric field of moderate intensity. Radical reconstruction in spectrum of individual helium atoms can be expected in condensed helium phases where each atom is deeply affected by interaction fields from neighbors. This result should be taken into account at interpretation of electrodynamic experiments on superfluid helium.