Dipole sum rules of a hydrogen atom in a Debye-Hückel plasma

Abstract

In this work, we carry out a study of the dipole oscillator strength sum rule, Sk, and the logarithmic, Lk, version, for a hydrogen atom embedded in a Debye-Huckel plasma. We solve the time-independent Schrodinger equation by means of a finite-differences approach to obtain the discrete and continuum spectrum of the atom embedded in the plasma, as a function of the screening parameter, λD. We find excellent agreement for the Sk and Lk sum rules for λD → ∞, i.e., no plasma, in comparison with exact theoretical results. For plasma interaction, we obtain the conditions for the delocalization of the hydrogen atom energy levels finding its effects on the Sk sum rules. We find that for k ≤ 0, Sk increases as the screening constant decreases until λ ~ 0.84 a.u., where the 1s ground state becomes delocalized due to the plasma weakening. For the static dipole polarizability, S−2, we find excellent agreement of our results for the discrete and continuum spectrum to available data in the literature for selected values of screening parameters. In the logarithmic counterpart, Lk, the sum rules decrease for lower values of the screening length for k ≤ 0. We observe a decrease of the mean excitation energy, I0 = eL0/S0, as the screening length decreases finding a sudden change for λD ~ 2 a.u. Furthermore, we obtain closure relations for the Sk sum rule with k = −1, 1, 2, 3 as a function of the Debye-Huckel screening and find excellent agreement with the sum over excited states for k = −1, 0, 1, and 2 and find that S3 sum rule diverges for a hydrogen atom immersed in a Debye-Huckel plasma. We conclude that the fulfillment of the closure relations requires a good description of the excitation states.