Highly excited states for the helium atom in the hyperspherical adiabatic approach

Abstract

The hyperspherical adiabatic approach is used to obtain the highly excited series 1sns 1 S e and 1s(n + 1)p 1 P o of the helium atom. The introduction of appropriate asymptotic conditions at large values of the hyperspherical radius results in a stable algorithm that allows the calculation of the full atomic spectrum with precision of a few parts per million. Comparison with the variational calculations available in the literature shows that the accuracy of the results improves with increasing principal quantum number. We present the energies up to n = 31 which is the typical value used in multiphoton excitation experiments.

S-states of helium-like ions

“…Very complicated basis functions are applied in other approaches [20,6,5,16,17,7]. A great deal of effort is dedicated to the derivation of simple (compact) and accurate wave functions [13][14][15]18,19,6].…”

Three-body systems with attractive1∕rpotentials

“…[12] give a differ-ence of about 10%. By comparison, for a system like the He atom [21], where the electronic repulsion plays an important rule, the relative difference between the lower and upper bounds estimated from hyperspherical potential curves is about 1%. …”

Electron affinity of the sodium atom within the coupled-channel hyperspherical approach

“…The hyperspherical method has been used in many fields of physics and chemistry, and an extensive application in atomic and molecular physics has been made. [27][28][29][30][31][32][33][34][35][36][37][38][39] The hyperspherical coordinates can also be found in nuclear physics [40][41][42][43][44][45] as well as in solid-state physics. 46 -51 The hyperspherical adiabatic representation of the wave function is well known to furnish a very good description of the correlation effects for twoelectron systems; its use has many motivations, such as universality, which permits its application to any few-body problem in an intuitive and elegant way with a description of physical states in terms of potential curves and their couplings, which are independent of the energy, similarly to the Born-Oppenheimer method.…”

“…54,55 This paper is organized as follows: In Sec. II we briefly describe the theoretical aspects of the coupled-channel hyperspherical adiabatic method, 27,31,[33][34][35][36] presenting the main equations. In Sec.…”