Short-range interactions in ground state H2+ using fluctuation theory techniques

Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

“…The first of these boundary conditions ensures that also x x -( ) ( ) / p 1 e 2 and consequently j(ξ), X(ξ) are analytical in the environment of ξ=1. 7 These coefficients were also evaluated in [17]. The present calculations of the expanded form are consistent with the results of that reference.…”

“…The separation of the 3-dimensional Schroedinger equation for + H 2 in confocal elliptic (spheroidal) coordinates x h j ( ) , , of the electron, with nuclei kept in fixed position [1][2][3][4][5][6][7][8][9][10][11][12][13], originates three one-dimensional differential equations, the outer ξ−equation, the inner η-equation and the j-equation. The subsequent variable transformation:…”

“…The coefficients a, b, c, d, e were evaluated in [8,10] 7 . The expanded form of these coefficients is the following, where it has been made use of appendix B:…”

“…The evaluation of the coefficients arising in the short-range expansion of the interaction in ground state + H 2 has been the object of many investigations [1][2][3][4][5][6][7][8][9][10][11]. In this paper we extend the calculations to the evaluation of the C 10 coefficient using our previous techniques.…”

“…The main principles and assumptions on which they are founded are examined and refined calculations are presented. In [7] perturbation theory was applied in conjunction with first-passage time techniques in order to solve both the so-called [4] inner and outer equations, while in subsequent work [8,10] it was found more suitable to make recourse to Hylleraas tridiagonal determinantal method [1] applied to the inner equation. This led straightforwardly to useful analytical results, although the physical picture of an electron stabilized by resonance in a double-well potential, which results from our transformed equations (2), (2ʹ) below, was somewhat hidden in that approach.…”