Dipole transition-matrix elements of the one-electron heterodiatomic quasimolecules

Abstract

The problem of dipole transition-matrix element calculation for optical transitions in multiply charged one-electron diatomic quasimolecules with unequal nuclear charges Z 1 and Z 2 has been stated and solved. The quasimolecule Z 1 eZ 2 is a unique example of a two-center system for which the energy terms and dipole transition moments have been calculated precisely in the frame of a nonrelativistic approach. Particular examples for the optical transitions with Z 1 = 1.5, 2 , 2.5, 3 and Z 2 = 1 and with the principal quantum number of the united ion n u =1,2,3,4 have been tabulated. The scaling rules make it possible to determine the matrix elements for quasimolecules having nuclear charge ratios such as 2:1, 3:1, 3:2, and 5:2. Zeros at intermediate R and zero limiting values at large R are the highlighted features of the matrix elements. The heteronucleus case generates a large number of asymptotically forbidden transitions corresponding to transitions of an electron from one ion to another.

Optical Transitions and Charge-Exchange in Highly Charged Quasi-Molecules

“…At this step it is important to notice that the dipole matrix elements for the one-electron heterodiatomic quasimolecules (Z 1 / = Z 2 ), in the frame of nonrelativistic approach, had not been calculated before the work done by Devdariani et al [21]; only the quasi-molecular energy terms had been reviewed in details by Komarov et al [22].…”

“…We emphasize that the calculation of the radiative characteristics for the quasi-molecules with smaller nucleus charges is timesaving and faced with smaller computational difficulties. [21]. It is well known that the Schrödinger equation of the two-coulomb-centre system is separable by using the prolate spheroïdal coordinate system (ξ, η, ϕ) related to the coordinates x, y, z of the electron position vector through…”

“…The wave functions have been expanded in various forms involving coefficients determined by recurrence relations [21] and yielding the relative accuracy of order 10 −12 for the energy terms and the accuracy of order 10 −8 − 10 −10 for the corresponding quasiradial and quasiangular wave functions. Thus, the accuracy of the calculated matrix elements can be estimated at 10 −8 [21].…”

“…As for the spectral features, an extremum in an energy term will then not necessarily produce a satellite. Of particular interest is the role of dipole transition moments [21,33], which can lead, in the case of zeros, to the formation of dips in the far wing spectral profiles [21]. This phenomenon has been discussed in two limiting cases, adiabatic and diabatic [34].…”

The continuous and discrete molecular orbital x-ray bands from Xeq+ (12≤q≤29) +Zn collisions

“…This is why a lot of experiments were devoted to x-ray emissions in slow collisions. Unfortunately, the molecular orbitals are difficult to calculate, especially for higher shells and multi-electrons systems 19 20 21 . Therefore, the precise theoretical calculations in electron promotion and MO transition processes are still lacking for slow highly charged ion-atom collisions.…”