Doubly excited¹S^e,¹D^eand¹G^estates of He, Li⁺, Be²⁺and B³⁺

Abstract

A newly proposed time-dependent variation-penurbatian theory (TDVPT) for double excitation is employed to study the Nlnl':' L' resonances (with N = 2,. . . , 5 : n = N , ..., 5; I = l ' = 0 , 1 . 2 a n d L = f + l ' ) f o r t h e i o n s f r a m Z = Z t o Z = 5 i n t h e helium isoelectronic sequence. The resonance positions are obtained from a study ofthe behaviour of a linearized variational functional with respect to driving frequency. Most of the results of this calculation are new and, for the old ones, reasonable agreement with other existing results is observed with much smaller basis sets. Analytic representations of the doubly excited states are obtained and the Coulomb repulsion terms in these states are estimated for checking up the consistency ofthe doubly excited state wavefunctions which may prove useful for evaluating physical properties of such states.

On the interpretation of two electron-one photon transitions in slow collisions between fully stripped ions and solid target

“…Since the Ki~ transition occurs between the states of helium like neon ion, the (Z + 1) approximation adopted by Mukherjee and Ghosh [6] is not necessary. Time-dependent perturbative method adopted by Ray et al [8,9] and by Ray and Mukherjee [ 10] has also been utilized to find the K~ transition in Ne 8 + which cross checks the result available from effective two particle model [6].…”

“…It appears that the most probable configurations associated with the experiment of Andriamonje et al [1] are the ones which gives the K~-lines. To have a cross check we have calculated the K:~ transition energy using time-dependent variation perturbation approach [8][9][10] with radially correlated basis sets. The transition energy is found to be 1.924 KeV which is in exact agreement with our two particle model calculation [6].…”

“…The theory for this has been discussed elsewhere [8][9][10]. This procedure is adopted to check the data for such transitions independently.…”

Calculations of 2<i>sns</i><sup>+1,3</sup><i>S</i><sup>e</sup>, 2<i>snp</i><sup>+1,3</sup><i>P<sup>0</sup></i>, 2<i>pnp</i><sup>+1,3</sup><i>D<sup>e</sup></i> Autoionizing Sta

“…For the calculation of doubly excited states for Helium-like ions, several authors have used different methods. Thus, Ho [3,23,31] used the method of complex rotation convoluted with a wave function of Hylleraas type, Dieng [4] used Special Forms of Hylleraas-Type Wave Functions, Ivanov and Safronova [24] performed calculation using double sum method over the complete hydrogen spectrum, Sakho [25] with the Screening Constant by Unit Nuclear Charge method, Lipsky et al [26], Ray and P. K. Mukherjee [27] with the time independent variation perturbation theory and Kar and Ho [28] the stabilization method, Drake and Dalgarno [29] the hydrogenic wave function for the continuum, Ho and A. Bathia [3] which have used the complex-coordinate rotation method.…”

Doubly excited states of highly stripped ions: a time dependent perturbation approach

“…The efficacy of the method was proved [65][66][67], albeit its simplicity. In this method the two electron charge cloud was considered as a single entity and its collective excitation modes are analysed using the time honored version of perturbation theory.…”