Imaginary-Time Time-Dependent Density Functional Calculation of Excited States of Atoms Using CWDVR Approach

We have calculated the energies of excited states for the He, Li, and Be atoms by the time dependent self-consistent Kohn Sham equation using the Coulomb Wave Function Discrete Variable Representation CWDVR) approach. The CWDVR approach was used the uniform and optimal spatial grid discretization to the solution of the Kohn-Sham equation for the excited states of atoms. Our results suggest that the CWDVR approach is an efficient and precise solutions of excited-state energies of atoms. We have shown that the calculated electronic energies of excited states for the He, Li, and Be atoms agree with the other researcher values.

Lemniscate and exponential starlikeness of regular Coulomb wave functions

In this study, a normalized form of regular Coulomb wave function is considered. By using the differential subordinations method due to Miller and Mocanu, we determine some conditions on the parameters such that the normalized regular Coulomb wave function is lemniscate starlike and exponential starlike in the open unit disk, respectively. In additon, by using the relationship between the regular Coulomb wave function and the Bessel function of the first kind we give some conditions for which the classical Bessel function of the first kind is lemniscate and exponential starlike in the unit disk 𝔻.

Nonresonant Cross-Section, Fano-Shape Parameter and Correlation Coefficient for the Photoionization of 2s2p (1P∘) in Heliumlike

The nonresonant cross-section, Fano-shape parameter q and coefficient parameter ρ2 have been calculated for the photoionization of helium and heliumlike under the n=2 threshold of the residual ions. Dipole matrix elements which correspond to the transitions from 1s2(S1e) to (0,1)22+ P1∘ state and from (0,1)22+ state to continuum state 1sεp (P1∘) were determined by choosing, for the ground state, the six-parameter Hylleraas wave function including electron correlation effects and a completely screened Coulomb wave function for the continuum. Energies and widths have been determined in the diagonalization method. The results are compared with available results obtained by other theoretical approaches.

Analytic formula for charged particle impact ionization cross-section

We derive an analytical formula for the first Born approximation amplitude for the ionization of general neutral atomic targets by charged particle impact. An orthogonalized Coulomb wave function is used to describe the ejected electron. The triple differential cross-section is written in a computationally efficient analytic form.