Investigation of 2snp^±1,3P^oresonances of two-electron systems using the screening constant by unit nuclear charge method

Abstract

The 2snp±1,3Po doubly excited states with n⩽6 of helium-like ions are investigated using screening constant by unit nuclear charge (SCUNC). Calculations are performed for total energies, excitation energies and total Coulomb interaction energies between the two electrons in He-isoelectronic series up to Z=10. The results obtained agree with the available theoretical and experimental literature values.

Energy Resonances for $^1P^o,$ $^1D^e,$ $^1F^o,$ $^1G^e,$ and $^1H^o$ Autoionizing States of the Helium Isoelectronic Series Below the $n=2-4$ Hydrogenic Thresholds

“…The results obtained are listed in Table 1. In Tables 2-4 Considering the results listed in Table 2 for 2s2p 1 P o , 3s3p 1 P o , 4s4p 1 P o and 3s3d 1 D e levels, the agreement between the present calculations and the double sums over the complete hydrogen spectrum values of Ivanov and Safronova [8], the complex rotation results of Ho [9,10], the Feshbach projection results of Bachau et al [14] and with our semi-empirical results obtained previously [16,17] is seen to be good. One can also remark that, the present variational results are close to that of the complex rotation calculations [9] for 2s2p 1 P o levels for Z =3∼9.…”

“…Besides, by use of the solution given by Eq. (17) and the value k = n, Eq. 16is written in the form of a sum of finites terms, namely…”

“…In this section, we apply the screening constant by unit nuclear charge formalism (SCUNC) to calculate the energy resonances of the helium-isoelectronic sequence converging to the n = 2 ∼ 4 hydrogenic thresholds. In the framework of the SCUNC -method, total energy of (N l,nl ′ ) 2S+1 L π excited states is expressed in the form (in Ryd) [16,17]…”

“…In this equation, the principal quantum numbers N and n, are respectively for the inner and the outer electron of He-isoelectronic series, the β-parameters are screening constants by unit nuclear charge expanded in inverse powers of Z and given by [16,17]…”

“…For autoionizing states in the helium isoelectronic series, many computational methods are employed. Among these methods are, the computing double sum method over the complete hydrogen spectrum [8], the complex-coordinate rotation [9][10][11][12], the density functional theory [24], the Feshbach-projection method [14], the screening constant by unit nuclear charge (SCUNC) method [15][16][17] (to name a few). Special type of trial wave functions combining Hylleraas and incomplete hydrogenic wave functions have also been used in the computations of energies for doubly excited states of two electron systems [18][19][20][21].…”