Spectral data of helium atoms with screened Coulomb potentials using the $B$-spline approach

In this work, we present spectral data of helium atoms with the screened Coulomb interactions using the $B$-spline configuration interaction approach. One of the challenges that we face is the electron-electron interaction under the screening effect. Instead of using explicitly correlated exponential wave functions which depend on the interelectron distance, we expand the screened electron-electron potential utilizing the Gegenbauers addition theorem for the separation of the radial variables. Several energies of the ${}^{1,3}S$, ${}^{1,3}P$, and ${}^{1,3}D$ states varying with screening parameters are reported. It is noted that the screening effects lead to the level crossings for high-lying states. We demonstrate the influence of screening on the oscillator strengths for the transitions of ${}^{1}S$-${}^{1}P$, ${}^{3}S{-}^{3}P$, ${}^{1}P{-}^{1}D$, and ${}^{3}P{-}^{3}D$. The variation of the multipole polarizabilities, such as dipole, quadrupole, and octupole, with the screening effect is reported.

Figure 1

Energy levels of 3 ${}^{1,3}S$, 3 ${}^{1,3}P$, and 3 ${}^{1,3}D$ states as functions of Debye screening lengths $D$ for helium atoms with the screened Coulomb potential. Two insets show the 3 ${}^{1}P$ level crossing through the states of 3 ${}^{1}D$ and 3 ${}^{3}D$, respectively.

Figure 2

Energy levels of 4 ${}^{1,3}S$, 4 ${}^{1,3}P$, and 4 ${}^{1,3}D$ states as functions of Debye screening lengths $D$ for helium atoms with the screened Coulomb potential. Two insets show the 4 ${}^{1}P$ level crossing through the states of 4 ${}^{1}D$ and 4 ${}^{3}D$, respectively.

Figure 3

Oscillator strengths for the 1 ${}^{1}S$–$n$ ${}^{1}P$ ($n=2$–7) transitions varying with the screening parameter $1/D$ (inverse Debye screening length).

Figure 4

Oscillator strengths for the 2 ${}^{1}S$–$n$ ${}^{1}P$ ($n=2$–7) transitions varying with the screening parameter $1/D$ (inverse Debye screening length).

Figure 5

Oscillator strengths for the 2 ${}^{3}S$–$n$ ${}^{3}P$ ($n=2$–7) transitions varying with the screening parameter $1/D$ (inverse Debye screening length).

Figure 6

Oscillator strengths for the 3 ${}^{1}P$–$n$ ${}^{1}D$ ($n=3$–7) transitions varying with the screening parameter $1/D$ (inverse Debye screening length).

Figure 7

Oscillator strengths for the 3 ${}^{3}P$–$n{}^{3}D$ ($n=3$–7) transitions varying with the screening parameter $1/D$ (inverse Debye screening length).

Figure 8

Dipole, quadrupole, and octupole polarizabilities as functions of the screening parameter $1/D$ (inverse Debye screening length).