Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

Abstract

ABSTRACT:We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound 1,3 D states and the doubly excited 1,3 D e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for 1 D e and 3 D e states) below the n ϭ 2 He ϩ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these 1,3 D e resonance states are reported along with the bound-excited 1s3d 1,3 D state energies. Overall behavior of the spectral profile of 1s3d 1 D state of helium atom due to electron-electron and electron-nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum.

Feshbach projection approach to study plasma effects on doubly excited autoionizing states in helium

“…We show the variation of resonance energies and widths against the screening parameter, i.e., (E r , r ) vs λ, in graphical form instead of voluminous tabular data, which are available from the authors upon request [40]. Nevertheless, to assess the quality and accuracy of our numerical data we choose to compare in Table III our results for the lowest singlet resonances ( 1 S e , 1 P o , and 1 D e ) with those reported by Ho et al [14,16,17,23], using the stabilization method. Due to the effectiveness of our computational method, we can provide values for higher resonances and for a much finer mesh of λ values, including also the values for λ used by Ho et al for the sake of comparison.…”

“…Recently, a plethora of papers released by the Y. K. Ho group have been dedicated to the study of bound and doubly excited states in two-electron atomic systems immersed in plasma environments (see [6,[12][13][14][15][16][17][18][19][20][21][22][23] and references therein). In particular, Kar and Ho first dealt with the 2s 2 1 S e resonance state without considering the screening between electrons in H − [12], then including it for the lowest 1 S e resonance in H − [13], in He [14], and Ps − [15]; they also studied the screening effect on 1,3 P o [16,17] and 1,3 D e resonances [23].…”

“…Recently, a plethora of papers released by the Y. K. Ho group have been dedicated to the study of bound and doubly excited states in two-electron atomic systems immersed in plasma environments (see [6,[12][13][14][15][16][17][18][19][20][21][22][23] and references therein). In particular, Kar and Ho first dealt with the 2s 2 1 S e resonance state without considering the screening between electrons in H − [12], then including it for the lowest 1 S e resonance in H − [13], in He [14], and Ps − [15]; they also studied the screening effect on 1,3 P o [16,17] and 1,3 D e resonances [23]. In these series of papers, the stabilization procedure [24] is widely used along with a configuration interaction (CI) method with explicitly correlated coordinates to uncover the resonances and to characterize their parameters by fitting the density of resonance states to a Lorentzian form.…”

Low-energy electron elastic scattering and impact ionization with hydrogenlike helium in Debye plasmas

“…Hashino et al have employed the variational method to study the bound states of heliumlike atoms in Debye plasmas in their early work [11]. Kar and Ho have investigated the effects of Debye plasmas on resonant states in electron-hydrogen-atom scattering (or hydrogen negative ion) and the doubly excited states of the helium atom and Ps − ion by using the stabilization method [12][13][14][15][16][17][18]. They have also calculated the energies of bound states of helium atom in Debye plasmas by using the Rayleigh-Ritz variational method [19,20].…”

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

“…Those nonorthogonal bases which can be approximately “complete” by a large number of basis functions are more frequently used in the atomic and molecular structure calculations. In the framework of configuration interaction (CI) approach, the nonorthogonal basis set can be constructed by the Slater‐type orbitals (STOs), the Gaussian‐type orbitals, the Coulomb Sturmian functions as well as the explicitly correlated Hylleraas‐like basis functions …”