Calculations of (nl)²and (3lnl′) autoionizing states in two-electron systems

Abstract

In this paper, we calculate energies for ns 2 1 S, np 2 1 D, nd 2 1 G, nf 2 1 I, 3snp 1,3 P • , 3s3d 1,3 D and 3p3d 1,3 F • doubly excited states (DES) of the helium isoelectronic sequence using the screening constant by unit nuclear charge (SCUNC) method in the framework of a semi-empirical procedure. Calculations are performed for total energies of low-lying DES (n 5) in He-like ions with 2 Z 10. The possibility of using the SCUNC method in the investigation of high-lying DES in two-electron systems is demonstrated in the present paper in the case of ns 2 1 S levels, where accurate energy positions are tabulated up to n = 20 and compared to the spin-dependent localized Hartree-Fock density functional (SLHF) with exchange-correlation (XC) potential calculations (Zhou and Chu 2005 Phys. Rev. A 71 022513) and to the works-function (WF)-based exchange (WF XC) potential approach values (Roy and Chu 2005 Phys. Rev. A 71 022513). In addition, the present method is used in the calculation of energy resonances for ns 2 1 S, np 2 1 D and nd 2 1 G excited states (n 5) in high-Z-helium-like ions (11 Z 19), and a comparison with the double sums over the complete hydrogen spectrum calculations (Ivanov and Safronova 1993 Opt. Spektrosk. 75 506) is made. All the results obtained in the present work agree with the available literature values.

The Singlet Doubly Excited (nl)<sup>2</sup> (n ≤ 7) States of He-Like Systems up to Z=10 and the Effect of Screen Constant (α) on the Nuclear Charge (Z)

“…In Table 7, we compare our results with those of Ivanov [33] using double sum method over the complete hydrogen spectrum, A. K. Roy [34] using density functional-theory results, S. Diehl [35]. With available experimental result of Li + obtained and for also doubly excited states we see excellent agreement between our values and those of Sakho [31] for the (np 2 ) 1 D e state. For these states, we note generally a quite good agreement between our results and those of Sakho, Ivanov and Roy for low values.…”

“…We find generally a satisfactory agreement between the present calculations with Z ≤ 7 and those of Biaye. Table 9 compares our results with the theoretical results of Sakho [31] and Biaye [36] for the (nf 2 ) 1 I e state. We note generally a satisfactory agreement between our results and those of Sakho and Biaye.…”

“…= 27.211396 eV and 1Ryd = 13.605698 eV. In the Table 6 our results are compared with those obtained by Gning [27] using a complex rotation method implemented in Scilab, Sakho [31] using the screening constant by unit nuclear charge method, Ho [32] using the complexcoordinate rotation method. Besides, for theoretical results, a good agreement is observed comparing our total energies for (ns 2 ) 1 S e , n ≤ 7 to those of the available.…”

“…We compare our results in Table 10 with those of Sakho [31] for the (ng 2 ) 1 K e and (nh 2 ) 1 M e state. We note generally a good agreement between our results with those of Sakho.…”

Modified atomic orbital theory applied to the calculation of high-lying <sub>2</sub>(K,T)<sub>n</sub><sup>±1,3</sup>P° rydberg series of he-like ions

“…In the description of the autoionizing states in two electron systems, various methods are used. Among these methods are the saddle-point complex-rotation method [6], the close-coupling method [7], the truncated-diagonalization method [8], the complex-coordinate rotation [9][10][11], the computing double sum over the complete hydrogen spectrum [12], the screening constant by unit nuclear charge formalism [13][14][15], the Debye screening model [16]. Except for the screening constant by unit nuclear charge method based on a semi-empirical formalism, most of the preceding methods present special theoretical and computational problems.…”