Application of Wave Functions Containing Interelectron Coordinates. I. The Ground-State Energy of Lithium

Abstract

As a check on some of the terms, values of y^ (nl -> /') were also obtained by means of Eq. (23) from the functions u{ determined in II. The results are as follows: y"(2p -> p)= -1.230, y"(3s -> i) = 0.303, Yoc(3p->£)= -17.83, -7oo(3#->/) = 0.485. It is seen that these values are in good agreement with those obtained from ?;/. The maximum deviation occurs for Too (3^->p), where the difference amounts to 4%. The present results for the terms due to the radial inp -> p) modes can be compared with those of Wikner and Das 22 who used a variational method and obtain: yJ rD {2p->p) = -1.22, y" WD (3p->p)=-13.03.

Fabrication and Characterization of Diffraction Gratings Using Photosensitive Al2O3 Gel Films

“…Indeed (see figure l), the node in the function uak,02(r12) occurs only for r12 = 48 au. In contrast, we find (see table 2 ) that the choice of a nodeless correlation function with k = 0, recommended by previous authors (Walsh andBorowitz 1959, Aubert-Frecon et a1 1981) leads to results that are less accurate compared either with experiment or (see table 2 ) the calculations of Jeung (1983Jeung ( , 1987. We should note however that when k is varied from 0 to 0.3, which is a wide range, the energies vary by less than lo%, the change in the binding energies of the upper states being less than 500 cm-I.…”

Helium atom in an external electric field: Exact diagonalization

“…An exact analytical solution of the two-particle equation (1) even at = 0 E is still unknown [12], let alone the case of nonzero external fields. Up to now the problem of free helium atom was analyzed with different approximate methods, among them in the most common use are direct Ritz variational approach [14][15][16][17][18][19][20][21][22], self-consistent (Hartree-Fock) approximation [9,10,[28][29][30][31][32][33][34] and perturbation theory [9,10]. An ef-Helium atom in an external electric field: Exact diagonalization fect of external electric fields was discussed exclusively within framework of standard perturbation theory with computation methods based on a certain variational procedure [39,40].…”

“…An exact analytical solution of this equation is still unknown [12], so that this problem was treated by a number of approximate approaches. Since the initial paper of Hylleraas [13] the Ritz variational approach based on artificial trial functions of different kind [14][15][16][17][18][19][20][21][22] predominates in the problem of helium states. It should be noted that all these results are the conditional variational solutions with reduced (as compared with initial six-coordinate statement) number of spatial variables, so that they are approximate solutions whose accuracy should be estimated by independent methods.…”

A two-electron atomic integral

“…In the case where only Coulomb forces occur between the electrons, this integral power will be greater than or equal to minus one. Several different methods [1][2][3][4][5][6][7] have been published for calculating the atomic multi-electron integrals, but no closed formula has yet been given in the literature for the integral mentioned above. We show below that this integral can be computed in closed form.…”