Doubly excited intershell states of two-electron atoms with large Z: exact wavefunctions and energies at N>>1

Abstract

Lower 1.3S and 1.3P states of the (N,n) manifold of two-electron atoms are studied. Analytical wavefunctions of these states diagonalizing the r-112 operator at N>>1 are found. These As-N-functions provide the excellent approximations of exact wavefunctions even at small and moderate N (for lower states the overlap integral is greater than 0.999 at N=4 and n<or=10). Using As-N functions permits the specific features of the electron distribution over l to be elucidated. Variations of (cos theta ) along the series with fixed N are investigated and it is proved that the angle correlation becomes stronger as n increases. The analytical dependence of (r-112) on quantum numbers is obtained. It is shown that there exists two systems of states ( nu =1 and nu =-1), energies of each system corresponding to that of the harmonic oscillator with different zero-point energies and vibrational quanta.