Helium atom doubly excited state

The development of a full angular momentum, three dimensional, smooth exterior complex dilated, finite element method for computing bound and resonant states in a wide class of quantum systems is described. Applications to the antiprotonic helium system, doubly excited states in the helium atom and to a model of a molecular van der Waals complex are discussed. 2001 by Academic Press. 

Notwithstanding, after hydrogen, helium is also the simplest naturally available atomic species, which, in contrast to one electron atoms, exhibits the additional electron-electron interaction, as a source of electronic correlations. Hence, helium is one of the simplest systems where electronic correlations can be studied. Direct manifestations of electronic correlations have been found, e.g., in doubly excited states of helium localized along highly asymmetric, though very stable, frozen planet configurations (FPC) (K. Richter et.al., 1990), or scarred by... 

The most recent advance in the theory of the helium atom was the discovery of its classically chaotic nature. In connection with modern semiclassical techniques, such as Gutzwiller s periodic orbit theory and cycle expansion techniques, it was possible to obtain substantial new insight into the structure of doubly excited states of two-electron atoms and ions. This new direction in the application of chaos in atomic physics was initiated by Ezra et al. (1991), Kim and Ezra (1991), Richter (1991), and Bliimel and Reinhardt (1992). The discussion of the manifestations of chaos in the helium atom is the focus of this chapter. 

The doubly excited states of helium are amenable to theoretical studies, and some of those states can be studied spectroscopically. Nevertheless, by any reasonable criterion, these transient states are rather exotic. They illustrate a phenomenon of atomic structure that was not heretofore expected, and, in so doing, open our minds to thinking of atomic structure in more general terms. They force us to ask whether other atoms, expecially atoms with two valence... 

Fragmenting levels for a known three-body problem - doubly excited states in the normal helium atom. 

The role of electron-electron interaction is one of the main topics of atomic, molecular physics and quantum chemistry. The normal helium atom is then naturally one of the most fundamental systems. Doubly excited states are as almost bound states of special interest since the role of the electron-electron interaction is important in describing energies and also autoionization rates. Dielectronic recombination processes where one of the two excited electrons falls down to a lower level while the other is ejected appears to be a fundamental process where electron-electron interaction plays a dominant role[6]. The recently built electron-cooler storage rings [7] have made it possible to study dielectronic recombination and thereby doubly excited states with high experimental accuracy. 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

A. Burgers, D. Wintgen, J.-M. Rost, Highly doubly excited S states of the helium atom, J. Phys. B 28 (1995) 3163. 

The metals in Group 1 have one unpaired electron in the valence shell s orbital. This AO may be combined with a or p spin functions to form two spin orbitals. It is therefore possible to write down two Slater determinant wavefunctions for these atoms the ground states are doubly degenerate. Atoms that contain two or more unpaired electrons are more difficult to describe. For these species one is forced to form wavefunctions by linear combination of two or more Slater determinants. In the next section we shall deal with the simplest atom of this kind, viz. a helium atom excited to the 1x 25 electron configuration. 

Next this problem is reduced to the Ritz method (see. pendices L, p. 984, and K, p. 982), and subsequently to the secular equations (H — sS)c = 0. It is worth noting here that, e.g., the CI wave function for the ground state of the helium atom would be linear combinations of the determinants where the largest c coefficient occurs in front of the 4>o determinant constructed from the spinorbitals Isa and lsj8, but a nonzero contribution would also come from the other determinants, e.g., constructed from the 2sa and 2sj8 spinorbitals (one of the doubly excited determinants). The CI wave functions for all states (ground and excited) are linear combinations of the same Slater determinants - they differ only in the c coefficients. 

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