Group theoretical treatments of strongly correlated atomic dynamics

Abstract

Applications of group theory in atomic physics have been dominated by Wigner-Racah algebra for angular momentum and the work pioneered by Racah in using Lie groups to disentangle complex atomic spectra. These studies concentrate on the spin and angular momentum coupling of several electrons in an open shell and on the classification of the resulting states. On the other hand, after the initial, and now very familiar, treatment of the symmetries of the hydrogen atom--in particular, the symmetry of 04, the group of four-dimensional rotations-further analysis of this group or of its extension to radial aspects through the non-compact group 0(4,2) faded into the background in the development of atomic physics. A revival has occurred in the past fifteen years, connected with the emergence of two challenging problems of atomic dynamics. One deals with high doubly excited states of atoms in which two slow electrons move in a Coulomb field. The second is the study of highly excited states of a single electron in a magnetic field. Both involve non-separable Hamiltonians and competing interactions that are not perturbative. Thereby, analysis through conventional single-particle bases requires the mixing of a diverging number of angular and radial configurations. This has motivated a search for quasi-good symmetries that may provide alternative bases and alternative quantum numbers. Group theoretical analysis, involving primarily variants of 04, has been largely successful in the program regarding angular mixings in both problems. This paper gives a unified review of this work, pointing out also what remains to be done, particularly regarding radial correlations which have seen essentia.lly no progress. Links are provided throughout between the group theoretical work and other approaches to these problems.

Calculation of Langmuir states in doubly excited helium

“…In the second step, we determine the single-particle / distribution which is distinctly different for different classes of resonances. LO states K= -(TV -1) are characterized by a large weight at high angular momenta (/^TV), which contrasts with the angular momentum distribution for K=N -\ states, where the high / components are exponentially suppressed [15]. Finally, we project the density of the wave function P(R,a,Q) = \<l>(R,a,0)\ 2 where ^=cos~1(fi,f 2 ), R=(r?…”

“…They describe two electrons "atop each other" [15]. The latter follows from the fact that the electrons spend most of their time near the turning point [ Fig.…”

Characterizing high-nquasi-one-dimensional strontium Rydberg atoms

“…Due to the strong mixing induced by the dc field, the low-contributions to the highly polarized states are relatively small. For high n, the excitation probability scales as ∼n −5 (i.e., ϕ n, =1,m |z|g ∼ n −3/2 and C n,m (k = n − 1, = 1) ∼ n −1 [23,24]), and therefore decreases rapidly with n, hindering the efficient production of the high-n polarized states.…”

Modified Atomic Orbital Calculations of Energy of the (2&lt;i&gt;s&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; &lt;sup&gt;1&lt;/sup&gt;&lt;i&gt;S&lt;/i&gt;) Ground-State, the (2&lt;i&gt;p&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; &lt;sup&gt;1&lt;/sup&gt;&lt;i&gt;D&lt;/i&gt;); (3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; &lt;sup&gt;1&lt;/sup&gt;&

“…Greatest attention have been concentrated on studying symmetric DES (nl 2 ) with excited electrons having equal values of principal quantum number n (intrashell states) where the electronic correlation effect may be predominant [18]. The investigations of the intrashell states of two-electrons systems are advanced and due to the group theoretical method [19] which allowed intrashell states to be approximatively classified and some of these properties studied [20]. Theoretical investigations of (nl 2 ) doubly excited states are performed by using various method.…”