The present review is devoted to the recent advances performed in alkaline-earth atoms by the selective laser preparation of autoionizing asymmetrical double Rydberg states which have, so far, not been observed in natural environments. Because the great amount of flexibility achieved by the sequential laser electron excitations, a wide choice of two-electron situations have been investigated and analyzed which exhibit spectral features due to long-range effects of the Coulomb electron-electron repulsion. To overcome the autoionization broadening of the lines, double Rydberg states with a non-core penetrating high-ℓ outer electron were produced by combining temporal laser excitation technique with the electric-field switching method. The study of the spectral correlation signatures in Nsn ℓ double Rydberg states versus ℓ allow to understand their evolution from simple spectra (ℓ ⩾ 10) due to long-range dipole interaction to more complex data (ℓ ⩽ 7) induced by short-range multipole effects when two electrons start to influence more each other.
We have calculated the cross section for Raman scattering of light from a hydrogenic atom, for a wide range of photon energies. The calculation assumes the photon encounters the atom in its ground state and excites it to the
2s state. Since various contributions to the matrix element may be isolated in the computation, the calculation allows one to obtain a notion of the relative importance of various classes of intermediate states in a given frequency range. We also point out that the Raman efficiency
S may be expressed in terms of the derivative of the electronic polarizability tensor with respect to a parameter that measures the degree of excitation of the atom. Thus, the formal expression for
S assumes an appearance identical to the expression encountered in the phenomenological theory of the first-order Raman effect in solids.
The dominant long-range interaction of an alkali-metal atom with charged particles at low energies is given for large separation R by the dispersive potential $W\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}{/R}^{4}$ in terms of the dipole polarizability ${\ensuremath{\alpha}}_{d}.$ For atoms prepared initially in Rydberg states of quantum numbers (n, l), the potential assumes a more complicated form due to the complete or near degeneracy of the n manifold. Contributions to the polarizability are treated in two parts, (a) one for the nondegenerate states and (b) the other for the degenerate or near degenerate cases. It is shown that ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}_{d}^{(b)}$ for case (b) is in general R dependent, and in the limit of complete degeneracy, diverges as
R2. That is, for a small energy gap \ensuremath{\Delta} between a pair of nearly degenerate states which are dipole coupled, the dispersion potential ${W}^{(b)}\ensuremath{\simeq}{D/R}^{2}$ for
R<Rx and ${W}^{(b)}\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}^{(b)}{/R}^{4}$ for
R>Rx, where D is the dipole moment, ${R}_{x}=[2|D/\ensuremath{\Delta}|{]}^{1/2},$ and ${\ensuremath{\alpha}}_{d}^{(b)}\ensuremath{\simeq}{D}^{2}/\ensuremath{\Delta}.$ They may also compete with a
1/R3 potential for Rydberg atoms with
l>0. The total ${\ensuremath{\alpha}}_{d}$ can be very large in magnitude for small \ensuremath{\Delta} and even assume negative values, but the corresponding
Rx also increases as \ensuremath{\Delta} decreases. The validity region in R of the ${R}^{\ensuremath{-}4}$ behavior of the potential recedes to larger R as the polarizability grows. A general formula for ${\ensuremath{\alpha}}_{d}$ is given, taking into account the effects of fine-structure splitting, the Lamb shift, and quantum defects.
The present Rapid Communication makes two points. (1) The exact matrix elements for the transitions between two hydrogenic states accompanied by the emission or absorption of one photon has been calculated in closed form without resorting to multiple expansions. Thus, retardation is taken into account exactly. (2) In addition to using these exact matrix elements to calculate transition probabilities, one can make estimates of the contribution to second-order processes of these matrix elements. In particular, it can be shown that the total contribution of bound-state matrix elements to the electromagnetic shift of the ground state is finite without renormalization.
We present experimental energy-level positions for Ba high-l Nsnl double Rydberg states with N=8 (n=13--15, l\ensuremath{\geqslant}7) and N=9 (n=13--15, l\ensuremath{\geqslant}7). These data as well as previously reported measurements for N=7 (n=12--15, l\ensuremath{\geqslant}5) and N=10 (n=13--15, l\ensuremath{\geqslant}10) are parametrized in order to yield values for the
Ba+ Ns effective dipole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ and quadrupole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ polarizabilities. The obtained ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ values are 1.25(5)\ifmmode\times\else\texttimes\fi{}
103, 7.05(4)\ifmmode\times\else\texttimes\fi{}
103, 2.95(4)\ifmmode\times\else\texttimes\fi{}
104, 9.39(15)\ifmmode\times\else\texttimes\fi{}
104 in
a03 units and the ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ values are 1.7(8)\ifmmode\times\else\texttimes\fi{}
104, 1.8(2)\ifmmode\times\else\texttimes\fi{}
105, -1.0(2)\ifmmode\times\else\texttimes\fi{}
106, -1.0(2)\ifmmode\times\else\texttimes\fi{}
107 in
a05 units for N=7, 8, 9, and 10, respectively. The ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ evolution with N is found to follow a
N∗6.9(1) power law, while calculated static polarizabilities present somewhat lower power dependence. From this small difference it is not possible to appreciate the importance of nonadiabatic effects between the two asymmetrically excited electrons. On the other hand, the larger discrepancies appearing between the calculated static and fitted quadrupole polarizabilities show clear evidence of nonadiabatic effects. Particularly the negative ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ sign for N\ensuremath{\geqslant}9 is attributed to the increasing strength of dynamical effects on the Ns core electron caused by the motion of the outer high-l electron. It gives evidence of the increasing importance of nonadiabatic radial correlation between two planetary electrons when the Ns inner electron is sufficiently radially extended to be characterized as an inner Rydberg electron without, nevertheless, any appreciable overlapping with the outer electron.
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron
R-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances
R from 20 to 400 bohrs and energies corresponding to
n from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers
n) and computations based on contact-potential models (higher quantum numbers
n).