Perturbed Rydberg series

One of the most intensively studied manifestations of channel interaction in the bound states is the perturbation of the regularity of the Rydberg series, which is evident if one simply measures the energies of the atomic states. Although measurements of Rydberg energy levels by classical absorption spectroscopy show the perturbations in the series which are optically accessible from the ground state, the tunable laser has made it possible to study series which are not connected to the ground state by electric dipole transitions as well. One of the approaches which has been used widely is that used by Armstrong et al. As shown in Fig. 22.1, a heat pipe oven contains Ba vapor at a pressure of ∼1 Torr. Three pulsed tunable dye laser beams pass through the oven. Two are fixed in frequency, to excite the Ba atoms from the ground 6s21So state to the 3P1 state and then to the 6s7s 3S1 state. The third laser is scanned in frequency over the 6s7s 3S1 → 6snp transitions. The Ba atoms excited to the 6snp states are ionized either by collisional ionization or by the absorption of another photon. The ions produced migrate towards a negatively biased electrode inside the heat pipe. The electrode has a space charge cloud of electrons near it which limits the emission current.

The autoionizing two electron states we have considered so far are those which can be represented sensibly by an independent electron picture. For example, an autoionizing Ba 6pnd state is predominantly 6pnd with only small admixtures of other states, and the departures from the independent electron picture can usually be described using perturbation theory or with a small number of interacting channels. In all these cases one of the electrons spends most of its time far from the core, in a coulomb potential, and the deviation of the potential from a coulomb potential occurs only within a small zone around the origin.

In contrast, in highly correlated states the noncoulomb potential seen by the outer electron is not confined to a small region. In most of its orbit the electron does not experience a coulomb potential, and an independent electron description based on nℓn′ℓ′ states becomes nearly useless. There are two ways in which this situation can arise. The first, and most obvious, is that the inner electron's wavefunction becomes nearly as large as that of the outer electron. If we assign the two electrons the quantum numbers niℓi and noℓo, this requirement is met when ni approaches no, which leads to what might be called radial correlation. The sizes of the two electron's orbits are related. The second way the potential seen by the outer electron can have a long range noncoulomb part is if the presence of the outer electron polarizes the inner electron states.

Information on orientational relaxation may be obtained by a wide range of techniques. Dielectric relaxation and magnetic resonance, neutron and light scattering, infrared spectroscopy and fluorescence depolarization are widely used. These different experimental probes of the phenomenon characterize it in different ways. The advantage of spectroscopic investigations is that they give information on relaxation times as well as on the corresponding correlation functions and their spectra. In particular, by combining the information in an absorption spectrum with that obtained from Raman scattering, one can determine the two lowest correlation functions of a molecule's axis position. A complete description of orientational relaxation is given by the infinite set of these functions.

The orientation of linear rotators in space is defined by a single vector directed along a molecular axis. The orientation of this vector and the angular momentum may be specified within the limits set by the uncertainty relation. In a rarefied gas angular momentum is well conserved at least during the free path. In a dense liquid it is a molecule's orientation that is kept fixed to a first approximation. Since collisions in dense gas and liquid change the direction and rate of rotation too often, the rotation turns into a process of small random walks of the molecular axis. Consequently, reorientation of molecules in a liquid may be considered as diffusion of the symmetry axis in angular space, as was first done by Debye.

It was demonstrated in Chapter 6 that impact theory is able to describe qualitatively the main features of the drastic transformations of gas-phase spectra into liquid ones for the case of a linear molecule. The corresponding NMR projection of spectral collapse is also reproduced qualitatively. Does this reflect any pronounced physical mechanism of molecular dynamics? In particular, can molecular rotation in dense media be thought of as free during short time intervals, interrupted by much shorter collisions?

It seems that an affirmative answer is hardly possible on the contemporary level of our general understanding of condensed matter physics. On the other hand, it is necessary to find a reason for numerous successful expansions of impact theory outside its applicability limits.

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the ‘continuation’ of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation–vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation.

As is seen from relations (2.5)–(2.8), isotropic scattering is independent of orientational relaxation. Since the isotropic component of the polarization tensor is invariant to a molecule's reorientation, the corresponding correlation function K0 describes purely vibrational relaxation. This invariance does not mean however that vibrational relaxation is completely insensitive to angular momentum relaxation. Interaction between vibrations and a molecule's rotation determines the rotational structure of the isotropic scattering spectra observed in highly rarefied gases. The heavier the molecule, the smaller is the constant αe of the Q-branch rotational structure. In fact this thin structure is easily resolved only in hydrogen and deuterium. The isotropic Raman spectrum of most other gases is usually unresolved even at rather low pressure and when describing its shape at higher densities one may consider J a classical (continuous) variable.

Within the framework of the impact theory J(t) is a purely discontinuous Markovian process. The same is valid for the corresponding frequency, or ‘rotational component’, which changes its position in the spectrum after each collision. This phenomenon, known as spectral diffusion or rotational frequency exchange, is accompanied by adiabatic dephasing of the vibrational transition caused by these same collisions. Both processes contribute to observed spectral transformation with increasing collision frequency, however they have opposite effects. While frequency exchange leads to collisional narrowing, dephasing results in the spectrum-broadening. If dephasing is weak and the collision frequency is small, the tendency for the spectrum to narrow prevails.