Quantum defects and fine structure

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of 2 quite accurately.25 

The quantum defects of the n = 10 states of He are given in Table 18.2. The quantum defects for the s and p states are derived from optical measurements, specifically from the term energies given by Martin.26 The quantum defects of the i = 8 and 9 (10 and 10m) states are calculated using Eq. (18.2), and the quantum defects of the 2 i 7 states are obtained from the calculated i = 8 quantum defect and the measured intervals reported by Hessels et a/.15 The quantum defects given by Table 18.2 are by no means indicative of the possible precision of the measurements. For example, Hessels etal. have reported measurements of n = 10 intervals which have precisions of parts per million.15 

Bethe and E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1957). 

Wing and K.B. MacAdam, in Progress in Atomic Spectroscopy, eds. W. Hanle and H. Kleinpoppen (Plenum, New York, 1978). 

---

In this section we survey the results obtained for quantum defects and fine structure intervals in such a way as to highlight the unifying features of the observations. 

The data can be represented either as quantum defects for each fine structure series or as a quantum defect for the center of gravity of the level and a fine structure splitting. For the moment we shall use the latter convention, although it is by no means universal. Explicitly, we represent the energy of an nij state, where j = ( + s and s is the electron spin, as... 

In order to unify, in fhe spirit of quantum defect theory, the treatment of discrefe and confinuous spectra in the presence of discrete Rydberg and valence states and of resonances, Komninos and Nicolaides [82, 83] developed K-mafrix-based Cl formalism that includes the bound states and the Rydberg series, and where the state-specific correlated wavefunc-tions (of the multi-state o) can be obtained by the methods of the SSA. The validity and practicality of fhis unified Cl approach was first demonstrated with the He P° Rydberg series of resonances very close to the n = 2 threshold [76], and subsequently in advanced and detailed computations in the fine-structure spectrum of A1 using fhe Breit-Pauli Hamiltonian [84, 85], which were later verified by experiment (See the references in Ref. [85]). 

Jun Jungen, Ch., Roche, A.L. Fine structure of the 4f complexes of ArH and KrH revisited Quantum defect theory used as a spectroscopic tool, J. Chem. Phys. 110 (1999) 10784-10791. 

From the optically pumped atomic or molecular Rydberg levels neighboring levels can be reached by microwave transitions, as was mentioned above. This triple resonance (two-step laser excitation plus microwave) is a very accurate method to measure quantum defects, fine-structure splitting, and Zeeman and Stark splitting in Rydberg states [592]. 

The measurements were extended to two-photon and three-photon absorption related to d-g and d-h transitions, respectively, in the n = 13-17 states of sodium. In the case of the three-photon transitions, a microwave frequency was swept while an rf frequency was fixed, and two rf photons and one microwave photon were absorbed. The detection scheme was the same as in Ref. 192. The measurements provided accurate quantum defect values and revealed hydrogenic fine structures for I <2. 

---