Fine structure intervals

Energy between adjacent n states Orbital radius Geometric cross section Dipole moment (nd er nf) Polarizability Radiative lifetime Fine-structure interval... 

The fine structure intervals of the alkali atoms often fall in the 1-10 MHz range, in which case the transition between spin orbit and uncoupled states can be made either diabatically or adiabatically. Jeys et al.16 have observed the transition from an adiabatic to a diabatic passage from the coupled fine structure states to the uncoupled states. With a pulsed laser, they excited Na atoms from the 3p1/2 state to the 34d3/2 state with o polarized light, which leads to 25% my = 1/2 atoms and... 

Measuring the M intervals by microwave resonance techniques generally yields the fine structure intervals as well. However, A = 0 transitions between the fine structure levels can also be examined by several other techniques. The first of these is rf resonance. Since the transition involves no change in Z it is not an electric dipole transition but rather a magnetic dipole transition, and a straightforward approach is magnetic resonance, which has been used by Farley and Gupta36 to measure the 6f and 7f fine structure intervals in Rb. Their approach is... 

Fig. 16.8 Schematic illustration of the magnetic resonance technique used to measure the Rb nf fine structure intervals. The Rb atoms in the n2F states are populated by spontaneous decay of the n D5/2 states, which are populated by stepwise excitation of the ground state atoms. The rf transitions, induced among the magnetic sublevels of the n2F states, are detected as a change in the intensity of the polarized n2F — 42D fluorescence. The lower part of the figure shows a sketch of the experimental arrangement (from ref. 36).

Both Aj = 0 and Aj = 1 transitions can be detected, the Aj = 1 intervals being more sensitive to the fine structure interval. 

A good example of the use of the electric resonance technique is the measurement of the Na nd fine structure intervals and tensor polarizabilities.38 These transitions were observed using selective field ionization, although they appear to be unlikely prospects for field ionization detection because of the small separations of the levels, 20 MHz. The nd3/2 states were selectively excited from the 3p1/2 state in a small static electric field and the = 0 transitions to the nd5/2 states induced by a... 

When the fine structure frequencies fall below 100 MHz they can also be measured by quantum beat spectroscopy. The basic principle of quantum beat spectroscopy is straightforward. Using a polarized pulsed laser, a coherent superposition of the two fine structure states is excited in a time short compared to the inverse of the fine structure interval. After excitation, the wavefunctions of the two fine structure levels evolve at different rates due to their different energies. For example if the nd3/2 and nd5/2 mf = 3/2 states are coherently excited from the 3p3/2 state at time t = 0, the nd wavefunction at a later time t can be written as40... 

The first measurements of Na nd fine structure intervals using quantum beats were the measurements of Haroche et al41 in which they detected the polarized time resolved nd-3p fluorescence subsequent to polarized laser excitation for n=9 and 10. Specifically, they excited Na atoms in a glass cell with two counterpropa-gating dye laser beams tuned to the 3s1/2—> 3p3/2 and 3p3/2— ndj transitions. The two laser beams had orthogonal linear polarization vectors et and e2 as shown in Fig. 16.9. 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

To put the alkali fine structure intervals in perspective it is useful to compare them to the hydrogenic intervals. For H the energy of Eq. (16.4) is valid if45... 

Egan, P.O., Hughes, V.W. and Yam, M.H. (1977). Precision determination of the fine-structure interval in the ground state of positronium. IV. Measurement of positronium fine-structure density shifts in noble gases. Phys. Rev. A 15 251-260. 

A comparison between theory and experiment for the fine structure intervals in helium holds the promise of providing a measurement of the fine structure constant a that would provide a significant test of other methods such as the ac Josephson effect the and quantum Hall effect. The latter two differ by 15 parts in 108 and are not in good agreement with each other [59]. 

Table 9 presents a summary of the known contributions to the fine structure intervals, and a comparison with several recent experiments. The theoretical uncertainty will remain at 15 kHz until the calculations described above have been completed. However, the present result is in remarkably good agreement with the measurement of Minardi et al. [67], which is within a factor of two of reaching the 1 kHz level for the larger i>oti interval. The measurements of Storry et al. [16] and Castilega et al. [18] at the 1 kHz level for the interval are not as sensitive to a, but they provide an important check on the theory. Once both theory and experiment are in place to the necessary accuracy, a new value for a can be derived. 

Fig. 7. Natural linewidth divided by the total transition energy for the ls2p 3Po — 3Pi, ls2p 3P2 — 3Pi and ls2p 3Pq — 3P2 fine structure intervals...

Table 4. Experimental results for the ls2p 3Pj j/ fine structure intervals compared with theory, units cm-1. (The calculations of Zhang et al. are incomplete at the level...

Abstract. We present a review of the helium spectroscopy, related to transitions between 23S and 23P states around 1083 nm. A detailed description of our measurements, that have produced the most accurate value of the 23Po — 23Pi fine structure interval, is given. It could produce an accurate determination (34 ppb) of the fine structure constant a. Improvements in the experimental set up are presented. In particular, a new frequency reference of the laser system has been developed by frequency lock of a 1083 nm diode laser to iodine hyperfine transitions around its double of frequency. The laser frequency stability, at 1 s timescale, has been improved of, at least, two orders of magnitude, and even better for longer time scales. Simultaneous 3He —4 He spectroscopy, as well as absolute frequency measurements of 1083 nm helium transitions can be allowed by using the Li-locked laser as frequency standard. We discuss the implication of these measurements for a new determination of the isotope and 23 5 Lamb shifts. 

Recently we developed a new approach which improves the sensitivity to a variation of a by more than an order of magnitude [1,2]. The relative value of any relativistic corrections to atomic transition frequencies is proportional to a2. These corrections can exceed the fine structure interval between the excited levels by an order of magnitude (for example, an s-wave electron does not have the spin-orbit splitting but it has the maximal relativistic correction to energy). The relativistic corrections vary very strongly from atom to atom and can have opposite signs in different transitions (for example, in s-p and d-p transitions). Thus, any variation of a could be revealed by comparing different transitions in different atoms in cosmic and laboratory spectra. 

This method provides an order of magnitude precision gain compared to measurements of the fine structure interval. Relativistic many-body calculations are used to reveal the dependence of atomic frequencies on a for a range of atomic species observed in quasar absorption spectra [1], It is convenient to present results for the transition frequencies as functions of a2 in the form... 

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