Hyperfine Structure and Isotope Shifts

We shall briefly review the relationship between spectroscopic observables and nuclear properties/ These properties include spins, magnetic dipole and electric quadrupole moments, as well as the variation in the mean square charge radius within a sequence of isotopes. They manifest themselves in the hyperfine structures and isotope shifts. The hyperfine energies of the different F states within a hyperfine multiplet / - / F J + I, given by the well-known formula 

The nuclear moments p,i and Qs can be extracted from A and B using empirical or theoretical values for the magnetic hyperfine field HdO) and the electric field gradient pjj 0) at the nucleus. Apart from hyperfine anomaly corrections He(0) is usually known from direct g,-factor measurements (g = iii/.IfiM) on the stable isotopes. pjj 0) is taken from semi-empirical or theoretical analyses, unless precise values are available from the hfs of muonic atoms. 

Similarly, the isotope shift of an optical transition is related to the change in the nuclear mean square charge radius between the 

Element Stable isotopes radioactive isotopes Production reactions Production facility Wavelength Transition (A) Reference  

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Nuclear properties (spins, moments, charge radii) revealed by the analysis of hyperfine structure and isotope shift of atomic levels have been obtained in decades of experiments. Since 1975 with the introduction of tunable dye laser, the rebirth of the methods, some already known since 1930, had led to many on line experiments on short lived isotopes not investigated before. I report here a sample of the experiments done by the Orsay, Mainz groups at CERN. Although experiments have been carried out by the Orsay group using the proton beam of the CERN Proton Synchrotron, most of the experiments have been done at Isolde, the on - line mass separator at CERN, whose radioactive beams are essential to the success of these experiments [RAV 84]. 

Hyperfine structure is another kind of electron-nuclear interaction and so also indicates the presence of an s-electron. In this case, the eflFect is not additive—the configuration s- gives no hyperfine structure. Hyperfine structure and isotope shift are somewhat complementary. 

Bohm, H-D.V. Michaelis, W. and Weitkamp, C., "Hyperfine Structure and Isotope Shift Measurements on 235jj anLaser-Separation of Uranium Isotopes by Two-Step Photoionization," Opt. Commun., 1978, 26, 177-182. 

Childs, W. J. and Goodman, L. S., "Hyperfine structure and isotope-shift measurements on Dy I 5988.562 using high-resolution laser spectroscopy and an atomic beam,"... 

In astrophysics much interest has in recent years been focussed on boron. Although its cosmic abundance is extremely low, it plays an important role in testing models of Big Bang Nucleosynthesis [10]. Optical spectroscopy is the only method for establishing B abundances in stellar objects, and thus a good knowledge of energy structure, transition probabilities, hyperfine structure and isotope shifts is needed [11]. 

Laser spectroscopic studies of radioactive isotopes have proved to be a valuable source in obtaining nuclear properties. The continuing developments promise a way of meeting challenge in measuring nuclear properties far from stability. It may also be so that new isotopes are discovered by optical rather than nuclear methods. The extreme high precision measurements in ionic traps make rather small nuclear effects such as hype ne anomaly interesting for tx experimental and theoretical studies. In ad(Ution the theories of hyperfine structure and isotope shift are well understood, so that detailed information on nuclear properties can be extracted. 

Fig. 4.8 Hyperfine structure and isotope shifts of radioactive Na-isotope [396]...

Precision measurements of hyperfine structure and isotope shifts yield information on nuclear spins, quadrapole moments, and nuclear deformations. The results of these experiments allow tests of nuclear models of the spatial distribution of protons and neutrons in highly deformed nuclei [467]. In Fig. 4.8 the hyperfine spectra of different Na isotopes are depicted, which had been produced by spallation of aluminum nuclei by proton bombardment according to the reaction Al(/ , 3p,xn) Na [468] and in Fig. 4.29 the hfs of 6 isotopes of the titanium ion H+ illustrates the good signal-to-noise ratio. Such precision measurements have been performed in several laboratories for different families of isotopes [466-469]. 

Fig. 9.23. Hyperfine structure and isotope shift of the D lines of radioactive Na isotopes [9.74]...

Many of the spectroscopic studies were performed to demonstrate the capability of the technique and of a number of variants which are specific for the combination of laser spectroscopy with fast beams of ions or atoms. An example has already been discussed in Section 3.3 Resonant two-photon exdtation becomes possible by adjusting the Doppler shifts for interaction with the direct and retroreflected laser beam to the atomic transition energies. Other features include the preparation of otherwise inaccessible atomic states, the separation of hyperfine structures from different isotopes by the Doppler shift, or the observation of time-resolved transient phenomena along the beam. The extensive research on nuclear moments and radii from the hyperfine structure and isotope shift constitutes a self-contained program, which will be discussed separately in Section 5. 

The motivation for hyperfine structure and isotope shift studies in the isoelectronic case of Ra II and in Ra I came originally from nuclear physics. After early measurements of the atomic energy levels on the long-lived Ra/ the isotope shifts and the hyperfine structures of the odd-A isotopes remained inaccessible until recentlyThe extraction of nuclear moments required the analysis of the electronic hyperfine fields which was performed in on-line collinear-beam studies of several transitions involving the 7s Si/2 and Ip Pi/2 states of Ra II and all states of the 7s7p configur-... 

Figure 1. Experimental setup for hyperfine structure and isotope shift measurements of Ba Rydberg states. (Taken from Ref. 28.)...

Quasiresonant two-step excitation was employed by Eliel and Hoger-vorst to study hyperfine structures and isotope shifts of 6sns and... 

At this point it is of interest to compare coherent two-photon with stepwise excitation, although the most suitable experimental scheme depends on the particular problem under study. In the case of Doppler-free coherent two-photon spectroscopy, only the initial and final state contribute to the recorded splittings and linewidths. Therefore, this technique offers better resolution, and generally simple spectra are obtained which are straightforward to interpret. On the contrary, the hyperfine structure of the intermediate state complicates the spectra recorded by resonant, two-step excitation, and a more involved analysis is required to deduce hyperfine structures and isotope shifts. Furthermore, the lifetime broadening of the intermediate state (At, )... 

Apart from the energy-level structures discussed above, molecules exhibit both the Zeeman and Stark effects. Further, hyperfine structure and isotopic shifts also occur. The occurrence of isotopic shifts is particularly simple to understand considering the substantially altered values of the reduced mass found in the vibrational and rotational energy expressions. 

E. Matthias, H. Rinneberg, R. Beigang, A. Timmermann, J. Neukammer, K. Liicke Hyperfine structure and isotope shifts in alkaline earth atoms, in Atomic Physics 5, ed. by I. Lindgren, A. Rosen, S. Svanberg (Plenum, New York 1983) p.543... 

Studies of the volmne effect yield information on the charge distribution in the nucleus. Hyperfine structure and isotopic shifts are of the same order of magnitude. Isotopic shifts can be studied in the visible region as weU as in the X-ray region. Particularly prominent isotopic shifts are obtained for muonic atoms, in which, for example, a p meson (m = 209me) has taken the place of an electron. The classical radius of the orbit is reduced by a factor of 209, and thus the nuclear influences are much greater than those pertaining to the electrons. Isotope shifts and their interpretation have been discussed m [2.57-2.59J. 

Because of small imperfections and the finite size of the circular aperture the practically achievable resolution is frequently reduced. Because of its high resolution the Fabry-Perot interferometer has been much used for measuring hyperfine structure and isotope shifts. The spectral line of interest is then first selected by a monochromator or an interference filter. First, a free spectral range of sufficient width to accomodate all the spectral components of the line is chosen to allow the correct order of components to be determined. Then the plates are moved fiurther apart, resulting in an increased resolution but also the mclusion of overlapping orders. 

Discuss hyperfine structure and isotopic shifts. What are the origins of these effects What can be learned from these phenomena Certain experimental teclmiques can be used for measuring hyperfine structures as well as isotopic shifts, while others are only useful for hyperfine-structure measurements. How does this arise ... 

C. Thibault, F. Touchard, S. Buttgenbach, R. Klapisch, M. de Saint Simon, H.T. Duong, P. Jacquinot, P. Juncar, S. Liberman, P. Pillet, J. Pinard, J.L. Vialle, A. Pesnelle, G. Huber, Hyperfine structure and isotope shift of the D line of... 

P. Grundevik, M. Gustavsson, G. Olsson, T. Olsson, Hyperfine-Structure and Isotope-Shift Measurements in the 6s5d 6p5d Transitions of Ba I in the Far-Red Spectral Region, preprint, 1982 R.E. Silverans, J-dependent Isotope Shifts in Ba Ions, (private communication, 1982). 

HYPERFINE STRUCTURE AND ISOTOPE SHIFTS OF RYDBERG STATES IN ALKALINE EARTH ATOMS... 

Moore s level list [8] is based on the results of van Kleef [2] who has found new levels in both parities, determined the g value of most of them and assigned tentative designations to a number of levels. As the studies of hyperfine structure and isotope shift and the theoretical calculations of the group of configurations (5d+6s) have led to the modification of some earlier designations, the lists of levels will be given (Tables 2/19 and 2/20, pp. 187/8). 

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