Zeeman hyperfine structure

By far the most important influence of a nuclear spin on the EPR spectrum is through the interaction between the electron spin S and the nuclear spin I. Usually, at X-band frequencies this interaction is weaker, by an order of magnitude or more, than the electronic Zeeman interaction, and so it introduces small changes in the EPR spectrum known as hyperfine structure. As a first orientation to these patterns, note that just like the electron spin S, also the nuclear spin / has a multiplicity ... 

With this procedure, as with the double-resonance methods in atomic physics, Zeeman and Stark splittings, hyperfine structures and A doublings in molecules can be measured with high precision, even if the observed level splittings are far less than the optical dopp-ler width. From the width of the rf resonance and from the time response of the pumped systems, orientation relaxation rates can be evaluated for individual v J") levels. Other possible applications of this promising technique have been outlined by Zare 30) Experiments to test some of these proposals are currently under investigation and their results will be reported elsewhere. 

This method is specially suited for measurements of closely spaced Zeeman or Stark splitting and fine and hyperfine structures, which are separated only within their doppler linewidth 5 ). 

BACK-GOUDSMIT EFFECT. An effect closely related to the Zeeman effect. It occurs in the spectrum of elements having a nuclear magnetic and mechanical moment. See also Hyperfine Structure and Paschen-Back Effect. 

Extensions allowing CPT and Lorentz invariance violations [23] lead to atomic models that reflect the symmetry violations as shifts in the atomic energy levels. It has been argued that such effects can be discovered in the fine-structure of Is — 2s transitions and also in the hyperfine structure of Zeeman transitions. 

II. GROUND STATE HYPERFINE STRUCTURE AND ZEEMAN EFFECT... 

The high-resolution spectroscopy of OH has been perhaps the most important test bed for the development of the theory of the molecular energy levels, both in zero field and in the presence of applied magnetic fields. In this section, we concentrate on the A-doubling and hyperfine structure, as probed by the molecular beam studies. In chapter 9 we discuss the complex theory of the Zeeman effect, and in chapter 10 deal with rotational transitions. Our discussion therefore follows a pattern similar to that adopted for the NO molecule. 

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

An alternative procedure for the Zeeman background corrector is to operate the hollow cathode continuously but to expose the sample to an alternating magnetic field. The sample atoms absorb at the resonance line when not exposed to the magnetic field, but develop hyperfine structure and do not absorb the resonance line when the magnet is turned on. With the magnetic field on, absorption of the resonance line is a measure of molecular background. From the combined data, the net atomic absorption can be measured. 

The collisional broadening rates are in good agreement with those observed in Na2 by Tsai ( ). The natural linewidths are larger than what one would expect from the lifetime measurements of Demtrdder et (10). The additional broadening (7 MHz for Na2 and 20 MHz for Li77 could result from an unresolved hyperfine structure or from the Zeeman effect produced by the oven heating wire. 

Radford (1961, 1962) and Radford and Broida (1962) presented a complete theory of the Zeeman effect for diatomic molecules that included perturbation effects. This led to a series of detailed investigations of the CN B2E+ (v — 0) A2II (v = 10) perturbation in which many of the techniques of modern high-resolution molecular spectroscopy and analysis were first demonstrated anticrossing spectroscopy (Radford and Broida, 1962, 1963), microwave optical double resonance (Evenson, et at, 1964), excited-state hyperfine structure with perturbations (Radford, 1964), effect of perturbations on radiative lifetimes and on inter-electronic-state collisional energy transfer (Radford and Broida, 1963). A similarly complete treatment of the effect of a magnetic field on the CO a,3E+ A1 perturbation complex is reported by Sykora and Vidal (1998). The AS = 0 selection rule for the Zeeman Hamiltonian leads to important differences between the CN B2E+ A2II and CO a/3E+ A1 perturbation plus Zeeman examples, primarily in the absence in the latter case of interference effects between the Zeeman and intramolecular perturbation terms. 

Urf being the selected radio frequency and H the homogeneous field applied. This original setup was then widely used for the determination of the magnetic and quadrupolar hyperfine structure (hfs) constants A and B. Hereby one has to consider that the additional magnetic field further splits the atomic energy levels now characterized by F into (2F + 1) sublevels and mixes states of the same Mp but different F values. A Zeeman term has therefore to be added to the hyperfine Hamiltonian according to... 

---