SO in the a 1A state

There are no nuclear spin magnetic moments in the predominant isotopic form of SO (i.e. 32S160), so that hyperfine interactions are absent. The orbital angular momentum vector L is coupled to the rotational angular momentum vector R to form the total angular momentum J. For a A state the projection of the value of L on the internuclear 

In a theoretical analysis of the Zeeman elfect for a diatomic molecule in a singlet state, Brown and Uehara [10] show that the effective Hamiltonian may be written, 

In these equations gi is the orbital g-factor corrected for quantum electrodynamic, relativistic and diamagnetic effects [11]. A gi is a small correction to the orbital g factor arising from non-adiabatic mixing of excited electronic states, whilst g v and ger are the nuclear and electronic contributions to the rotational g-factor, gr. 

In the second line of (9.4) we have transformed from space to molecule-fixed axes (q). If we now retain only terms diagonal in the 1A state by putting q = 0, we obtain the diagonal and off-diagonal Zeeman matrix elements, as follows  

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). 

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