Relative intensities in L-S coupling and

The relative intensities of a group of spectral lines which arise in electric dipole transitions between one L-S fine structure multiplet and another may be calculated from equation (5.26). The angular factors in this expression depend on the quantum numbers (S,L,J) and (S, L, J ) of the levels involved and may be calculated by vector coupling techniques. Unfortunately the formulae so derived are themselves rather complicated and the reader is referred to standard works on atomic spectroscopy, for instance Condon and Shortley (1967), where tabulations of the relative intensities may be found. 

Magnetic dipole and electric quadrupole transitions, which we have ignored so far, will be discussed in detail in Chapter 7. However, it should be noted that the selection rules governing these forbidden types of radiation can be derived by the application of the techniques already discussed here. The results are summarized in Table 7.1 together with the rules for electric dipole radiation previously derived in this chapter. 

In spherical polar coordinates show that the unit vectors (r, , ) are related to the cartesian unit vectors by 

4 669 cm. Calculate the relative intensities of the Zeeman components viewed in directions parallel and perpendicular to the applied magnetic field using a classical argument and compare with the results obtained from equation (5.9) and Table 5.1. 

Hence show that in a magnetic field will be split into 

---