CsF in the A 1 X ground state

Now for CsF in its X ground state the value of A is zero the second 3-j symbol in (8.278) is then non-zero only if 1 + J + J is even, so that. / =. / I is a requirement. In other words, there can be no first-order Stark effect in this case. Equation (8.278) tells us that each rotational level J is mixed by the electric field with the adjacent rotational levels. / 1, and the Stark behaviour may therefore be represented by the following 3x3 truncated matrix. 

B is the rotational constant, and M remains a good quantum number. The above 3x3 matrix is, of course, something of an approximation since, in reality, the Stark matrix is infinite and the accuracy with which the electric field mixing is calculated depends upon the number of rotational states included in the calculation. 

The energies of the levels in an electric field can be calculated by numerical diagonalisation of the above matrix for different values of the electric field and the J, M quantum numbers. However, perturbation theory has also often been used and we may readily derive an expression for the second-order Stark energy using the above matrix elements. The result is as follows  

This is a very well-known and often quoted result, first presented by Kronig [49]. For 

Diagonalisation of the Stark matrices enables us to plot the Stark energies, given values of B and /M), and the results are shown in figure 8.27 for the first three rotational levels, J = 0, 1 and 2. The parameter X is defined by A.2 = iJ E jB. In figure 8.28 we show plots of the effective electric moment of the molecule in the different J, M states listed in figure 8.27. With the aid of both diagrams, we are able to understand the principles of electric state selection, and the electric resonance transitions. 

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