Principles of electric resonance methods

As the name suggests, electric resonance experiments make use of electric fields to achieve molecular state selection. Fignre 8.25 shows a schematic diagram ofamolecular beam electric resonance instrument, which we wUl discuss in more detail when we describe experiments on the CsF molecule. In contrast to the magnetic resonance apparatus discussed earher, the A, B and C fields in figure 8.25 are all elecfric fields. In 

The first successful electric resonance experiment was reported by Hughes [48] who studied the CsF molecule, an appropriate beam being produced from a hot oven. He used both A and B electric dipole fields, separated by a homogeneous electric C field combined with a radio fi equency electric field at right angles to the static field. In order to understand both the deflection and state selection in the dipole fields, as well as the electric resonance spectrum, we first consider the details of the Stark effect. 

An applied electric field ( ) interacts with the electric dipole moment (fx ) of a polar diatomic molecule, which lies along the direction of the intemuclear axis. The applied field defines the space-fixed p = 0 direction, or Z direction, whilst the molecule-fixed = 0 direction corresponds to the intemuclear axis. Transformation from one axis system to the other is accomplished by means of a first-rank rotation matrix, so that the interaction may be represented by the effective Hamiltonian as follows  

We choose to work in the simple basis set rj, A J, Mj) where A is the component of electronic angular momentum along the intemuclear axis rj represents all relevant unspecified quantum numbers, including the vibrational quantum number. We use J, which is appropriate for E molecules, rather than N tiiere is no distinction between J and N for molecules in singlet states. The mattix elements of (8.277) in this basis are given by 

Now for CsF in its E+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 J = J 1 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 J 1, and the Stark behaviour may therefore be represented by the following 3x3 truncated matrix. 

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