Positions of the Stark levels

As already mentioned, we define the positions of the Stark levels as the energies for which (OJ/QJ )2 assumes its maxima for fixed F, m and n. When the energy dependence of the //-dependent quantities in (5.17b) is much smaller than that of tanv, it is seen that the resonances, i.e., the minima of (fT /Q )2, occur when approximately 

According to the approximate version of (5.18b) it follows from (5.32) that 

The values of v for which (fl /Q)2 assumes its maxima and minima are obtained from the equation 

The positions of the Stark levels En, where n = m + 1 + n + n2, are obtained from the two simultaneous quantization conditions (5.9) and (5.44) along with (5.42). 

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Values of the energy E and the half-width T for different states of a hydrogen atom in an electric field F[= F according to (2.17)] of various strengths, obtained both in previous work by other authors and in the present work with the use of the phase-integral formulas, are presented in the tables of the present chapter. We use atomic units (au), i.e., such units that p = e = h = 1. The positions E of the Stark levels were obtained from (5.33) except for the state with n = 30 in Table 8.7, where the more accurate formula (5.40) along with (5.42) has been used. The half-widths T were obtained from (5.54) along with (5.55) and are therefore accurate only when the barrier is sufficiently thick, which means that T is sufficiently small. 

Representation of the Stark sub-level position in energy (cm ) for each site according to the excitation energy (cm ) ... 

Fig. 6.13 Part of the excitation spectrum oftheNaw = 29 Stark levels from the 3d state in an electrostatic field of 20.5 V/cm corresponding to nj values of n — 3, n — 4, and n — 5. The energy splitting between m = 0 (highest energy fine in the doublets) and m = 1 states is of the order of 180 MHz. The arrows indicate theoretical positions of energy levels obtained by a numerical diagonalization of the Stark Hamiltonian (from ref. 28).

Meerts and Dymanus [142, 153] extended their studies of the OH and SH radicals by examining the Stark effect and determining the electric dipole moments, but an even more extensive study of the Stark effect for OH and OD in several different vibrational levels was described by Peterson, Fraser and Klemperer [154], The effect of an applied electric field on the hyperfine components of the A-doublets for the. 7 = 3 /2 level of the 2n3/2 state is illustrated in figure 8.47. Measurements were made of the MF = 2, A MF = 0 transition in a calibrated electric field of approximately 700 V cnr1 and the Stark shift from the zero-field line position measured. The observations were made on resonances from 0 = 0, I and 2 for OH, and v = 0 and 1 for OD. 

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