Optical spectra of autoionizing Rydberg states

First we consider the two channel problem shown in Fig. 21.1. Our present interest is in the region above limit 1, i.e. the autoionizing states of channel 2. Later we shall consider the similarity of the interactions above and below the limit. A typical quantum defect surface obtained from Eq. (20.12) or (20.40) for all energies below the second limit is shown in Fig. 21.2. The surface of Fig. 21.2 may be obtained with either of two sets of parameters, dj = 0.56, d2 = 0.53, and R[2 - 0.305, R n — R22 = 0or/q = 0.4,/ = 0.6, and Un = U22 = cosO and Ul2 = — U21 = sin, with 6 = 0.6 rad. 1,2To conform to the usual convention, in Fig. 21.2 the Vj axis is inverted. The wavefunction is given in terms of the collision channels by 

Between limit 1 and limit 2, since j i is open, A = 1. If we choose At = 1, it is straight forward to show that 

The probability of finding an autoionizing state of channel 2 at any energy is given by A2, which we shall term the spectral density. Squaring Eq. (21.2) we find 

Thus the FWHM is given by 2(R[2)2/ji or in terms of the energy width1 

6) shows both the expected v 3 scaling of the autoionization rates and the utility of the parametrization in terms of 51, d2, and R 2. 

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