Schematic illustration of rotational autoionization in para

For autoionization of the Jth level, which belongs to the series converging to the second (N+ = 2) ionization limit and autoionized by the continuum of (iV+ = 0), Eq. (8.4.7) gives (see Herzberg and Jungen, 1972) 

The interval 2B(2J +1) between the two ionization limits becomes small for heavy molecules and low values of J. 

Type of autoionization Molecule State r(cm-1) (obs) /(calc) Vibrational selection rules 

In this expression, da /dR reflects the difference in the Re values of the ion and Rydberg state potential curves and d2a /dR reflects the difference in the harmonic constants (u e) or in the dissociation energies of these two curves. If one defines n = n — ax (R=R+y using a truncated Taylor expansion as in Eq. (8.5.8) and keeping only the linear term of Eq. (8.6.2), one obtains 

Converting to the usual off-diagonal form [Eq. (8.4.4)] of Rydberg Rydberg matrix elements between members of the same IA series but with different vibrational factors, the matrix element can be written as 

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Figure 8.11 Schematic illustration of rotational autoionization in para-H2 showing the transition from case (b) to case (d). The electronic continua associated with X2Ej (u+ = 0, N+ = 0 and 2) are depicted by light horizontal lines. The stable and autoionizing levels of the H2 np Rydberg series with v = 0 and J = 1 are shown as heavy horizontal lines.

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