Autoionising Rydberg series in a flat continuum

It is interesting to study how the three shape parameters R, C and D can alter the shapes of the line profiles. Since the numerator in the formula for j v) is a perfect square, there must be a zero for tantti = —B. This defines a Rydberg series of transmission windows (one cycle of the series is shown in fig. 8.7). 

Likewise, one can readily show that the peak cross section occurs for tan7ri/ = (D2 — BC)/(B — C). There are also bounds on the value of C which one can find by rearranging the formula as 

Since a cross section is positive definite, by choosing D positive (no loss of generality), we have —D C D. 

Since B is fully determined by a single point on the profile (the zero in the cross section), it is convenient to explore changes in a(v) by varying the parameters C and D for fixed B. 

We begin with C. Clearly, there exist just three points on the profile within any cycle (a Rydberg cycle is defined by an increase of 2tt in 

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