# CCL: Slater orbital p - d transition probabilities

*From*: "James J. P. Stewart"
<jstewart|at|fujitsu.com>
*Subject*: CCL: Slater orbital p - d transition probabilities
*Date*: Mon, 19 Jan 2004 10:17:20 -0700

`Help! I'm trying to derive the oscillator integral, os, for p to d
``transitions in an atom, and have come up with the expression:
` os = (np+nd+1)!*2**(np+nd+1)*exp(p)**(np+1/2)*exp(d)**(nd+1/2)
--------------------------------------------------------
sqrt(5)*(exp(p)+exp(d)**(np+nd+2)*sqrt( (2*np)! * (2*nd)! )

`where the Slater orbital principal quantum numbers are "np"
and "nd", and
``the exponents are "p" and "d".
`

`Can anyone confirm or dispute this expression, please. Evidence
either way
``would be appreciated.
`

`My concern is that the integral becomes very large for large values of
"np"
``and "nd".
` Thanks,
Jimmy