Calculation of Form Factor for the Rydberg Atoms.

Abstract

Calculations Of the Scaled Form Factor for the transition from one bound state to another bound state in the case of the Hydrogen atom are presented in this article. Firstly we have to choose the best approximation available in the mathematical literature for the Terminating Hypergeometric Functions (THFs) as several numerical expressions are available of the Form Factor containing THFs and dealing with the large values of the principal quantum number (n) is a challenging task as numerical computation programs give overflow and can- cellation errors for large n. Here we analyzed and discussed Jacobi polynomial approximation and Tricomi Expansion Approximation methods through numer- ical computation calculations. Moreover, we found out that using numerous properties and recurrence relations of Jacobi Polynomials, we can compute the form factor expressions even for large n values with much accuracy and precision which is not that smooth when expressions are in the Hypergeometric Functions.