August 18th, 2020

лошадь, диаграмма, Фейнман

Интеграл от двух сферических бесселей с гауссианой

The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian:
Rami Mehrem
In this paper, the integral (λ10λ20λ30)∫∞0rλ3+2exp(−αr2)jλ1(k1r)jλ2(k2r)dr, where k1, k2 and α are positive, is evaluated analytically. The result is a finite sum over the modified spherical Bessel function of the first kind. This result will be useful for nuclear scattering calculations, where harmonic oscillator nuclear wavefunctions are used or when evaluating momentum space matrix elements for a Gaussian potential.
Comments: 7 pages