An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor

Abstract

The integrals $\text{threej}\text{Llo}\text{Llt}\text{Llth}000{\int }_0^{\infty }{r}^{\text{Llth}+1}{e}^{-\alpha r}{j}_{\text{Llo}}(k_{1}r)j_{\text{Llt}}(k_{2}r)dr$ and $\text{threej}\text{Llo}\text{Llt}\text{Llth}000{\int }_0^{\infty }{r}^{\text{Llth}+2}{e}^{-\alpha r}{j}_{\text{Llo}}(k_{1}r)j_{\text{Llt}}(k_{2}r)dr$ are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind.

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