Corpus ID: 201103759

The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian.

  title={The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian.},
  author={R. Mehrem},
  journal={arXiv: Nuclear Theory},
  • R. Mehrem
  • Published 2019
  • Physics
  • arXiv: Nuclear Theory
In this paper, the integral $\pmatrix{\lambda_1 &\lambda_2 &\lambda_3\cr 0 &0 &0\cr}\, \int_0^\infty \, r^{\lambda_3+2}\, \exp{(-\alpha r^2)}\, j_{\lambda_1}(k_1r) \,j_{\lambda_2}(k_2r) \,dr$, where $k_1$, $k_2$ and $\alpha$ 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… Expand


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