Non-relativistic scattering by a shield barrier and by an elliptical aperture

Schmidt, Alexandre G. M.; Jesus, Anderson L. de

doi:10.1088/1402-4896/ac7e7e

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2023

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“…It is necessary to evaluate integrals of the product of sBFs in many scattering calculations (e.g. [22][23][24][25][26]). Such integrals may include Gaussian damping to ensure convergence at infinity.…”

Section: Introductionmentioning

confidence: 99%

Triple-spherical Bessel function integrals with exponential and Gaussian damping: towards an analytic N-point correlation function covariance model

Chellino,

Slepian

2023

Proc. R. Soc. A.

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Spherical Bessel functions (sBFs) appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here, we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially damped case) and Gamma, incomplete Gamma, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of sBFs with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions.

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