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Problem with Fourier bessel transform of Yukawa potential

  1. Jun 16, 2015 #1

    I am trying to find Fourier Bessel Transform (i.e. Hankel transform of order zero) for Yukuwa potential of the form
    f(r) = - e1*e2*exp(-kappa*r)/(r) (e1, e2 and kappa are constants). I am using the discrete sine transform routine from FFTW ( with dst routine). For this potential there is analytical result - f^hat (k) = - 4*pi *e1*e2/(kappa^2 + k^2).

    I was comparing the results from numerical and analytical transform. However, I see that there is a significant difference (delR =0.3, 1st point is at 0.1, 4096 points are used for the numerical transform but the error remains even if I increase it 16384). Is there any trick to get better numerical transform for (screened) coulomb potential?

    analytical numerical r
    -711437635.18197799 -748996019.05573177 0.1
    -275116156.66050136 -261467385.57794687 0.4
    -136050696.75080600 -143418942.44284841 0.7
    -79670334.886979684 -75837581.595151573 1.0
    -51976687.575621709 -54872935.399959348 1.3


  2. jcsd
  3. Jun 21, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Jul 5, 2015 #3


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    A sine transform is a poor choice since your function is not zero at r=0. You might have better luck with a cosine transform. In any case you will have a problem with a numerical transform since the function is infinite at the origin.
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