# Problem with Fourier bessel transform of Yukawa potential

1. Jun 16, 2015

### praban

Hello,

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

thanks,

2. Jun 21, 2015