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y = sf_hard_spheres(p, x, [y]) : Hard Sphere structure factor [Percus-Yevick]


function y=sf_hard_spheres(varargin)


 y = sf_hard_spheres(p, x, [y]) : Hard Sphere structure factor [Percus-Yevick]

   iFunc/sf_hard_spheres Hard Sphere structure factor, suited for simple liquids
     The 'x' wave-vector/momentum axis is usually in nm-1 or Angs-1.
     The parameter RHS is given in inverse unit of the axis (that is nm or Angs).
     Typical values for parameters are R=3-50 Angs, rho=0.2.
     The Hard Sphere model corresponds with the Sticky Hard Sphere model with large tau.
     The model returns the S(q) structure factor.

     Ref: J. K. Percus and G. J. Yevick., Phys. Rev., 110(1):1–13, 1958.
          A. Vrij., J. Chem. Phys., 71(8):3267–3270, 1979.
          Extracted from sasfit/sasfit_sq/sasfit_sq_HardSphere.c
     I. Bressler, et al, Journal of Applied Crystallography, 2015, 48 (5), 1587-1598

 input:  p: hard sphere model parameters (double)
            p = [ R=Hard_Sphere_Radius rho=Volume_Fraction ]
          or 'guess'
         x: wave-vector/momentum axis (double, e.g. nm-1 or Angs-1)
         y: when values are given and p='guess', a guess of the parameters is performed (double)
 output: y: model value (intensity)
 ex:     y=sf_hard_spheres([10 0.2], 0:0.01:1); or plot(sf_hard_spheres,[10 0.1],0:0.01:1)

 Version: Aug. 22, 2017
 See also iFunc, iFunc/fits, iFunc/plot
 (c) E.Farhi, ILL. License: EUPL.


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