.. _HayterMSAsq:

HayterMSAsq
=======================================================

Hayter-Penfold MSA charged sphere interparticle S(Q) structure factor

============= ================================================================ ======= =============
Parameter     Description                                                      Units   Default value
============= ================================================================ ======= =============
scale         Source intensity                                                 None                1
background    Source background                                                |cm^-1|             0
effect_radius effective radius of hard sphere                                  |Ang|           20.75
charge        charge on sphere (in electrons)                                  e                  19
volfraction   volume fraction of spheres                                       None           0.0192
temperature   temperature, in Kelvin, for Debye length calculation             K              318.16
saltconc      conc of salt, 1:1 electolyte, for Debye length                   M                   0
dielectconst  dielectric constant of solvent (default water), for Debye length None            71.08
============= ================================================================ ======= =============

The returned value is a dimensionless structure factor, $S(q)$.


This calculates the structure factor (the Fourier transform of the pair
correlation function $g(r)$) for a system of charged, spheroidal objects
in a dielectric medium. When combined with an appropriate form factor
(such as sphere, core+shell, ellipsoid, etc), this allows for inclusion
of the interparticle interference effects due to screened coulomb repulsion
between charged particles.

**This routine only works for charged particles**. If the charge is set to
zero the routine will self-destruct! For non-charged particles use a hard
sphere potential.

The salt concentration is used to compute the ionic strength of the solution
which in turn is used to compute the Debye screening length. At present
there is no provision for entering the ionic strength directly nor for use
of any multivalent salts. The counterions are also assumed to be monovalent.

For 2D data, the scattering intensity is calculated in the same way as 1D,
where the $q$ vector is defined as

.. math::

    q = \sqrt{q_x^2 + q_y^2}

.. figure:: img/HayterMSAsq_227.jpg

    1D plot using the default values (in linear scale).

**References**

J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118

J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656