.. _hayter-msa:

hayter_msa
=======================================================

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

================== ======================================================================================= ======= =============
Parameter          Description                                                                             Units   Default value
================== ======================================================================================= ======= =============
scale              Source intensity                                                                        None                1
background         Source background                                                                       |cm^-1|         0.001
radius_effective   effective radius of charged sphere                                                      |Ang|           20.75
volfraction        volume fraction of spheres                                                              None           0.0192
charge             charge on sphere (in electrons)                                                         e                  19
temperature        temperature, in Kelvin, for Debye length calculation                                    K              318.16
concentration_salt conc of salt, moles/litre, 1:1 electolyte, for Debye length                             M                   0
dielectconst       dielectric constant (relative permittivity) 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 may 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, though it should be possible to simulate the effect
of this by increasing the salt concentration. The counterions are also
assumed to be monovalent.

In sasview the effective radius may be calculated from the parameters
used in the form factor $P(q)$ that this $S(q)$ is combined with.

The computation uses a Taylor series expansion at very small rescaled $qR$, to
avoid some serious rounding error issues, this may result in a minor artefact
in the transition region under some circumstances.

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/hayter_msa_autogenfig.png

    1D plot corresponding to the default parameters of the model.

**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

