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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Sample/LibFF/SomeFormfactor.cpp
//! @brief Implements namespace someff with some form factor functions.
//!
//! @homepage http://www.bornagainproject.org
//! @license GNU General Public License v3 or higher (see COPYING)
//! @copyright Forschungszentrum Jülich GmbH 2018
//! @authors Scientific Computing Group at MLZ (see CITATION, AUTHORS)
//
// ************************************************************************************************
#include "Sample/LibFF/SomeFormfactor.h"
#include <numbers>
using std::numbers::pi;
//! Returns the form factor of a sphere of radius R.
//!
//! Used by the hard sphere and by several soft sphere classes.
complex_t SampleUtil::someff::ffSphere(C3 q, double R)
{
complex_t q1 =
sqrt(q.x() * q.x() + q.y() * q.y() + q.z() * q.z()); // NO sesquilinear dot product!
complex_t qR = q1 * R;
if (std::abs(qR) < 1e-4) { // relative error is O(qR^4) with small prefactor
// expand sin(qR)-qR*cos(qR) up to qR^5
return 4 * pi / 3 * pow(R, 3) * (1. - 0.1 * pow(qR, 2));
}
return 4 * pi * pow(q1, -3) * (sin(qR) - qR * cos(qR));
}
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