celeritas::UUNuclearFormFactor Class Reference

Uniform-uniform folded nuclear form factor. More...

#include <NuclearFormFactors.hh>

Inheritance diagram for celeritas::UUNuclearFormFactor:

Public Member Functions
CELER_FUNCTION	UUNuclearFormFactor (AtomicMassNumber a_mass)
	Construct from atomic mass number.
CELER_FUNCTION real_type	operator() (MomentumSq target_momsq) const
	Calculate the uniform-uniform folded form factor by calculating momentum.
CELER_FUNCTION real_type	operator() (Momentum target_mom) const
	Calculate the uniform-uniform folded form factor.

Static Public Member Functions
static CELER_CONSTEXPR_FUNCTION FFType	ff_type ()
	Form factor type corresponding to this distribution.
Static Public Member Functions inherited from celeritas::NuclearFormFactorTraits
static CELER_CONSTEXPR_FUNCTION InvMomentum	fm_par_hbar ()
	Momentum transfer prefactor: 1 fm / hbar.

Additional Inherited Members
Public Types inherited from celeritas::NuclearFormFactorTraits
using	AtomicMassNumber = AtomicNumber
using	Momentum = units::MevMomentum
using	MomentumSq = units::MevMomentumSq
using	InvMomentum = Quantity< UnitInverse< Momentum::unit_type > >
using	InvMomentumSq = Quantity< UnitInverse< MomentumSq::unit_type > >
using	FFType = NuclearFormFactorType

Detailed Description

Uniform-uniform folded nuclear form factor.

This nuclear form factor corresponds NuclearFormFactorType::flat and assumes a uniform nuclear charge at the center with a smoothly decreasing charge at the surface. This leads to a form factor:

\[ F(q) = F'(x(R_0, q)) F'(x(R_1, q)) \]

where \( x \equiv q R / \hbar \) uses the effective nuclear radius \( R_0 = 1.2 A^{1/3} \,\mathrm{fm} \) and nuclear surface skin \( R_1 = 2.0 \,\mathrm{fm} \), and

\[ F'(x) = \frac{3}{x^3} ( \sin x - x \cos x) \]

is the form factor for a uniformly charged sphere.

Warning

This form factor suffers from catastrophic numerical cancellation for small radii and momenta so should only be used for large nuclei or large momentum transfers.

[LR16] C. Leroy and P.G. Rancoita. Principles of Radiation Interaction in Matter and Detection. World Scientific (Singapore), 4th edition, 2016.

[H56] R.H. Helm, Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei, Phys. Rev. 104 (1956) 1466–1475. https://doi.org/10.1103/PhysRev.104.1466.

[FMS93] J.M. Fernández-Varea, R. Mayol, F. Salvat, Cross sections for elastic scattering of fast electrons and positrons by atoms, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 82 (1993) 39–45. https://doi.org/10.1016/0168-583X(93)95079-K.

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The documentation for this class was generated from the following file:

• NuclearFormFactors.hh