calculation of moessbauer spectra More...

#include <Moesscalc.h>

Public Member Functions
void	calc ()
	fill Hamiltonian, solve and precalculate transition propabilities

double	get_Egamma (int f, int i)
	get Transition Energy from initial state i to final State f

double	Vzz_mms (double Vzz)
	transform V/Angstroem^2 into mm/s at axialsymmetric field gradient

double	get_dv_Douplett ()
	get current quadrupol splitting in mm/s

double	I (double beta, double gamma, int f, int i)
	Transition propability from i to f in crystal geometry. More...

void	I (double beta, double gamma, double alpha, int f, int i, double Int, double phi, double *xi)
	Transition propability of polarized radiation in crystal geometry. More...

double	Idiag (double beta, int f, int i)
	transition propabilities for a diagonal hamitonian More...

double	I (int f, int i)
	powder transition propabilities for the current hamiltonian

double	f_lorenz (double x, double dx, double x0, double I)
	Lorentz functions I/(pidx)1/(1+((x-x0)/dx)^2)

double	f_lorenz_fast (double x, double invdx, double x0, double I)
	Lorentz functions Iinvdx/((1+((x-x0)invdx)^2)*M_PI)

void	get_SC_spectrum (double I, int cc, double v, double *p)
	single crystal spectrum, static Hamiltonian

void	get_Powder_spectrum (double I, int cc, double v, double *p)
	powder spectrum, static Hamiltonian

void	get_SrcFld_spectrum (double I, int cc, double v, double *p)
	static Hamiltonian with source in field

void	get_fm_Powder_spectrum (double I, int cc, double v, double *p)
	ferromagnet in transverse field spectrum

void	get_afm_Powder_spectrum (double I, int cc, double v, double *p)
	antiferromagnet in transverse field spetrum

void	get_PseudoVoigt_profile (double I, int cc, double v, double *p)

void	get_FeCal_spectrum (double I, int cc, double v, double *p, double U)
	iron calibrations, recalculates sin-velocity using monitur voltage U

void	get_Dyn_spectrum (double I, int cc, double v, double *p)
	Blume-Jones model with arbitrary number of intermediate states. More...

void	get_MLR_spectrum (double I, int cc, double v, double *p)
	multi level relaxation model, asuming a potential barrier More...

void	get_DynDiagDiag_spectrum (double I, int cc, double v, double *p)
	Fast Blume Jones for two states with diagonal Hamiltonian.

void	get_DynDiagDiagDiag_spectrum (double I, int cc, double v, double *p)
	Fast Blume Jones for three states with diagonal Hamiltonian.

void	add_noise (double *I, int cc)
	adds gaussian noise to spectrum I with standard deviation sqrt(I)

void	get_FeCaltriang_spectrum (double I, int cc, double v, double *p, double U)
	iron calibrations, recalculates triangular-velocity

void	get_FeAs_spectrum (double I, int cc, double v, double *p)
	calculates FeAs spectrum (Europhys. Lett., 9 (l), pp. 87-92 (1989))

void	SimpleInvert (double x, double y, int count, int steps, double *Mspec, double rho)
	Hesse Ruebartsch without smoothing parameter. More...

double	baseline (double x, double y, int count, double Baseline, double Face, double bperx, double omega, double rho, double rhox, int rhosteps, double INew)
	determination of baseline and absorption area More...

void	MEM_Cambridge (double *M0, double rho, double rhoerr, double y, double I0, int steps, int cc, double stepsize, int MaxIterations, double MaxLambda, double MaxDif, double status[5])
	Maximum Entroy method using Cambridge algorithm to track MEM path. More...

void	HesseRuebartsch (double *M0, double rho, double *y, int steps, int cc, double smooth)
	Hesse Ruebartsch parameter distribution. More...

void	LeCear (double *M0, double rho, double *y, int steps, int cc, double smooth)
	Hesse Ruebartsch, but restricted to positive weights. More...

double	dv_Debye (double T, double TD, double Meff)
	quadratic dopplereffect in Debye approximation

double	Abs_Debye (double T, double TD, double Meff)
	Debye Waller factor in Debye approximation.

double	sWave_SuperfluidDensity (double SF0, double Tc, double T, double delta0)
	superfluid density in s-wave symmetry More...

double	Hc2_WHH (double T, double Tc, double dHc2dT, double alpha, double lambdaSO)
	Werthamer-Helfand-Honenberg (WHH) model for upper critial field. More...

double	OrderParameterDistr (double T, double Tn, double sigma, double alpha, double beta)
	order parameter temperature dependence More...

double	errorfunction (double arg)
	Gaussian error function f(x)=2/sqrt(pi)*int(0,x)[exp(-a^2)]da.

void	TransmissionIntegral (double SHI, double v, int count, double A, double I0, double ta, double omegasrc, double omegaabs, double fr)
	Convolution of source line with absorber spectrum. More...

void	afm_flipflop (double Bex, double BJ, double BA, double zeta, double theta1, double theta2)
	calculates tilting of antiferromagnetic (afm) moments in field More...

void	fm_flip (double Bex, double BA, double zeta, double *theta1)
	see afm_fliflop, but without antiferromagnetic coupling

Detailed Description

calculation of moessbauer spectra

spectrum constructors of the form spectrum(I,cc,v,p) need the following arguments

Parameters

I,:	intensity, array of length cc for output
cc,:	channel count
v,:	velocity array of length cc
	parameters array

Member Function Documentation

void MoessCalc::afm_flipflop	(	double	Bex,
		double	BJ,
		double	BA,
		double	zeta,
		double *	theta1,
		double *	theta2
	)

calculates tilting of antiferromagnetic (afm) moments in field

Parameters

Bex,:	external field
BJ,:	afm coupling constant
BA,:	anisotropy field
zeta,:	tilting of anisotropy axis with respect to Bex
theta1,:	polar angle of moment 1 to Bex
theta2,:	polar angle of moment 2 to Bex

double MoessCalc::baseline	(	double *	x,
		double *	y,
		int	count,
		double *	Baseline,
		double *	Face,
		double	bperx,
		double	omega,
		double **	rho,
		double **	rhox,
		int *	rhosteps,
		double *	INew
	)

determination of baseline and absorption area

simulates the spectrum with a high number of Lorentzian singlets using SimpleInvert function

void MoessCalc::get_Dyn_spectrum	(	double *	I,
		int	cc,
		double *	v,
		double *	p
	)

Blume-Jones model with arbitrary number of intermediate states.

Physical Review 174.2 (1968): 351

void MoessCalc::get_MLR_spectrum	(	double *	I,
		int	cc,
		double *	v,
		double *	p
	)

multi level relaxation model, asuming a potential barrier

Journal of Physics: Condensed Matter 23 (2011), Nr. 42, S.426003

double MoessCalc::Hc2_WHH	(	double	T,
		double	Tc,
		double	dHc2dT,
		double	alpha,
		double	lambdaSO
	)

Werthamer-Helfand-Honenberg (WHH) model for upper critial field.

see Collings, EW: Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys: Volume 1: Fundamentals. Bd. 1. Springer 1986

void MoessCalc::HesseRuebartsch	(	double **	M0,
		double *	rho,
		double *	y,
		int	steps,
		int	cc,
		double	smooth
	)

Hesse Ruebartsch parameter distribution.

(1974 J. Phys. E: Sci. Instrum. 7 526), uses Linear Algebra to weihght a number of subspectra to meet both best fitting and a smooth weight histogram

Parameters

M0,:	Matrix of subspectra
rho,:	spectra weights to be find
y,:	data points
steps,:	subspectra count
cc,:	channel count of each subspectrum
smooth,:	smoothing parameter

double MoessCalc::I	(	double	beta,
		double	gamma,
		int	f,
		int	i
	)

Transition propability from i to f in crystal geometry.

Parameters

beta,:	polar angle of gamma beam to field gradient z-axis
gamma,:	azimutal angle of gamma beam to field gradient z-axis
f,:	final state index
i,:	initial state index

void MoessCalc::I	(	double	beta,
		double	gamma,
		double	alpha,
		int	f,
		int	i,
		double *	Int,
		double *	phi,
		double *	xi
	)

Transition propability of polarized radiation in crystal geometry.

Parameters

beta,:	polar angle of gamma beam to field gradient z-axis
gamma,:	azimutal angle of gamma beam to field gradient z-axis
alpha,:	azimutal angle between source and sample z-axis
f,:	final state index
i,:	initial state index
Int,:	intensity output
phi,:	tilting of the polarisation ellipse with respect to z-axis
xi,:	eccentricity of the polarization matrix

double MoessCalc::Idiag	(	double	beta,
		int	f,
		int	i
	)

transition propabilities for a diagonal hamitonian

Parameters

beta,:	incoming polar angle
f,:	finale state index
i,:	initial state index

void MoessCalc::LeCear	(	double **	M0,
		double *	rho,
		double *	y,
		int	steps,
		int	cc,
		double	smooth
	)

Hesse Ruebartsch, but restricted to positive weights.

Journal of Physics E: Scientifc Instruments 12 (1979), Nr. 11, S. 1083
Instead of using linear algebra the determination of the weight histogram might be achieved by numeric minimization. For parameters see HesseRuebartsch

void MoessCalc::MEM_Cambridge	(	double **	M0,
		double *	rho,
		double *	rhoerr,
		double *	y,
		double	I0,
		int	steps,
		int	cc,
		double	stepsize,
		int	MaxIterations,
		double	MaxLambda,
		double	MaxDif,
		double	status[5]
	)

Maximum Entroy method using Cambridge algorithm to track MEM path.

ambridge algorithm: Mon. Not. R Astr. Soc. (1984) 211, 111-124
MEM in Moessbauer: Brand, R. A., and G. Le Caër. "Improving the validity of Mössbauer hyperfine parameter distributions: the maximum entropy formalism and its applications."

Parameters

M0,:	subspectra to be weighted
rho,:	weight histogram to be smoothed
rhoerr,:	errors of the weights
y,:	experimental spectrum
I0,:	base line
steps,:	subspectra counts
cc,:	channel count
stepsize,:	of algorithm
MaxLambda,:	maximum fitting weight
MaxDif,:	maximum accepted divergence off entropy gradient and chi2 gradient

double MoessCalc::OrderParameterDistr	(	double	T,
		double	Tn,
		double	sigma,
		double	alpha,
		double	beta
	)

order parameter temperature dependence

with two critical exponents and a gaussian distributed transition temperature:
OP(T)=int(0,)[Gauss(t,Tn,sigma)*(1-(T/t)^alpha)^beta]dt

Parameters

T,:	temperature
Tn,:	transition temperature mean
sigma,:	standarrd deviation of the transition temperature
alpha,:	first critical exponent
beta,:	second critical exponent

void MoessCalc::SimpleInvert	(	double *	x,
		double *	y,
		int	count,
		int	steps,
		double **	Mspec,
		double *	rho
	)

Hesse Ruebartsch without smoothing parameter.

a number of subspectra are weighted to fit the total spectrum in the best way using linear algebra in the same way as Hesse-Ruebartsch, but without smoothing

Parameters

x,:	velocity data
y,:	intensity data
count,:	channel count of each spectrum
steps,:	subspectra count
Mspec,:	count*steps Matrix with subspectra
rho,:	weights of the subspectra

double MoessCalc::sWave_SuperfluidDensity	(	double	SF0,
		double	Tc,
		double	T,
		double	delta0
	)

superfluid density in s-wave symmetry

Supercond. Sci. Technol.21(2008) 082003 (3pp)

Parameters

SF0,:	superfluid density at T=0
Tc,:	critical temperature
T,:	temperature
delta0,:	gap value

void MoessCalc::TransmissionIntegral	(	double *	SHI,
		double *	v,
		int	count,
		double	A,
		double	I0,
		double	ta,
		double	omegasrc,
		double	omegaabs,
		double	fr
	)

Convolution of source line with absorber spectrum.

acording to the transmission integral the final absorption spectrum is the convolution of the Lorentzian source line with the absorber spectrum. The absorber spectrum represents the crosssection for i.e. it appears in the exponent of an exponential function.
A symmetric velocity specing considerably can reduce the calculation costs for the convolution process. However the function can deal with asymmetric spacing as well.

Parameters

SHI,:	thin absorber spectrum
v,:	velocities
count,:	channel count
A,:	spectral area of the thin-absorber-spectrum
I0,:	baseline
ta,:	effective thickness
omegasrc,:	source line width
omegaabs,:	absorber line width
fr,:	resonant fraction, i.e. the part of the photon count rate which in principle is able to be resonantly absorbed, i.e. it's not background radiation, it hits the sample, and it respects both source and sample Debye Waller factor

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

Moesscalc.h
Moesscalc.cpp

Public Member Functions

Detailed Description

Member Function Documentation