Functions
Double_t	chiosi_Z (Double_t x, Double_t par)

Double_t	fede (Double_t x, Double_t par)

Double_t	pawlowski_A (Double_t x, Double_t par)

Double_t	pawlowski_Z (Double_t x, Double_t par)

Double_t	pichon_Z (Double_t x, Double_t par)

Double_t	starting_points_A (Double_t x, Double_t par)

Double_t	starting_points_Z (Double_t x, Double_t par)

Double_t	tassangot_A (Double_t x, Double_t par)

Double_t	tassangot_Z (Double_t x, Double_t par)

Detailed Description

Contains Tassan-Got functionals for mass and charge identification used for Si-CsI, Si150-CsI and ChIo-CsI, and ChIo-Si matrices.

For xxx-CsI telescopes:
tassangot_A and tassangot_Z are the original 10 parameter functionals
(corresponds to Eq.10 with Eq.12 (E vs. h) from Nucl.Instrum.Meth. B194 (2002) 503-512).
pawlowski_A and pawlowski_Z are modified functionals with 11 parameters.

In all cases here is the correspondance between par[] and the formulae
given in Nucl.Instrum.Meth. B194 (2002) 503-512 (with initial values and limits used when fitting
parameters from same publication) :

   par[0] : lambda
   par[1] : alpha (1: 0.5 - 1.5)
   par[2] : beta (0.5: 0.2 - 1)
   par[3] : mu (1: 0.2 - 1.5)
   par[4] : nu (1: 0.1 - 4)
   par[5] : xi (>0)
   par[6] : g
   par[7] : pedestal of x-coordinate
   par[8] : pedestal of y-coordinate

In case of xxx-CsI telescopes, the relationship between E and h introduces an additional parameter:

   par[9] : eta (Eq.11)

lambda and g are determined from starting points (E=0) and initial slopes of lines, respectively, and their ranges are given as between 0.25 and 4 times these values. If no A identification is given, beta is fixed at beta=0.5
With the Pawlowski modification, we have also:

 par[10] : Pawlowski correction

Function Documentation

◆ chiosi_Z()

Double_t KVTGIDFunctions::chiosi_Z	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula used for Z identification in ChIo-Si telescopes. Charity EAL mass used for Z>5

Returns difference between measured ChIo energy (dE) and that calculated for given (Z, Si energy (E)).

Arguments are x[0] Z of nucleus considered par[0], ..., par[8] 9 parameters of Tassan-Got formula par[9] Si energy (in MeV) X-coordinate = dE par[10] ChIo energy (in MeV) Y-coordinate = E

Definition at line 301 of file KVTGIDFunctions.cpp.

◆ fede()

Double_t KVTGIDFunctions::fede	(	Double_t *	x,
		Double_t *	par
	)

General Tassan-Got functional used with KVTGIDFitter It gives Y as a function of X and Z or A (depending on parameters).

par[0] = ixt --—> type of functional

ixt : =0->basic functional <>0->extended functional
* For the basic formula :
yy = ((g*E)**(mu+1)+lambda**(mu+1)*Z**2*A**mu)**(1/(mu+1))-g*E + pdy
* For the extended formula :
yy = ((g*E)**(mu+nu+1)+(lambda*Z**alpha*A**beta)**(mu+nu+1)+
xi*Z*Z*A**mu*(g*E)**nu)**(1/(mu+nu+1))-g*E + pdy

par[1] = ih --—> treatment of CsI total light output

ih : =0->no non-linear light response <>0->non-linear light response included
* If ih=0 no non-linear light response : E=xx-pdx
* If ih<>0 non-linear light response included :
E = sqrt(h**2+2*rho*h*(1+log(1+h/rho)))
rho=eta*Z**2*A and h=xx-pdx

par[2] = ZorA --—> whether x[0]=Z or x[0]=A

ZorA : =0->x[0]=A <>0->x[0]=Z
* If ZorA=1, we calculate A using the mass formula indicated
by the value of MassForm=par[3]
* If ZorA=0, Z is given by the value of par[3]

par[3] = mass formula or Z

If ZorA=1, par[3] = mass formula, for values see KVNucleus::GetAFromZ
If ZorA=0, par[3] = Z

par[4] = X coordinate par[5] = Y coordinate

The number & order of remaining parameters depend on ixt and ih.

ixt=0 ih=0 5 parameters: lambda, mu, g, pdx, pdy
ixt=0 ih<>0 6 parameters: lambda, mu, g, pdx, pdy, eta
ixt<>0 ih=0 9 parameters: lambda, alpha, beta, mu, nu,
xi, g, pdx, pdy
ixt<>0 ih<>0 10 parameters: lambda, alpha, beta, mu, nu,
xi, g, pdx, pdy, eta

Therefore:

ixt=0, ih=0: Double_t par[11];

par[6] = lambda par[7] = mu par[8] = g par[9] = pdx par[10] = pdy

ixt=0, ih<>0: Double_t par[12];

par[6] = lambda par[7] = mu par[8] = g par[9] = pdx par[10] = pdy par[11] = eta

ixt<>0, ih=0: Double_t par[15];

par[6] = lambda par[7] = alpha par[8] = beta par[9] = mu par[10] = nu par[11] = xi par[12] = g par[13] = pdx par[14] = pdy

ixt<>0, ih<>0: Double_t par[16];

par[6] = lambda par[7] = alpha par[8] = beta par[9] = mu par[10] = nu par[11] = xi par[12] = g par[13] = pdx par[14] = pdy par[15] = eta

Definition at line 109 of file KVTGIDFunctions.cpp.

◆ pawlowski_A()

Double_t KVTGIDFunctions::pawlowski_A	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula with Pawlowski correction (11th parameter) for A identification (Z known). Returns difference between measured ChIo/Si PG/GG channel and that calculated for given (Z, A, CsI light output) 14 parameters in all Arguments are x[0] A of nucleus considered par[0], ..., par[10] 11 parameters of corrected Tassan-Got formula par[11] Z of nucleus considered par[12] measured total light output of CsI - X coord par[13] measured ChIo/Si PG or GG channel - Y coord

Definition at line 616 of file KVTGIDFunctions.cpp.

◆ pawlowski_Z()

Double_t KVTGIDFunctions::pawlowski_Z	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula with Pawlowski correction (11th parameter) for Z identification A = 2*Z + 1 13 parameters in all. Returns difference between measured Si PG/GG channel and that calculated for given (Z, CsI light output).

Arguments are x[0] Z of nucleus considered par[0], ..., par[10] 11 parameters of corrected Tassan-Got formula par[11] measured total light output of CsI - X coord par[12] measured ChIo/Si PG or GG channel - Y coord

Definition at line 555 of file KVTGIDFunctions.cpp.

◆ pichon_Z()

Double_t KVTGIDFunctions::pichon_Z	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula (10 parameters) used for Z identification in Si-CsI or ChIo-CsI 5th campaign telescopes - 12 parameters As per Matthieu Pichon's these, we use A = 2Z for the mass. Returns difference between measured ChIo/Si PG/GG channel and that calculated for given (Z, CsI light output).

Corresponds to Eq.11 of NIM B194 (2002) 503 with Eq.13 for the light-energy dependence

Arguments are x[0] Z of nucleus considered par[0] : lambda par[1] : alpha (1: 0.5 - 1.5) par[2] : beta (0.5: 0.2 - 1) par[3] : mu (1: 0.2 - 1.5) par[4] : nu (1: 0.1 - 4) par[5] : zeta (?? squiggly epsilon thingy ??) (>0) par[6] : g par[7] : pedestal of x-coordinate par[8] : pedestal of y-coordinate par[9] : eta par[10] measured total light output of CsI - X coord par[11] measured ChIo/Si PG or GG channel - Y coord

Definition at line 426 of file KVTGIDFunctions.cpp.

◆ starting_points_A()

Double_t KVTGIDFunctions::starting_points_A	(	Double_t *	x,
		Double_t *	par
	)

Function used to fit starting points' y-coordinate as a function of A and get initial values for lambda, alpha and beta Function is : DE(E=0) = lambda * (Z**alpha) * (A**beta)

par0 = lambda par1 = alpha par2 = beta par3 = Z

Definition at line 696 of file KVTGIDFunctions.cpp.

◆ starting_points_Z()

Double_t KVTGIDFunctions::starting_points_Z	(	Double_t *	x,
		Double_t *	par
	)

Function used to fit starting points' y-coordinate as a function of Z and get initial values for lambda, alpha Function is : DE(E=0) = lambda * (Z**alpha) * (A**0.5)

par0 = lambda par1 = alpha

Definition at line 670 of file KVTGIDFunctions.cpp.

◆ tassangot_A()

Double_t KVTGIDFunctions::tassangot_A	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula (13 parameters) for A identification (known Z) Returns difference between measured ChIo/Si PG/GG channel and that calculated for given (Z, A, CsI light output)

Arguments are x[0] A of nucleus considered par[0], ..., par[9] 10 parameters of corrected Tassan-Got formula par[10] Z of nucleus considered par[11] measured total light output of CsI - X coord par[12] measured ChIo/Si PG or GG channel - Y coord

Definition at line 499 of file KVTGIDFunctions.cpp.

◆ tassangot_Z()

Double_t KVTGIDFunctions::tassangot_Z	(	Double_t *	x,
		Double_t *	par
	)

Tassan-Got formula (10 parameters) used for Z identification in Si-CsI or ChIo-CsI telescopes - 12 parameters Charity EAL mass used for Z>5 Returns difference between measured ChIo/Si PG/GG channel and that calculated for given (Z, CsI light output).

Arguments are x[0] Z of nucleus considered par[0], ..., par[9] 10 parameters of Tassan-Got formula par[10] measured total light output of CsI - X coord par[11] measured ChIo/Si PG or GG channel - Y coord

Definition at line 354 of file KVTGIDFunctions.cpp.