Probability density function of photon emission from EM-shower as a function of cosine of the emission angle. More...

#include <JGeanx.hh>

Public Member Functions
	JGeanx (const double __a, const double __b, const double __n=getIndexOfRefractionPhase())
	Constructor. More...

double	operator() (const double ct) const
	Number of photons from EM-shower as a function of emission angle. More...

double	operator() (const double xmin, const double xmax) const
	Integral number of photons from EM-shower between two emission angles. More...

double	evaluate (const double ct) const
	Functional dependence. More...

double	evaluate (const double xmin, const double xmax) const
	Integral. More...

Public Attributes
const double	a
	power More...

const double	b
	slope More...

const double	n
	index of refraction More...

Private Attributes
double	c
	normalisation constant More...

Detailed Description

Probability density function of photon emission from EM-shower as a function of cosine of the emission angle.

     \f[P(\cos(\theta))  =  c \times e^{b \times |\cos(\theta) - 1/n|^a}\f]

where $c$ is a normalisation constant such that the integral of $P$ over the full solid angle is one.

The parametrisation is taken from reference: R. Mirani, "Parametrisation of EM-showers in the ANTARES detector volume.", Doctoral thesis in computational physics, University of Amsterdam.

Definition at line 35 of file JGeanx.hh.

Constructor & Destructor Documentation

◆ JGeanx()

JPHYSICS::JGeanx::JGeanx	(	const double	__a,
		const double	__b,
		const double	__n = `getIndexOfRefractionPhase()`
	)

inline

Constructor.

Parameters

__a	power
__b	exponential slope
__n	index of refraction

Definition at line 45 of file JGeanx.hh.

                                                            :
       a(__a),
       b(__b),
       n(__n)
     {
       using JTOOLS::PI;
  
       const double y = evaluate(-1.0, +1.0);
  
       c  = 1.0 / (y * 2*PI);
     }

Member Function Documentation

◆ operator()() [1/2]

double JPHYSICS::JGeanx::operator() ( const double ct ) const

inline

Number of photons from EM-shower as a function of emission angle.

The integral over full solid angle is normalised to one.

Parameters

ct	cosine angle of emmision

Returns: d^2P/dcos()dphi

Definition at line 67 of file JGeanx.hh.

     {
       return c * evaluate(ct);
     }

◆ operator()() [2/2]

double JPHYSICS::JGeanx::operator()	(	const double	xmin,
		const double	xmax
	)		const

inline

Integral number of photons from EM-shower between two emission angles.

The integral over full solid angle is normalised to one.

Parameters

xmin	minimal cosine angle of emmision
xmax	maximal cosine angle of emmision

Returns: dnpe/dphi

Definition at line 81 of file JGeanx.hh.

     {
       return c * evaluate(xmin, xmax);
     }

◆ evaluate() [1/2]

double JPHYSICS::JGeanx::evaluate ( const double ct ) const

inline

Functional dependence.

In this, the normalisation constant c = 1.

Parameters

ct	cosine angle of emmision

Returns: f()

Definition at line 95 of file JGeanx.hh.

     {
       const double x = fabs(ct - 1.0/n);
  
       return exp(b * pow(x,a));
     }

◆ evaluate() [2/2]

double JPHYSICS::JGeanx::evaluate	(	const double	xmin,
		const double	xmax
	)		const

inline

Integral.

In this, the normalisation constant c = 1.

Parameters

xmin	minimal cosine angle of emmision
xmax	maximal cosine angle of emmision

Returns: integral f() x dcos()

Definition at line 111 of file JGeanx.hh.

     {
       const double x  = 1.0 / n;
       
       const double ai = 1.0 / a;
       const double bi = 1.0 / b;
       
       const double xl = pow(fabs(x - xmin), a) * -b;
       const double xr = pow(fabs(x - xmax), a) * -b;
       
       const double gp = TMath::Gamma(ai);
       
       double yl = TMath::Gamma(ai, xl) * gp;
       double yr = TMath::Gamma(ai, xr) * gp;
       
       if (xmin > x) 
         yl = -yl;
       if (xmax < x)
         yr = -yr;
       
       return ai * pow(-bi,ai) * (yl + yr);
     }