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.

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

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 31 of file JGeanx.hh.

Constructor & Destructor Documentation

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 41 of file JGeanx.hh.

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

Member Function Documentation

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 61 of file JGeanx.hh.

     {
       return c * evaluate(ct);
     }

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 75 of file JGeanx.hh.

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

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 89 of file JGeanx.hh.

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

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 105 of file JGeanx.hh.

     {
       using namespace std;
       using namespace JPP;
 
       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 = tgamma(ai);
       
       double yl = Gamma(ai, xl) * gp;
       double yr = Gamma(ai, xr) * gp;
       
       if (xmin > x) 
         yl = -yl;
       if (xmax < x)
         yr = -yr;
       
       return ai * pow(-bi,ai) * (yl + yr);
     }

Member Data Documentation

const double JPHYSICS::JGeanx::a

power

Definition at line 133 of file JGeanx.hh.

const double JPHYSICS::JGeanx::b

slope

Definition at line 134 of file JGeanx.hh.

const double JPHYSICS::JGeanx::n

index of refraction

Definition at line 135 of file JGeanx.hh.

double JPHYSICS::JGeanx::c

private

normalisation constant

Definition at line 138 of file JGeanx.hh.

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

JGeanx.hh

Public Member Functions

Public Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation