JPHYSICS::JGeanx Class Reference

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.
double	operator() (const double ct) const
	Number of photons from EM-shower as a function of emission angle.
double	operator() (const double xmin, const double xmax) const
	Integral number of photons from EM-shower between two emission angles.
double	evaluate (const double ct) const
	Functional dependence.
double	evaluate (const double xmin, const double xmax) const
	Integral.

Public Attributes
const double	a
	power
const double	b
	slope
const double	n
	index of refraction

Private Attributes
double	c
	normalisation constant

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 is a normalisation constant such that the integral of 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

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 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

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 61 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 75 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 89 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 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

a

const double JPHYSICS::JGeanx::a

power

Definition at line 133 of file JGeanx.hh.

b

const double JPHYSICS::JGeanx::b

slope

Definition at line 134 of file JGeanx.hh.

n

const double JPHYSICS::JGeanx::n

index of refraction

Definition at line 135 of file JGeanx.hh.

c

double JPHYSICS::JGeanx::c

private

normalisation constant

Definition at line 138 of file JGeanx.hh.

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

• JGeanx.hh