Jpp
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Pages
Public Member Functions | Public Attributes | Private Attributes | List of all members
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=getIndexOfRefraction())
 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 35 of file JGeanx.hh.

Constructor & Destructor Documentation

JPHYSICS::JGeanx::JGeanx ( const double  __a,
const double  __b,
const double  __n = getIndexOfRefraction() 
)
inline

Constructor.

Parameters
__apower
__bexponential slope
__nindex of refraction

Definition at line 45 of file JGeanx.hh.

47  :
48  a(__a),
49  b(__b),
50  n(__n)
51  {
52  using JTOOLS::PI;
53 
54  const double y = evaluate(-1.0, +1.0);
55 
56  c = 1.0 / (y * 2*PI);
57  }
JTOOLS::PI
static const double PI
Constants.
Definition: JConstants.hh:20
JPHYSICS::JGeanx::b
const double b
slope
Definition: JGeanx.hh:137
JPHYSICS::JGeanx::n
const double n
index of refraction
Definition: JGeanx.hh:138
JPHYSICS::JGeanx::c
double c
normalisation constant
Definition: JGeanx.hh:141
JPHYSICS::JGeanx::a
const double a
power
Definition: JGeanx.hh:136
JPHYSICS::JGeanx::evaluate
double evaluate(const double ct) const
Functional dependence.
Definition: JGeanx.hh:95

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
ctcosine angle of emmision
Returns
d^2P/dcos()dphi

Definition at line 67 of file JGeanx.hh.

68  {
69  return c * evaluate(ct);
70  }
JPHYSICS::JGeanx::c
double c
normalisation constant
Definition: JGeanx.hh:141
JPHYSICS::JGeanx::evaluate
double evaluate(const double ct) const
Functional dependence.
Definition: JGeanx.hh:95
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
xminminimal cosine angle of emmision
xmaxmaximal cosine angle of emmision
Returns
dnpe/dphi

Definition at line 81 of file JGeanx.hh.

83  {
84  return c * evaluate(xmin, xmax);
85  }
JPHYSICS::JGeanx::c
double c
normalisation constant
Definition: JGeanx.hh:141
JPHYSICS::JGeanx::evaluate
double evaluate(const double ct) const
Functional dependence.
Definition: JGeanx.hh:95
double JPHYSICS::JGeanx::evaluate ( const double  ct) const
inline

Functional dependence.

In this, the normalisation constant c = 1.

Parameters
ctcosine angle of emmision
Returns
f()

Definition at line 95 of file JGeanx.hh.

96  {
97  const double x = fabs(ct - 1.0/n);
98 
99  return exp(b * pow(x,a));
100  }
JPHYSICS::JGeanx::b
const double b
slope
Definition: JGeanx.hh:137
JPHYSICS::JGeanx::n
const double n
index of refraction
Definition: JGeanx.hh:138
JPHYSICS::JGeanx::a
const double a
power
Definition: JGeanx.hh:136
double JPHYSICS::JGeanx::evaluate ( const double  xmin,
const double  xmax 
) const
inline

Integral.

In this, the normalisation constant c = 1.

Parameters
xminminimal cosine angle of emmision
xmaxmaximal cosine angle of emmision
Returns
integral f() x dcos()

Definition at line 111 of file JGeanx.hh.

113  {
114  const double x = 1.0 / n;
115 
116  const double ai = 1.0 / a;
117  const double bi = 1.0 / b;
118 
119  const double xl = pow(fabs(x - xmin), a) * -b;
120  const double xr = pow(fabs(x - xmax), a) * -b;
121 
122  const double gp = TMath::Gamma(ai);
123 
124  double yl = TMath::Gamma(ai, xl) * gp;
125  double yr = TMath::Gamma(ai, xr) * gp;
126 
127  if (xmin > x)
128  yl = -yl;
129  if (xmax < x)
130  yr = -yr;
131 
132  return ai * pow(-bi,ai) * (yl + yr);
133  }
JPHYSICS::JGeanx::b
const double b
slope
Definition: JGeanx.hh:137
JPHYSICS::JGeanx::n
const double n
index of refraction
Definition: JGeanx.hh:138
JPHYSICS::JGeanx::a
const double a
power
Definition: JGeanx.hh:136

Member Data Documentation

const double JPHYSICS::JGeanx::a

power

Definition at line 136 of file JGeanx.hh.

const double JPHYSICS::JGeanx::b

slope

Definition at line 137 of file JGeanx.hh.

const double JPHYSICS::JGeanx::n

index of refraction

Definition at line 138 of file JGeanx.hh.

double JPHYSICS::JGeanx::c
private

normalisation constant

Definition at line 141 of file JGeanx.hh.

The documentation for this class was generated from the following file:
Generated by   doxygen 1.8.5