Class nucmass_radius (o2scl)

O2scl : Class List

class nucmass_radius

Compute the RMS radius of a Fermi-Dirac density distribution with fixed diffusiveness.

This class computes the RMS radius given either the central density or the radius specified in the Fermi function. This class assumes the density distribution function is of the form

\[ N = 4 \pi \rho_0 \int r^2~dr~\left\{1+\exp \left[\left(r-R_{\mathrm{fermi}}\right)/d\right]\right\}^{-1} \]

where \( N \) is the total number of particles, \( d \) is the diffusiveness, \( R_{\mathrm{fermi}} \) is the half-height radius, and \( \rho_0 \) is the central density.

The radius assuming constant density,

\[ R_{\mathrm{cd}} = \left(\frac{3 N}{4 \pi \rho_0}\right)^3 \, , \]

is also given.

Public Functions

nucmass_radius()

void eval_rms_rho(double rho0, double N, double d, double &Rcd, double &Rfermi, double &Rrms)

Compute the RMS radius from the central density.

Computes the RMS radius Rrms from the central density rho0, the number of particles N, and the diffusiveness d. This function also computes the radius in the Fermi distribution function, Rfermi and the radius assuming constant density, Rcd.

void eval_rms_rsq(double Rfermi, double N, double d, double &rho0, double &Rcd, double &Rrms)

Compute the RMS radius from the Fermi distribution radius.

Computes the RMS radius Rrms from the radius Rfermi in the Fermi distribution assuming a total number of particles N, a diffusiveness paramter d. This function also produces the central density rho0, and the radius assuming constant density, Rcd.

double density(double r, double Rfermi, double d, double rho0)

The radial density distribution.

double iand2_new(double r, double Rfermi, double d, double rho0)

The radial density distribution times radius squared.

void eval_N_err(double Rfermi, double d, double rho0, double &N, double &N_err)

Compute the total number of particles with numerical uncertainty.

double eval_N(double Rfermi, double d, double rho0)

Compute the total number of particles.

Protected Functions

double iand(double r)

The function \( 4 \pi r^4 \rho(r) \).

double iand2(double r)

The function \( 4 \pi r^2 \rho(r) \).

double solve(double x)

The function to fix the total number of particles.

Protected Attributes

double urho0

The central denstiy.

double ud

The diffusiveness.

double uRfermi

Store the user-specified value of the radius in the Fermi distribution.

This is used in the integrands iand() and iand2().

double uN

The total number of particles.

inte_qagiu_gsl it

The integrator.

root_cern cr

The solver.