Particles and Nuclei Sub-Library: Version 0.910
Public Member Functions | Data Fields | Protected Attributes
frdm_mass Class Reference

FRDM semi-empirical mass formula (macroscopic part only with no deformation) More...

#include <frdm_mass.h>

Inheritance diagram for frdm_mass:
nuclear_mass_fit nuclear_mass_cont nuclear_mass nuclear_mass_info

Detailed Description

The macroscopic part of the finite-range droplet model from Moller95 .

Using the relations

\[ \bar{\delta} = (n_n - n_p)/n \]

and

\[ \bar{\epsilon} = - (n-n_0)/3/n_0 \]

we get

\[ n_n = \frac{1}{2} (1+\bar{\delta}) (1-3 \bar{\epsilon}) n_0 \]

and

\[ n_p = \frac{1}{2} (1-\bar{\delta}) (1-3 \bar{\epsilon}) n_0 \]

Assuming that

\[ \frac{4 \pi}{3} R_n^3 n_n = N \]

and

\[ \frac{4 \pi}{3} R_p^3 n_p = Z \]

we get

\[ R_n^3 = 3 N / \alpha_n \]

\[ R_p^3 = 3 Z / \alpha_p \]

where $ \alpha $'s are

\[ \alpha_n = 2 \pi (1+ \bar{\delta})(1 - 3 \bar{\epsilon}) n_0 \]

\[ \alpha_p = 2 \pi (1- \bar{\delta})(1 - 3 \bar{\epsilon}) n_0 \]

Note that the above relations are somehow self-consistent because they imply

\[ R^3 n = R_n^3 n_n + R_p^3 n_p \]

Since we're using (is there a better way?)

\[ R = r_0 A^{1/3} \]

with $ r_0 = 1.16 $ fm, then $ n_0 = 0.152946 \mathrm{fm}^{-3} $.

Todo:

Fix pairing energy and double vs. int

Document drip_binding_energy(), etc.

Decide on number of fit parameters (10 or 12?) or let the user decide

Document the protected variables

Set the neutron and proton masses and hbarc to Moller et al.'s values

Idea for Future:
Add microscopic part.

Definition at line 103 of file frdm_mass.h.

Public Member Functions

virtual double mass_excess_d (double Z, double N)
 Given Z and N, return the mass excess in MeV.
virtual int fit_fun (size_t nv, const ovector_base &x)
 Fix parameters from an array for fitting.
virtual int guess_fun (size_t nv, ovector_base &x)
 Fill array with guess from present values for fitting.
virtual double drip_binding_energy_d (double Z, double N, double npout, double nnout, double chi)
 Return the binding energy in MeV.
virtual double drip_mass_excess_d (double Z, double N, double np_out, double nn_out, double chi)
 Given Z and N, return the mass excess in MeV.

Data Fields

double a1
 Volume-energy constant in MeV (default 16.247)
double J
 Symmetry-energy constant in MeV (default 32.73)
double K
 Nuclear compressibility constant in MeV (default 240)
double a2
 Surface-energy constant in MeV (default 22.92)
double Q
 Effective surface-stiffness constant in MeV (default 29.21)
double a3
 Curvature-energy constant in MeV (default 0)
double ca
 Charge-asymmetry constant in MeV (default 0.436)
double W
 Wigner constant in MeV (default 30)
double ael
 electronic-binding constant in MeV (default $ 1.433 \times 10^{-5} $ ).
double rp
 Proton root-mean-square radius in fm (default 0.80)
double r0
 Nuclear-radius constant in fm (default 1.16)
double MH
 Hydrogen atom mass excess, 7.289034 MeV.
double Mn
 Neutron mass excess, 8.071431 MeV.
double e2
 Electronic charge squared, 1.4399764 MeV fm.
double a
 Range of Yukawa-plus-exponential potential, 0.68 fm.
double aden
 Range of Yukawa function used to generate nuclear charge distribution, 0.70 fm.
double rmac
 Average pairing-gap constant, 4.80 MeV.
double h
 Neutron-proton interaction constant, 6.6 MeV.
double L
 Density-symmetry constant, 0 MeV.
double C
 Pre-exponential compressibility-term constant, 60 MeV.
double gamma
 Exponential compressibility-term range constant, 0.831.
double amu
 Atomic mass unit, 931.5014 MeV.
double nn
 Internal average neutron density.
double np
 Internal average proton density.
double Rn
 Neutron radius.
double Rp
 Proton radius.

Protected Attributes

double Deltap
 Proton pairing coefficient.
double Deltan
 Neutron pairing coefficient.
double deltanp
 Isovector pairing coefficient.
double deltabar
 Average bulk nuclear asymmetry.
double epsbar
 Average relative deviation of bulk density.
double Bs
 Desc.
double Bk
 Desc.
double Br
 Desc.
double Bw
 Desc.
double Bv
 Desc.
double c1
 Coulomb energy coefficient.
double c2
 Volume redistribution energy coefficient.
double c4
 Coulomb exchange correction coefficient.
double c5
 Surface redistribution energy coefficient.
double f0
 Coefficient for the proton form-factor correction to the Coulomb energy.
double a0
 Desc.
double B1
 Desc.
double B2
 Desc.
double B3
 Desc.
double B4
 Desc.

The documentation for this class was generated from the following file:
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Friends

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).

Get Object-oriented Scientific Computing
Lib at SourceForge.net. Fast, secure and Free Open Source software
downloads.