Class nucmass_frdm (o2scl)¶

O2scl : Class List

class nucmass_frdm : public o2scl::nucmass_fit_base ¶

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

The spherically-symmetric, 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

In class nucmass_frdm:

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.

Subclassed by o2scl::nucmass_frdm_shell

Public Functions

nucmass_frdm()¶

virtual double mass_excess_d(double Z, double N)¶: Given Z and N, return the mass excess in MeV.

inline virtual double mass_excess(int Z, int N)¶: Given Z and N, return the mass excess in MeV.

virtual int fit_fun(size_t nv, const ubvector &x)¶: Fix parameters from an array for fitting.

virtual int guess_fun(size_t nv, ubvector &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 in a many-body environment.

This is an experimental version of mass_excess_d which removes pairing, computes nn, np, Rn, and Rp, and attempts to correct the surface. This function probably doesn’t work at the moment. It’s not currently used by drip_binding_energy_d().

Public Members

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 kg_to_invfm¶: Conversion from kg to inverse fm.

double Deltap¶: Proton pairing coefficient.

double Deltan¶: Neutron pairing coefficient.

double deltanp¶: Isubvector 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.