Class nucmass_frdm (o2scl)¶
-
class
o2scl
::
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:
Fix pairing energy and double vs. int
- Todo:
Document drip_binding_energy(), etc.
- Todo:
Decide on number of fit parameters (10 or 12?) or let the user decide
- Todo:
Document the protected variables
- Todo:
Set the neutron and proton masses and hbarc to Moller et al.’s values
- Idea for Future:
Add microscopic part.
Public Functions
-
nucmass_frdm
()¶
-
double
mass_excess_d
(double Z, double N)¶ Given
Z
andN
, return the mass excess in MeV.
-
double
mass_excess
(int Z, int N)¶ Given
Z
andN
, return the mass excess in MeV.
-
int
fit_fun
(size_t nv, const ubvector &x)¶ Fix parameters from an array for fitting.
-
int
guess_fun
(size_t nv, ubvector &x)¶ Fill array with guess from present values for fitting.
-
double
drip_binding_energy_d
(double Z, double N, double npout, double nnout, double chi)¶ Return the binding energy in MeV.
-
double
drip_mass_excess_d
(double Z, double N, double np_out, double nn_out, double chi)¶ Given
Z
andN
, 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.