nucmass_frdm.h
Go to the documentation of this file.
1 /*
2  -------------------------------------------------------------------
3 
4  Copyright (C) 2006-2020, Andrew W. Steiner
5 
6  This file is part of O2scl.
7 
8  O2scl is free software; you can redistribute it and/or modify
9  it under the terms of the GNU General Public License as published by
10  the Free Software Foundation; either version 3 of the License, or
11  (at your option) any later version.
12 
13  O2scl is distributed in the hope that it will be useful,
14  but WITHOUT ANY WARRANTY; without even the implied warranty of
15  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16  GNU General Public License for more details.
17 
18  You should have received a copy of the GNU General Public License
19  along with O2scl. If not, see <http://www.gnu.org/licenses/>.
20 
21  -------------------------------------------------------------------
22 */
23 #ifndef NUCMASS_FRDM_H
24 #define NUCMASS_FRDM_H
25 
26 /** \file nucmass_frdm.h
27  \brief File defining \ref o2scl::nucmass_frdm, \ref o2scl::nucmass_mnmsk,
28  and \ref o2scl::nucmass_mnmsk_exp
29 */
30 
31 #include <cmath>
32 
33 #include <o2scl/nucleus.h>
34 #include <o2scl/nucmass.h>
35 #include <o2scl/constants.h>
36 
37 #ifndef DOXYGEN_NO_O2NS
38 namespace o2scl {
39 #endif
40 
41  /** \brief FRDM semi-empirical mass formula (macroscopic part only
42  with no deformation)
43 
44  The spherically-symmetric, macroscopic part of the finite-range
45  droplet model from \ref Moller95 .
46 
47  Using the relations
48  \f[
49  \bar{\delta} = (n_n - n_p)/n
50  \f]
51  and
52  \f[
53  \bar{\epsilon} = - (n-n_0)/3/n_0
54  \f]
55  we get
56  \f[
57  n_n = \frac{1}{2} (1+\bar{\delta}) (1-3 \bar{\epsilon}) n_0
58  \f]
59  and
60  \f[
61  n_p = \frac{1}{2} (1-\bar{\delta}) (1-3 \bar{\epsilon}) n_0
62  \f]
63  Assuming that
64  \f[
65  \frac{4 \pi}{3} R_n^3 n_n = N
66  \f]
67  and
68  \f[
69  \frac{4 \pi}{3} R_p^3 n_p = Z
70  \f]
71  we get
72  \f[
73  R_n^3 = 3 N / \alpha_n
74  \f]
75  \f[
76  R_p^3 = 3 Z / \alpha_p
77  \f]
78  where \f$ \alpha \f$'s are
79  \f[
80  \alpha_n = 2 \pi (1+ \bar{\delta})(1 - 3 \bar{\epsilon}) n_0
81  \f]
82  \f[
83  \alpha_p = 2 \pi (1- \bar{\delta})(1 - 3 \bar{\epsilon}) n_0
84  \f]
85  Note that the above relations are somehow self-consistent
86  because they imply
87  \f[
88  R^3 n = R_n^3 n_n + R_p^3 n_p
89  \f]
90 
91  Since we're using (is there a better way?)
92  \f[
93  R = r_0 A^{1/3}
94  \f]
95  with \f$ r_0 = 1.16 \f$ fm, then
96  \f$ n_0 = 0.152946 \mathrm{fm}^{-3} \f$.
97 
98  \todo Fix pairing energy and double vs. int
99  \todo Document drip_binding_energy(), etc.
100  \todo Decide on number of fit parameters (10 or 12?) or
101  let the user decide
102  \todo Document the protected variables
103  \todo Set the neutron and proton masses and hbarc to Moller et al.'s
104  values
105 
106  \future Add microscopic part.
107  */
109 
110  public:
111 
112  nucmass_frdm();
113 
114  /// Volume-energy constant in MeV (default 16.247)
115  double a1;
116  /// Symmetry-energy constant in MeV (default 32.73)
117  double J;
118  /// Nuclear compressibility constant in MeV (default 240)
119  double K;
120  /// Surface-energy constant in MeV (default 22.92)
121  double a2;
122  /// Effective surface-stiffness constant in MeV (default 29.21)
123  double Q;
124  /// Curvature-energy constant in MeV (default 0)
125  double a3;
126  /// Charge-asymmetry constant in MeV (default 0.436)
127  double ca;
128  /// Wigner constant in MeV (default 30)
129  double W;
130  /** \brief electronic-binding constant in MeV
131  (default \f$ 1.433 \times 10^{-5} \f$ ).
132  */
133  double ael;
134  /// Proton root-mean-square radius in fm (default 0.80)
135  double rp;
136  /// Nuclear-radius constant in fm (default 1.16)
137  double r0;
138  /// Hydrogen atom mass excess, 7.289034 MeV
139  double MH;
140  /// Neutron mass excess, 8.071431 MeV
141  double Mn;
142  /// Electronic charge squared, 1.4399764 MeV fm
143  double e2;
144  /// Range of Yukawa-plus-exponential potential, 0.68 fm
145  double a;
146  /** \brief Range of Yukawa function used to generate nuclear
147  charge distribution, 0.70 fm
148  */
149  double aden;
150  /// Average pairing-gap constant, 4.80 MeV
151  double rmac;
152  /// Neutron-proton interaction constant, 6.6 MeV
153  double h;
154  /// Density-symmetry constant, 0 MeV
155  double L;
156  /// Pre-exponential compressibility-term constant, 60 MeV
157  double C;
158  /// Exponential compressibility-term range constant, 0.831
159  double gamma;
160  /// Atomic mass unit, 931.5014 MeV
161  double amu;
162 
163  /// Internal average neutron density
164  double nn;
165 
166  /// Internal average proton density
167  double np;
168 
169  /// Neutron radius
170  double Rn;
171 
172  /// Proton radius
173  double Rp;
174 
175  /// Given \c Z and \c N, return the mass excess in MeV
176  virtual double mass_excess_d(double Z, double N);
177 
178  /// Given \c Z and \c N, return the mass excess in MeV
179  virtual double mass_excess(int Z, int N) {
180  return mass_excess_d(Z,N);
181  }
182 
183  /// Fix parameters from an array for fitting
184  virtual int fit_fun(size_t nv, const ubvector &x);
185 
186  /// Fill array with guess from present values for fitting
187  virtual int guess_fun(size_t nv, ubvector &x);
188 
189  /** \brief Return the binding energy in MeV
190  */
191  virtual double drip_binding_energy_d(double Z, double N,
192  double npout, double nnout,
193  double chi);
194 
195  /** \brief Given \c Z and \c N, return the mass excess in MeV
196  in a many-body environment
197 
198  This is an experimental version of mass_excess_d which removes
199  pairing, computes nn, np, Rn, and Rp, and attempts to correct
200  the surface. This function probably doesn't work at the
201  moment. It's not currently used by \ref
202  drip_binding_energy_d().
203  */
204  virtual double drip_mass_excess_d(double Z, double N,
205  double np_out, double nn_out,
206  double chi);
207 
208  protected:
209 
210  /// Conversion from kg to inverse fm
211  double kg_to_invfm;
212 
213  /// Proton pairing coefficient
214  double Deltap;
215  /// Neutron pairing coefficient
216  double Deltan;
217  /// Isubvector pairing coefficient
218  double deltanp;
219 
220  /// Average bulk nuclear asymmetry
221  double deltabar;
222  /// Average relative deviation of bulk density
223  double epsbar;
224 
225  /// Desc
226  double Bs;
227  /// Desc
228  double Bk;
229  /// Desc
230  double Br;
231  /// Desc
232  double Bw;
233  /// Desc
234  double Bv;
235 
236  /// Coulomb energy coefficient
237  double c1;
238  /// Volume redistribution energy coefficient
239  double c2;
240  /// Coulomb exchange correction coefficient
241  double c4;
242  /// Surface redistribution energy coefficient
243  double c5;
244 
245  /** \brief Coefficient for the proton form-factor correction to the
246  Coulomb energy
247  */
248  double f0;
249 
250  /// Desc
251  double a0;
252 
253  /// Desc
254  double B1;
255  /// Desc
256  double B2;
257  /// Desc
258  double B3;
259  /// Desc
260  double B4;
261 
262  };
263 
264  /** \brief Mass formula from Moller, Nix, Myers, Swiatecki and Kratz
265 
266  This is based on the tables given in \ref Moller95 and \ref
267  Moller97. To load data from the \o2 HDF5 data files, use
268  <tt>o2scl_hdf::mnmsk_load()</tt>.
269 
270  The data containing an object of type \ref entry for 8979
271  nuclei is automatically loaded by the constructor. If the file
272  (nucmass/mnmsk.o2) is not found, then is_loaded() will return
273  <tt>false</tt> and all calls to get_ZN() will return an object
274  with \c N=Z=0.
275 
276  There are several entries in the original table which are
277  blank because they are in some way not known, measured, or
278  computable. To distinguish these values from zero, blank entries
279  have been replaced by the number \c 1.0e99. For convenience,
280  this value is returned by \ref blank().
281 
282  \note This class requires data stored in an HDF file and
283  thus requires HDF support for normal usage.
284  */
285  class nucmass_mnmsk : public nucmass_table {
286 
287  public:
288 
289  nucmass_mnmsk();
290 
291  virtual ~nucmass_mnmsk();
292 
293  /** \brief Entry structure for Moller, et al. masses
294  */
295  struct entry {
296 
297  /// Neutron number
298  int N;
299 
300  /// Proton number
301  int Z;
302 
303  /// Atomic number
304  int A;
305 
306  /** \name Ground state deformations (perturbed-spheroid parameterization)
307  */
308  //@{
309  /// Quadrupole
310  double eps2;
311  /// Octupole
312  double eps3;
313  /// Hexadecapole
314  double eps4;
315  /// Hexacontatetrapole
316  double eps6;
317  /// Hexacontatetrapole without mass asymmetry
318  double eps6sym;
319  //@}
320 
321  /** \name Ground state deformations in the spherical-harmonics expansion
322  */
323  //@{
324  /// Quadrupole
325  double beta2;
326  /// Octupole
327  double beta3;
328  /// Hexadecapole
329  double beta4;
330  /// Hexacontatetrapole
331  double beta6;
332  //@}
333 
334  /// The ground-state microscopic energy
335  double Emic;
336 
337  /// The theoretical mass excess (in MeV)
338  double Mth;
339 
340  /// The experimental mass excess (in MeV)
341  double Mexp;
342 
343  /// Experimental mass excess error
344  double sigmaexp;
345 
346  /// The ground-state microscopic energy in the FRLDM
347  double EmicFL;
348 
349  /// The theoretical mass excess in the FRLDM
350  double MthFL;
351 
352  /// Spin and pairity of odd proton
353  char spinp[6];
354 
355  /// Spin and pairity of odd neutron
356  char spinn[6];
357 
358  /// Lipkin-Nogami proton gap
359  double gapp;
360 
361  /// Lipkin-Nogami neutron gap
362  double gapn;
363 
364  /// Total binding energy
365  double be;
366 
367  /// One neutron separation energy
368  double S1n;
369 
370  /// Two neutron separation energy
371  double S2n;
372 
373  /** \brief Percentage of daughters generated in beta decay after
374  beta-delayed neutron emission
375  */
376  double PA;
377 
378  /// Desc
379  double PAm1;
380 
381  /// Desc
382  double PAm2;
383 
384  /// Energy released in beta-decay
385  double Qbeta;
386 
387  /// Half-life w.r.t. GT beta-decay
388  double Tbeta;
389 
390  /// One proton separation energy
391  double S1p;
392 
393  /// Two proton separation energy
394  double S2p;
395 
396  /// Energy released in alpha-decay
397  double Qalpha;
398 
399  /// Half-life w.r.t. alpha-decay
400  double Talpha;
401 
402  };
403 
404  /** \brief Return false if the mass formula does not include
405  specified nucleus
406  */
407  virtual bool is_included(int Z, int N);
408 
409  /// Given \c Z and \c N, return the mass excess in MeV
410  virtual double mass_excess(int Z, int N);
411 
412  /** \brief Get the entry for the specified proton and neutron number
413 
414  This method searches the table using a cached binary search
415  algorithm. It is assumed that the table is sorted first by
416  proton number and then by neutron number.
417  */
418  nucmass_mnmsk::entry get_ZN(int l_Z, int l_N);
419 
420  /// The value which corresponds to a blank entry
421  double blank() { return 1.0e99; };
422 
423  /// Neither beta+ or beta- is possible
424  double neither() { return 1.0e98; };
425 
426  /// The value which corresponds to a blank entry
427  double beta_stable() { return 1.0e97; };
428 
429  /// Both beta+ and beta- are possible
430  double beta_plus_and_minus() { return 1.0e96; };
431 
432  /// The value is greater than 100
433  double greater_100() { return 1.0e95; };
434 
435  /// The value is greater than \f$ 10^{20} \f$
436  double very_large() { return 1.0e94; };
437 
438  /// Return the type, \c "nucmass_mnmsk".
439  virtual const char *type() { return "nucmass_mnmsk"; }
440 
441  /** \brief Set data
442 
443  This function is used by the HDF I/O routines.
444  */
445  int set_data(int n_mass, nucmass_mnmsk::entry *m, std::string ref);
446 
447 #ifndef DOXYGEN_INTERNAL
448 
449  protected:
450 
451  /// The reference for the original data
452  std::string reference;
453 
454  /// The array containing the mass data of length ame::n
456 
457  /// The last table index for caching
458  int last;
459 
460 #endif
461 
462  };
463 
464  /** \brief The experimental values from Moller, Nix, Myers and Swiatecki
465 
466  This mass formula only includes the experimental mass
467  excesses tabulated in \ref Moller95 and \ref Moller97 .
468 
469  \note This class requires data stored in an HDF file and
470  thus requires HDF support for normal usage.
471  */
473 
474  public:
475 
476  /** \brief Return false if the mass formula does not include
477  specified nucleus
478  */
479  virtual bool is_included(int Z, int N);
480 
481  /// Given \c Z and \c N, return the mass excess in MeV
482  virtual double mass_excess(int Z, int N);
483 
484  };
485 
486 #ifndef DOXYGEN_NO_O2NS
487 }
488 #endif
489 
490 #endif
491 
o2scl::nucmass_frdm::drip_mass_excess_d
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.
o2scl::nucmass_mnmsk::entry::gapp
double gapp
Lipkin-Nogami proton gap.
Definition: nucmass_frdm.h:359
o2scl::nucmass_frdm::Bs
double Bs
Desc.
Definition: nucmass_frdm.h:226
o2scl::nucmass_mnmsk::entry::beta3
double beta3
Octupole.
Definition: nucmass_frdm.h:327
o2scl::nucmass_frdm::fit_fun
virtual int fit_fun(size_t nv, const ubvector &x)
Fix parameters from an array for fitting.
o2scl::nucmass_mnmsk_exp::is_included
virtual bool is_included(int Z, int N)
Return false if the mass formula does not include specified nucleus.
o2scl::nucmass_frdm::r0
double r0
Nuclear-radius constant in fm (default 1.16)
Definition: nucmass_frdm.h:137
o2scl::nucmass_mnmsk::entry::S2p
double S2p
Two proton separation energy.
Definition: nucmass_frdm.h:394
o2scl::nucmass_mnmsk::entry::Z
int Z
Proton number.
Definition: nucmass_frdm.h:301
o2scl::nucmass_mnmsk_exp
The experimental values from Moller, Nix, Myers and Swiatecki.
Definition: nucmass_frdm.h:472
o2scl::nucmass_mnmsk::entry::PAm1
double PAm1
Desc.
Definition: nucmass_frdm.h:379
o2scl::nucmass_mnmsk::entry::spinn
char spinn[6]
Spin and pairity of odd neutron.
Definition: nucmass_frdm.h:356
o2scl::nucmass_frdm::K
double K
Nuclear compressibility constant in MeV (default 240)
Definition: nucmass_frdm.h:119
o2scl::nucmass_mnmsk::type
virtual const char * type()
Return the type, "nucmass_mnmsk".
Definition: nucmass_frdm.h:439
o2scl::nucmass_frdm::MH
double MH
Hydrogen atom mass excess, 7.289034 MeV.
Definition: nucmass_frdm.h:139
o2scl::nucmass_mnmsk::entry::be
double be
Total binding energy.
Definition: nucmass_frdm.h:365
o2scl::nucmass_frdm::deltabar
double deltabar
Average bulk nuclear asymmetry.
Definition: nucmass_frdm.h:221
o2scl::nucmass_frdm::Rn
double Rn
Neutron radius.
Definition: nucmass_frdm.h:170
o2scl::nucmass_mnmsk::last
int last
The last table index for caching.
Definition: nucmass_frdm.h:458
o2scl::nucmass_frdm::B4
double B4
Desc.
Definition: nucmass_frdm.h:260
o2scl::nucmass_frdm::B1
double B1
Desc.
Definition: nucmass_frdm.h:254
o2scl::nucmass_mnmsk::neither
double neither()
Neither beta+ or beta- is possible.
Definition: nucmass_frdm.h:424
o2scl::nucmass_mnmsk::entry::gapn
double gapn
Lipkin-Nogami neutron gap.
Definition: nucmass_frdm.h:362
o2scl::nucmass_frdm::ca
double ca
Charge-asymmetry constant in MeV (default 0.436)
Definition: nucmass_frdm.h:127
o2scl::nucmass_mnmsk::beta_stable
double beta_stable()
The value which corresponds to a blank entry.
Definition: nucmass_frdm.h:427
o2scl::nucmass_mnmsk::entry::EmicFL
double EmicFL
The ground-state microscopic energy in the FRLDM.
Definition: nucmass_frdm.h:347
o2scl::nucmass_frdm::a
double a
Range of Yukawa-plus-exponential potential, 0.68 fm.
Definition: nucmass_frdm.h:145
o2scl::nucmass_frdm::drip_binding_energy_d
virtual double drip_binding_energy_d(double Z, double N, double npout, double nnout, double chi)
Return the binding energy in MeV.
o2scl::nucmass_mnmsk::blank
double blank()
The value which corresponds to a blank entry.
Definition: nucmass_frdm.h:421
o2scl::nucmass_frdm::Deltan
double Deltan
Neutron pairing coefficient.
Definition: nucmass_frdm.h:216
o2scl::nucmass_mnmsk::entry::S1n
double S1n
One neutron separation energy.
Definition: nucmass_frdm.h:368
o2scl::nucmass_frdm::c5
double c5
Surface redistribution energy coefficient.
Definition: nucmass_frdm.h:243
o2scl::nucmass_frdm::gamma
double gamma
Exponential compressibility-term range constant, 0.831.
Definition: nucmass_frdm.h:159
o2scl::nucmass_mnmsk::mass
nucmass_mnmsk::entry * mass
The array containing the mass data of length ame::n.
Definition: nucmass_frdm.h:455
o2scl::nucmass_frdm::Br
double Br
Desc.
Definition: nucmass_frdm.h:230
o2scl::nucmass_mnmsk::entry::Mexp
double Mexp
The experimental mass excess (in MeV)
Definition: nucmass_frdm.h:341
o2scl::nucmass_mnmsk::get_ZN
nucmass_mnmsk::entry get_ZN(int l_Z, int l_N)
Get the entry for the specified proton and neutron number.
o2scl::nucmass_frdm::L
double L
Density-symmetry constant, 0 MeV.
Definition: nucmass_frdm.h:155
o2scl::nucmass_mnmsk::entry::PA
double PA
Percentage of daughters generated in beta decay after beta-delayed neutron emission.
Definition: nucmass_frdm.h:376
o2scl::nucmass_frdm::h
double h
Neutron-proton interaction constant, 6.6 MeV.
Definition: nucmass_frdm.h:153
o2scl::nucmass_frdm::c1
double c1
Coulomb energy coefficient.
Definition: nucmass_frdm.h:237
o2scl::nucmass_frdm::a1
double a1
Volume-energy constant in MeV (default 16.247)
Definition: nucmass_frdm.h:115
o2scl::nucmass_mnmsk::entry::beta4
double beta4
Hexadecapole.
Definition: nucmass_frdm.h:329
o2scl::nucmass_mnmsk::entry::Talpha
double Talpha
Half-life w.r.t. alpha-decay.
Definition: nucmass_frdm.h:400
o2scl::nucmass_frdm::c2
double c2
Volume redistribution energy coefficient.
Definition: nucmass_frdm.h:239
o2scl::nucmass_frdm
FRDM semi-empirical mass formula (macroscopic part only with no deformation)
Definition: nucmass_frdm.h:108
o2scl::nucmass_mnmsk::entry::eps2
double eps2
Quadrupole.
Definition: nucmass_frdm.h:310
o2scl::nucmass_frdm::mass_excess
virtual double mass_excess(int Z, int N)
Given Z and N, return the mass excess in MeV.
Definition: nucmass_frdm.h:179
o2scl::nucmass_frdm::Bk
double Bk
Desc.
Definition: nucmass_frdm.h:228
o2scl::nucmass_frdm::mass_excess_d
virtual double mass_excess_d(double Z, double N)
Given Z and N, return the mass excess in MeV.
o2scl::nucmass_frdm::np
double np
Internal average proton density.
Definition: nucmass_frdm.h:167
o2scl::nucmass_fit_base
Fittable mass formula [abstract base].
Definition: nucmass.h:375
o2scl::nucmass_frdm::B2
double B2
Desc.
Definition: nucmass_frdm.h:256
o2scl::nucmass_frdm::rp
double rp
Proton root-mean-square radius in fm (default 0.80)
Definition: nucmass_frdm.h:135
o2scl::nucmass_frdm::rmac
double rmac
Average pairing-gap constant, 4.80 MeV.
Definition: nucmass_frdm.h:151
o2scl::nucmass_frdm::aden
double aden
Range of Yukawa function used to generate nuclear charge distribution, 0.70 fm.
Definition: nucmass_frdm.h:149
o2scl::nucmass_frdm::Deltap
double Deltap
Proton pairing coefficient.
Definition: nucmass_frdm.h:214
o2scl::nucmass_mnmsk::entry::eps6sym
double eps6sym
Hexacontatetrapole without mass asymmetry.
Definition: nucmass_frdm.h:318
o2scl::nucmass_mnmsk::entry::Tbeta
double Tbeta
Half-life w.r.t. GT beta-decay.
Definition: nucmass_frdm.h:388
o2scl::nucmass_mnmsk::entry::MthFL
double MthFL
The theoretical mass excess in the FRLDM.
Definition: nucmass_frdm.h:350
o2scl::nucmass_frdm::a0
double a0
Desc.
Definition: nucmass_frdm.h:251
o2scl::nucmass_frdm::kg_to_invfm
double kg_to_invfm
Conversion from kg to inverse fm.
Definition: nucmass_frdm.h:211
o2scl::nucmass_mnmsk::entry::beta6
double beta6
Hexacontatetrapole.
Definition: nucmass_frdm.h:331
o2scl::nucmass_mnmsk::entry::Mth
double Mth
The theoretical mass excess (in MeV)
Definition: nucmass_frdm.h:338
o2scl::nucmass_mnmsk::entry
Entry structure for Moller, et al. masses.
Definition: nucmass_frdm.h:295
o2scl::nucmass_mnmsk::reference
std::string reference
The reference for the original data.
Definition: nucmass_frdm.h:452
o2scl::nucmass_mnmsk::entry::beta2
double beta2
Quadrupole.
Definition: nucmass_frdm.h:325
o2scl::nucmass_frdm::a3
double a3
Curvature-energy constant in MeV (default 0)
Definition: nucmass_frdm.h:125
o2scl::nucmass_mnmsk::entry::A
int A
Atomic number.
Definition: nucmass_frdm.h:304
o2scl::nucmass_frdm::amu
double amu
Atomic mass unit, 931.5014 MeV.
Definition: nucmass_frdm.h:161
o2scl::nucmass_mnmsk::entry::Qbeta
double Qbeta
Energy released in beta-decay.
Definition: nucmass_frdm.h:385
o2scl::nucmass_mnmsk::is_included
virtual bool is_included(int Z, int N)
Return false if the mass formula does not include specified nucleus.
o2scl::nucmass_frdm::Mn
double Mn
Neutron mass excess, 8.071431 MeV.
Definition: nucmass_frdm.h:141
o2scl::nucmass_mnmsk::entry::N
int N
Neutron number.
Definition: nucmass_frdm.h:298
o2scl::nucmass_mnmsk::entry::eps6
double eps6
Hexacontatetrapole.
Definition: nucmass_frdm.h:316
o2scl::nucmass_mnmsk::set_data
int set_data(int n_mass, nucmass_mnmsk::entry *m, std::string ref)
Set data.
o2scl::nucmass_mnmsk
Mass formula from Moller, Nix, Myers, Swiatecki and Kratz.
Definition: nucmass_frdm.h:285
o2scl::nucmass_frdm::epsbar
double epsbar
Average relative deviation of bulk density.
Definition: nucmass_frdm.h:223
o2scl::nucmass_mnmsk::entry::PAm2
double PAm2
Desc.
Definition: nucmass_frdm.h:382
o2scl::nucmass_frdm::e2
double e2
Electronic charge squared, 1.4399764 MeV fm.
Definition: nucmass_frdm.h:143
o2scl::nucmass_frdm::Bw
double Bw
Desc.
Definition: nucmass_frdm.h:232
o2scl::nucmass_frdm::nn
double nn
Internal average neutron density.
Definition: nucmass_frdm.h:164
o2scl::nucmass_mnmsk::beta_plus_and_minus
double beta_plus_and_minus()
Both beta+ and beta- are possible.
Definition: nucmass_frdm.h:430
o2scl::nucmass_frdm::B3
double B3
Desc.
Definition: nucmass_frdm.h:258
o2scl::nucmass_mnmsk::entry::S2n
double S2n
Two neutron separation energy.
Definition: nucmass_frdm.h:371
o2scl::nucmass_mnmsk_exp::mass_excess
virtual double mass_excess(int Z, int N)
Given Z and N, return the mass excess in MeV.
o2scl::nucmass_mnmsk::entry::Emic
double Emic
The ground-state microscopic energy.
Definition: nucmass_frdm.h:335
o2scl::nucmass_frdm::f0
double f0
Coefficient for the proton form-factor correction to the Coulomb energy.
Definition: nucmass_frdm.h:248
o2scl::nucmass_mnmsk::greater_100
double greater_100()
The value is greater than 100.
Definition: nucmass_frdm.h:433
o2scl::nucmass_frdm::Q
double Q
Effective surface-stiffness constant in MeV (default 29.21)
Definition: nucmass_frdm.h:123
o2scl::nucmass_mnmsk::very_large
double very_large()
The value is greater than .
Definition: nucmass_frdm.h:436
o2scl::nucmass_frdm::W
double W
Wigner constant in MeV (default 30)
Definition: nucmass_frdm.h:129
o2scl::nucmass_frdm::a2
double a2
Surface-energy constant in MeV (default 22.92)
Definition: nucmass_frdm.h:121
o2scl::nucmass_table
Tabulated nuclear masses [abstract base].
Definition: nucmass.h:330
o2scl::nucmass_mnmsk::entry::eps3
double eps3
Octupole.
Definition: nucmass_frdm.h:312
o2scl::nucmass_frdm::J
double J
Symmetry-energy constant in MeV (default 32.73)
Definition: nucmass_frdm.h:117
o2scl::nucmass_mnmsk::mass_excess
virtual double mass_excess(int Z, int N)
Given Z and N, return the mass excess in MeV.
o2scl::nucmass_frdm::c4
double c4
Coulomb exchange correction coefficient.
Definition: nucmass_frdm.h:241
o2scl::nucmass_mnmsk::entry::sigmaexp
double sigmaexp
Experimental mass excess error.
Definition: nucmass_frdm.h:344
o2scl::nucmass_mnmsk::entry::spinp
char spinp[6]
Spin and pairity of odd proton.
Definition: nucmass_frdm.h:353
o2scl::nucmass_frdm::deltanp
double deltanp
Isubvector pairing coefficient.
Definition: nucmass_frdm.h:218
o2scl::nucmass_frdm::Rp
double Rp
Proton radius.
Definition: nucmass_frdm.h:173
o2scl::nucmass_frdm::guess_fun
virtual int guess_fun(size_t nv, ubvector &x)
Fill array with guess from present values for fitting.
o2scl::nucmass_frdm::C
double C
Pre-exponential compressibility-term constant, 60 MeV.
Definition: nucmass_frdm.h:157
o2scl::nucmass_mnmsk::entry::S1p
double S1p
One proton separation energy.
Definition: nucmass_frdm.h:391
o2scl::nucmass_frdm::ael
double ael
electronic-binding constant in MeV (default ).
Definition: nucmass_frdm.h:133
o2scl::nucmass_mnmsk::entry::Qalpha
double Qalpha
Energy released in alpha-decay.
Definition: nucmass_frdm.h:397
o2scl::nucmass_mnmsk::entry::eps4
double eps4
Hexadecapole.
Definition: nucmass_frdm.h:314
o2scl::nucmass_frdm::Bv
double Bv
Desc.
Definition: nucmass_frdm.h:234

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