eos_had_skyrme.h
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4  Copyright (C) 2006-2018, Andrew W. Steiner
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23 /** \file eos_had_skyrme.h
24  \brief File defining \ref o2scl::eos_had_skyrme
25 */
26 #ifndef O2SCL_SKYRME_EOS_H
27 #define O2SCL_SKYRME_EOS_H
28 
29 #include <iostream>
30 #include <string>
31 #include <cmath>
32 
33 #include <o2scl/constants.h>
34 #include <o2scl/mroot.h>
35 #include <o2scl/eos_had_base.h>
36 #include <o2scl/part.h>
37 #include <o2scl/fermion_nonrel.h>
38 #include <o2scl/fermion_deriv_nr.h>
39 
40 #ifndef DOXYGEN_NO_O2NS
41 namespace o2scl {
42 #endif
43 
44  /** \brief Object to store second derivatives of \f$ P(\mu,T) \f$
45  */
47  public:
48  /// The quantity \f$ (\partial^2 P)/(\partial T^2) \f$
49  double dsdT;
50  /// The quantity \f$ (\partial^2 P)/(\partial T \partial \mu_n) \f$
51  double dnndT;
52  /// The quantity \f$ (\partial^2 P)/(\partial T \partial \mu_p) \f$
53  double dnpdT;
54  /// The quantity \f$ (\partial^2 P)/(\partial \mu_n^2) \f$
55  double dnndmun;
56  /// The quantity \f$ (\partial^2 P)/(\partial \mu_n \partial \mu_p) \f$
57  double dndmu_mixed;
58  /// The quantity \f$ (\partial^2 P)/(\partial \mu_p^2) \f$
59  double dnpdmup;
60  };
61 
62  /** \brief Skyrme hadronic equation of state
63 
64  Equation of state of nucleonic matter based on
65  the Skryme interaction from \ref Skyrme59 .
66 
67  \hline
68  \b Background:
69 
70  The Hamiltonian is defined (using the notation of
71  \ref Steiner05b ) as
72  \f[
73  {\cal H} =
74  {\cal H}_{k1} +
75  {\cal H}_{k2} +
76  {\cal H}_{k3} +
77  {\cal H}_{p1} +
78  {\cal H}_{p2} +
79  {\cal H}_{p3} +
80  {\cal H}_{g1} +
81  {\cal H}_{g2} \, .
82  \f]
83 
84  The kinetic terms are:
85  \f[
86  {\cal H}_{k1} = \frac{\tau_n}{2 m_n} +
87  \frac{\tau_p}{2 m_p}
88  \f]
89  \f[
90  {\cal H}_{k2} =
91  n \left(\tau_n + \tau_p \right) \left[ \frac{t_1}{4}
92  \left( 1 + \frac{x_1}{2} \right)
93  + \frac{t_2}{4} \left( 1 + \frac{x_2}{2} \right) \right]
94  \f]
95  \f[
96  {\cal H}_{k3} =
97  \left( \tau_n n_n + \tau_p n_p \right) \left[ \frac{t_2}{4}
98  \left( \frac{1}{2} + x_2 \right)
99  - \frac{t_1}{4} \left( \frac{1}{2} + x_1 \right) \right]
100  \f]
101  where \f$ \tau_i \f$ is the Fermi gas energy density
102  of particle \f$ i \f$ .
103 
104  The potential terms are:
105  \f[
106  {\cal H}_{p1} =
107  \frac{t_0}{2}
108  \left[ \left( 1 + \frac{x_0}{2} \right) n^2 -
109  \left( {\textstyle \frac{1}{2}} + x_0 \right)
110  \left( n_n^2 + n_p^2 \right) \right]
111  \f]
112  \f[
113  {\cal H}_{p2} =
114  \frac{a t_3}{6} \left[ \left( 1 + \frac{x_3}{2} \right) n^{\alpha}
115  n_n n_p + 2^{\alpha-2} \left(1 - x_3\right)
116  \left(n_n^{\alpha+2} + n_p^{\alpha+2}\right) \right]
117  \f]
118  \f[
119  {\cal H}_{p3} =
120  \frac{b t_3}{12} \left[ \left(1 + \frac{x_3}{2} \right) n^{\alpha+2} -
121  \left(\frac{1}{2} + x_3 \right) n^{\alpha}
122  \left( n_n^2+n_p^2 \right) \right]
123  \f]
124 
125  The gradient terms are displayed here for completeness even though
126  they are not computed in the code:
127  \f[
128  {\cal H}_{g1} =
129  \frac{3}{32} \left[ t_1 \left(1 - x_1 \right) -
130  t_2 \left(1 + x_2 \right) \right] \left[ \left( \nabla n_n\right)^2 +
131  \left( \nabla n_p \right)^2 \right]
132  \f]
133  \f[
134  {\cal H}_{g2} =
135  \frac{1}{8} \left[ 3 t_1 \left( 1 +
136  \frac{x_1}{2} \right) - t_2 \left(1 + \frac{x_2}{2} \right) \right]
137  \nabla n_n \nabla n_p
138  \f]
139 
140  The values \f$ a=0, b=1 \f$ give the standard definition of the
141  Skyrme Hamiltonian \ref Skyrme59, while \f$a=1, b=0\f$ contains
142  the modifications suggested by \ref Onsi94.
143 
144  The spin-orbit term is (following \ref Steiner05)
145  \f[
146  {\cal H}_{J} = -\frac{W_0}{2} \left( n_n \vec{\nabla} \cdot
147  \vec{J}_n + n_p \vec{\nabla} \cdot \vec{J}_p + n \vec{\nabla}
148  \cdot \vec{J} \right) + \frac{t_1}{16} \left(\vec{J}_n^2 +
149  \vec{J}_p^2 - x_1 \vec{J}^2\right) - \frac{t_2}{16}
150  \left(\vec{J}_n^2 + \vec{J}_p^2 + x_2 \vec{J}^2\right)
151  \f]
152  where sometimes the \f$ \vec{J}^2 \f$ terms are not included.
153  Alternatively, one can separate the isoscalar and isovector
154  parts in the first term
155  \f[
156  {\cal H}_{J} = - b_4 n \vec{\nabla} \cdot \vec{J} -
157  b_4^{\prime} n_n \vec{\nabla} \cdot \vec{J}_n -
158  b_4^{\prime} n_p \vec{\nabla} \cdot \vec{J}_p
159  \f]
160  then the earlier Skyrme interactions have \f$ b_4 =
161  b_4^{\prime} = W_0/2 \f$. For example, for SLy4,
162  \f$ b_4 = b_4^{\prime} = W_0/2 = 61.5~\mathrm{MeV} \f$.
163 
164  Also, couple useful definitions
165  \f[
166  t_3^{\prime} = \left(a + b\right) t_3 \, ,
167  \f]
168  \f[
169  C = \frac{3 }{10 m} \left( \frac{3 \pi^2 }{2} \right)^{2/3} \, ,
170  \f]
171  and
172  \f[
173  \beta = \frac{M}{2} \left[ \frac{1}{4} \left( 3 t_1 + 5 t_2 \right) \, .
174  + t_2 x_2 \right] \\
175  \f]
176 
177  \hline
178  \b Units:
179 
180  Quantities which have units containing powers of energy are
181  divided by \f$\hbar c\f$ to ensure all quantities are in units
182  of \f$ \mathrm{fm} \f$. The \f$x_i\f$ and \f$\alpha\f$ are
183  unitless, while the original units of the \f$t_i\f$ are:
184  - \f$t_0\f$ - \f$\mathrm{MeV}\f$ \f$\mathrm{fm}^3\f$
185  - \f$t_1\f$ - \f$\mathrm{MeV}\f$ \f$\mathrm{fm}^5\f$
186  - \f$t_2\f$ - \f$\mathrm{MeV}\f$ \f$\mathrm{fm}^5\f$
187  - \f$t_3\f$ - \f$\mathrm{MeV}\f$ \f$\mathrm{fm}^{3(1+\alpha)}\f$
188 
189  These are stored internally with units of:
190  - \f$t_0\f$ - \f$\mathrm{fm}^2\f$
191  - \f$t_1\f$ - \f$\mathrm{fm}^4\f$
192  - \f$t_2\f$ - \f$\mathrm{fm}^4\f$
193  - \f$t_3\f$ - \f$\mathrm{fm}^{2+3 \alpha}\f$
194 
195  \hline
196  \b Misc:
197 
198  The functions for the usual saturation properties are based
199  partly on \ref Brack85.
200 
201  Models are taken from the references: \ref Bartel79, \ref
202  Beiner75, \ref Chabanat95, \ref Chabanat97, \ref Danielewicz09,
203  \ref Dobaczewski94, \ref Dutta86, \ref Friedrich86, \ref Onsi94,
204  \ref Reinhard95, and \ref Tondeur84, and \ref VanGiai81 .
205 
206  The variables \f$ \nu_n\f$ and \f$ \nu_p\f$ contain the
207  expressions \f$ (-\mu_n+V_n)/T \f$ and \f$ (-\mu_p+V_p)/T \f$
208  respectively, where \f$ V \f$ is the potential part of the
209  single particle energy for particle i (i.e. the derivative of
210  the Hamiltonian w.r.t. density while energy density held
211  constant). Equivalently, \f$ \nu_n\f$ is just \f$ -k_{F_n}^2/ 2
212  m^{*} \f$.
213 
214  \note The finite temperature code does not include attempt to
215  include antiparticles and uses \ref
216  o2scl::fermion_nonrel::calc_density(). At finite temperature,
217  pure neutron matter implies a zero proton number density which
218  would imply that the proton chemical potential is \f$ - \infty
219  \f$ . This class handles this situation by just setting \f$
220  \nu_p \f$ to zero. The case of pure proton matter is handled
221  similarly.
222 
223  \note Since this EOS uses the effective masses and chemical
224  potentials in the fermion class, the values of
225  <tt>part::non_interacting</tt> for neutrons and protons are set
226  to false in many of the functions.
227 
228  \hline
229 
230  \todo
231  - Convert W0 to b4 and b4p everywhere
232  - Remove use of mnuc in calparfun()?
233  - Document \ref o2scl_hdf::skyrme_load() file format.
234  - Update reference list.
235 
236  \future
237  - There is some code duplication between calc_e() and
238  calc_temp_e() which could be simplified.
239  - This EOS typically converges very well. One exception seems
240  to be using <tt>calc_temp_p()</tt> at very low densities. I have
241  had problems, for example, with <tt>mun=5.0, mup=6.5</tt>
242  at <tt>T=1.0/197.33</tt>.
243 
244  \hline
245 
246  */
248 
249  public:
250 
251  /// \name Basic usage
252  //@{
253  /// Create a blank Skyrme EOS
254  eos_had_skyrme();
255 
256  /// Destructor
257  virtual ~eos_had_skyrme() {};
258 
259  /** \brief Evaluate the effective masses for neutrons and
260  protons
261  */
262  void eff_mass(fermion &ne, fermion &pr);
263 
264  /** \brief Equation of state as a function of densities
265 
266  \note Runs the zero temperature code if \c temper is less
267  than or equal to zero.
268  */
269  virtual int calc_temp_e(fermion &ne, fermion &pr, double temper,
270  thermo &th);
271 
272  /** \brief Equation of state including second derivatives
273  as a function of the densities
274  */
275  virtual int calc_deriv_temp_e(fermion_deriv &ne, fermion_deriv &pr,
276  double temper, thermo &th,
277  thermo_np_deriv &thd);
278 
279  /// Equation of state as a function of density.
280  virtual int calc_e(fermion &ne, fermion &pr, thermo &lt);
281  //@}
282 
283  /// \name Basic Skyrme model parameters
284  //@{
285  double t0,t1,t2,t3,x0,x1,x2,x3,alpha,a,b;
286  //@}
287 
288  /** \brief Spin-orbit splitting (in \f$ \mathrm{fm}^{-1} \f$)
289 
290  This is unused, but included for possible future use and
291  present in the internally stored models.
292  */
293  double W0;
294 
295  /// Isoscalar spin-orbit term (in \f$ \mathrm{fm}^{-1} \f$)
296  double b4;
297 
298  /// Isovector spin-orbit term (in \f$ \mathrm{fm}^{-1} \f$)
299  double b4p;
300 
301  /// Bibliographic reference
302  std::string reference;
303 
304  /** \name Saturation properties
305 
306  These calculate the various saturation properties exactly from
307  the parameters at any density. These routines often assume that
308  the neutron and proton masses are equal.
309  */
310  //@{
311  /** \brief Calculate binding energy
312 
313  \f[
314  \frac{E}{A} = C n_B^{2/3} \left( 1 + \beta n_B \right) +
315  \frac{3 t_0}{8} n_B + \frac{t_3^{\prime}}{16} n_B^{\alpha+1}
316  \f]
317  */
318  virtual double feoa(double nb);
319 
320  /** \brief Calculate effective mass
321 
322  \f[
323  M^{*}/M = \left(1+ \beta n_B \right)^{-1} \\
324  \f]
325  */
326  virtual double fmsom(double nb);
327 
328  /** \brief Calculate compressibility
329 
330  \f[
331  K = 10 C n_B^{2/3} + \frac{27}{4} t_0 n_B + 40 C \beta n_B^{5/3} +
332  \frac{9 t_3^{\prime}}{16}
333  \alpha \left( \alpha+1 \right) n_B^{1 + \alpha} +
334  \frac{9 t_3^{\prime}}{8} \left( \alpha+1 \right) n_B^{1 + \alpha}
335  \f]
336  */
337  virtual double fcomp(double nb);
338 
339  /** \brief Calculate symmetry energy
340 
341  If pf=0.5, then the exact expression below is used.
342  Otherwise, the method from class eos_had_base is used.
343 
344  \f[
345  E_{sym} = \frac{5}{9} C n^{2/3} + \frac{10 C m}{3}
346  \left[ \frac{t_2}{6} \left(1 + \frac{5}{4} x_2 \right) -
347  \frac{1}{8} t_1 x_1 \right] n^{5/3}
348  - \frac{t_3^{\prime}}{24}
349  \left({\textstyle \frac{1}{2}} + x_3 \right) n^{1+\alpha} -
350  \frac{t_0}{4} \left( {\textstyle \frac{1}{2}} + x_0 \right) n
351  \f]
352  */
353  virtual double fesym(double nb, double alpha=0.0);
354 
355  /** \brief skewness
356 
357  \f[
358  2 C n_B^{2/3} \left(9-5/M^{*}/M\right)+
359  \frac{27 t_3^{\prime}}{16} n^{1+\alpha} \alpha
360  \left(\alpha^2-1\right)
361  \f]
362  */
363  virtual double fkprime(double nb);
364  //@}
365 
366  /** \brief Calculate \f$ t_0,t_1,t_2,t_3 \f$ and \f$ \alpha \f$ from
367  the saturation properties.
368 
369  In nuclear matter:
370 
371  \f$ E_b=E_b(n_0,M^{*},t_0,t_3,\alpha) \f$ \n
372  \f$ P=P(n_0,M^{*},t_0,t_3,\alpha) \f$ \n
373  \f$ K=K(n_0,M^{*},t_3,\alpha) \f$
374  (the \f$ t_0 \f$ dependence vanishes) \n
375  \f$ M^{*}=M^{*}(n_0,t_1,t_2,x_2) \f$
376  (the \f$ x_1 \f$ dependence cancels), \n
377  \f$ E_{sym}=E_{sym}(x_0,x_1,x_2,x_3,t_0,t_1,t_2,t_3,\alpha) \f$
378 
379  To fix the couplings from the saturation properties, we take
380  \f$ n_0, M^{*}, E_b, K \f$ as inputs, and we can fix \f$
381  t_0,t_3,\alpha \f$ from the first three relations, then use
382  \f$ M^{*}, E_b \f$ to fix \f$ t_2 \f$ and \f$ t_1 \f$. The
383  separation into two solution steps should make for better
384  convergence. All of the x's are free parameters and should be
385  set before the function call.
386 
387  The arguments \c gt0, \c gt3, \c galpha, \c gt1, and \c gt2
388  are used as initial guesses for skyme_eos::t0, eos_had_skyrme::t3,
389  eos_had_skyrme::alpha, eos_had_skyrme::t1, and eos_had_skyrme::t2
390  respectively.
391 
392  \todo Does this work for both 'a' and 'b' non-zero?
393 
394  \todo Compare to similar formulas in \ref Margueron02
395  */
396  int calpar(double gt0=-10.0, double gt3=70.0, double galpha=0.2,
397  double gt1=2.0, double gt2=-1.0);
398 
399  // Unfinished.
400  /* \brief
401  From \ref Margueron02
402  */
403  // int calpar_new(double m);
404 
405  /** \brief Use eos_had_base methods for saturation properties
406 
407  This can be set to true to check the difference between
408  the exact expressions and the numerical values from
409  class eos_had_base.
410  */
412 
413  /** \brief Check the Landau parameters for instabilities
414 
415  This returns zero if there are no instabilities.
416  */
417  int check_landau(double nb, double m);
418 
419  /** \brief Calculate the Landau parameters for nuclear matter
420 
421  Given \c n0 and \c m, this calculates the Landau parameters in
422  nuclear matter as given in \ref Margueron02
423 
424  \todo This needs to be checked.
425 
426  (Checked once on 11/05/03)
427  */
428  void landau_nuclear(double n0, double m,
429  double &f0, double &g0, double &f0p,
430  double &g0p, double &f1, double &g1,
431  double &f1p, double &g1p);
432 
433  /** \brief Calculate the Landau parameters for neutron matter
434 
435  Given 'n0' and 'm', this calculates the Landau parameters in
436  neutron matter as given in \ref Margueron02
437 
438  \todo This needs to be checked
439 
440  (Checked once on 11/05/03)
441  */
442  void landau_neutron(double n0, double m, double &f0, double &g0,
443  double &f1, double &g1);
444 
445  /// Return string denoting type ("eos_had_skyrme")
446  virtual const char *type() { return "eos_had_skyrme"; }
447 
448  /** \brief Set using alternate parameterization
449 
450  From \ref Bender03 as in, e.g. \ref Kortelainen14
451  \f{eqnarray*}
452  C^{\rho \rho}_{00} &=& 3 t_0/8 \nonumber \\
453  C^{\rho \rho}_{10} &=& -t_0/4 \left(\frac{1}{2}+x_0 \right)
454  \nonumber \\
455  C^{\rho \rho}_{0D} &=& t_3/16 \nonumber \\
456  C^{\rho \rho}_{1D} &=& -t_3/24 \left(\frac{1}{2}+x_3\right)
457  \nonumber \\
458  C^{\rho \tau}_{0} &=& 3 t_1/16+t_2/4\left(\frac{5}{4}+x_2\right)
459  \nonumber \\
460  C^{\rho \tau}_{1} &=& -t_1/8 \left(\frac{1}{2}+x_1\right) +
461  t_2/8 \left(\frac{1}{2}+x_2\right) \nonumber \\
462  C^{\rho \Delta \rho}_{0} &=& -9/64 t_1+t_2/16
463  \left(\frac{5}{4}+x_2\right) \nonumber \\
464  C^{\rho \Delta \rho}_{1} &=& 3/32 t_1 \left(\frac{1}{2}+x_1\right) +
465  t_2/32 \left(\frac{1}{2}+x_2\right) \nonumber \\
466  C^{\rho \nabla J}_{0} &=& -b_4 -b_4^{\prime}/2 \nonumber \\
467  C^{\rho \nabla J}_{1} &=& -b_4^{\prime}/2
468  \f}
469 
470  The parameters should have the following units
471  - <tt>Crr00</tt>: \f$ \mathrm{fm}^2 \f$
472  - <tt>Crr10</tt>: \f$ \mathrm{fm}^2 \f$
473  - <tt>Crr0D</tt>: \f$ \mathrm{fm}^{3 \alpha+2} \f$
474  - <tt>Crr1D</tt>: \f$ \mathrm{fm}^{3 \alpha+2} \f$
475  - <tt>Crt0</tt>: \f$ \mathrm{fm}^4 \f$
476  - <tt>Crt1</tt>: \f$ \mathrm{fm}^4 \f$
477  - <tt>CrDr0</tt>: \f$ \mathrm{fm}^4 \f$
478  - <tt>CrDr1</tt>: \f$ \mathrm{fm}^4 \f$
479  - <tt>CrnJ0</tt>: \f$ \mathrm{fm}^{-1} \f$
480  - <tt>CrnJ1</tt>: \f$ \mathrm{fm}^{-1} \f$
481  - <tt>alpha2</tt>: unitless
482 
483  \todo These expressions are not exactly the same
484  as those in \ref Bender03, so I need to find out why
485  and make this more clear.
486  */
487  void alt_params_set
488  (double Crr00, double Crr10, double Crr0D, double Crr1D,
489  double Crt0, double Crt1, double CrDr0, double CrDr1,
490  double CrnJ0, double CrnJ1, double alpha2);
491 
492  /** \brief Get alternate parameterization
493 
494  The parameters will have the following units
495  - <tt>Crr00</tt>: \f$ \mathrm{fm}^2 \f$
496  - <tt>Crr10</tt>: \f$ \mathrm{fm}^2 \f$
497  - <tt>Crr0D</tt>: \f$ \mathrm{fm}^{3 \alpha+2} \f$
498  - <tt>Crr1D</tt>: \f$ \mathrm{fm}^{3 \alpha+2} \f$
499  - <tt>Crt0</tt>: \f$ \mathrm{fm}^4 \f$
500  - <tt>Crt1</tt>: \f$ \mathrm{fm}^4 \f$
501  - <tt>CrDr0</tt>: \f$ \mathrm{fm}^4 \f$
502  - <tt>CrDr1</tt>: \f$ \mathrm{fm}^4 \f$
503  - <tt>CrnJ0</tt>: \f$ \mathrm{fm}^{-1} \f$
504  - <tt>CrnJ1</tt>: \f$ \mathrm{fm}^{-1} \f$
505  - <tt>alpha2</tt>: unitless
506 
507  See \ref eos_had_skyrme::alt_params_set().
508  */
509  void alt_params_get
510  (double &Crr00, double &Crr10, double &Crr0D, double &Crr1D,
511  double &Crt0, double &Crt1, double &CrDr0, double &CrDr1,
512  double &CrnJ0, double &CrnJ1, double &alpha2);
513 
514  /** \brief Use the specified saturation properties and couplings
515  and the function \ref alt_params_set() to set the
516  Skyrme coefficients
517 
518  This function uses the relations in \ref Kortelainen10 .
519  The parameters should have the following units
520  - <tt>n0</tt>: \f$ \mathrm{fm}^{-3} \f$
521  - <tt>EoA</tt>: \f$ \mathrm{fm}^{-1} \f$
522  - <tt>K</tt>: \f$ \mathrm{fm}^{-1} \f$
523  - <tt>Ms_star</tt>: unitless
524  - <tt>a</tt>: \f$ \mathrm{fm}^{-1} \f$
525  - <tt>L</tt>: \f$ \mathrm{fm}^{-1} \f$
526  - <tt>Mv_star</tt>: unitless
527  - <tt>CrDr0</tt>: \f$ \mathrm{fm}^{-3} \f$
528  - <tt>CrDr1</tt>: \f$ \mathrm{fm}^{-3} \f$
529  - <tt>CrnJ0</tt>: \f$ \mathrm{fm}^{-3} \f$
530  - <tt>CrnJ1</tt>: \f$ \mathrm{fm}^{-3} \f$
531 
532  \ref Kortelainen10 assumed equal neutron and proton masses, so
533  this function uses \f$ \hbar^2/(2m) = \hbar^2/(m_n+m_p) \f$
534  and the neutron and proton masses in \ref
535  eos_had_base::def_neutron and \ref eos_had_base::def_proton,
536  respectively. To obtain the results in the original paper, set
537  neutron and proton masses to ensure that \f$ \hbar^2/(2m) =
538  20.73553~\mathrm{MeV}~\mathrm{fm}^2 \f$ .
539  */
540  void alt_params_saturation
541  (double n0, double EoA, double K, double Ms_star, double a, double L,
542  double Mv_star, double CrDr0, double CrDr1, double CrnJ0, double CrnJ1);
543 
544  /// Thermodynamics of non-relativistic fermions
546 
547  /// Thermodynamics of non-relativistic fermions
549 
550 #ifndef DOXYGEN_NO_O2NS
551 
552  protected:
553 
554  /// \name Functions and parameters for calpar()
555  //@{
556  int calparfun(size_t nv, const ubvector &x, ubvector &y);
557  int calparfun2(size_t nv, const ubvector &x, ubvector &y);
558  double fixn0, fixeoa, fixesym, fixcomp, fixmsom;
559  //@}
560 
561 #endif
562 
563  };
564 
565 #ifndef DOXYGEN_NO_O2NS
566 }
567 #endif
568 
569 #endif
double dnpdmup
The quantity .
double dsdT
The quantity .
fermion_deriv_nr nrfd
Thermodynamics of non-relativistic fermions.
fermion_nonrel nrf
Thermodynamics of non-relativistic fermions.
std::string reference
Bibliographic reference.
virtual ~eos_had_skyrme()
Destructor.
virtual const char * type()
Return string denoting type ("eos_had_skyrme")
double W0
Spin-orbit splitting (in )
double dndmu_mixed
The quantity .
A hadronic EOS at finite temperature based on a function of the densities [abstract base]...
double dnpdT
The quantity .
Skyrme hadronic equation of state.
Object to store second derivatives of .
bool parent_method
Use eos_had_base methods for saturation properties.
double b4
Isoscalar spin-orbit term (in )
double dnndT
The quantity .
double b4p
Isovector spin-orbit term (in )
double dnndmun
The quantity .

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