eos_had_rmf_delta.h
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1 /*
2  -------------------------------------------------------------------
3 
4  Copyright (C) 2006-2017, 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 /** \file eos_had_rmf_delta.h
24  \brief File defining \ref o2scl::eos_had_rmf_delta
25 */
26 #ifndef O2SCL_RMF_DELTA_EOS_H
27 #define O2SCL_RMF_DELTA_EOS_H
28 
29 #include <o2scl/eos_had_rmf.h>
30 
31 #ifndef DOXYGEN_NO_O2NS
32 namespace o2scl {
33 #endif
34 
35  /** \brief Field-theoretical EOS with scalar-isovector meson,
36  \f$ \delta \f$.
37 
38  This essentially follows the notation in \ref Kubis97, except
39  that our definitions of \c b and \c c follow their \f$ \bar{b}
40  \f$ and \f$ \bar{c} \f$, respectively.
41 
42  Also discussed in \ref Gaitanos04, where they take
43  \f$ m_{\delta}=980 \f$ MeV.
44 
45  The full Lagragian is:
46 
47  \f[
48  {\cal L} = {\cal L}_{Dirac} + {\cal L}_{\sigma} +
49  {\cal L}_{\omega} + {\cal L}_{\rho} + {\cal L}_{\delta}
50  \f]
51 
52  \f{eqnarray*}
53  {\cal L}_{Dirac} &=&
54  \bar{\Psi} \left[ i {{\partial}\!\!\!{\slash}} -
55  g_{\omega} {{\omega}\!\!\!{\slash}} - \frac{g_{\rho}}{2}
56  {{\vec{\rho}}\!\!\!{\slash}}~
57  \vec{\tau} - M + g_{\sigma} \sigma - \frac{e}{2}
58  \left( 1 + \tau_3 \right) A_{\mu} \right] \Psi \nonumber \\
59  {\cal L}_{\sigma} &=&
60  {\textstyle \frac{1}{2}} \left( \partial_{\mu} \sigma \right)^2
61  - {\textstyle \frac{1}{2}} m^2_{\sigma} \sigma^2
62  - \frac{b M}{3} \left( g_{\sigma} \sigma\right)^3
63  - \frac{c}{4} \left( g_{\sigma} \sigma\right)^4 \nonumber \\
64  {\cal L}_{\omega} &=&
65  - {\textstyle \frac{1}{4}} f_{\mu \nu} f^{\mu \nu}
66  + {\textstyle \frac{1}{2}} m^2_{\omega}\omega^{\mu}\omega_{\mu}
67  + \frac{\zeta}{24} g_{\omega}^4 \left(\omega^\mu \omega_\mu\right)^2
68  \nonumber \\
69  {\cal L}_{\rho} &=&
70  - {\textstyle \frac{1}{4}} \vec{B}_{\mu \nu} \cdot \vec{B}^{\mu \nu}
71  + {\textstyle \frac{1}{2}} m^2_{\rho} \vec{\rho}^{~\mu} \cdot
72  \vec{\rho}_{~\mu}
73  + \frac{\xi}{24} g_{\rho}^4 \left(\vec{\rho}^{~\mu}\right) \cdot
74  \vec{\rho}_{~\mu}
75  + g_{\rho}^2 f (\sigma, \omega) \vec{\rho}^{~\mu} \cdot
76  \vec{\rho}_{~\mu} \nonumber \\
77  \f}
78  where the additional terms are
79 
80  \f[
81  {\cal L}_{\delta} = \bar{\Psi} \left( g_{\delta} \vec{\delta} \cdot
82  \vec{\tau} \right) \Psi
83  + \frac{1}{2} (\partial_{\mu} \vec{\delta})^2 -
84  \frac{1}{2} m_{\delta}^2 \vec{\delta}^{~2}
85  \f]
86 
87  The new field equation for the delta meson is
88  \f[
89  m_{\delta}^2 \delta = g_{\delta} (n_{s,p} - n_{s,n})
90  \f]
91 
92  \future Finish the finite temperature EOS
93 
94  */
95  class eos_had_rmf_delta : public eos_had_rmf {
96  public:
97 
98  /// The mass of the scalar-isovector field
99  double md;
100 
101  /// The coupling of the scalar-isovector field to the nucleons
102  double cd;
103 
104  /// The value of the scalar-isovector field
105  double del;
106 
107  /** \brief Equation of state as a function of density
108  */
109  virtual int calc_e(fermion &ne, fermion &pr, thermo &lth);
110 
111  /** \brief Equation of state as a function of chemical potentials
112  */
113  virtual int calc_p(fermion &neu, fermion &p,
114  double sig, double ome, double rho, double delta,
115  double &f1, double &f2, double &f3, double &f4,
116  thermo& th);
117 
118  /** \brief Finite temperature (unfinished)
119  */
120  int calc_temp_p(fermion &ne, fermion &pr, double temper,
121  double sig, double ome, double lrho,
122  double delta, double &f1, double &f2,
123  double &f3, double &f4, thermo& lth);
124 
125  /** \brief Set a guess for the fields for the next call to calc_e(),
126  calc_p(), or saturation()
127  */
128  virtual int set_fields(double sig, double ome, double lrho,
129  double delta) {
130  sigma=sig;
131  omega=ome;
132  rho=lrho;
133  del=delta;
134  guess_set=true;
135  return 0;
136  }
137 
138  /** \brief Calculate saturation properties for nuclear matter
139  at the saturation density
140 
141  This requires initial guesses to the chemical
142  potentials, etc.
143  */
144  virtual void saturation();
145 
146 #ifndef DOXYGEN_INTERNAL
147 
148  protected:
149 
150  /// The function for calc_e()
151  virtual int calc_e_solve_fun(size_t nv, const ubvector &ex,
152  ubvector &ey);
153 
154  /// Compute matter at zero pressure (for saturation())
155  virtual int zero_pressure(size_t nv, const ubvector &ex,
156  ubvector &ey);
157 
158 
159  private:
160 
161  /** \brief Forbid setting the guesses to the fields unless all four
162  fields are specified
163  */
164  virtual int set_fields(double sig, double ome, double lrho) {
165  return 0;
166  }
167 
168 #endif
169 
170  };
171 
172 #ifndef DOXYGEN_NO_O2NS
173 }
174 #endif
175 
176 #endif
virtual int calc_e(fermion &ne, fermion &pr, thermo &lth)
Equation of state as a function of density.
double del
The value of the scalar-isovector field.
bool guess_set
True if a guess for the fields has been given.
Definition: eos_had_rmf.h:796
double md
The mass of the scalar-isovector field.
Relativistic mean field theory EOS.
Definition: eos_had_rmf.h:295
virtual void saturation()
Calculate saturation properties for nuclear matter at the saturation density.
virtual int zero_pressure(size_t nv, const ubvector &ex, ubvector &ey)
Compute matter at zero pressure (for saturation())
virtual int set_fields(double sig, double ome, double lrho, double delta)
Set a guess for the fields for the next call to calc_e(), calc_p(), or saturation() ...
Field-theoretical EOS with scalar-isovector meson, .
virtual int set_fields(double sig, double ome, double lrho)
Forbid setting the guesses to the fields unless all four fields are specified.
int calc_temp_p(fermion &ne, fermion &pr, double temper, double sig, double ome, double lrho, double delta, double &f1, double &f2, double &f3, double &f4, thermo &lth)
Finite temperature (unfinished)
double cd
The coupling of the scalar-isovector field to the nucleons.
virtual int calc_p(fermion &neu, fermion &p, double sig, double ome, double rho, double delta, double &f1, double &f2, double &f3, double &f4, thermo &th)
Equation of state as a function of chemical potentials.
virtual int calc_e_solve_fun(size_t nv, const ubvector &ex, ubvector &ey)
The function for calc_e()

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