![]() |
Equation of State Sub-Library: Version 0.910
|
00001 /* 00002 ------------------------------------------------------------------- 00003 00004 Copyright (C) 2006-2012, Andrew W. Steiner 00005 00006 This file is part of O2scl. 00007 00008 O2scl is free software; you can redistribute it and/or modify 00009 it under the terms of the GNU General Public License as published by 00010 the Free Software Foundation; either version 3 of the License, or 00011 (at your option) any later version. 00012 00013 O2scl is distributed in the hope that it will be useful, 00014 but WITHOUT ANY WARRANTY; without even the implied warranty of 00015 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00016 GNU General Public License for more details. 00017 00018 You should have received a copy of the GNU General Public License 00019 along with O2scl. If not, see <http://www.gnu.org/licenses/>. 00020 00021 ------------------------------------------------------------------- 00022 */ 00023 #ifndef O2SCL_RMF_DELTA_EOS_H 00024 #define O2SCL_RMF_DELTA_EOS_H 00025 00026 #include <o2scl/rmf_eos.h> 00027 00028 #ifndef DOXYGENP 00029 namespace o2scl { 00030 #endif 00031 00032 /** \brief Field-theoretical EOS with scalar-isovector meson, 00033 \f$ \delta \f$. 00034 00035 This essentially follows the notation in \ref Kubis97, except 00036 that our definitions of \c b and \c c follow their \f$ \bar{b} 00037 \f$ and \f$ \bar{c} \f$, respectively. 00038 00039 Also discussed in \ref Gaitanos04, where they take 00040 \f$ m_{\delta}=980 \f$ MeV. 00041 00042 The full Lagragian is: 00043 00044 \f[ 00045 {\cal L} = {\cal L}_{Dirac} + {\cal L}_{\sigma} + 00046 {\cal L}_{\omega} + {\cal L}_{\rho} + {\cal L}_{\delta} 00047 \f] 00048 00049 \f{eqnarray*} 00050 {\cal L}_{Dirac} &=& 00051 \bar{\Psi} \left[ i {{\partial}\!\!\!{\slash}} - 00052 g_{\omega} {{\omega}\!\!\!{\slash}} - \frac{g_{\rho}}{2} 00053 {{\vec{\rho}}\!\!\!{\slash}}~ 00054 \vec{\tau} - M + g_{\sigma} \sigma - \frac{e}{2} 00055 \left( 1 + \tau_3 \right) A_{\mu} \right] \Psi \nonumber \\ 00056 {\cal L}_{\sigma} &=& 00057 {\textstyle \frac{1}{2}} \left( \partial_{\mu} \sigma \right)^2 00058 - {\textstyle \frac{1}{2}} m^2_{\sigma} \sigma^2 00059 - \frac{b M}{3} \left( g_{\sigma} \sigma\right)^3 00060 - \frac{c}{4} \left( g_{\sigma} \sigma\right)^4 \nonumber \\ 00061 {\cal L}_{\omega} &=& 00062 - {\textstyle \frac{1}{4}} f_{\mu \nu} f^{\mu \nu} 00063 + {\textstyle \frac{1}{2}} m^2_{\omega}\omega^{\mu}\omega_{\mu} 00064 + \frac{\zeta}{24} g_{\omega}^4 \left(\omega^\mu \omega_\mu\right)^2 00065 \nonumber \\ 00066 {\cal L}_{\rho} &=& 00067 - {\textstyle \frac{1}{4}} \vec{B}_{\mu \nu} \cdot \vec{B}^{\mu \nu} 00068 + {\textstyle \frac{1}{2}} m^2_{\rho} \vec{\rho}^{~\mu} \cdot 00069 \vec{\rho}_{~\mu} 00070 + \frac{\xi}{24} g_{\rho}^4 \left(\vec{\rho}^{~\mu}\right) \cdot 00071 \vec{\rho}_{~\mu} 00072 + g_{\rho}^2 f (\sigma, \omega) \vec{\rho}^{~\mu} \cdot 00073 \vec{\rho}_{~\mu} \nonumber \\ 00074 \f} 00075 where the additional terms are 00076 00077 \f[ 00078 {\cal L}_{\delta} = \bar{\Psi} \left( g_{\delta} \vec{\delta} \cdot 00079 \vec{\tau} \right) \Psi 00080 + \frac{1}{2} (\partial_{\mu} \vec{\delta})^2 - 00081 \frac{1}{2} m_{\delta}^2 \vec{\delta}^{~2} 00082 \f] 00083 00084 The new field equation for the delta meson is 00085 \f[ 00086 m_{\delta}^2 \delta = g_{\delta} (n_{s,p} - n_{s,n}) 00087 \f] 00088 00089 \future Finish the finite temperature EOS 00090 00091 */ 00092 class rmf_delta_eos : public rmf_eos { 00093 public: 00094 00095 /// The mass of the scalar-isovector field 00096 double md; 00097 00098 /// The coupling of the scalar-isovector field to the nucleons 00099 double cd; 00100 00101 /// The value of the scalar-isovector field 00102 double del; 00103 00104 /** \brief Equation of state as a function of density 00105 */ 00106 virtual int calc_e(fermion &ne, fermion &pr, thermo <h); 00107 00108 /** \brief Equation of state as a function of chemical potentials 00109 */ 00110 virtual int calc_p(fermion &neu, fermion &p, 00111 double sig, double ome, double rho, double delta, 00112 double &f1, double &f2, double &f3, double &f4, 00113 thermo& th); 00114 00115 /** \brief Finite temperature (unfinished) 00116 */ 00117 int calc_temp_p(fermion &ne, fermion &pr, double temper, 00118 double sig, double ome, double lrho, 00119 double delta, double &f1, double &f2, 00120 double &f3, double &f4, thermo& lth); 00121 00122 /** \brief Set a guess for the fields for the next call to calc_e(), 00123 calc_p(), or saturation() 00124 */ 00125 virtual int set_fields(double sig, double ome, double lrho, 00126 double delta) { 00127 sigma=sig; 00128 omega=ome; 00129 rho=lrho; 00130 del=delta; 00131 guess_set=true; 00132 return 0; 00133 } 00134 00135 /** \brief Calculate saturation properties for nuclear matter 00136 at the saturation density 00137 00138 This requires initial guesses to the chemical 00139 potentials, etc. 00140 */ 00141 virtual int saturation(); 00142 00143 #ifndef DOXYGEN_INTERNAL 00144 00145 protected: 00146 00147 /// The function for calc_e() 00148 virtual int calc_e_solve_fun(size_t nv, const ovector_base &ex, 00149 ovector_base &ey); 00150 00151 /// Compute matter at zero pressure (for saturation()) 00152 virtual int zero_pressure(size_t nv, const ovector_base &ex, 00153 ovector_base &ey); 00154 00155 00156 private: 00157 00158 /** \brief Forbid setting the guesses to the fields unless all four 00159 fields are specified 00160 */ 00161 virtual int set_fields(double sig, double ome, double lrho) { 00162 return 0; 00163 } 00164 00165 #endif 00166 00167 }; 00168 00169 #ifndef DOXYGENP 00170 } 00171 #endif 00172 00173 #endif
Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).