00001 /* 00002 ------------------------------------------------------------------- 00003 00004 Copyright (C) 2006, 2007, 2008, 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 00034 \f$ \delta \f$. 00035 00036 This essentially follows the notation in PLB 399 (1997) 191, except 00037 that our definitions of \c b and \c c follow their \f$ \bar{b} \f$ 00038 and \f$ \bar{c} \f$, respectively. 00039 00040 Also discussed in NPA 732 (2004) 24, where they take 00041 \f$ m_{\delta}=980 \f$ MeV. 00042 00043 The full Lagragian is: 00044 00045 \f[ 00046 {\cal L} = {\cal L}_{Dirac} + {\cal L}_{\sigma} + 00047 {\cal L}_{\omega} + {\cal L}_{\rho} + {\cal L}_{\delta} 00048 \f] 00049 00050 \f{eqnarray*} 00051 {\cal L}_{Dirac} &=& 00052 \bar{\Psi} \left[ i {{\partial}\!\!\!{\slash}} - 00053 g_{\omega} {{\omega}\!\!\!{\slash}} - \frac{g_{\rho}}{2} 00054 {{\vec{\rho}}\!\!\!{\slash}}~ 00055 \vec{\tau} - M + g_{\sigma} \sigma - \frac{e}{2} 00056 \left( 1 + \tau_3 \right) A_{\mu} \right] \Psi \nonumber \\ 00057 {\cal L}_{\sigma} &=& 00058 {\textstyle \frac{1}{2}} \left( \partial_{\mu} \sigma \right)^2 00059 - {\textstyle \frac{1}{2}} m^2_{\sigma} \sigma^2 00060 - \frac{b M}{3} \left( g_{\sigma} \sigma\right)^3 00061 - \frac{c}{4} \left( g_{\sigma} \sigma\right)^4 \nonumber \\ 00062 {\cal L}_{\omega} &=& 00063 - {\textstyle \frac{1}{4}} f_{\mu \nu} f^{\mu \nu} 00064 + {\textstyle \frac{1}{2}} m^2_{\omega}\omega^{\mu}\omega_{\mu} 00065 + \frac{\zeta}{24} g_{\omega}^4 \left(\omega^\mu \omega_\mu\right)^2 00066 \nonumber \\ 00067 {\cal L}_{\rho} &=& 00068 - {\textstyle \frac{1}{4}} \vec{B}_{\mu \nu} \cdot \vec{B}^{\mu \nu} 00069 + {\textstyle \frac{1}{2}} m^2_{\rho} \vec{\rho}^{~\mu} \cdot 00070 \vec{\rho}_{~\mu} 00071 + \frac{\xi}{24} g_{\rho}^4 \left(\vec{\rho}^{~\mu}\right) \cdot 00072 \vec{\rho}_{~\mu} 00073 + g_{\rho}^2 f (\sigma, \omega) \vec{\rho}^{~\mu} \cdot 00074 \vec{\rho}_{~\mu} \nonumber \\ 00075 \f} 00076 where the additional terms are 00077 00078 \f[ 00079 {\cal L}_{\delta} = \bar{\Psi} \left( g_{\delta} \vec{\delta} \cdot 00080 \vec{\tau} \right) \Psi 00081 + \frac{1}{2} (\partial_{\mu} \vec{\delta})^2 - 00082 \frac{1}{2} m_{\delta}^2 \vec{\delta}^{~2} 00083 \f] 00084 00085 The new field equation for the delta meson is 00086 \f[ 00087 m_{\delta}^2 \delta = g_{\delta} (n_{s,p} - n_{s,n}) 00088 \f] 00089 00090 \todo Finish finite temperature 00091 00092 */ 00093 class rmf_delta_eos : public rmf_eos { 00094 public: 00095 00096 /// The mass of the scalar-isovector field 00097 double md; 00098 00099 /// The coupling of the scalar-isovector field to the nucleons 00100 double cd; 00101 00102 /// The value of the scalar-isovector field 00103 double del; 00104 00105 /** 00106 \brief Equation of state as a function of density 00107 */ 00108 virtual int calc_e(fermion &ne, fermion &pr, thermo <h); 00109 00110 /** 00111 \brief Equation of state as a function of chemical potentials 00112 */ 00113 virtual int calc_p(fermion& neu, fermion& p, 00114 double sig, double ome, double rho, double delta, 00115 double &f1, double &f2, double &f3, double &f4, 00116 thermo& th); 00117 00118 /** \brief Finite temperature (unfinished) 00119 */ 00120 int calc_temp_p(fermion& ne, fermion& pr, double temper, 00121 double sig, double ome, double lrho, 00122 double delta, double &f1, double &f2, 00123 double &f3, double &f4, thermo& lth); 00124 00125 /** \brief Set a guess for the fields for the next call to calc_e(), 00126 calc_p(), or saturation() 00127 */ 00128 virtual int set_fields(double sig, double ome, double lrho, 00129 double delta) { 00130 sigma=sig; 00131 omega=ome; 00132 rho=lrho; 00133 del=delta; 00134 guess_set=true; 00135 return 0; 00136 } 00137 00138 /** \brief Calculate saturation properties for nuclear matter 00139 at the saturation density 00140 00141 This requires initial guesses to the chemical 00142 potentials, etc. 00143 */ 00144 virtual int saturation(); 00145 00146 #ifndef DOXYGEN_INTERNAL 00147 00148 protected: 00149 00150 /// The function for calc_e() 00151 virtual int calc_e_solve_fun(size_t nv, const ovector_view &ex, 00152 ovector_view &ey, void *&pa); 00153 00154 /// Compute matter at zero pressure (for saturation()) 00155 virtual int zero_pressure(size_t nv, const ovector_view &ex, 00156 ovector_view &ey, void *&pa); 00157 00158 00159 private: 00160 00161 /** \brief Forbid setting the guesses to the fields unless all four 00162 fields are specified 00163 */ 00164 virtual int set_fields(double sig, double ome, double lrho) { 00165 return 0; 00166 } 00167 00168 #endif 00169 00170 }; 00171 00172 #ifndef DOXYGENP 00173 } 00174 #endif 00175 00176 #endif
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