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 /** \mainpage 00024 00025 \htmlonly 00026 <a href="../latex/refman.pdf">PDF documentation</a> 00027 \endhtmlonly 00028 00029 All equations of state inherit from \ref eos (except for the TOV 00030 solver \ref tov_solve and \ref cold_nstar). The \c o2scl_eos 00031 library contains all of the classes mentioned in this documentation. 00032 00033 \hline 00034 \section dcsect User's Guide 00035 - \ref hadronic 00036 - \ref quark_matter 00037 - \ref tovtoc 00038 - \ref cnstar 00039 - \ref nrTeos_section 00040 - \ref eossource_section 00041 - \ref eosref_section 00042 00043 \hline 00044 \section hadronic Hadronic equations of state 00045 00046 The hadronic equations of state are all inherited from 00047 hadronic_eos: schematic_eos, skyrme_eos, rmf_eos, apr_eos, and 00048 gen_potential_eos. 00049 00050 hadronic_eos includes several methods that can be used 00051 to calculate the saturation properties of nuclear matter. 00052 These methods are sometimes overloaded in descendants when 00053 exact formulas are available. 00054 00055 There is also a set of classes to modify the quartic term 00056 of the symmetry energy: rmf4_eos, apr4_eos, skyrme4_eos, and 00057 mdi4_eos all based on sym4_eos_base which can be used 00058 in sym4_eos. 00059 00060 \hline 00061 \section quark_matter Equations of state of quark matter 00062 00063 The equations of state of quark matter are all inherited from 00064 quark_eos: bag_eos is a simple bag model, nambujl_eos is the 00065 Nambu--Jona-Lasinio model. 00066 00067 \hline 00068 \section tovtoc Solution of the Tolman-Oppenheimer-Volkov equations 00069 00070 The class \ref tov_solve provide a solution to the 00071 Tolman-Oppenheimer-Volkov (TOV) equations given an equation of 00072 state. This is particularly useful for static neutron star 00073 structure: given any equation of state one can calculate the mass 00074 vs. radius curve and the properties of any star of a given 00075 mass. An adaptive integration is employed and calculates the 00076 gravitational mass, the baryonic mass (if the baryon density is 00077 supplied), and the gravitational potential. The remaining columns 00078 is the equation of state are also interpolated into the solution, 00079 e.g. if a chemical potential is given, then the radial dependence 00080 of the chemical potential for a 1.4 solar mass star can be 00081 automatically computed. The equation of state may be specified in 00082 arbitrary units so long as an appropriate conversion factor is 00083 supplied. An equation of state for low densities (baryon density < 00084 0.08 \f$ \mathrm{fm}^{-3} \f$ ) is provided and can be 00085 automatically appended to the user-defined equation of state. 00086 00087 This is still experimental. 00088 00089 \hline 00090 \section cnstar Naive Cold Neutron Stars 00091 00092 There is also a class to calculate zero-temperature neutron 00093 stars: \ref cold_nstar. It uses \ref tov_solve to compute 00094 the structure, given a hadronic equation of state (of type 00095 \ref hadronic_eos). It also computes the adiabatic index, the 00096 speed of sound, and determines the possibility of the 00097 direct Urca process as a function of density or radius. 00098 00099 This is still experimental. 00100 00101 \hline 00102 \section nrTeos_section Non-relativistic Finite Temperature Approximations 00103 00104 This is taken from the \ref Prakash87. 00105 00106 The entropy is 00107 \f[ 00108 s = -\sum_k \left[ n_k \ln n_k + \left(1-n_k\right) \ln 00109 \left(1-n_k\right)\right] 00110 \f] 00111 00112 The low-temperature (degenerate) approximation to the entropy is 00113 \f[ 00114 s=\pi^2/3 N(0) T 00115 \f] 00116 where the density of states at the Fermi surface is 00117 \f[ 00118 N(0)=\sum_k \delta(\epsilon_k -\mu) = \frac{3 \rho }{k_F v_F} 00119 \f] 00120 where the Fermi velocity is 00121 \f[ 00122 v_F = \left.\frac{\partial \epsilon_k}{\partial k}\right|_{k_F} 00123 = \frac{k_F}{m^{*}} 00124 \f] 00125 The latter equation defines the effective mass. 00126 The level density parameter is given by 00127 \f[ 00128 a=\frac{\pi^2 N(0)}{6 \rho} 00129 \f] 00130 Defining the Fermi temperature: 00131 \f[ 00132 T_F=\frac{1}{2} k_F v_F = k_F^2/2/m^{*} 00133 \f] 00134 another expression for the entropy is 00135 \f[ 00136 s=\frac{\pi^2}{2} \rho (T/T_F) 00137 \f] 00138 Expressions for the remaining quantities are 00139 \f[ 00140 P=P(T=0)+\frac{\rho}{3} 00141 a T^2 \left(1+\frac{d \ln v_F}{d \ln k_F }\right) 00142 \f] 00143 \f[ 00144 E/A=E/A(T=0)+a T^2 00145 \f] 00146 \f[ 00147 \mu=\mu(T=0)-\frac{1}{3} a T^2\left(2-\frac{d \ln v_F}{d \ln k_F }\right) 00148 \f] 00149 Typically, the leading correction to 00150 \f[ 00151 s=\frac{\pi^2}{2} \rho (T/T_F) 00152 \f] 00153 is of order \f$ (T/T_F)^2 \f$ unless soft collective modes give 00154 rise to a \f$ (T/T_F)^3 \ln (T/T_F) \f$ correction. 00155 00156 At high temperature (non-degenerate approximation), 00157 a stationary phase approximation gives 00158 \f{eqnarray*} 00159 \rho(T) &\sim& \frac{\gamma}{2 \pi^2} e^{\mu/T} \cdot k^2 00160 e^{-\epsilon_k/T} \sqrt{2 \pi} \left[\frac{2}{k^2}+ 00161 \frac{1}{T}\frac{\partial v_k}{\partial k}\right]^{-1/2} \\ 00162 &=& e^{\mu/T} \left.f(T)\right|_{k=k_{\rho}} 00163 \f} 00164 where \f$ \gamma \f$ is the spin and isospin degeneracy and the 00165 velocity function is \f$ v_k=\partial \epsilon_k/\partial k \f$ . 00166 The function \f$ f(T) \f$ is evaluated at momentum \f$ k_{\rho} \f$ 00167 which is obtained by solving \f$ T-k v_k/2=0 \f$ . 00168 The chemical potential is obtained by inverting the above 00169 relation for \f$ \rho(T) \f$ : 00170 \f[ 00171 \mu \sim T \ln \rho - T \ln f(T) 00172 \f] 00173 From this value of \f$ \mu \f$ we can derive the entropy density 00174 using 00175 \f[ 00176 T s \sim \sum_k n_k \epsilon_k + \rho T - \mu \rho 00177 \f] 00178 Using the stationary phase method: 00179 \f{eqnarray*} 00180 \sum_k n_k \epsilon_k &\sim& \frac{\gamma}{2 \pi^2} e^{\mu/T} 00181 \cdot k^2 \epsilon_k e^{-\epsilon_k/T} \sqrt{2 \pi} 00182 \left[\frac{2}{k^2}-\left(\frac{1}{\epsilon_k}-\frac{1}{T}\right) 00183 \frac{\partial v_k}{\partial k}+ 00184 \left(\frac{v_k}{\epsilon_k}\right)^2\right]^{-1/2} \\ 00185 &=& e^{\mu/T} \left.g(T)\right|_{k=k_E} 00186 \f} 00187 where \f$ k_E \f$ is the solution of 00188 \f[ 00189 \frac{2}{k}+v_k \left(\frac{1}{\epsilon_k}-\frac{1}{T}\right)=0 00190 \f] 00191 This provides a first approximation to the energy and together 00192 with the thermodynamic identity gives the pressure. 00193 00194 \hline 00195 \section eossource_section Example source code 00196 00197 \b Example \b list 00198 00199 - \ref ex_cold_nstar_sect 00200 00201 \subsection ex_cold_nstar_sect Cold neutron star example 00202 00203 \dontinclude ex_cold_nstar.cpp 00204 \skip Example: 00205 \until End of example 00206 00207 \hline 00208 \section todo_section Other Todos 00209 00210 \todo Right now, the equation of state classes depend on the 00211 user to input the correct value of \c non_interacting 00212 for the particle inputs. This is not very graceful... 00213 \todo Document the "n15" models. What where they for? 00214 00215 \hline 00216 \section eosref_section Bibliography 00217 00218 Some of the references which contain links should direct you to 00219 the work referred to directly through dx.doi.org. 00220 00221 \anchor Akmal98 Akmal98: 00222 \htmlonly 00223 <a href="http://dx.doi.org/10.1103/PhysRevC.58.1805"> 00224 Akmal, Pandharipande, and Ravenhall</a>, 00225 \endhtmlonly 00226 \latexonly 00227 \href{http://dx.doi.org/10.1103/PhysRevC.58.1805}{ 00228 Akmal, Pandharipande, and Ravenhall}, 00229 \endlatexonly 00230 Phys. Rev. C \b 58, 1805 (1998). 00231 00232 \anchor Bartel79 Bartel79: 00233 \htmlonly 00234 <a href="http://dx.doi.org/10.1016/0375-9474(82)90403-1"> 00235 J. Bartel, P. Quentin, M. Brack, C. Guet, and Håkansson</a>, 00236 \endhtmlonly 00237 \latexonly 00238 \href{http://dx.doi.org/10.1016/0375-9474(82)90403-1}{ 00239 J. Bartel, P. Quentin, M. Brack, C. Guet, and H{\aa}kansson}, 00240 \endlatexonly 00241 Nucl. Phys. A \b 386 (1982) 79. 00242 00243 \anchor Baym71 Baym71: 00244 G. Baym, C. Pethick, and P. Sutherland, Astrophys. J. \b 170 (1971) 299. 00245 00246 \anchor Beiner75 Beiner75: 00247 \htmlonly 00248 <a href="http://dx.doi.org/10.1016/0375-9474(75)90338-3"> 00249 M. Beiner, H. Flocard, Nguyen van Giai, and P. Quentin</a>, 00250 \endhtmlonly 00251 \latexonly 00252 \href{http://dx.doi.org/10.1016/0375-9474(75)90338-3}{ 00253 M. Beiner, H. Flocard, Nguyen van Giai, and P. Quentin}, 00254 \endlatexonly 00255 Nucl. Phys. A \b 238 (1975) 29. 00256 00257 \anchor Bernard88 Bernard88: 00258 \htmlonly 00259 <a href="http://dx.doi.org/10.1016/0550-3213(88)90127-7"> 00260 V. Bernard, R.L. Jaffe, and U.-G. Meissner</a>, 00261 \endhtmlonly 00262 \latexonly 00263 \href{http://dx.doi.org/10.1016/0550-3213(88)90127-7}{ 00264 V. Bernard, R.~L. Jaffe, and U.-G. Meissner}, 00265 \endlatexonly 00266 Nucl. Phys. B \b 308 (1988) 753. 00267 00268 \anchor Bombaci01 Bombaci01: 00269 I. Bombaci, "Equation of State for Dense Isospin Asymmetric 00270 Nuclear Matter for Astrophysical Applications Equation of 00271 State for Isospin-Asymmetric Nuclear Matter and Neutron Star 00272 Properties", in "Isospin physics in heavy-ion collisions at 00273 intermediate energies" 00274 \htmlonly 00275 ed. by B-A. Li and W. U. Schröder (2001) Nova Science, New York. 00276 \endhtmlonly 00277 \latexonly 00278 ed. by B-A. Li and W. U. Schr\"{o}der (2001) Nova Science, New York. 00279 \endlatexonly 00280 00281 \anchor Brack85 Brack85: 00282 \htmlonly 00283 <a href="http://dx.doi.org/10.1016/0370-1573(86)90078-5"> 00284 M. Brack, C. Guet, and H.-B. Håkansson</a> 00285 \endhtmlonly 00286 \latexonly 00287 \href{http://dx.doi.org/10.1016/0370-1573(86)90078-5}{ 00288 M. Brack, C. Guet, and H.-B. H{\aa}kansson}, 00289 \endlatexonly 00290 Phys. Rep. \b 123 (1985) 275. 00291 00292 \anchor Buballa99 Buballa99: 00293 \htmlonly 00294 <a href="http://dx.doi.org/10.1016/S0370-2693(99)00533-X"> 00295 M. Buballa and M. Oertel</a>, 00296 \endhtmlonly 00297 \latexonly 00298 \href{http://dx.doi.org/10.1016/S0370-2693(99)00533-X}{ 00299 M. Buballa and M. Oertel}, 00300 \endlatexonly 00301 Phys. Lett. B \b 457 (1999) 261. 00302 00303 \anchor Buballa04 Buballa04: 00304 \htmlonly 00305 <a href="http://dx.doi.org/10.1016/j.physrep.2004.11.004"> 00306 M. Buballa</a>, 00307 \endhtmlonly 00308 \latexonly 00309 \href{http://dx.doi.org/10.1016/j.physrep.2004.11.004}{ 00310 M. Buballa}, 00311 \endlatexonly 00312 Phys. Rep. \b 407 (2005) 205-376. 00313 00314 \anchor Chabanat95 Chabanat95: 00315 E. Chabanat, Ph. D. Thesis 1995 00316 00317 \anchor Chabanat97 Chabanat97: 00318 \htmlonly 00319 <a href="http://dx.doi.org/10.1016/S0375-9474(97)00596-4"> 00320 E. Chabanat, J. Meyer, P. Bonche, R. Schaeffer, and P. Haensel</a>, 00321 \endhtmlonly 00322 \latexonly 00323 \href{http://dx.doi.org/10.1016/S0375-9474(97)00596-4}{ 00324 E. Chabanat, J. Meyer, P. Bonche, R. Schaeffer, and P. Haensel}, 00325 \endlatexonly 00326 Nucl. Phys. A \b 627 (1997) 710. 00327 00328 \anchor Das03 Das03: 00329 \htmlonly 00330 <a href="http://dx.doi.org/10.1103/PhysRevC.67.034611"> 00331 C.B. Das, S. Das Gupta, C. Gale, and B.-A. Li</a>, 00332 \endhtmlonly 00333 \latexonly 00334 \href{http://dx.doi.org/10.1103/PhysRevC.67.034611}{ 00335 C.B. Das, S. Das Gupta, C. Gale, and B.-A. Li}, 00336 \endlatexonly 00337 Phys. Rev. C \b 67 (2003) 034611. 00338 00339 \anchor Dobaczewski94 Dobaczewski94: 00340 \htmlonly 00341 <a href="http://dx.doi.org/10.1016/0375-9474(84)90433-0"> 00342 J. Dobaczewski, H. Flocard, and J. Treiner</a>, 00343 \endhtmlonly 00344 \latexonly 00345 \href{http://dx.doi.org/10.1016/0375-9474(84)90433-0}{ 00346 J. Dobaczewski, H. Flocard, and J. Treiner}, 00347 \endlatexonly 00348 Nucl. Phys. A \b 422 (1984) 103. 00349 00350 \anchor Dutta86 Dutta86: 00351 \htmlonly 00352 <a href="http://dx.doi.org/10.1016/0375-9474(86)90283-6"> 00353 A.K.Dutta, J.-P.Arcoragi, J.M.Pearson, R.Behrman, F.Tondeur</a>, 00354 \endhtmlonly 00355 \latexonly 00356 \href{http://dx.doi.org/10.1016/0375-9474(86)90283-6}{ 00357 A.K.Dutta, J.-P.Arcoragi, J.M.Pearson, R.Behrman, F.Tondeur}, 00358 \endlatexonly 00359 Nucl. Phys. A \b 458 (1986) 77. 00360 00361 \anchor Friedrich86 Friedrich86: 00362 \htmlonly 00363 <a href="http://dx.doi.org/10.1103/PhysRevC.33.335"> 00364 J. Friedrich, and P.-G. Reinhard</a>, 00365 \endhtmlonly 00366 \latexonly 00367 \href{http://dx.doi.org/10.1103/PhysRevC.33.335}{ 00368 J. Friedrich, and P.-G. Reinhard}, 00369 \endlatexonly 00370 Phys. Rev. C \b 33 (1986) 335. 00371 00372 \anchor Gale87 Gale87: 00373 \htmlonly 00374 <a href="http://dx.doi.org/10.1103/PhysRevC.35.1666"> 00375 C. Gale, G. Bertsch, and S. Das Gupta</a>, 00376 \endhtmlonly 00377 \latexonly 00378 \href{http://dx.doi.org/10.1103/PhysRevC.35.1666}{ 00379 C. Gale, G. Bertsch, and S. Das Gupta}, 00380 \endlatexonly 00381 Phys. Rev. C \b 35 (1986) 1666. 00382 00383 \anchor Hatsuda94 Hatsuda94: 00384 \htmlonly 00385 <a href="http://dx.doi.org/10.1016/0370-1573(94)90022-1"> 00386 T. Hatsuda and T. Kunihiro</a>, 00387 \endhtmlonly 00388 \latexonly 00389 \href{http://dx.doi.org/10.1016/0370-1573(94)90022-1}{ 00390 T. Hatsuda and T. Kunihiro}, 00391 \endlatexonly 00392 Phys. Rep. \b 247 (1994) 221. 00393 00394 \anchor Horowitz01 Horowitz01: 00395 \htmlonly 00396 <a href="http://dx.doi.org/10.1103/PhysRevLett.86.5647"> 00397 Horowitz and Piekrewicz</a>, 00398 \endhtmlonly 00399 \latexonly 00400 \href{http://dx.doi.org/10.1103/PhysRevLett.86.5647}{ 00401 Horowitz and Piekarewicz}, 00402 \endlatexonly 00403 Phys. Rev. Lett. \b 86 (2001) 5647. 00404 00405 \anchor Margueron02 Margueron02: 00406 \htmlonly 00407 <a href="http://dx.doi.org/10.1103/PhysRevC.66.014303"> 00408 J. Margueron, J. Navarro, and N.V. Giai</a>, 00409 \endhtmlonly 00410 \latexonly 00411 \href{http://dx.doi.org/10.1103/PhysRevC.66.014303}{ 00412 J. Margueron, J. Navarro, and N.~V. Giai}, 00413 \endlatexonly 00414 Phys. Rev. C \b 66 (2002) 014303. 00415 00416 \anchor Muller96 Muller96: 00417 \htmlonly 00418 <a href="http://dx.doi.org/10.1016/0375-9474(96)00187-X"> 00419 H. Muller and B. D. Serot</a>, 00420 \endhtmlonly 00421 \latexonly 00422 \href{http://dx.doi.org/10.1016/0375-9474(96)00187-X}{ 00423 H. Muller and B.~D. Serot}, 00424 \endlatexonly 00425 Nucl. Phys. A \b 606 (1996), 508. 00426 00427 \anchor Osni94 Osni94: 00428 \htmlonly 00429 <a href="http://dx.doi.org/10.1103/PhysRevC.50.460"> 00430 M. Onsi, H. Przysiezniak, J.M. Pearson</a>, 00431 \endhtmlonly 00432 \latexonly 00433 \href{http://dx.doi.org/10.1103/PhysRevC.50.460}{ 00434 M. Onsi, H. Przysiezniak, J.M. Pearson}, 00435 \endlatexonly 00436 Phys. Rev. C \b 50 (1994) 460. 00437 00438 \anchor Pethick95 Pethick95: 00439 \htmlonly 00440 <a href="http://dx.doi.org/10.1016/0375-9474(94)00506-I"> 00441 C.J. Pethick, D.G. Ravenhall, and C.P. Lorenz</a>, 00442 \endhtmlonly 00443 \latexonly 00444 \href{http://dx.doi.org/10.1016/0375-9474(94)00506-I}{ 00445 C.~J. Pethick, D.~G. Ravenhall, and C.~P. Lorenz}, 00446 \endlatexonly 00447 Nucl. Phys. A \b 584 (1995) 675. 00448 00449 \anchor Prakash87 Prakash87: 00450 \htmlonly 00451 M. Prakash, T.L. Ainsworth, J.P. Blaizot, and H. Wolter, 00452 in Windsurfing the Fermi Sea, Volume II 00453 edited by T.T.S. Kuo and J. Speth, Elsevier 1987, pg. 357. 00454 \endhtmlonly 00455 \latexonly 00456 M. Prakash, T.~L. Ainsworth, J.~P. Blaizot, and H. Wolter, 00457 in Windsurfing the Fermi Sea, Volume II 00458 edited by T.~T.~S. Kuo and J. Speth, Elsevier 1987, pg. 357. 00459 \endlatexonly 00460 00461 \anchor Prakash88 Prakash88: 00462 \htmlonly 00463 <a href="http://dx.doi.org/10.1103/PhysRevLett.61.2518"> 00464 M. Prakash, T. L. Ainsworth, and J. M. Lattimer</a>, 00465 \endhtmlonly 00466 \latexonly 00467 \href{http://dx.doi.org/10.1103/PhysRevLett.61.2518}{ 00468 M. Prakash, T.~L. Ainsworth, and J.~M. Lattimer}, 00469 \endlatexonly 00470 Phys. Rev. Lett. \b 61 (1988) 2518. 00471 00472 \anchor Prakash97 Prakash97: 00473 \htmlonly 00474 <a href="http://dx.doi.org/10.1016/S0370-1573(96)00023-3"> 00475 Madappa Prakash, I. Bombaci, Manju Prakash, P.J. Ellis, J.M. Lattimer, 00476 and R. Knorren</a>, 00477 \endhtmlonly 00478 \latexonly 00479 \href{http://dx.doi.org/10.1016/S0370-1573(96)00023-3}{ 00480 Madappa Prakash, I. Bombaci, Manju Prakash, P.~J. Ellis, J.~M. Lattimer, 00481 and R. Knorren}, 00482 \endlatexonly 00483 Phys. Rep. \b 280 (1997) 1. 00484 00485 \anchor Reinhard95 Reinhard95: 00486 \htmlonly 00487 <a href="http://dx.doi.org/10.1016/0375-9474(94)00770-N"> 00488 P.-G. Reinhard and H. Flocard</a>, 00489 \endhtmlonly 00490 \latexonly 00491 \href{http://dx.doi.org/10.1016/0375-9474(94)00770-N}{ 00492 P.-G. Reinhard and H. Flocard}, 00493 \endlatexonly 00494 Nucl. Phys. A \b 584 (1995) 467. 00495 00496 \anchor Reinhard99 Reinhard99: 00497 \htmlonly 00498 <a href="http://dx.doi.org/10.1103/PhysRevC.60.014316"> 00499 P.-G. Reinhard, D.J. Dean, W. Nazarewicz, J. Dobaczewski, 00500 J.A. Maruhn, M.R. Strayer</a>, 00501 \endhtmlonly 00502 \latexonly 00503 \href{http://dx.doi.org/10.1103/PhysRevC.60.014316}{ 00504 P.-G. Reinhard, D.J. Dean, W. Nazarewicz, J. Dobaczewski, 00505 J.A. Maruhn, M.R. Strayer}, 00506 \endlatexonly 00507 Phys. Rev. C \b 60, (1999) 014316. 00508 00509 \anchor Shapiro83 Shapiro83: 00510 S. L. Shapiro and S. A. Teukolsky, "Black Holes, White Dwarfs, 00511 and Neutron Stars: The Physics of Compact Objects", John 00512 Wiley and Sons, New York, 1983. 00513 00514 \anchor Tondeur84 Tondeur84: 00515 \htmlonly 00516 <a href="http://dx.doi.org/10.1016/0375-9474(84)90444-5"> 00517 F. Tondeur, M. Brack, M. Farine, and J.M. Pearson</a>, 00518 \endhtmlonly 00519 \latexonly 00520 \href{http://dx.doi.org/10.1016/0375-9474(84)90444-5}{ 00521 F. Tondeur, M. Brack, M. Farine, and J.M. Pearson}, 00522 \endlatexonly 00523 Nucl. Phys. A \b 420 (1984) 297. 00524 00525 \anchor Typel99 Typel99: 00526 S. Typel and H. H. Wolter, 00527 \htmlonly 00528 <a href="">Nucl. Phys. <b>A</b> 656 (1999) 331</a>. 00529 \endhtmlonly 00530 \latexonly 00531 \href{}{Nucl. Phys. A \bf{656} (1999) 331}. 00532 \endlatexonly 00533 00534 \anchor VanGiai81 VanGiai81: 00535 \htmlonly 00536 <a href="http://dx.doi.org/10.1016/0370-2693(81)90646-8"> 00537 Nguyen van Giai and H. Sagawa</a>, 00538 \endhtmlonly 00539 \latexonly 00540 \href{http://dx.doi.org/10.1016/0370-2693(81)90646-8}{ 00541 Nguyen van Giai and H. Sagawa}, 00542 \endlatexonly 00543 Phys. Lett. B \b 106 (1981) 379. 00544 00545 \anchor Zimanyi90 Zimanyi90: 00546 \htmlonly 00547 <a href="http://dx.doi.org/10.1103/PhysRevC.42.1416"> 00548 Zimanyi and Moszkowski</a>, 00549 \endhtmlonly 00550 \latexonly 00551 \href{http://dx.doi.org/10.1103/PhysRevC.42.1416}{ 00552 Zimanyi and Moszkowski}, 00553 \endlatexonly 00554 Phys. Rev. C \b 42 (1990) 1416. 00555 00556 */
Documentation generated with Doxygen and provided under the GNU Free Documentation License. See License Information for details.
Project hosting provided by
,
O2scl Sourceforge Project Page