THE THERMODYNAMIC PROPERTIES OF COMPRESSED GASEOUS AND LIQUID FLUORINE

By DANIEL LEE

CONTENTS I QUANTUM-STATISTICAL SELF-CONSISTENT ?ELD MODELS THE GENERALIZED THOMAS-FERMI MODEL THE THOMAS-FERMI MODEL FOR MATTER WITH GIVEN TEMPERATURE AND DENSITY THE FERMI-DIRAC STATISTICS FOR SYSTEMS OF INTERACTING PARTICLES DERIVATION OF THE POISSON-FERMI-DIRAC EQUATION FOR THE ATOMIC POTENTIAL FORMULATION OF THE BOUNDARY VALUE PROBLEM THE THOMAS-FERMI POTENTIAL AS A SOLUTION OF THE POISSON EQUATION DEPENDING ON ONLY TWO VARIABLES BASIC PROPERTIES OF THE FERMI-DIRAC INTEGRALS THE UNIFORM FREE-ELECTRON DENSITY MODEL THE THOMAS-FERMI MODEL AT TEMPERATURE ZERO METHODS FOR THE NUMERICAL INTEGRATION OF THE THOMAS-FERMI EQUATION THE SHOOTING METHOD LINEARIZATION OF THE EQUATION AND A DI?ERENCE SCHEME DOUBLE-SWEEP METHOD WITH ITERATIONS THE THOMAS-FERMI MODEL FOR MIXTURES SETTING UP OF THE PROBLEM THERMODYNAMIC EQUILIBRIUM CONDITION LINEARIZATION OF THE SYSTEM OF EQUATIONS ITERATION SCHEME AND THE DOUBLE-SWEEP METHOD DISCUSSION OF COMPUTATIONAL RESULTS ELECTRON WAVE FUNCTIONS IN A GIVEN POTENTIAL DESCRIPTION OF ELECTRON STATES IN A SPHERICAL AVERAGE ATOM CELL CLASSI?CATION OF ELECTRON STATES WITHIN THE AVERAGE ATOM CELL MODEL OF AN ATOM WITH AVERAGE OCCUPATION NUMBERS DERIVATION OF THE EXPRESSION FOR THE ELECTRON DENSITY BY MEANS OF THE SEMICLASSICAL APPROXIMATION FOR WAVE FUNCTIONS AVERAGE DEGREE OF IONIZATION CORRECTIONS TO THE THOMAS-FERMI MODEL BOUND-STATE WAVE FUNCTIONS NUMERICAL METHODS FOR SOLVING THE SCHR¨ODINGER EQUATION HYDROGEN-LIKE AND SEMICLASSICAL WAVE FUNCTIONS RELATIVISTIC WAVE FUNCTIONS CONTINUUM WAVE FUNCTIONS THE SCHR¨ODINGER EQUATION THE DIRAC EQUATIONS QUANTUM-STATISTICAL SELF-CONSISTENT ?ELD MODELS QUANTUM-MECHANICAL RE?NEMENT OF THE GENERALIZED THOMAS-FERMI MODEL FOR BOUND ELECTRONS THE HARTREE SELF-CONSISTENT ?ELD FOR AN AVERAGE ATOM COMPUTATIONAL ALGORITHM ANALYSIS OF COMPUTATIONAL RESULTS FOR IRON THE RELATIVISTIC HARTREE MODEL THE HARTREE-FOCK SELF-CONSISTENT ?ELD MODEL FOR MATTER WITH GIVEN TEMPERATURE AND DENSITY VARIATIONAL PRINCIPLE BASED ON THE MINIMUM CONDITION FOR THE GRAND THERMODYNAMIC POTENTIAL THE SELF-CONSISTENT ?ELD EQUATION IN THE HARTREE-FOCK APPROXIMATION THE HARTREE-FOCK EQUATIONS FOR A FREE ION THE MODI?ED HARTREE-FOCK-SLATER MODEL SEMICLASSICAL APPROXIMATION FOR THE EXCHANGE INTERACTION THE EQUATIONS OF THE HARTREE-FOCK-SLATER MODEL THE EQUATIONS OF THE HARTREE-FOCK-SLATER MODEL IN THE CASE WHEN THE SEMICLASSICAL APPROXIMATION IS USED FOR CONTINUUM ELECTRONS THE THERMODYNAMIC CONSISTENCY CONDITION THE HARTREE-FOCK-SLATER MODEL FOR THE AVERAGE ATOM THE HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS IN A SPHERICAL CELL THE HARTREE-FOCK-SLATER ?ELD PERIODIC BOUNDARY CONDITIONS IN THE AVERAGE SPHERICAL CELL APPROXIMATION THE ELECTRON DENSITY AND THE ATOMIC POTENTIAL IN THE HARTREE-FOCK-SLATER MODEL WITH BANDS THE RELATIVISTIC HARTREE-FOCK-SLATER MODEL AN ITERATION METHOD FOR SOLVING THE HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS ALGORITHM BASICS COMPUTATION OF THE BAND STRUCTURE OF THE ENERGY SPECTRUM COMPUTATIONAL RESULTS THE UNIFORM-DENSITY APPROXIMATION FOR FREE ELECTRONS IN THE CASE OF A RARE?ED PLASMA SOLUTION OF THE HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS FOR A MIXTURE OF ELEMENTS PROBLEM SETTING ITERATION SCHEME EXAMPLES OF COMPUTATIONS ACCOUNTING FOR THE INDIVIDUAL STATES OF IONS DENSITY FUNCTIONAL OF THE ELECTRON SYSTEM WITH THE INDIVIDUAL STATES OF IONS ACCOUNTED FOR THE HARTREE-FOCK-SLATER EQUATIONS OF THE ION METHOD IN THE CELL AND PLASMA APPROXIMATIONS WAVE FUNCTIONS AND ENERGY LEVELS OF IONS IN A PLASMA II RADIATIVE AND THERMODYNAMICAL PROPERTIES OF HIGH-TEMPERATURE DENSE PLASMA INTERACTION OF RADIATION WITH MATTER RADIATIVE HEAT CONDUCTIVITY OF PLASMA THE RADIATIVE TRANSFER EQUATION THE DI?USION APPROXIMATION THE ROSSELAND MEAN OPACITY THE PLANCK MEAN RADIATION OF AN OPTICALLY THIN LAYER QUANTUM-MECHANICAL EXPRESSIONS FOR THE E?ECTIVE PHOTON ABSORPTION CROSS-SECTIONS ABSORPTION IN SPECTRAL LINES PHOTOIONIZATION INVERSE BREMSSTRAHLUNG COMPTON SCATTERING THE TOTAL ABSORPTION CROSS-SECTION PECULIARITIES OF PHOTON ABSORPTION IN SPECTRAL LINES PROBABILITY DISTRIBUTION OF EXCITED ION STATES POSITION OF SPECTRAL LINES ATOM WAVE FUNCTIONS AND ADDITION OF MOMENTA SHAPE OF SPECTRAL LINES DOPPLER E?ECT ELECTRON BROADENING IN THE IMPACT APPROXIMATION THE NONDEGENERATE CASE ACCOUNTING FOR DEGENERACY METHODS FOR CALCULATING RADIATION AND ELECTRON BROADENING ION BROADENING THE VOIGT PRO?LE LINE PRO?LES OF A HYDROGEN PLASMA IN A STRONG MAGNETIC ?ELD STATISTICAL METHOD FOR LINE-GROUP ACCOUNTING SHIFT AND BROADENING PARAMETERS OF SPECTRAL LINES IN PLASMA FLUCTUATIONS OF OCCUPATION NUMBERS IN A DENSE HOT PLASMA STATISTICAL DESCRIPTION OF OVERLAPPING MULTIPLETS E?ECTIVE PRO?LE FOR A GROUP OF LINES STATISTICAL DESCRIPTION OF THE PHOTOIONIZATION PROCESS COMPUTATIONAL RESULTS FOR ROSSELAND MEAN PATHS AND SPECTRAL PHOTON-ABSORPTION COE?CIENTS COMPARISON OF THE STATISTICAL METHOD WITH DETAILED COMPUTATION DEPENDENCE OF THE ABSORPTION COE?CIENTS ON THE ELEMENT NUMBER, TEMPERATURE AND DENSITY OF THE PLASMA SPECTRAL ABSORPTION COE?CIENTS RADIATIVE AND ELECTRON HEAT CONDUCTIVITY DATABASES OF ATOMIC DATA AND SPECTRAL PHOTON ABSORPTION COE?CIENTS ABSORPTION OF PHOTONS IN A PLASMA WITH NONEQUILIBRIUM RADIATION ?ELD BASIC PROCESSES AND RELAXATION TIMES JOINT CONSIDERATION OF THE PROCESSES OF PHOTON TRANSPORT AND LEVEL KINETICS OF ELECTRONS AVERAGE-ATOM APPROXIMATION RATES OF RADIATION AND COLLISION PROCESSES RADIATION PROPERTIES OF A PLASMA WITH NONEQUILIBRIUM RADIATION ?ELD RADIATIVE HEAT CONDUCTIVITY OF MATTER FOR LARGE GRADIENTS OF TEMPERATURE AND DENSITY THE EQUATION OF STATE DESCRIPTION OF THERMODYNAMICS OF MATTER BASED ON QUANTUM-STATISTICAL MODELS FORMULAS FOR THE PRESSURE, INTERNAL ENERGY AND ENTROPY ACCORDING TO THE THOMAS-FERMI MODEL QUANTUM, EXCHANGE AND OSCILLATION CORRECTIONS TO THE THOMAS-FERMI MODEL THE IONIZATION EQUILIBRIUM METHOD THE GIBBS DISTRIBUTION FOR THE ATOM CELL THE SAHA APPROXIMATION AN ITERATION SCHEME FOR SOLVING THE SYSTEM OF EQUATIONS OF IONIZATION EQUILIBRIUM CORONAL EQUILIBRIUM THERMODYNAMIC PROPERTIES OF MATTER IN THE HARTREE-FOCK-SLATER MODEL ELECTRON THERMODYNAMIC FUNCTIONS ACCOUNTING FOR THE THERMAL MOTION OF IONS IN THE CHARGED HARD-SPHERE APPROXIMATION E?ECTIVE RADIUS OF THE AVERAGE ION ON METHODS FOR DERIVING WIDE-RANGE EQUATIONS OF STATE GENERAL DESCRIPTION COLD COMPRESSION CURVES SHOCK ADIABATS COMPARISON WITH THE SAHA MODEL APPROXIMATION OF THERMOPHYSICAL-DATA TABLES CONSTRUCTION OF AN APPROXIMATING SPLINE THAT PRESERVES GEOMETRIC PROPERTIES OF THE INITIAL FUNCTION NUMERICAL RESULTS