Quantum statistical models of hot dense matter methods for computation opacity and equation of state
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| Format: | Buch |
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Basel u.a.
Birkhäuser
2005
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| Schriftenreihe: | Progress in mathematical physics
37 |
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| 245 | 1 | 0 | |a Quantum statistical models of hot dense matter |b methods for computation opacity and equation of state |c A. F. Nikiforov ; V. G. Novikov ; V. B. Uvarov |
| 246 | 1 | 3 | |a Quantum-statistical models of hot dense matter |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 2005 | |
| 300 | |a XVII, 428 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Progress in mathematical physics |v 37 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Equations of state | |
| 650 | 4 | |a High temperature plasmas | |
| 650 | 4 | |a Plasma density | |
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Datensatz im Suchindex
| _version_ | 1819611975496237056 |
|---|---|
| adam_text | A.F. NIKIFOROV VG. NOVIKOV VB. UVAROV QUANTUM-STATISTICAL MODELS OF HOT
DENSE MATTER METHODS FOR COMPUTATION OPACITY AND EQUATION OF STATE
TRANSLATED FROM THE RUSSIAN BY ANDREI IACOB BIRKHAUSER VERLAG BASEL *
BOSTON * BERLIN CONTENTS PREFACE XIII QUANTUM-STATISTICAL
SELF-CONSISTENT FIELD MODELS 1 THE GENERALIZED THOMAS-FERMI MODEL 3 1.1
THE THOMAS-FERMI MODEL FOR MATTER WITH GIVEN TEMPERATURE AND DENSITY 4
1.1.1 THE FERMI-DIRAC STATISTICS FOR SYSTEMS OF INTERACTING PARTICLES 4
1.1.2 DERIVATION OF THE POISSON-FERMI-DIRAC EQUATION FOR THE ATOMIC
POTENTIAL 7 1.1.3 FORMULATION OF THE BOUNDARY VALUE PROBLEM 9 1.1.4 THE
THOMAS-FERMI POTENTIAL AS A SOLUTION OF THE POISSON EQUATION DEPENDING
ON ONLY TWO VARIABLES 10 1.1.5 BASIC PROPERTIES OF THE FERMI-DIRAC
INTEGRALS 11 1.1.6 THE UNIFORM FREE-ELECTRON DENSITY MODEL 13 1.1.7 THE
THOMAS-FERMI MODEL AT TEMPERATURE ZERO 15 1.2 METHODS FOR THE NUMERICAL
INTEGRATION OF THE THOMAS-FERMI EQUATION 16 1.2.1 THE SHOOTING METHOD
. .... 16 1.2.2 LINEARIZATION OF THE EQUATION AND A DIFFERENCE SCHEME
... 19 1.2.3 DOUBLE-SWEEP METHOD WITH ITERATIONS 20 1.3 THE THOMAS-FERMI
MODEL FOR MIXTURES 22 1.3.1 SETTING UP OF THE PROBLEM. THERMODYNAMIC
EQUILIBRIUM CONDITION 22 1.3.2 LINEARIZATION OF THE SYSTEM OF EQUATIONS
23 1.3.3 ITERATION SCHEME AND THE DOUBLE-SWEEP METHOD 24 1.3.4
DISCUSSION OF COMPUTATIONAL RESULTS 27 VI CONTENTS 2 ELECTRON WAVE
FUNCTIONS IN A GIVEN POTENTIAL 29 2.1 DESCRIPTION OF ELECTRON STATES IN
A SPHERICAL AVERAGE ATOM CELL ... 29 2.1.1 CLASSIFICATION OF ELECTRON
STATES WITHIN THE AVERAGE ATOM CELL 30 2.1.2 MODEL OF AN ATOM WITH
AVERAGE OCCUPATION NUMBERS . . . . 33 2.1.3 DERIVATION OF THE EXPRESSION
FOR THE ELECTRON DENSITY BY MEANS OF THE SEMICLASSICAL APPROXIMATION FOR
WAVE FUNCTIONS . . . . 35 2.1.4 AVERAGE DEGREE OF IONIZATION 39 2.1.5
CORRECTIONS TO THE THOMAS-FERMI MODEL 41 2.2 BOUND-STATE WAVE FUNCTIONS
42 2.2.1 NUMERICAL METHODS FOR SOLVING THE SCHRODINGER EQUATION . . 43
2.2.2 HYDROGEN-LIKE AND SEMICLASSICAL WAVE FUNCTIONS 43 2.2.3
RELATIVISTIC WAVE FUNCTIONS 50 2.3 CONTINUUM WAVE FUNCTIONS 58 2.3.1 THE
SCHRODINGER EQUATION 58 2.3.2 THE DIRAC EQUATIONS 61 3
QUANTUM-STATISTICAL SELF-CONSISTENT FIELD MODELS 65 3.1
QUANTUM-MECHANICAL REFINEMENT OF THE GENERALIZED THOMAS-FERMI MODEL FOR
BOUND ELECTRONS 66 3.1.1 THE HARTREE SELF-CONSISTENT FIELD FOR AN
AVERAGE ATOM . . . . 66 3.1.2 COMPUTATIONAL ALGORITHM 68 3.1.3 ANALYSIS
OF COMPUTATIONAL RESULTS FOR IRON 72 3.1.4 THE RELATIVISTIC HARTREE
MODEL 76 3.2 THE HARTREE-FOCK SELF-CONSISTENT FIELD MODEL FOR MATTER
WITH GIVEN TEMPERATURE AND DENSITY 80 3.2.1 VARIATIONAL PRINCIPLE BASED
ON THE MINIMUM CONDITION FOR THE GRAND THERMODYNAMIC POTENTIAL 80 3.2.2
THE SELF-CONSISTENT FIELD EQUATION IN THE HARTREE-FOCK APPROXIMATION 83
3.2.3 THE HARTREE-FOCK EQUATIONS FOR A FREE ION 86 3.3 THE MODIFIED
HARTREE-FOCK-SLATER MODEL 92 3.3.1 SEMICLASSICAL APPROXIMATION FOR THE
EXCHANGE INTERACTION . . 92 3.3.2 THE EQUATIONS OF THE
HARTREE-FOCK-SLATER MODEL 96 3.3.3 THE EQUATIONS OF THE
HARTREE-FOCK-SLATER MODEL IN THE CASE WHEN THE SEMICLASSICAL
APPROXIMATION IS USED FOR CONTINUUM ELECTRONS 99 3.3.4 THE THERMODYNAMIC
CONSISTENCY CONDITION 103 CONTENTS VII 4 THE HARTREE-FOCK-SLATER MODEL
FOR THE AVERAGE ATOM 107 4.1 THE HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS
IN A SPHERICAL CELL . . 107 4.1.1 THE HARTREE-FOCK-SLATER FIELD 107
4.1.2 PERIODIC BOUNDARY CONDITIONS IN THE AVERAGE SPHERICAL CELL
APPROXIMATION ILL 4.1.3 THE ELECTRON DENSITY AND THE ATOMIC POTENTIAL IN
THE HARTREE-FOCK-SLATER MODEL WITH BANDS 114 4.1.4 THE RELATIVISTIC
HARTREE-FOCK-SLATER MODEL 115 4.2 AN ITERATION METHOD FOR SOLVING THE
HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS 117 4.2.1 ALGORITHM BASICS 117
4.2.2 COMPUTATION OF THE BAND STRUCTURE OF THE ENERGY SPECTRUM 118 4.2.3
COMPUTATIONAL RESULTS 120 4.2.4 THE UNIFORM-DENSITY APPROXIMATION FOR
FREE ELECTRONS IN THE CASE OF A RAREFIED PLASMA 122 4.3 SOLUTION OF THE
HARTREE-FOCK-SLATER SYSTEM OF EQUATIONS FOR A MIXTURE OF ELEMENTS 123
4.3.1 PROBLEM SETTING 123 4.3.2 ITERATION SCHEME 125 4.3.3 EXAMPLES OF
COMPUTATIONS 129 4.4 ACCOUNTING FOR THE INDIVIDUAL STATES OF IONS 131
4.4.1 DENSITY FUNCTIONAL OF THE ELECTRON SYSTEM WITH THE INDIVIDUAL
STATES OF IONS ACCOUNTED FOR 132 4.4.2 THE HARTREE-FOCK-SLATER EQUATIONS
OF THE ION METHOD IN THE CELL AND PLASMA APPROXIMATIONS 134 4.4.3 WAVE
FUNCTIONS AND ENERGY LEVELS OF IONS IN A PLASMA . . . . 138 II RADIATIVE
AND THERMODYNAMICAL PROPERTIES OF HIGH-TEMPERATURE DENSE PLASMA X 143 5
INTERACTION OF RADIATION WITH MATTER 145 5.1 RADIATIVE HEAT CONDUCTIVITY
OF PLASMA 146 5.1.1 THE RADIATIVE TRANSFER EQUATION 146 5.1.2 THE
DIFFUSION APPROXIMATION 150 5.1.3 THE ROSSELAND MEAN OPACITY 154 5.1.4
THE PLANCK MEAN. RADIATION OF AN OPTICALLY THIN LAYER . . . 155 VIII
CONTENTS 5.2 QUANTUM-MECHANICAL EXPRESSIONS FOR THE EFFECTIVE PHOTON
ABSORPTION CROSS-SECTIONS 156 5.2.1 ABSORPTION IN SPECTRAL LINES 156
5.2.2 PHOTOIONIZATION 164 5.2.3 INVERSE BREMSSTRAHLUNG 168 5.2.4 COMPTON
SCATTERING 170 5.2.5 THE TOTAL ABSORPTION CROSS-SECTION 171 5.3
PECULIARITIES OF PHOTON ABSORPTION IN SPECTRAL LINES 172 5.3.1
PROBABILITY DISTRIBUTION OF EXCITED ION STATES 172 5.3.2 POSITION OF
SPECTRAL LINES 174 5.3.3 ATOM WAVE FUNCTIONS AND ADDITION OF MOMENTA 176
5.4 SHAPE OF SPECTRAL LINES 183 5.4.1 DOPPLER EFFECT , . . 184 5.4.2
ELECTRON BROADENING IN THE IMPACT APPROXIMATION 185 5.4.3 THE
NONDEGENERATE CASE 186 5.4.4 ACCOUNTING FOR DEGENERACY 194 5.4.5 METHODS
FOR CALCULATING RADIATION AND ELECTRON BROADENING . 198 5.4.6 ION
BROADENING 205 5.4.7 THE VOIGT PROFILE 213 5.4.8 LINE PROFILES OF A
HYDROGEN PLASMA IN A STRONG MAGNETIC FIELD . . 214 5.5 STATISTICAL
METHOD FOR LINE-GROUP ACCOUNTING 219 5.5.1 SHIFT AND BROADENING
PARAMETERS OF SPECTRAL LINES IN PLASMA 220 5.5.2 FLUCTUATIONS OF
OCCUPATION NUMBERS IN A DENSE HOT PLASMA . 226 5.5.3 STATISTICAL
DESCRIPTION OF OVERLAPPING MULTIPLETS 228 5.5.4 EFFECTIVE PROFILE FOR A
GROUP OF LINES 238 5.5.5 STATISTICAL DESCRIPTION OF THE PHOTOIONIZATION
PROCESS . . . . 243 5.6 COMPUTATIONAL RESULTS FOR ROSSELAND MEAN PATHS
AND SPECTRAL PHOTON-ABSORPTION COEFFICIENTS 245 5.6.1 COMPARISON OF THE
STATISTICAL METHOD WITH DETAILED COMPUTATION 245 5.6.2 DEPENDENCE OF THE
ABSORPTION COEFFICIENTS ON THE ELEMENT NUMBER, TEMPERATURE AND DENSITY
OF THE PLASMA 250 5.6.3 SPECTRAL ABSORPTION COEFFICIENTS 259 5.6.4
RADIATIVE AND ELECTRON HEAT CONDUCTIVITY 265 5.6.5 DATABASES OF ATOMIC
DATA AND SPECTRAL PHOTON ABSORPTION COEFFICIENTS 266 CONTENTS IX 5.7
ABSORPTION OF PHOTONS IN A PLASMA WITH NONEQUILIBRIUM RADIATION FIELD
267 5.7.1 BASIC PROCESSES AND RELAXATION TIMES 268 5.7.2 JOINT
CONSIDERATION OF THE PROCESSES OF PHOTON TRANSPORT AND LEVEL KINETICS OF
ELECTRONS 271 5.7.3 AVERAGE-ATOM APPROXIMATION 272 5.7.4 RATES OF
RADIATION AND COLLISION PROCESSES 274 5.7.5 RADIATION PROPERTIES OF A
PLASMA WITH NONEQUILIBRIUM RADIATION FIELD 277 5.7.6 RADIATIVE HEAT
CONDUCTIVITY OF MATTER FOR LARGE GRADIENTS OF TEMPERATURE AND DENSITY
280 6 THE EQUATION OF STATE 285 6.1 DESCRIPTION OF THERMODYNAMICS OF
MATTER BASED ON QUANTUM-STATISTICAL MODELS 286 6.1.1 FORMULAS FOR THE
PRESSURE, INTERNAL ENERGY AND ENTROPY ACCORDING TO THE THOMAS-FERMI
MODEL 286 6.1.2 QUANTUM, EXCHANGE AND OSCILLATION CORRECTIONS TO THE
THOMAS-FERMI MODEL 294 6.2 THE IONIZATION EQUILIBRIUM METHOD 300 6.2.1
THE GIBBS DISTRIBUTION FOR THE ATOM CELL 300 6.2.2 THE SAHA
APPROXIMATION 301 6.2.3 AN ITERATION SCHEME FOR SOLVING THE SYSTEM OF
EQUATIONS OF IONIZATION EQUILIBRIUM 303 6.2.4 CORONAL EQUILIBRIUM 305
6.3 THERMODYNAMIC PROPERTIES OF MATTER IN THE HARTREE-FOCK-SLATER MODEL
307 6.3.1 ELECTRON THERMODYNAMIC FUNCTIONS 309 6.3.2 ACCOUNTING FOR THE
THERMAL MOTION OF IONS IN THE CHARGED HARD-SPHERE APPROXIMATION 314
6.3.3 EFFECTIVE RADIUS OF THE AVERAGE ION ,317 6.3.4 ON METHODS FOR
DERIVING WIDE-RANGE EQUATIONS OF STATE . . . 318 6.4 COMPUTATIONAL
RESULTS 319 6.4.1 GENERAL DESCRIPTION 319 6.4.2 COLD COMPRESSION CURVES
322 6.4.3 SHOCK ADIABATS 324 6.4.4 COMPARISON WITH THE SAHA MODEL 327
6.5 APPROXIMATION OF THERMOPHYSICAL-DATA TABLES 330 6.5.1 CONSTRUCTION
OF AN APPROXIMATING SPLINE THAT PRESERVES GEOMETRIC PROPERTIES OF THE
INITIAL FUNCTION 331 6.5.2 NUMERICAL RESULTS 334 X CONTENTS III APPENDIX
METHODS FOR SOLVING THE SCHRODINGER AND DIRAC EQUATIONS 337 ANALYTIC
METHODS 339 A.I QUANTUM MECHANICAL PROBLEMS THAT CAN BE SOLVED
ANALYTICALLY . . 339 A. 1.1 EQUATIONS OF HYPERGEOMETRIC TYPE 339 A. 1.2
BOUND STATE WAVE FUNCTIONS AND CLASSICAL ORTHOGONAL POLYNOMIALS 343 A.
1.3 SOLUTION OF THE SCHRODINGER EQUATION IN A CENTRAL FIELD . . . 345
A.1.4 RADIAL PART OF THE WAVE FUNCTION IN A COULOMB FIELD . . . . 347
A.2 SOLUTION OF THE DIRAC EQUATION FOR THE COULOMB POTENTIAL 355 A.2.1
THE SYSTEM OF EQUATIONS FOR THE RADIAL PARTS OF THE WAVE FUNCTIONS 356
A.2.2 REDUCTION OF THE SYSTEM OF EQUATIONS FOR THE RADIAL FUNCTIONS TO
AN EQUATION OF HYPERGEOMETRIC TYPE 359 A.2.3 EQUATIONS OF HYPERGEOMETRIC
TYPE FOR THE BOUND STATES AND THEIR SOLUTION 362 A.2.4 ENERGY LEVELS AND
RADIAL FUNCTIONS V . 365 A.2.5 CONNECTION WITH THE NONRELATIVISTIC
THEORY 367 APPROXIMATION METHODS 371 A.3 THE VARIATIONAL METHOD AND THE
METHOD OF THE TRIAL POTENTIAL . . . 371 A.3.1 MAIN FEATURES OF THE
VARIATIONAL METHOD 371 A.3.2 CALCULATION OF HYDROGEN-LIKE WAVE FUNCTIONS
374 A.3.3 METHOD OF THE TRIAL POTENTIAL FOR THE SCHRODINGER AND DIRAC
EQUATIONS 377 A.4 THE SEMICLASSICAL APPROXIMATION 380 A.4.1
SEMICLASSICAL APPROXIMATION IN THE ONE-DIMENSIONAL CASE . . 380 A.4.2
APPLICATION OF THE WKB METHOD TO AN EQUATION WITH SINGULARITY.
SEMICLASSICAL APPROXIMATION FOR A CENTRAL FIELD . 387 A.4.3 THE
BOHR-SOMMERFELD QUANTIZATION RULE 388 A.4.4 USING THE SEMICLASSICAL
APPROXIMATION TO NORMALIZE THE CONTINUUM WAVE FUNCTIONS 391 CONTENTS XI
NUMERICAL METHODS 392 A.5 THE PHASE METHOD FOR CALCULATING ENERGY
EIGENVALUES AND WAVE FUNCTIONS 392 A.5.1 EQUATION FOR THE PHASE AND THE
CONNECTION WITH THE SEMICLASSICAL APPROXIMATION 392 A.5.2 CONSTRUCTION
OF AN ITERATION SCHEME FOR THE CALCULATION OF EIGENVALUES 394 A.5.3
DIFFERENCE SCHEMES FOR CALCULATING RADIAL FUNCTIONS 399 A.5.4 THE RADIAL
FUNCTIONS NEAR ZERO AND FOR LARGE VALUES OF R . . . 401 A.5.5
COMPUTATIONAL RESULTS 403 A.5.6 THE PHASE METHOD FOR THE DIRAC EQUATION
406 BIBLIOGRAPHY 409 INDEX 427
|
| any_adam_object | 1 |
| author | Nikiforov, Arnol'd F. 1930- Novikov, Vladimir G. Uvarov, Vasilij B. 1929-1997 |
| author_GND | (DE-588)123298075 (DE-588)11086932X |
| author_facet | Nikiforov, Arnol'd F. 1930- Novikov, Vladimir G. Uvarov, Vasilij B. 1929-1997 |
| author_role | aut aut aut |
| author_sort | Nikiforov, Arnol'd F. 1930- |
| author_variant | a f n af afn v g n vg vgn v b u vb vbu |
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| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV017323164 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T16:19:52Z |
| institution | BVB |
| isbn | 3764321830 9783764321833 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010441741 |
| oclc_num | 57594533 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-11 |
| owner_facet | DE-703 DE-384 DE-11 |
| physical | XVII, 428 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spellingShingle | Nikiforov, Arnol'd F. 1930- Novikov, Vladimir G. Uvarov, Vasilij B. 1929-1997 Quantum statistical models of hot dense matter methods for computation opacity and equation of state Progress in mathematical physics Equations of state High temperature plasmas Plasma density Quantum statistics Zustandsgleichung (DE-588)4068158-0 gnd Opazität (DE-588)4494369-6 gnd Dichtes Plasma (DE-588)4149626-7 gnd Heißes Plasma (DE-588)4350270-2 gnd Self-consistent Field (DE-588)4180911-7 gnd Quantenstatistik (DE-588)4047991-2 gnd |
| subject_GND | (DE-588)4068158-0 (DE-588)4494369-6 (DE-588)4149626-7 (DE-588)4350270-2 (DE-588)4180911-7 (DE-588)4047991-2 |
| title | Quantum statistical models of hot dense matter methods for computation opacity and equation of state |
| title_alt | Quantum-statistical models of hot dense matter |
| title_auth | Quantum statistical models of hot dense matter methods for computation opacity and equation of state |
| title_exact_search | Quantum statistical models of hot dense matter methods for computation opacity and equation of state |
| title_full | Quantum statistical models of hot dense matter methods for computation opacity and equation of state A. F. Nikiforov ; V. G. Novikov ; V. B. Uvarov |
| title_fullStr | Quantum statistical models of hot dense matter methods for computation opacity and equation of state A. F. Nikiforov ; V. G. Novikov ; V. B. Uvarov |
| title_full_unstemmed | Quantum statistical models of hot dense matter methods for computation opacity and equation of state A. F. Nikiforov ; V. G. Novikov ; V. B. Uvarov |
| title_short | Quantum statistical models of hot dense matter |
| title_sort | quantum statistical models of hot dense matter methods for computation opacity and equation of state |
| title_sub | methods for computation opacity and equation of state |
| topic | Equations of state High temperature plasmas Plasma density Quantum statistics Zustandsgleichung (DE-588)4068158-0 gnd Opazität (DE-588)4494369-6 gnd Dichtes Plasma (DE-588)4149626-7 gnd Heißes Plasma (DE-588)4350270-2 gnd Self-consistent Field (DE-588)4180911-7 gnd Quantenstatistik (DE-588)4047991-2 gnd |
| topic_facet | Equations of state High temperature plasmas Plasma density Quantum statistics Zustandsgleichung Opazität Dichtes Plasma Heißes Plasma Self-consistent Field Quantenstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441741&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
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