Scattering theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture Notes in Physics
872 |
| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783642382826 9783642382819 |
| DOI: | 10.1007/978-3-642-38282-6 |
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Datensatz im Suchindex
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| adam_text | CONTENTS
XV
1 CLASSICAL SCATTERING THEORY 1
1.1 RELATIVE MOTION OF PROJECTILE AND TARGET 1
1.2 DEFLECTION FUNCTION 2
1.2.1 KEPLER-COULOMB POTENTIAL 5
1.2.2 INVERSE-POWER POTENTIALS 6
1.2.3 LENNARD-JONES POTENTIAL 9
1.3 SCATTERING ANGLE AND SCATTERING CROSS SECTIONS 11
1.3.1 KEPLER-COULOMB POTENTIAL 13
1.3.2 INVERSE-POWER POTENTIALS 14
1.3.3 LENNARD-JONES POTENTIAL 16
1.4 CLASSICAL SCATTERING IN TWO SPATIAL DIMENSIONS 17
REFERENCES- 21
2 ELASTIC SCATTERING BY A CONSERVATIVE POTENTIAL 23
2.1 SCATTERING AMPLITUDE AND SCATTERING CROSS SECTION 23
2.2 LIPPMANN-SCHWINGER EQUATION AND BORN APPROXIMATION 26
2.3 RADIALLY SYMMETRIC POTENTIALS 28
2.3.1 ANGULAR MOMENTUM 28
2.3.2 PARTIAL-WAVES EXPANSION 29
2.3.3 SCATTERING PHASE SHIFTS 30
2.3.4 NORMALIZATION OF RADIAL WAVE FUNCTIONS 33
2.3.5 RADIAL LIPPMANN-SCHWINGER EQUATION 34
2.3.6 S-MATRIX 36
2.3.7 DETERMINATION OF THE SCATTERING PHASE SHIFTS 37
2.3.8 NEAR-THRESHOLD BEHAVIOUR OF THE SCATTERING PHASE SHIFTS . 38
2.3.9 LEVINSON S THEOREM 45
2.3.10 POTENTIAL RESONANCES (SHAPE RESONANCES) 49
2.3.11 SCATTERING CROSS SECTIONS 55
2.4 THE WKB APPROXIMATION 58
2.4.1 DEFINITION AND ACCURACY OF WKB WAVE FUNCTIONS 58
2.4.2 CONNECTION ACROSS A CLASSICAL TURNING POINT 60
IX
HTTP://D-NB.INFO/1033487902
X CONTENTS
2.4.3 WKB PHASE SHIFTS 67
2.5 COULOMBIC POTENTIALS 70
2.5.1 PURE COULOMB POTENTIAL 71
2.5.2 MODIFIED COULOMB POTENTIAL; GENERAL CONSIDERATIONS ... 75
2.5.3 MODIFIED REPULSIVE COULOMB POTENTIAL 78
2.5.4 MODIFIED ATTRACTIVE COULOMB POTENTIAL, QUANTUM-DEFECT
THEORY 81
2.6 POTENTIALS FALLING OFF AS 1 /R
A
,A 2 90
2.6.1 NEAR-THRESHOLD BEHAVIOUR OF SCATTERING PHASE SHIFTS ... 90
2.6.2 THE SPECIAL CASE 21 + 3 = A 93
2.6.3 MODIFIED EFFECTIVE-RANGE EXPANSIONS 95
2.6.4 PERIPHERAL SCATTERING 98
2.6.5 THE LENNARD-JONES POTENTIAL 99
2.7 POTENTIALS WITH INVERSE-SQUARE TAILS 101
2.7.1 PURE INVERSE-SQUARE POTENTIAL 101
2.7.2 MODIFIED INVERSE-SQUARE POTENTIAL 106
2.7.3 EXAMPLE: INVERSE-SQUARE POTENTIAL WITH HARD SPHERE . ... 110
2.8 NONVANISHING ANGULAR MOMENTUM OF PROJECTILE AND/OR TARGET ... 113
2.8.1 GENERAL FORMALISM FOR TREATING SPINS 113
2.8.2 SPIN-J PROJECTILE WITH SPIN-ZERO TARGET 119
2.8.3 APPLICATION TO MIXED SPIN STATES 124
2.9 WHEN PROJECTILE AND TARGET ARE INDISTINGUISHABLE 126
2.9.1 SPINLISS BOSONS LL26
2.9.2 SPIN-J FERMIONS 130
REFERENCES 133
3 INTERNAL EXCITATION, INELASTIC SCATTERING 137
3.1 COUPLED-CHANNEL EQUATIONS AND SCATTERING CROSS SECTIONS 137
3.2 COUPLED-CHANNEL LIPPMANN-SCHWINGER EQUATION AND BORN
APPROXIMATION 140
3.3 RADIAL COUPLED-CHANNEL EQUATIONS 142
3.4 ABSORPTION 146
3.5 FESHBACH RESONANCES 147
3.5.1 SINGLE ISOLATED FESHBACH RESONANCE 148
3.5.2 INTERFERING RESONANCES 156
3.5.3 RESONANCES IN THE PRESENCE OF SEVERAL OPEN CHANNELS . . . 161
3.6 COULOMBIC POTENTIALS, GENERAL THEORY 163
3.6.1 SCATTERING CROSS SECTIONS 163
3.6.2 PARTIAL-WAVES EXPANSION 164
3.7 ATTRACTIVE COULOMB POTENTIALS, MULTICHANNEL QUANTUM-DEFECT
THEORY 166
3.7.1 PERTURBED RYDBERG SERIES 167
3.7.2 TWO COUPLED COULOMBIC CHANNELS 169
3.7.3 MORE THAN TWO COUPLED COULOMBIC CHANNELS 177
REFERENCES 183
CONTENTS XI
4 SPECIAL TOPICS 185
4.1 DEEP POTENTIALS FALLING OFF FASTER THAN /R
2
ASYMPTOTICALLY .... 185
4.1.1 NEAR-THRESHOLD QUANTIZATION 185
4.1.2 QUANTUM REFLECTION 209
4.1.3 ELASTIC SCATTERING 220
4.1.4 NONVANISHING ANGULAR MOMENTUM 229
4.1.5 SUMMARY 232
4.1.6 RELATION TO OTHER APPROACHES 234
4.2 NEAR-THRESHOLD FESHBACH RESONANCES 236
4.2.1 MOTIVATION 236
4.2.2 THRESHOLD-INSENSITIVE PARAMETRIZATION OF A FESHBACH
RESONANCE 238
4.2.3 INFLUENCE ON THE SCATTERING LENGTH 241
4.2.4 INFLUENCE ON THE BOUND-STATE SPECTRUM 243
4.2.5 RELATION TO THE EMPIRICAL FORMULA (4.156) 246
4.3 QUANTUM DESCRIPTION OF SCATTERING IN TWO SPATIAL DIMENSIONS . . 248
4.3.1 SCATTERING AMPLITUDE AND SCATTERING CROSS SECTION 249
4.3.2 LIPPMANN-SCHWINGER EQUATION AND BORN APPROXIMATION . 250
4.3.3 PARTIAL-WAVES EXPANSION AND SCATTERING PHASE SHIFTS . ... 251
4.3.4 NEAR-THRESHOLD BEHAVIOUR OF THE SCATTERING PHASE SHIFTS . 254
4.3.5 THE CASE M = 0,
A
-WAVES IN TWO DIMENSIONS 255
4.3.6 RUTHERFORD SCATTERING IN TWO DIMENSIONS 259
REFERENCES 261
APPENDIX A SCALING 267
A.L CLASSICAL MECHANICS 267
A.2 QUANTUM MECHANICS 269
REFERENCES 271
APPENDIX B SPECIAL FUNCTIONS 273
B.L LEGENDRE POLYNOMIALS, SPHERICAL HARMONICS 273
B.2 ERROR FUNCTION 274
B.3 GAMMA FUNCTION 274
B.4 BESSEL FUNCTIONS 275
B.5 CONFLUENT HYPERGEOMETRIC FUNCTIONS, COULOMB FUNCTIONS,
WHITTAKER S FUNCTION 279
REFERENCES 281
INDEX 283
SCATTERING THEORY
/ FRIEDRICH, HARALD
: 2013
ABSTRACT / INHALTSTEXT
THIS BOOK PRESENTS A CONCISE AND MODERN COVERAGE OF SCATTERING THEORY.
IT IS MOTIVATED BY THE FACT THAT EXPERIMENTAL ADVANCES HAVE SHIFTED AND
BROADENED THE SCOPE OF APPLICATIONS WHERE CONCEPTS FROM SCATTERING
THEORY ARE USED, E.G. TOTHE FIELD OF ULTRACOLD ATOMS AND MOLECULES,
WHICH HAS BEEN EXPERIENCING ENORMOUS GROWTH IN RECENT YEARS, LARGELY
TRIGGERED BY THE SUCCESSFUL REALIZATION OF BOSE-EINSTEIN CONDENSATES OF
DILUTE ATOMIC GASES IN 1995. IN THE PRESENT TREATMENT, SPECIAL
ATTENTION IS GIVEN TO THE ROLE PLAYED BY THE LONG-RANGE BEHAVIOUR OF THE
PROJECTILE-TARGET INTERACTION, AND A THEORY IS DEVELOPED, WHICH IS WELL
SUITED TODESCRIBE NEAR-THRESHOLD BOUND AND CONTINUUM STATES IN
REALISTIC BINARY SYSTEMS SUCH AS DIATOMIC MOLECULES OR MOLECULAR IONS.
THE LEVEL OF ABSTRACTION IS KEPTAS LOW AS AT ALL POSSIBLE,AND DEEPER
QUESTIONS RELATED TOMATHEMATICAL FOUNDATIONS OF SCATTERING THEORY ARE
PASSED BY. THE BOOKSHOULD BEUNDERSTANDABLE FOR ANYONE WITH A BASIC
KNOWLEDGE OF NONRELATIVISTIC QUANTUM MECHANICS. IT IS INTENDED FOR
ADVANCED STUDENTS AND RESEARCHERS, AND IT IS HOPED THAT IT WILL BE
USEFUL FOR THEORISTS AND EXPERIMENTALISTS ALIKE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
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| discipline | Physik |
| doi_str_mv | 10.1007/978-3-642-38282-6 |
| format | Electronic eBook |
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| spelling | Friedrich, Harald 1947-2017 Verfasser (DE-588)11819738X aut Scattering theory Harald Friedrich Berlin [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Physics 872 Streutheorie (DE-588)4183697-2 gnd rswk-swf Streutheorie (DE-588)4183697-2 s DE-604 Lecture Notes in Physics 872 (DE-604)BV013615055 872 https://doi.org/10.1007/978-3-642-38282-6 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026074642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026074642&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Friedrich, Harald 1947-2017 Scattering theory Lecture Notes in Physics Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4183697-2 |
| title | Scattering theory |
| title_auth | Scattering theory |
| title_exact_search | Scattering theory |
| title_full | Scattering theory Harald Friedrich |
| title_fullStr | Scattering theory Harald Friedrich |
| title_full_unstemmed | Scattering theory Harald Friedrich |
| title_short | Scattering theory |
| title_sort | scattering theory |
| topic | Streutheorie (DE-588)4183697-2 gnd |
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