ATOMIC AND LASER SPECTROSCOPY

Transcription

1 ALAN CORNEY ATOMIC AND LASER SPECTROSCOPY CLARENDON PRESS OXFORD 1977

2 Contents 1. INTRODUCTION 1.1. Planck's radiation law The photoelectric effect Early atomic spectroscopy The postulates of Bohr's theory of 7 atomic structure 1.5. Development of quantum mechanics g 1.6. Interaction of atoms and radiation n Optical physics since The present situation (1975) 12 Problems References 15 General references and further reading REVIEW.OF CLASSICAL ELECTRODYNAMICS <: Maxwell's equations The electromagnetic wave equations Plane wave solutions Linear and circular polarizations The energy density and the Poynting vector Vector and scalar potentials Electric dipole radiation Rate of radiation by an electric dipole 39 oscillator 2.9. Angular momentum of dipole radiation Magnetic dipole radiation Electric quadrupole radiation Multipole fields 48 Problems 49 General references and further reading 51

3 x CONTENTS 3. REVIEW OF QUANTUM MECHANICS The Schrodinger-wave equation Expectation values and matrix elements Solution of Schrodinger's equation for spherically symmetric potentials Orbital angular momentum Hydrogenic wavefunctions Spin angular momentum Coupling of two angular momenta Spin-orbit interaction and the vector model Many-electron atoms 77 Problems 88 General references and further reading THE SPONTANEOUS EMISSION OF RADIATION The classical atomic model Radiative lifetime of a classical atom Spontaneous emission probability, A, Spontaneous emission according to quantum electrodynamics Spontaneous transitions between degenerate levels Radiative lifetimes of excited atoms Intensity of light emitted by optically thin sources Oscillator strengths The line strength, S, Oscillator strengths in hydrogenic systems Theoretical oscillator strengths in complex atoms 114 Problems 115 References 118 General references and further reading 118

4 CONTENTS xi 5. SELECTION RULES FOR ELECTRIC DIPOLE TRANSITIONS Introduction One-electron atoms without spin One-electron atoms with spin "Tensor properties of the electric dipole 129 operator 5.5. Many-electrun atoms Relative intensities in L-S coupling and forbidden transitions 138.Problems 139 General references and further reading MEASUREMENT OF 1 RADIATIVE LIFETIMES OF ATOMS AND MOLECULES The beam-foil method Fast beam experiments using laser excitation The delayed-coincidence method using electron excitation 160, 6.4. Delayed-coincidence experiments using 171 optical excitation References 176 GeneraFreferences and further reading FORBIDDEN TRANSITIONS AND METASTABLE ATOMS Magnetic dipole transitions Electric quadrupole radiation Selection rules for magnetic dipole and electric quadrupole transitions Two-photon decay of hydrogenic systems Forbidden transitions in helium-like systems " Collision processes involving metastable 214 : a t o m s " Problems 224 References 226 General references and further reading, 228

5 xii CONTENTS 8. THE WIDTH AND SHAPE OF SPECTRAL LINES 2 2P 8.1. The natural.or radiative lineshape The pressure broadening of spectral lines Doppler broadening Comparison of Doppler, collision, and natural widths Voigt profiles Effect of the instrumental profile Line profile measurements and temperatures at low pressures 257 Problems 266 References 269 General references and further reading THE ABSORPTION AND STIMULATED EMISSION OF RADIATION Classical description of absorption by electric dipole oscillator Einstein's treatment of stimulated emission and absorption The semi-classical treatment of absorption and induced emission Einstein B-coefficients terms of intensity defined in ' Relations between Einstein B-coefficients and f-values The integral of the total absorption cross-section 285 ' 9.7. Introduction of the atomic response frequency 285 Problems 286 References 288 General references and further reading 28R 10. RADIATIVE TRANSFER AND THE FORMATION OF SPECTRAL LINES Derivation of the equation of transfer Solution of the transfer equation uniformly excited sources for Non-uniform sources 296 cont

6 CONTENTS. xiii Chapter 10 continued Equivalent widths of absorption lines Measurement of relative f-values by absorption techniques Determination of chemical composition 308 and atomic densities by absorption techniques Problems 315 References 317 General references and further reading POPULATION' INVERSION MECHANISMS IN GAS LASERS Introduction Population inversion and the atomic gain coefficient Transient "and steady state population inversion Population inversion mechanisms in gas lasers 329 * Problems. 351 References 353 General references and further reading RESONANT MODES OF OPTICAL CAVITIES Introduction Numerical solution of cavity mode problem ^ Approximate analytic solutions for transverse modes Mode size and cavity stability Design considerations for practical systems Cavity Q-factor and resonance linewidth 370 Problems 372 References 375 General references and further reading 376

7 xiv CONTENTS 13. SATURATION CHARACTERISTICS AND SINGLE-FREQUENCY 377 OPERATION OF GAS LASERS Frequencies of the resonant cavity 378 modes Gain required for oscillation, Gain saturation : homogeneously- 383 broadened transitions Gain saturation : inhomogeneously- 388 broadened transitions Measurement of gain coefficients Mode-locking of gas lasers Single-frequency operation of gas. 402 lasers Output power versus tuning curves 409 for single-frequency gas lasers Saturated absorption spectroscopy 414 using tunable gas lasers Frequency stabilization of single- 420 frequency gas lasers Problems 432 References 436 General references and further reading TUNABLE DYE LASERS AND ATOMIC SPECTROSCOPY Introduction Tunable organic dye lasers Saturated absorption spectroscopy ' 454, using tunable dye lasers Two-photon absorption spectros- 462 copy > References " 470 General references and further reading THE HANLE EFFECT AND THE THEORY OF RESONANCE 4 73 FLUORESCENCE EXPERIMENTS Resonance radiation and resonance 474 fluorescence Magnetic depolarization of resonance radiation - the Hanle effect 477 cont

8 CONTENTS xv Chapter 15 continued Excitation by electron impact Range and accuracy of lifetime measurements Theory of resonance fluorescence experiments " Theory of the Hanle effect Theory of resonance fluorescence in 506 the J =1**J =0 case eg Resonance fluorescence experiments using pulsed excitation Resonance fluorescence experiments using modulated excitation 520 Problems 526 References 530 General references and further reading OPTICAL DOUBLE RESONANCE EXPERIMENTS ' Magnetic resonance and excited atoms 534,16.2. theory of the Brossel-Bitter experiment Discussion of the optical doubleresonance method Radiation trapping and coherence narrowing Collision broadening in resonance fluorescence experiments Light modulation in double-resonance experiments Magnetic resonance in the density matrix formalism Expansion of the density matrix in 584 terms of irreducible tensor operators Problems 586 References 589 General references and further reading 590 y

9 xvi CONTENTS 17. OPTICAL PUMPING EXPERIMENTS Introduction Principles of optical'pumping Effect of relaxation processes Investigation of longitudinal relaxation times Spin-exchange collisions ' Optical pumping of metastabie atoms Optical pumping and magnetic resonance Transverse magnetization and Hertzian 629 coherence in optical pumping experiments Quantum theory of the optical pumping 639 cycle Problems 654 References 658 General references and further reading THE HYPERFINE STRUCTURE OF ATOMS AND ITS INVES TIGATION BY MAGNETIC RESONANCE METHODS Theory of hyperfine structure Investigation of hyperfine structure 676 of ground-state atoms by optical pumping Hyperfine pumping and the measurement 682 o V HFS,., Optically.pumped rubidium frequency 689 standards The atomic beam magnetic, resonance technique Hyperfine structure investigations by the atomic beam technique Cesium beam atomic clock Hyperfine structure of atomic hydrogen Investigation of the hyperfine structure of excited states Conclusion i Problems References General references and further reading

10 CONTENTS xv 11 APPENDIX: TABLE OF FUNDAMENTAL CONSTANTS 742 AUTHOR INDEX * 745 SUBJECT INDEX 754