The Theory of Atomic Spectra Book

	Preface to the 1963 impression	xiii
	Preface	xiv
Chapter I	Introduction	1
Chapter II	The Quantum Mechanical Method	12
Section 1	Symbolic algebra of states and observables	12
Section 2	Representations of states and observables	15
Section 3	Continuous eigenvalues and the Schrodinger representation	20
Section 4	The statistical interpretation	24
Section 5	The laws of quantum mechanics	25
Section 6	Schrodinger's equation	26
Section 7	Matrix mechanics	27
Section 8	Perturbation theory	30
Section 9	Resume of the perturbation theory	34
Section 10	Remarks on the perturbation theory	35
Section 11	Perturbation caused by a single state	37
Section 12	The analysis of non-commuting vectors	43
Chapter III	Angular Momentum	45
Section 1	Definition of angular momentum	45
Section 2	Allowed values of angular momentum	46
Section 3	The matrices of angular momentum	48
Section 4	Orbital angular momentum	50
Section 5	Spin angular momentum	54
Section 6	Vector addition of angular momenta	56
Section 7	The matrix of [characters not reproducible]	58
Section 8	Matrix of T in the j m scheme. Selection rule on j	59
Section 9	Dependence of the matrix of T on m	61
Section 10	The matrices of J[subscript 1] and J[subscript 2], where J[subscript 1] + J[subscript 2] = J	64
Section 11	Matrix of a vector P which commutes with J[subscript 1]	67
Section 12	Matrix of P.Q	70
Section 13	Sum rules	71
Section 14	Transformation amplitudes for vector addition	73
Chapter IV	The Theory of Radiation	79
Section 1	Transition probabilities	79
Section 2	Classical electromagnetic theory	83
Section 3	Expansion of the retarded potential	84
Section 4	The correspondence principle for emission	87
Section 5	The dipole-radiation field	90
Section 6	The quadrupole-radiation field	93
Section 7	Spectral lines in natural excitation	97
Section 8	Induced emission and absorption	100
Section 9	Dispersion theory. Scattering. Raman effect	103
Section 10	Natural shape of absorption lines	109
Chapter V	One-Electron Spectra	112
Section 1	Central-force problem	112
Section 2	Radial functions for hydrogen	114
Section 3	The relativity correction	118
Section 4	Spin-orbit interaction	120
Section 5	Sketch of the relativistic theory	125
Section 6	Intensities in hydrogen	131
Section 7	Experimental results for hydrogenic spectra	137
Section 8	General structure of the alkali spectra	141
Section 9	Intensities in alkali spectra	147
Section 10	Zeeman effect	149
Chapter VI	The Central-Field Approximation	158
Section 1	The Hamiltonian for many-electron atoms	158
Section 2	Equivalence degeneracy	160
Section 3	The dynamical equivalence of the electrons	162
Section 4	The Pauli exclusion principle	166
Section 5	Conventions concerning quantum numbers. Closed shells	168
Section 6	Matrix components for [Sigma subscript i]f(i)	169
Section 7	Matrix components for [Sigma subscript i,j]g(i, j)	171
Section 8	Matrix components of electrostatic interaction	174
Section 9	Specialization for closed shells	177
Section 10	One electron outside closed shells	183
Section 11	Odd and even states	185
Chapter VII	The Russell-Saunders Case: Energy Levels	187
Section 1	The LS-coupling scheme	188
Section 2	Term energies	191
Section 3	The Lande interval rule	193
Section 4	Absolute term intervals	195
Section 5	Formulas and experimental comparison	197
Section 6	Terms in the nl[superscript x] configurations	207
Section 7	The triplet terms of helium	210
Chapter VIII	The Russell-Saunders Case: Eigenfunctions	213
Section 1	Vector coupling in antisymmetric states	213
Section 2	Genealogical characterization of LS-coupling terms	216
Section 3	Lande intervals for terms of coupled groups	219
Section 4	Calculation of eigenfunctions by direct diagonalization	220
Section 5	Calculation of eigenfunctions using angular-momentum operators	226
Section 6	Calculation of eigenfunctions from vector-coupling formulas	228
Section 7	Separation of the [superscript 2]D's of d[superscript 3]	233
Chapter IX	The Russell-Saunders Case: Line Strengths	236
Section 1	Configuration selection rules	236
Section 2	Line strengths in Russell-Saunders multiplets	237
Section 3	Multiplet strengths in a transition array	244
Section 4	Multiplet strengths obtained from spectroscopic stability	249
Section 5	Quadrupole multiplets	252
Chapter X	jj Coupling	257
Section 1	The jj-coupling scheme and the spin-orbit interaction	257
Section 2	The addition of a weak electrostatic interaction	259
Section 3	Eigenfunctions	262
Section 4	Line strengths	264
Chapter XI	Intermediate Coupling	266
Section 1	Matrix of spin-orbit interaction for configurations consisting of coupled groups	266
Section 2	Matrix of spin-orbit interaction obtained from the eigenfunctions	270
Section 3	Illustrations of the transition from LS to jj coupling	271
Section 4	Line strengths in intermediate coupling	277
Section 5	The forbidden lines of astrophysical interest	282
Chapter XII	Transformations in the Theory of Complex Spectra	284
Section 1	Configurations containing almost closed shells	284
Section 2	The transformation to LS coupling	285
Section 3	The transformation to jj coupling	287
Section 4	The transformation between zero-order states	287
Section 5	The transformation nlm[subscript s]m[subscript i] [left harpoon over right] nljm	290
Section 6	The transformation jjJM [left harpoon over right] SLJM	291
Chapter XIII	Configurations Containing Almost Closed Shells. X-Rays	295
Section 1	The electrostatic energy in LS coupling	295
Section 2	The spin-orbit interaction	299
Section 3	Pure almost-closed-shell configurations	300
Section 4	The rare-gas spectra	301
Section 5	The configurations p[superscript 5]s and d[superscript 9]s	304
Section 6	The configuration p[superscript 5]p in the rare gases	306
Section 7	The configuration p[superscript 5]d in the rare gases	312
Section 8	Line strengths	316
Section 9	X-ray spectra	316
Section 10	Line strengths in X-ray spectra	322
Section 11	X-ray satellites	323
Chapter XIV	Central Fields	327
Section 1	The periodic system	327
Section 2	The statistical method of Fermi-Thomas	335
Section 3	The Wentzel-Brillouin-Kramers approximation	339
Section 4	Numerical integration of the radial equation	344
Section 5	Normal state of helium	345
Section 6	Excited levels in helium	348
Section 7	Normal states of first-row atoms	351
Section 8	Hartree's self-consistent fields	354
Section 9	Survey of consistent-field results	358
Section 10	Self-consistent fields for oxygen	362
Chapter XV	Configuration Interaction	365
Section 1	Interaction of sd and p[superscript 2] in magnesium	366
Section 2	Perturbed series	367
Section 3	Auto-ionization	369
Section 4	Many-electron jumps	375
Section 5	Spin-orbit perturbation of doublet intensities	376
Chapter XVI	The Zeeman Effect	378
Section 1	The 'normal' Zeeman effect	378
Section 2	The weak-field case: Russell-Saunders terms	380
Section 3	Weak fields: general case	384
Section 4	Intensities in the Zeeman pattern: weak fields	386
Section 5	The Paschen-Back effect	388
Section 6	The Paschen-Back effect: illustrative examples	390
Section 7	Quadrupole lines	395
Chapter XVII	The Stark Effect	397
Section 1	Hydrogen	398
Section 2	Stark effect at the series limit	404
Section 3	General theory for non-hydrogenic atoms	409
Section 4	Helium	413
Section 5	Alkali metals	415
Chapter XVIII	The Nucleus in Atomic Spectra	418
Section 1	Effect of finite mass	418
Section 2	Local nuclear fields	420
Section 3	Nuclear spin in one-electron spectra	421
Section 4	The hyperfine structure of two-electron spectra	424
Section 5	Zeeman effect of hyperfine structure	426
Appendix	Universal Constants and Natural Atomic Units	428
	List of Principal Tables	434
	Index of Subjects	435
	Index of Names	439