Electromagnetic excitation: theory of Coulomb excitation with heavy ions

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North-Holland Pub. Co., 1975 - Science - 364 pages
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Ellipsometry is a unique optical technique of great sensitivity for in situ non-destructive characterization of surface (inter-facial) phenomena (reactions) utilizing the change in the state of polarization of a light-wave probe. Although known for almost a century, the use of ellipsometry has increased rapidly in the last two decades. Among the most significant recent developments are new applications, novel and automated instrumentation and techniques for error-free data analysis. This book provides the necessary analytical and experimental tools needed for competent understanding and use of these developments. It is directed to those who are already working in the field and, more importantly, to the newcomer who would otherwise have to sift through several hundred published papers. The authors first present a comprehensive study of the different mathematical representations of polarized light and how such light is processed by optical systems, going on to show how these tools are applied to the analysis of ellipsometer systems. To relate ellipsometric measurements to surface properties, use is then made of electromagnetic theory. Experimental techniques and apparatus are described and the many interesting applications of ellipsometry to surface and thin-film phenomena are reviewed. This reference work is addressed to researchers and students with a strong interest in surface and thin-film physics and optics and their applications. It is a must for libraries in the fields of solid state physics, physical chemistry, electro-chemistry, metallurgy and optical engineering.

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Contents

INTRODUCTION
1
SEMICLASSICAL EQUATIONS OF MOTION
14
Semiclassical picture
17
Smatrix formalism
21
Coupled differential equations
28
Coupled equations in Fourier components
33
Effect of highlying states
35
Effects of decaying states
38
The diagonalization procedure
175
The sudden approximation
178
Deviations from the sudden approximation
184
Deviations from the xapproximation
186
Excitation of two weakly coupled groups of states
187
Simultaneous and mutual excitation
189
Symmetrization of the parameters
191
CHAPTER VTI MULTIPLE EXCITATION OF VIBRATIONAL STATES
194

Symmetries invariances and coordinate systems
43
Parametrization of orbital motion
49
CROSS SECTIONS AND ANGULAR DISTRIBUTIONS
56
Polarization in Coulomb excitation
58
Angular distribution of gamma rays
63
Gamma cascades following Coulomb excitation
69
Perturbation of angular distribution
74
FIRSTORDER PERTURBATION THEORY
77
Classical orbital integrals
80
Excitation probabilities
89
Cross section and angular distribution
93
Magnetic excitation
108
Multipolemultipole excitation
115
Quantum mechanical effects
118
HIGHERORDER PERTURBATION THEORY
121
Double integrals
125
Excitation probabilities and cross sections
129
Angular distribution of gamma rays
131
Double excitations
134
Effects of static moments
149
Polarization effects
158
Higherorder perturbation theory
162
MULTIPLE EXCITATIONS
165
The coupled differential equations
168
Evaluation of the excitation amplitude
198
Vibrational excitation of spherical nuclei
201
Vibrational excitation of deformed nuclei
203
Classical treatment of vibrational excitations
206
MULTIPLE EXCITATION OF DEFORMED NUCLEI
210
Excitation in the sudden approximation
215
Excitation of the ground state band
217
Excitation of other rotational bands
222
Deviation from the sudden approximation
229
Classical treatment
233
Effects of higher multipole moments
235
QUANTUM MECHANICAL TREATMENT
237
Perturbation theory
241
The WKB approximation
248
Discussion of quantum mechanical corrections
257
APPLICATION TO EXPERIMENTS
263
TORBEN units
268
Projectile and target excitation
274
Range of parameters
277
Thick targets
285
APPENDICES
297
ALPHABETICAL LIST OF SYMBOLS
344
REFERENCES
359
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