Corso di laurea in Fisica

 

 

X-rays and Diffraction Optics

 

The course of 48 hours is divided in two-parts.

The first part, of 35 hours, is dedicated to X-rays physics.

            Röntgen’s discovery of X-rays in 1895 launched a tool essential to the development of modern physics and to the verification of many of the predictions of quantum theory. Incredible is the influence exerted in fields as diverse as chemical physics, nuclear physics, solid state physics, medical physics, astrophysics.The course, conceived for a one semestre-course, would provide the basic arguments to the understanding of the X-ray physics, and provide some general background information useful to participate in the recent growing research activity of this field.

The lectures follow the scheme:

1. Introduction: historical description.
2. Elementary notions for technical use: The electromagnetic spectrum.Characteristics of the electromagnetic waves.  Production of X rays. Continuos X-rays. Characteristic X-rays. X-ray absorption. Filters. X-ray tubes. Detection of X-rays. Safety problems.
3. The photon: the duality: wave and particle. Relation between energy and momentum in special relativity.  Experiments with photons as particle and as wave. Corpuscular and wave mechanical interpretation. Compton scattering. Bremsstrahlung radiation. Pair annihilation. Scattering and diffraction experiments with photons.
4. Inertial systems. Field of a point charge at rest. Field of a point charge moving with uniform velocity. Radiation from an accelerated or decelerated charged particle. Transverse radiation field due to the acceleration of an electron at low velocity.
5. Maxwell equations. Coulomb potential. Retarded potentials. Lienard-Wiechert potentials.
6. Radiation from an accelerated charge. Radiation field at low velocity. Poynting vector. Larmor law. Radiation power in terms of electric dipole moment. Radiation field at relativistic velocity. Polarization of continuous X-rays.
7. Sommerfeld’s classical theory of the spatial distribution of continuous X-rays. Radiation in acceleration and in deceleration regimes. Frequency spectrum of continuous X-rays. Ultraviolet catastrophe.
8. Radiation experimental spectra and spatial distributions. Experimental measurement of Urley, of Kulenkampff, of Seeman, of Honerjager, of Harworth and Kirkpatrick, of Boersch et al.. Schortcomings of classical theory.
9. Kramer’s semiclassical theory. The correspondence principle. Spectral distribution of radiation from thin targets. The Thomson-Widdington law. Spectral distribution from thick targets.
10. Quantum mechanical considerations. Born approximation. Sommerfeld’s quantum mechanical treatment. Polarization of the X-ray spectrum.
11. Characteristic X-rays: Line emission. Moseley law. Classical oscillator model. Ionization function: classical theory, quantum theory, intensity. Ratio of characteristics to continuous radiation. Nomeclature of X-ray lines.
12. The synchrotron radiation. Historical notes. Synchroton radiation laboratories in the World. Main characteristics of the Electra  at Trieste and of the Europen Synchrotron Radiation Facility (ESRF) at Grenoble. Characteristics of the synchrotron radiation: time structure, angular distribution, frequency distribution. Relativistic expression of the Larmor law. Schwinger’s treatment of the radiation from high energy accelerated electrons; high frequency radiation by energetic electrons; radiation by an electron in uniform circular motion. Experimental measurements of Corson.
13. Bending magnets. Wigglers. Undulators. Historical notes. Charatcteristics of the radiation form such insertion devices: radiation brilliance, source size, source divergence, critical energy .
14. Natural sources of X-ray radiation. Commercial X-ray tubes for small research laboratories.
15. Interaction of X-rays with matter: photelectric effect, Compton scattering and the Klein-Nishina  cross-section.
16. Experimental techniques and method. X-rays detectors: emulsion plate, ionization chambers, gas caunters, scitillation detectors, solid state detectors.
17. Interaction of X-rays with matter:  free and damped oscillator, form and width of lines.
18. Scattering of X-rays. Classical theory of Thomson and Rayleigh (coherent) scattering. Compton (incoerent) scattering. Raman scattering. Plasmon scattering.
19. X-rays absorption: experimental techniques and fields of application.

20.  Complex dielectric constant. Refracticve index. Bragg equation. Measurement of refratctive index: the method of critical angle of refraction, of symmetrical reflection, of unsymmetrical reflection, of refraction in a prism.

21.  X-rays diffraction: experimental techniques and fields of application.

 

The second part of the lectures are dedicated to topics in Optics of the visible spectrum. Some arguments are known from the undergraduate school.

1. Wave motion. One dimensional waves. Harmonic waves. Phase velocity. The superposition principle.The complex representation. Plane waves. The one, two and three dimensional differential wave equation. Plane waves. Spherical waves, Cylindrical waves.
2. Superposition of waves. Linear response. Addition of waves: the algebraic method, the complex method. Standing waves. Addition of waves of different frequency: beats, group velocity. Anharmonic  periodic waves: Fourier series. Non periodic waves: Fourier integrals. Pulses and waves packets: the cosine wavetrain, frequency bandwidth. Coherence length. The discrete Fourier transform.
3. Polarization of light: linear, circular, elliptical. Natural light. Polarizers. Malus’s law. Dichroism: the wire-grid polarizer, dichroic crystals, polaroid. Birefringence: calcite, birefringent crystals, birefringent polarizers. Scattering and polarization: polarization by scattering, by reflection. The half-wave plate. The quarter-wave plate. Compensators. Polarization of polychromatic light. Optical activity.
4. Interference. Conditions for interference. Wavefront-splitting interferometers: Young’s experiment. Interferometers. Waveamplitude-splitting interferometers. The Michelson-Morley interferometer. The Mach-Zehnder interferometer.
5. Diffraction. The Huygens-Fresnel principle. Several coherent oscillators. Fraunhofer diffraction: single slit diffraction, double slit diffraction, many slits diffraction, circular aperture diffraction. Resolution of imaging systems. Diffraction grating. Fresnel diffraction. Diffraction by a slit. Diffraction by a narrow obstacle
6. Fourier optics. Optical applications.
7. Basic of coherence theory.