Alessandro Bettini

Status of the Germanium Detector Array (GERDA) in the search of neutrinoless ββ decays of 76Ge at LNGS

The Germanium Detector Array (GERDA) in the search for neutrinoless ββ decays of 76Ge at LNGS will operate bare germanium diodes enriched in 76Ge in an (optional active) cryogenic fluid shield to investigate neutrinoless ββ decay with a sensitivity of T1/2 > 2 × 1026 yr after an exposure of 100 kg yr. Recent progress includes the installation of the first underground infrastructures at Gran Sasso, the completion of the enrichment of 37.5 kg of germanium material for detector construction, prototyping of low-mass detector support and contacts, and front-end and DAQ electronics, as well as the preparation for construction of the cryogenic vessel and water tank.

Oscillations of Systems with One Degree of Freedom

Oscillations are periodic or quasi-periodic motions, or, more generally, the evolution, of a large number of physical systems, which may be very different from one another. However, the principal characteristics of the oscillatory phenomena are similar. This is because the differential equation describing those systems is the same. In this chapter, we study the oscillations of systems with one degree of freedom, both mechanical and electric. We deal with free, damped and forced oscillations and study the resonance phenomenon.

Diffraction, Interference, Coherence

In this chapter, we study different types of interference phenomena. Interference happens when two or more waves having a phase relation with one another fixed in time overlap in a region of space. We study Young’s two-slit experiment and then the coherence conditions, namely the conditions that must be satisfied for interference phenomena to be observable. After having introduced diffraction with Grimaldi’s discovery, we treat the phenomenon under Fraunhofer conditions in the important cases of the slit, the circular aperture, randomly distributed centers and the diffraction grating. Finally, we study the close relations between the physics of diffraction and the mathematics of the Fourier transform.

Images and Diffraction

In this chapter, we discuss two subjects in which diffraction is the dominant process in image formation. The first argument, developed in the first two sections, is the Abbe theory of image formation. The theory is valid in general, but is easier to understand under conditions of coherence. The second argument, developed in the subsequent sections, deals with those actual three-dimensional images known as holograms. In a hologram, both the amplitude and the phase of the wave produced by the object are recorded, using coherent illumination.

Oscillations of Systems with Several Degrees of Freedom

In the first part of this chapter, we study oscillating systems with two (and subsequently with n) degrees of freedom. We learn the existence of particular motions, the normal modes, in which all parts of the system oscillate together harmonically. The number of modes, and the number of resonances, is equal to the number of degrees of freedom. We then study the modes of a vibrating sting. In the second part of the chapter, we study Fourier analysis, in regard to both periodic and non-periodic functions and for functions of both time and space.

Magnetic Properties of Matter

This chapter deals with the magnetic properties of matter. We consider three classes of material: diamagnetic, paramagnetic and ferromagnetic. Two new vector fields are introduced, needed to describe magnetism in matter: magnetization, which is the magnetic moment per unit volume, and the auxiliary H-field. The latter is somewhat similar to the D-field in electricity but its role is much more relevant. The magnetic phenomena in matter are due to the behavior of the atomic and molecular constituents. Even if the correct laws are those of quantum physics, we try to give an approximate classical description. We conclude with a discussion of ferromagnetic materials and their uses.

Microscopic Interpretation of Thermodynamics

Thermodynamics and statistical mechanics give complementary descriptions of the physical processes, from a macroscopic and microscopic point of view respectively. Matter is made of an enormous number of molecules. Statistical mechanics starts from the laws of mechanics to extract the equations governing the mean values of the molecular kinematical quantities and their statistical distributions. We develop the kinetic model of gases and learn the physical meaning of pressure and internal energy. We experimentally control the predictions of the model and see how classical mechanics reaches its validity limits. We study the molecule kinetic energy and velocity distributions, and the fundamental Boltzmann law. We finally demonstrate the physical reasons of why microscopic phenomena are reversible, macroscopic ones are not and understand the physical meanings of entropy and of the second law of thermodynamics.

Thermodynamic Properties of Real Fluids

The ideal gas studied in the previous chapters is a very useful idealization, but does not exist in nature. The molecules are small but have non-zero dimensions and exert forces on one another, called van der Waals forces. Consequently, at low temperatures or high pressures real gases behave very differently from ideal ones up to the point to change aggregation phase and become liquid. We shall see how a state equation, the van der Waals equation, approximately describes the real fluids. We shall then study the aggregation phase transitions. In the final sections we deal with the capillary phenomena, which appear at the interfaces between different aggregation phases, finally treating boiling and vaporization..

Space, Time and Motion

Physical laws must always be experimentally verified. Experiment is the sole judge of the scientific truth. Consequently, any physical quantity must be measurable, namely the set of operations to be performed to measure it must be defined. In particular, a system of units of measurement must be defined. The International Unit system will be described. The mathematical properties of vectors will be discussed. In the second part of the chapter we shall deal with the kinematics of the point like particle, namely the study of its motion, independently of its causes. We shall introduce the vector quantities velocity, angular velocity and acceleration.

Dynamics of a Material Point

In this chapter we study the dynamics of the material point, namely the laws governing motion to its causes, which are the forces. These laws were discovered by Galilei and by Newton and assumed by Newton as postulates in his development of mechanics. After having operationally defined the concept of force, we shall state the three laws of Newton. We shall study the motion of pendulums and see the equivalence of inertial and gravitational mass. We shall introduce the concepts of work and of kinetic and potential energies and meet the fundamental law of energy conservation.