Introduction

The interaction between cosmic rays and the Galactic interstellar medium produces a non-thermal emission which is very intense in the high-energy gamma-ray band, making the Milky way the most prominent source in the sky at energies greater than 100 MeV.
Studies of gamma emission from the interstellar medium, by means of high-energy gamma-ray telescopes, provide important information on the distribution of both cosmic rays and interstellar medium. In particular observations with the EGRET instrument on board of the NASA Compton Gamma-Ray Observatory (CGRO) led to important conclusions concerning, for example, the galactic origin of cosmic rays. Nonetheless, many questions concerning the cosmic rays and interstellar medium components remain open. The gamma-ray telescope AGILE, to be launched in 2005 and operating in the band 30 MeV - 30 GeV and 15-45 KeV will be able to improve our knowledge of the gamma-ray diffuse emission, because of its large field of view (covering one fourth of the sky), and its angular resolution much better than that of previous instruments. In order to explain the observations of the diffuse gamma-ray emission a set of theoretical models is required to be considered in detail.
Moreover, the galactic diffuse gamma-ray emission represents a background component for the study of discrete gamma-ray sources, even at high galactic latitudes. The data analysis for any source in the gamma band requires a likelihood analysis, for which a model of the background due to galactic emission is a crucial input.
In chapters 1 and 2 of this thesis I describe the development of a model of the diffuse gamma-ray emission to be used in the forthcoming AGILE observations. This new model is represented by a 4-dimensional matrix g(l,b,r,E), in which the spatial coordinates map the whole Galaxy, while the fourth dimension gives, for each cell, the gamma emissivity spectrum. The latter is evaluated as the sum of different contributions due to three production processes (pp scattering, Bremsstrahlung and inverse Compton). The model is built first by obtaining the three-dimensional distributions of cosmic rays and of the components of interstellar medium relevant for the gamma-ray production: HI regions, molecular clouds and interstellar radiation field. Using these distributions, the emission spectra in the gamma-ray band for the three process are calculated, and finally the predicted intensity of the gamma-ray sky is obtained by integrating the gamma-ray emissivity along the line of sight.
In Chapter 3, I present an original method that I propose to extract information on the cosmic-rays galactic distribution from the diffuse gamma-ray observations. This technique uses the matter distribution obtained from the model presented in the previous chapters, but it does not assume any cosmic-ray distribution. It can therefore be used to test theoretical cosmic-ray models. This method, that we have tested on EGRET data, can be easily applied to future observations from other satellites.
In chapter 4, I describe the work done for the optimization of the AGILE science performance. In particular, I report on the development of techniques aimed at improving the angular and spectral resolution in the energy band 30 MeV - 30 GeV, and the development of techniques for the rejection of the particle background, an essential step in order to detect the diffuse gamma-ray emission of the Galaxy.