Unstable states in quantum many-body theory

Unstable states of a general type of many-body system characterized by a combination of outgoing waves and bound states in all channels are investigated. It is seen, that the time-development in general will contain both oscillating and exponentially decaying terms

On the Relativistic Description of the Nucleus

We present here a formalism able to generalise to a relativistically covariant scheme the standard nuclear shell model. We show that, using some generalised nuclear Green's functions and their Lehmann representation we can define the relativistic equivalent of the non relativistic single particle wave function (not loosing, however, the physical contribution of other degrees of freedom, like mesons and antinucleons). It is shown that the mass operator associated to the nuclear Green's function can be approximated with the equivalent of a shell-model potential and that the corresponding ``single particle wave functions'' can be easily derived in a specified frame of reference and then boosted to any other system, thus fully restoring the Lorentz covarianc

On the Relativistic Description of the Nucleus

We discuss a relativistic theory of the atomic nuclei in the framework of the hamiltonian formalism and of the mesonic model of the nucleus. Attention is paid to the translational invariance of the theory. Our approach is centered on the concept of spectral amplitude, a function in the Dirac spinor space. We derive a Lorentz covariant equation for the latter, which requires as an input the baryon self-energy. For this we either postulate the most general Lorentz-Poincar\'e invariant expression or perform a calculation via a Bethe-Salpeter equation starting from a nucleon-nucleus interaction. We discuss the features of the nuclear spectrum obtained in the first instance. Finally the general constraints the self-energy should satisfy because of analyticity and Poincar\'e covariance are discussed

Deep inelastic electron scattering on nuclei within a fully relativistic model

In a recent paper we have developed a theoretical frame suitable to handle finite systems in a fully covariant way preserving translational invariance. Further, we have also introduced the relativistic counterpart of the shell model displaying the same invariance properties. We apply now the above theory to a practical case, by investigating how a covariant single-particle description of a nucleus can be implemented on 4He , 12C and 16O and how the inelastic electron scattering, within the frame of the Plane-Wave Impulse Approximation (PWIA), can be recovered, still preserving the Poincaré invariance