In this work we perform quasiparticle-rotor coupling model calculations within the usual BCS and the projected BCS for the carbon isotopes 15C, 17C and 19C using 13C as the building block. Owing to the pairing correlation, we find that 13C as well as the cores of the other isotopes, namely 14C, 16C and 18C acquire strong and varied deformations. The deformation parameter is large and negative for 12C, very small (or zero) for 14C and large and positive for 16C and 18C. This finding casts a doubt about the purity of the supposed simple one-neutron halo nature of 19C.

The high momentum transfer electron-nucleus scattering cross section is evaluated within the plane wave impulse approximation (PWIA) supplemented by the relativistic Hartree approximation (RHA). Binding effects on the struck nucleon are introduced through the scalar and vector meson-exchange fields within the framework of quantum hadrodynamics. This model naturally satisfies the current conservation, with the off-shell nucleons behaving as being on the mass shell but having an effective mass. The nucleon inelastic response is included via different parameterizations of the structure function measured at SLAC, while the smearing of the Fermi surface is introduced through a momentum distribution obtained from a perturbative nuclear matter calculation. Recent CEBAF data on inclusive scattering of 4.05 GeV electrons on 56Fe are well reproduced for all measured geometries by the first time. Scaling effects are analyzed as well, and the scaling properties of the nuclear response in terms of the y variable associated to the PWIA within the RHA framework are discussed. The theoretical scaling function obtained in our approach also significantly improves previous PWIA calculations within the multi-GeV electron scattering regime, and describes properly the CEBAF scaling data.

The neutrino-nucleus cross-section and the muon capture rate are discussed within a simple formalism which facilitates the nuclear structure calculations. The corresponding formulae only depend on four types of nuclear matrix elements, which are currently used in the nuclear beta decay. We have also considered the non-locality effects arising from the velocity-dependent terms in the hadronic current. We show that for both observables in 12C the higher order relativistic corrections are of the order of ~ 4% only, and therefore do not play a significant role.

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak lambda-core coupling formalism. The hypernuclei are grouped having in view their A - 1 cores, that is in those with even-even, even-odd and odd-oddcores. It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates, gamman and gammap, which does not involve the spectroscopic factors. For the strangeness-changing weak lambda N ->N N transition potential we use the One-Meson-Exchange Model (OMEM), which comprises the exchange of the complete pseudoscalar and vector meson octets (pi, <FONT FACE=Symbol>h,</FONT>K<FONT FACE=Symbol>, r</FONT>, omega, K*).We evaluate ³H, 4H, 4lambdaHe, 5lambdaHe, 11B, 12lambdaC, 16lambdaO, 17lambdaO, and 28Si hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information. The calculated rates gammaNM = gamman + gammap are consistent with the data, but the measurements of gamman/p = gamman/gammap are not well accounted for by the theory. It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.