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Applying Jarlskog's treatment of the CKM matrix, to the neutralino mass matrix in MSSM for real soft gaugino SUSY breaking and µ-parameters, we construct explicit analytical expressions for the four projectors which acting on any neutralino state project out the mass eigenstates. Analytical expressions for the neutralino mass eigenvalues in terms of the various SUSY parameters, are also given. It is shown that these projectors and mass eigenvalues are sufficient to describe any physical observable involving neutralinos, to any order of perturbation theory. As an example, the e − e + →χ 0 iχ 0 j cross section at tree level is given in terms of these projectors. The expected magnitude of their various matrix elements in plausible SUSY scenarios is also discussed.PACS number(s): 12.60.Jv † Partially supported by EU contracts HPMF-CT-1999-00363 and HPRN-CT-2000-00149.

For neutrinos of O(10keV) energies, their oscillation lengths are less than a few hundred meters, thereby suggesting the fascinating idea of oscillation experiments of small geometrical size. To help evaluating this idea, a formalism is developed for calculating the neutrino ionization cross sections for H as well as the noble atoms. This formalism is based on the use of spin-independent atomic wave functions, and should very accurately describe the ionization spectra for H, He, Ne and Ar. The accuracy is considerably reduced for the Xe case though, where the spin dependence in the wave functions is non-negligible. Nevertheless, even for Xe the results remain qualitatively correct. In all cases, the atomic ionizations cross section per electron is found to be smaller than the neutrino cross section off free electrons, approaching it from below as the energy increases to the 100 keV region. At the 10-20 keV range though, the atomic binding effects in the cross sections and the spectra are very important and increasing with the atomic number. They are cancelling out though, when total ionization cross section ratios, like ν µ /ν e orν µ /ν e , are considered.