Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.
Neutrino-nucleus reactions at low energies play an important role in many phenomena in nuclear and particle physics, as well as astrophysics. These reactions present extremely subtle physical processes, not only because they involve the weak interaction, but also because they are very sensitive to the structure of nuclear ground states and excitations, i.e. to the solution of the nuclear many-body problem that includes the strong and electromagnetic interactions. The use of microscopic nuclear structure models in a consistent theoretical framework is therefore essential for a quantitative description of neutrino-nucleus reactions [1]. Detailed predictions of neutrino-nucleus cross sections are crucial for the interpretation of neutrino experiments, detection of neutrinos produced in supernova explosions and understanding the underlying nature of these explosions [2]. Neutrino-nucleus reactions which occur in a type II supernova could also contribute to the nucleosynthesis [3,4], but more data on cross sections are necessary for a more complete understanding of this process, as well as the supernova dynamics.
Data on neutrino-nucleus cross sections have been obtained by the LSND [5,6] and KARMEN [7,8,9] collaborations, and at LAMPF [10,11], but only for 12 C and 56 Fe target nuclei. New experimental programs are being planned which will provide essential data on the neutrino-nucleus reactions, and also help to improve the reliability of present cross-section calculations. These include the spallation neutron source (SNS) at ORNL, where neutrinos produced by pion decay at rest will enable measurements of cross sections for a wide range of target nuclei [12,13], and the promising “beta-beams” method for the production of pure electron neutrino-beams by using the β-decay of boosted radioactive ions [14,15]. Cross sections for neutrino energies in the range of tens of MeV could be measured, and these reactions are particularly interesting for supernova studies [16].
Weak interaction rates at low energies have been analyzed employing a variety of microscopic approaches, principally in the frameworks of the shell model [17,18,19], the random phase approximation (RPA) [20,21,22,23], continuum RPA (CRPA) [24,25,26,27,28], hybrid models of CRPA and shell model [29,30], and the Fermi gas model [31,32,33]. The shell model provides a very accurate description of ground state wave functions. The description of high-lying excitations, however, necessitates the use of large model spaces and this often leads to computational difficulties, making the approach applicable essentially only to light and medium-mass nuclei. For systematic studies of weak interaction rates throughout the nuclide chart, microscopic calculations must therefore be performed using models based on the RPA.
Hybrid models combine the shell-model and CRPA in such a way that occupation probabilities of single-particle states in a specific nucleus are determined by shell model calculations, and then inserted into the CRPA [29]. In general the CRPA employs different interactions for the calculation of the nuclear ground state (for instance, the Woods-Saxon potential), and in the residual CRPA interaction (G matrix from the Bonn potential, or the Landau-Migdal interaction), and thus additional parameters are required in order to adjust the calculated rates to data. A more consistent approach, based on the quasiparticle RPA with Skyrme effective interactions, has been employed in calculations of weak interaction rates [22]. Although in this framework the residual RPA interaction is derived from the same energy functional which determines the nuclear ground state, some terms are usually omitted, and pairing correlations require the adjustment of additional factors. A fully consistent theoretical framework for the description of charge-exchange excitations in open shell nuclei, based on Skyrme effective interactions, has only recently been developed [34], but not yet employed in the analysis of neutrino-nucleus reactions. Neutrino-nucleus cross sections have also been calculated using the ab-initio no-core shell model based on realistic NN and three-body interactions [35], and the shell model with an improved Hamiltonian which properly takes into account the spin-isospin interactions [36]. The importance of improved calculations of neutrino-nucleus cross sections for neutrino-oscillation studies has been demonstrated in the recent reanalysis of the LSND experiment [37], using the particle-number projected quasiparticle RPA [38], which has shown an enhancement of the neutrino-oscillation probability when compared to previous studies.
Although the general expressions for the transition matrix elements relevant for the calculation of neutrino-nucleus cross sections have been known since many years [39,40], it is only more recently that systematic calculations have been performed in open-shell nuclei by making use of modern effective interactions in the descript
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