Nuclear structure issues determining neutrino-nucleus cross sections
Introduction
Several of the searches for neutrino oscillations involve measuring the interaction of neutrinos with the nucleus. A primary example is the recently announced evidence [1] for neutrino oscillations at Super-Kamiokande, which comes from comparing the ratio of muons to electrons created by the scattering of atmospheric neutrinos from oxygen in the Cherenkov water detector. Another detector based on neutrino-nucleus scattering is the Sudbury Neutrino Observatory (SNO) which will measure the interaction of 8B solar neutrinos with deuterium in heavy water. Both the Liquid Scintillator Neutrino Detector (LSND) and KARMEN experiments involve neutrino scattering from carbon in mineral oil. The search for neutrino oscillations (νμ→νe and ) at the BooNE experiment at Fermi Lab will be a search for νeC→e−N and quasi-elastic scattering. In addition to acting as a signal for neutrino oscillations, neutrino-nucleus reactions appear as background cross sections in these experiments and provide important checks on neutrino flux or detector efficiency. Crucial to all these experiments is our understanding of neutrino-nucleus scattering and our ability to predict the cross sections to sufficiently high accuracy.
Another field in which neutrino-nucleus scattering plays a significant role is that of nucleosynthesis. As the core of a massive star collapses to form a neutron star, the flux of neutrinos is so large that significant nuclear spallation occurs, despite the small cross-sections. It has been pointed out by Woosley et al. [2] that neutrinos of all flavors excite nuclei to particle unbound states through the neutral current, and the A(ν,ν′X)A′ reaction, or the ν-process, may be an important process for nucleosynthesis of a number of elements. The temperature of the neutrinos is flavor-dependent and is MeV and –5 MeV. This translates to transferring an average of 25 MeV of energy to the nucleus, with a Fermi–Dirac tail up to ∼80 MeV. Thus, an understanding of both the neutral-current excitation and the subsequent multi-particle breakup of the nucleus are needed.
Neutrino-nucleus scattering also plays an important role in r-process nucleosynthesis, which is responsible for the formation of half of the elements with A>70. In a stellar environment where a neutron gas exists alongside nuclei, neutron capture becomes the dominant mode for synthesizing medium and heavy mass nuclei. Under stellar conditions where the neutron capture rate is fast compared to β-decay, the conditions for the rapid or r-process, the nucleosynthesis rate becomes proportional to the the β-decay rate. The r-process is thought to take place in the expanding ‘hot bubble’ of a type II supernova, which would mean that the flux of neutrinos is sufficiently intense to cause significant neutrino-nucleus reactions. The competition between neutron capture and neutrino scattering can be used to determine the distance of the r-process site from the neutron star and to estimate the time scale for the process. Extracting information on the issues requires knowledge of the neutrino capture cross sections by the very neutron-rich nuclei lying along the r-process path.
The physics determining the various neutrino-nucleus cross sections of interest to particle and astrophysics varies with neutrino energy and with the structure of the nuclei involved. In this article we discuss the main nuclear physics issues involved and examine the dependence of the predicted cross-sections on models of nuclear structure.
Section snippets
Formalism
Neutrino absorption on the nucleus occurs through the charged-current of the weak interactionwhere the incoming flux is a beam of either neutrinos or anti-neutrinos, and the leptons are either electrons or muons or their anti-particles. The expression for neutrino absorption on the nucleus in terms of nuclear structure matrix elements has been derived by O'Connell [3] and by Walecka [4].where G is the weak interaction coupling
Atmospheric neutrinos
The most recent evidence (1) for neutrino oscillations comes from the anomaly in the number of μ- and e-type neutrinos reaching the Super-Kamiokande detector after being produced in the atmosphere by cosmic rays. The observed ratio of muons to electrons is about a factor of two less than expected. The addition of a significant zenith angle dependence in the ratio of muon to electron events, where muon neutrino coming from larger distances (zenith angle 90°) evidence larger depletion, while muon
Solar neutrino detection
Four of the five solar neutrino experiments involve detecting neutrino-nucleus reactions, namely, Homestake, SAGE, GALLEX, and SNO. At Kamiokande solar neutrinos are detected via neutrino–electron scattering. The neutrino-nucleus cross sections measured in these detectors have been examined in detail in [9]. For completeness we summarize the key issues involved here.
The primary source of neutrinos from the sun is the proton–proton burning chain, with an additional weaker source of neutrinos
Neutrino–Carbon scattering at LSND and KARMEN
At both LSND and KARMEN the signal for neutrino oscillations involves neutrino interactions in mineral oil (CH2), and understanding neutrino scattering from carbon is important for these experiments. The neutrino source at both these experiments comes from the decay of pions produced in the beam stop. The vast majority of the pions decay at rest producing one muon neutrino, muon anti-neutrino and electron neutrino. Of these only the electron neutrino has enough energy to cause a nuclear
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