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Unformatted text preview: freedom into effective operators which are expanded in powers of some cutoff momentum. Such effective operators can then be related directly to some observable or constraint that fixes the expansion. In the case of d scattering, the expansion is often carried out as an expansion of the pion mass q=m . EFT separates the two-body current process such that it is dependent on one single parameter, referred to in the literature as L1;A . This low-energy constant can be experimentally constrained, and in doing so provides an overall regularization for the entire cross section. Comparisons between these two different methods agree to within 1%–2% for energies relevant for solar neutrinos (< 20 MeV) (Nakamura et al., 2001; Mosconi, Ricci, and Truhlik, 2006; Mosconi et al., 2007). In general, the EFT approach has been extremely successful in providing a solid prediction of the deuterium cross section, and central to the reduction in the theoretical uncertainties associated with the reaction (Adelberger et al., 2010). Given the precision of such cross sections, one must often include radiative corrections (Towner, 1998; Beacom and Parke, 2001; Kurylov, Ramsey-Musolf, and Vogel, 2002). D. Other nuclear targets So far we have only discussed the most simple of reactions; that is, scattering of antineutrinos off of free protons and scattering of neutrinos off of deuterium, both of which do not readily involve any bound states. In such circumstances, the uncertainties involved are small and well understood. But what happens when we expand our arsenal and attempt to evaluate more complex nuclei or nuclei at higher momenta transfer? The specific technique used depends in part on the type of problem that one is attempting to solve, but it usually falls in one of three main categories: (1) For the very lowest energies, one must consider the exclusive scattering to particular nuclear bound states and provide an appropriate description of the nuclear response and correlations among nucleons. The shell model is often invoked here, given its success in describing Fermi and Gamow-Teller amplitudes (Caurier et al., 2005). (2) At higher energies, enumeration of all states becomes difficult and cumbersome. However, at this stage one can begin to look at the collective excitation of the nucleus. Several theoretical tools, such as the random phase approximation (RPA) (Auerbach and Klein, 1983) and extensions of the theory, including continuous random phase approximation (CRPA) (Kolbe, Langanke, and Vogel, 1999), and quasiparticle random phase approximation (QRPA) (Volpe et al., 2000), have been developed along this strategy. (3) Beyond a certain energy scale, it is possible to begin describing the nucleus in terms of individual, quasifree nucleons. Techniques in this regime are discussed later in the text. Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 We first turn our attention to the nature of the matrix elements which describe the cross section amplitu...
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