*This preview shows
page 1. Sign up
to
view the full content.*

**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...

View
Full
Document