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**Unformatted text preview: **rocess 37 Caðþ Þ37 K are prime example of this last
constraint technique (Aufderheide et al., 1994).
C. Theoretical calculations of neutrino-deuterium cross sections Next to hydrogen, no nuclear target is better understood
than deuterium. Neutrino-deuterium scattering plays an important role in experimental physics, as heavy water (D2 O)
was the primary target of SNO (Ahmad et al., 2001, 2002a,
2002b, 2004; Aharmin et al., 2005, 2007, 2008). The SNO
experiment is able to simultaneously measure the electron
and nonelectron component of the solar neutrino spectrum by
comparing the charged current and neutral-current neutrino
reactions on deuterium
e þ d ! e À þ p þ p ðcharged currentÞ; (38) x þ d ! x þ n þ p ðneutral currentÞ: (39) Results from the experiment allowed conﬁrmation of the
ﬂavor-changing signature of neutrino oscillations and veriﬁcation of the Mikheyev-Smirnov-Wolfenstein mechanism
(Wolfenstein, 1978; Mikheyev and Smirnov, 1989).
Deuterium with its extremely small binding energy
(Ebind ’ 2:2 MeV) has no bound ﬁnal state after scattering.
There exist two prominent methods for calculating such cross
sections. The ﬁrst method, sometimes referred to in the
literature as the elementary-particle treatment (EPT) or at
times the standard nuclear physics approach, was ﬁrst introduced by Fujii and Yamaguchi (1964) and Kim and Primakoff
(1965). The technique treats the relevant nuclei as fundamental particles with assigned quantum numbers. A transition
matrix element for a given process is parametrized in terms of
the nuclear form factors solely based on the transformation
properties of the nuclear states, which in turn are constrained
from complementary experimental data. Such a technique
provides a robust method for calculating d scattering.
Typically one divides the problem into two parts; the onebody impulse approximation terms and two-body exchange
currents acting on the appropriate nuclear wave functions. In
general, the calculation of these two-body currents presents
the most difﬁculty in terms of veriﬁcation. However, data
gathered from n þ p ! d þ scattering provide one means
of constraining any terms which may arise in d scattering.
An additional means of veriﬁcation, as discussed previously,
involves the reproduction of the experimental tritium beta
decay width, which is very precisely measured.
An alternative approach to such calculations has recently
emerged on the theoretical scene based on effective ﬁeld
theory (EFT) which has proven to be particularly powerful 1316 Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . . in the calculations of d scattering (Butler and Chen, 2000;
Butler, Chen, and Kong, 2001). EFT techniques make use of
the gap between the long-wavelength and short-range properties of nuclear interactions. Calculations separate the
long-wavelength behavior of the interaction, which can be
readily calculated, while absorbing the omitted degrees of...

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