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B. Neutrino capture on radioactive nuclei Neutrino capture on radioactive nuclei, sometimes referred
to as enhanced or stimulated beta decay emission, constitutes
another thresholdless mechanism in our library of possible
neutrino interactions. The process is similar to that of ordinary beta decay
A Z ! A Zþ 1 þ e À þ e ;
Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 (30) 1313 except the neutrino is interacting with the target nucleus
e þ AZ ! eÀ þ AZþ1 :
N À1 (31) This reaction has the same observable ﬁnal states as its beta
decay counterpart. What sets this reaction apart from other
neutrino interactions is that the process is exothermic and
hence no energy is required to initiate the reaction.3 The cross
section amplitude is directly related to that of beta decay.
Using the formalism of Beacom and Vogel (1999), the cross
section can be written as
G2 jV j2 FðZf ;Ee Þ
¼ F ud
Ee pe fV ð0Þ ð1 þ e cosÞ
þ 32 1 À e cos ;
where e and are the electron and neutrino velocities,
respectively, Ee , pe , and cos are the electron energy, momentum, and scattering angle, 2 is the axial-to-vector coupling ratio, and jVud j2 is the Cabbibo angle. The Fermi
function FðZf ; EÞ encapsulates the effects of the Coulomb
interaction for a given lepton energy Ee and ﬁnal-state proton
number Zf . We discuss the coupling strengths fV ð0Þ and
In Eq. (32), we no longer assume that ! c. If the
neutrino ﬂux is proportional to the neutrino velocity, then
the product of the cross section and the ﬂux results in a ﬁnite
number of observable events. If the neutrino and the nucleus
each possess negligible energy and momentum, the ﬁnal-state
electron is ejected as a monoenergetic particle whose energy
is above the end-point energy of the reaction.
The interaction cross section of very low-energy neutrinos
was ﬁrst suggested by Weinberg (1962). Recently, this process has attracted particular interest thanks to the work by
Cocco, Mangano, and Messina (2007), where they considered
the process as a means to detect cosmological neutrinos. The
reaction has received attention partially due to the advancement of beta decay experiments in extending the reach on
neutrino mass scales. The mechanism, like its coherent counterpart, remains to be observed.
IV. LOW-ENERGY NUCLEAR PROCESSES:
E $ 1–100 MeV As the energy of the neutrino increases, it is possible to
probe the target nucleus at smaller and smaller length scales.
Whereas coherent scattering only allows one to ‘‘see’’ the
nucleus as a single coherent structure, higher energies allow
one to access nucleons individually. These low-energy interactions have the same fundamental characteristics as those
of lepton scattering, though the manner in which they are
gauged and calibrated is very different. And, unlike the
thresholdless scattering mechanisms discussed previously,
these low-energy nuclear processes have b...
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