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**Unformatted text preview: **corrections and effects due to ﬁnite momentum transfer have
been evaluated. From a theoretical standpoint, therefore, the
inverse beta decay cross section is well predicted, with uncertainties around Æ0:5%.5
The ability for measured beta decay rates to assist in the
evaluation of neutrino cross sections is not limited solely to
inverse beta decay. Beta decay transitions also play a pivotal
role in the evaluation of neutrino cross sections for a variety
of other target nuclei. Nuclei which relate back to superallowed nuclear transitions stand as one excellent example.
Isotopes that undergo superallowed Fermi transitions
(0þ ! 0þ ) provide the best test of the conserved vector
current (CVC) hypothesis (Gerstein and Zeldovich, 1956;
Feynman and Gell-Mann, 1958) and, if one includes measurements of the muon lifetime, the most accurate measurements of the quark mixing matrix element of the CabibboKobayashi-Maskawa matrix Vud (Hardy and Towner, 1999).
Typically, the value for Vud can be extracted by looking at the
combination of the statistical rate function (F ) and the partial
half-life (t) of a given superallowed transition. Because the
axial current cannot contribute in lowest order to transitions
between spin-0 states, the experimental F t value is related
directly to the vector coupling constant. For an isospin-1
multiplet, one obtains
jVud j2 ¼ K
;
2G2 ð1 þ ÁR ÞF t
F (37) where ÁR are the nucleus-independent radiative corrections in
0þ ! 0þ transitions and K is deﬁned as K 23 ln2=m5 ¼
e
ð8120:271 Æ 0:012Þ Â 10À10 GeVÀ4 s. The F t value from
various transitions are very precisely measured (down to the
0.1% level) to be 3072:3 Æ 2:0, while the radiative corrections
enter at the 2.4% level (Towner, 1998). The process is not
directly relatable to that of inverse beta decay because of the
lack of the axial form factor, but it provides a strong constraint
on the validity of the CVC hypothesis.
Even excluding neutron decay and superallowed transitions, beta decay measurements also play an important role in
5
Some caution should be taken, as currently the most accurate
value for the neutron lifetime is 6:5 away from the PDG average
value (Serebrov et al., 2005). Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 1315 the calculation of low-energy cross sections simply because
they represent a readily measurable analog to their neutrino
interaction counterpart. For example, the þ decay from 12 N
to the ground state of 12 C is often used to calibrate calculations of the exclusive cross section of 12 Cðe ; eÀ Þ12 N
(Fukugita, Kohyama, and Kubodera, 1988). In the case of
deuterium targets, the decay width of tritium beta decay
provides an extremely strong constraint on the d cross
section (Nakamura et al., 2001). Finally, though not least,
both allowed and forbidden Æ decays often allow a direct
measure of the Gamow-Teller contribution to the total cross
section. Comparisons of neutrino reactions on 37 Cl and the
decay p...

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