Inner radiative corrections additional radiative

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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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This document was uploaded on 09/28/2013.

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