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Beta Spectrum

In the process of β-decay the changing of a neutron into a proton within the nucleus is accompanied by the ejection of an electron and an electron-antineutrino, which share the momentum and energy of the decay. There is a spectrum of energies for the electron depending upon what fraction of the fixed reaction energy (Q) it carries away. This total amount of reaction energy results from the total mass difference between the original atom (the decay mother) and the decay product atom (the decay daughter).

Empirical Beta Energy Spectrum of Bismuth 210


 

Experimental energy spectrum for decay electrons from 210Bi,

From G. J. Neary, Proc. Phys. Soc. (London), A175, 71 (1940).

From the Fermi theory of beta decay, the shape of the energy distribution for this "allowed" transition is given approximately by the expression

 

betadecayshape.png
 

where F(Z',Te) is called the Fermi function, Te here is the kinetic energy of the electron, C a collection of constants and mν the neutrino mass. The Fermi function accounts for the nuclear coulomb interaction which shifts this distribution toward lower energies because of the coulomb attraction between the daughter nucleus and the emitted electron (it shifts the distribution upward for positrons in β+ decay because they are repelled by the nucleus). Q represents the energy yield of the transition and as such is the upper bound on the kinetic energy of the electron.

The Q-values of many β-decays are well understood and accurately measured. The aim of AMBER is to measure the energies of the electrons in the high energy tail of the spectrum and compare this spectrum shape to that expected for the case of a zero neutrino mass. Any deviation consistent with a finite value for the neutrino mass, as given in the equation above, would be a strong indication for a measured neutrino mass value.

Adapted from Fermi Theory of Beta Decay by R. Nave, from Hyperphysics.

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