beta_spectroscopy_sp_2010

beta_spectroscopy_sp_2010 - HOM, 12/14/05 Beta Spectrum...

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HOM, 12/14/05 1 Beta Spectrum Goal: to investigate the spectrum of β rays emitted by a 137 Cs source. The instrument used is a so-called 180 o magnetic spectrometer that separates β rays of different momenta by using a magnetic field. 1 Introduction 1.1 Beta decay The continuous spectrum of β rays (electrons) from a radioactive source is explained by the fact that with each β , also a neutrino ( υ ) is emitted, and the total decay energy is shared between them. The decay energy equals the largest possible β energy, T β ,max . The decay scheme of 137 Cs is shown in fig.1. + 2 / 11 + 2 / 7 Cs 137 55 E γ = 661.7 keV Ba 137 56 30 y 95% 5% T β ,max = 1176 keV T β ,max = 511.6 keV 2.5 ms Fig.1: decay scheme of 137 Cs (from Ref. [LED78]) The main β decay branch is to a meta-stable excited state of 137 Ba, which in turn decays by γ emission to the ground state. We ignore the much less probable (5%) β decay branch directly to the ground state. Competing with the γ decay of the meta-stable level is a process called ‘Internal Conversion’, in which the excitation energy is transferred to an atomic electron, which emerges with a discrete energy. The ratio between conversion electrons and gammas is called the conversion coefficient α . In our case, α = 0.092. In about 80% of the cases, a K-electron is converted. The rest mostly involves an L I electron, and the shells L II , L III , M, etc. play a minor role. The binding energy E B of a K (L B I ) electron in Ba is 37.4 keV (6.0 keV). The energy of the emitted conversion electrons is then T 137 conv = E γ – E B B . We expect two sharp peaks in the observed spectrum, corresponding to internal conversion with K- or L-shell electrons. 1.2 Charged particles in magnetic fields A particle of charge e , and momentum p , in a uniform magnetic field B travels on a circle with radius ρ . The following relationship holds ) ( ) ( 2998 . 0 ) / ( cm Gauss B c keV p ρ = (1) In our spectrometer, the radius ρ is fixed, and B is varied, to select a given momentum.
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The mass of the electron is m = 511 keV/c 2 . The kinetic energy is measured in keV. These units are non-S.I., but very practical (setting the speed of light c = 1). To convert energy to momentum, and vice versa, we use the relations m m p T + = 2 2 , mT T p 2 2 + = . (2) As an example for eqs. 1 and 2, an electron of T = 600 keV has a momentum of p = 986.5 keV/c. The field necessary to achieve a bending radius of 15 cm is B = 219 Gauss. 1.3
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beta_spectroscopy_sp_2010 - HOM, 12/14/05 Beta Spectrum...

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