Sec. 3.11] BETA PARTICLES 65 



If the proton or neutron that is transformed remains in nearly the same 

 quantum state after beta emission, Q is nearly unity. If the initial and final 

 quantum states are markedly different, Q is smaller than unity, and it is zero 

 when a transition between two states is impossible; i.e., the transformation of 

 a proton or neutron in state n to a neutron or proton in state m is forbidden. 

 For most light elements in which comparatively few states exist at ordinary 

 levels of excitation, it can be regarded generally as unity (or zero if it is 

 energetically impossible). The factor f(Z, E) includes the relativity correc- 

 tion and the appropriate wave function of the electron in the presence of the 

 strong coulomb field of the nucleus. 



In light elements /(Z, E) is of the order of unity; for Z = 0,/(O, E) = 1. 

 In heavy nuclei, however, this factor increases the probability for beta 

 emission by an order of magnitude over that for light nuclei emitting beta 

 particles of the same maximum energy. 



The Fermi theory provides for a continuous distribution in kinetic energy 

 for the ejected particles from zero to a maximum energy corresponding to the 

 total transition energy for the particular nucleus and the specific transition. 

 The most probable beta energy is found to be E /2, and near both zero 

 kinetic and the maximum energy very few particles are to be expected. A 

 difference in the numbers of positrons and beta particles should be found in 

 the low-energy end of the spectrum for medium and heavy elements because 

 of the strong effect of the nuclear coulomb field. Fewer low-energy positrons 

 will be observed since, once formed, they derive additional energy from the 

 repulsive electrostatic field. Conversely, a greater number of slow negative 

 particles are observed because faster particles lose energy to the field and are 

 then observed at relatively lower energy. 



Measurements of beta-energy spectra are sometimes complicated in radio- 

 isotopes in which two or more beta particles are emitted or when conversion 

 electrons (line spectra) are present (see Gamma Rays, Chap. 2). When a 

 nucleus can decay by one of several possible beta transitions, the observed 

 energy distribution is a superposition of the several Fermi curves [11]. 

 Conversion electrons, on the other hand, can be readily identified since 

 they form peaks with small energy spread and often high intensity super- 

 imposed on the continuous distributions. 



An approximate expression for the energy distribution when E < 2 mev 

 has been given in the form [12] 



PdE = AEHl + 2E)(1 + E)»(Eo - E) 2 dE 



where A = constant for each isotope 



A form more useful for plotting experimental data is to be found in the 

 reduced equation given by Kurie [13]. 



