The Doppler broadening of gamma-ray peaks due to nuclear recoil from beta-delayed nucleon emission can be used to measure the energies of the nucleons. The purpose of this Thesis is to test and apply this Doppler broadening method using gamma-ray peaks from the 26P(betapgamma) 25Al decay sequence. A fast beam of 26P was implanted into a planar Ge detector, which was used as a 26P beta-decay trigger. The SeGA array of high-purity Ge detectors was used to detect gamma rays from the 26P(betapgamma)25Al decay sequence. Radiative Doppler broadening in beta-delayed proton-gamma decay was observed for the first time. The Doppler broadening analysis method was verified using the 1613 keV gamma-ray line for which the proton energies were previously known. The 1776 keV gamma ray de-exciting the 2720 keV 25Al level was observed in 26P(betapgamma) 25Al decay for the first time and used to determine that the center-of-mass energy of the proton emission feeding the 2720-keV level is 5.1 +/- 1.0 (stat.) +/- 0.6 (syst.) MeV, corresponding to a 26Si excitation energy of 13.3 +/- 1.0 (stat.) +/- 0.7 (syst.) MeV for the proton-emitting level. The Doppler broadening method has been demonstrated to provide practical measurements of the energies for beta-delayed nucleon emissions populating excited states of nuclear recoils at least as heavy as A = 25.
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