Study of Single Pion Production by Weak Charged Currents in Low-energy Neutrino $d$ Interactions

This paper gives the results of a study of single-pion production by the weak charged current utilizing the wide-band muon-type-neutrino beam at the Argonne Zero Gradient Synchrotron. The data were obtained from hydrogen and deuterium fillings of the 12-foot bubble chamber. The methods of event selection and separation from background are given as are the details of the corrections and systematic effects in the data sample. The energy-dependent cross sections and differential distributions are presented for the three single-pion production reactions ..nu..p..--> mu../sup -/p..pi../sup +/, ..nu..n..--> mu../sup -/p..pi../sup 0/, and ..nu..n..--> mu../sup -/n..pi../sup +/. An isospin decomposition shows that the ratio of I = 1/2 to I = 3/2 amplitudes is 0.68 +- 0.04 with a relative phase of (90.7 +- 4.6)/sup 0/ for M(N..pi..) mu../sup -/p..pi../sup +/, the characteristic mass of the nucleon axial-vector elastic form factor is measured to be 0.98/sup +0.06//sub -0.03/ GeV when analyzed within the context of the Adler model. The data are also compared to other parametrizations of the nucleon axial-vector form factor.