Measurements have been made of high-energy neutron capture gamma ray spectra from the ¹⁰³Rh(n, gamma )¹⁰⁴Rh reaction for discrete resonances up to 850 eV and for unresolved regions up to 6 keV, with the aim of investigating the reaction mechanism. Spins of stronger resolved s-wave resonances up to 1272 eV were assigned using low-energy capture gamma rays, and in some cases also using high energy gamma rays. A value was obtained for the neutron binding energy, and a level scheme was constructed for ¹⁰⁴Rh states up to 1 MeV populated by primary transitions. The distribution of a sample of 1938 reduced partial radiation widths in spin 1 resonances were found. The averaged gamma -ray spectra up to 6 keV showed an enhancement in the region 6.0-6.2 MeV, confirming previous observations. No correlations were found between resonance reduced neutron widths and reduced partial radiation widths in any part of the gamma -ray spectrum.