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We have determined some of the phonon spectral parameters for Pu and Ga in the {open_quotes}stabilized{close_quotes} {delta} phase (fcc) of the Pu-3.6thinspat.thinsp{percent}thinspGa alloy by measuring the Doppler broadening of neutron resonances as a function of temperature. We find the mean phonon energy (first moment of the phonon spectrum) of Pu to be {l_angle}h{nu}{r_angle}=8.22{plus_minus}0.12thinspmeV and the second moment to be {l_angle}(h{nu}){sup 2}{r_angle}=(7.2{plus_minus}0.3){times}10{sup {minus}5}thinspeV{sup 2}. These moments and the value of the ({minus}1)st moment determined from Debye-Waller factors from neutron powder diffraction are consistent with a Debye model with a Debye temperature of 127.2{plus_minus}1.7thinspK. For Ga in the Pu-Ga alloy, {l_angle}h{nu}{r_angle}=16.3{plus_minus}1.4thinspmeV, which is slightly larger than the m{sup 1/2}-weighted value of 15.3 meV expected from the value for Pu (however, the measured value cannot be distinguished from the latter value within experimental error). These results show that Pu-3.6thinspat.thinsp{percent}thinspGa behaves very much like a Debye solid at ambient pressures and low temperature and that the Ga impurity experiences approximately the same (or a slightly stiffer) force field compared with the Pu it replaces. {copyright} {ital 1998} {ital The American Physical Society}