Angular distribution of stretched E2 transitions for Gaussian substate population of side feeding in (particle, xn γ) reactions

Abstract

In (particle, xn γ) reactions the population of magnetic substates of a given level of spin J in the ground state quasirotational band resulting from the preceding neutrons and gammas from outside the band (i.e. side feeding) can be described by a mixture of Gaussians of various widths. The resulting angular distribution of the stretched E2 (denoted E2 ) gammas with respect to the direction of the particle beam is analysed here. It is not approximated that an E2 transition from a Gaussian distribution of substates of level J produces a Gaussian distribution for the final level J−2. The ( A 2, A 4) results are discussed for a state populated by previous E2 transitions plus a single Gaussian side feeding. The results are extended to include side feeding producing substate populations of any mixture of Gaussians. A method of exact solution is given for cases where the experimental data are sufficiently accurate. The region of the ( A 2, A 4) space which can result from any mixture of Gaussian side feedings is derived. The results of various assumed substate populations of side feeding are compared to experiments by Newton et al. on 182W(α, 2n) 184Os, 165Ho( 11B, 4n) 172Hf and 159Tb( 14N, 5n) 168Hf. The comparison is quite satisfactory for single Gaussian side feeding of width σ = 2.8 for each level of spin J. The qualitative differences in the angular distributions for these experimental cases are caused by different experimental intensities of side feeding. For 74Ge(α, 2n) 76Se a width σ = 1.6+0.1 J gives good agreement with our experimental angular distributions of the transitions 10 → 8, 8 → 6, 6 → 4, 4 → 2 and 2 → 0. The angular distribution is also derived for a case where the population of substates increases with M.