W.J. Thompson

Direct and compound nuclear reaction mechanisms in 26Mg(p, p)26Mg

Abstract The reaction 26 Mg(p, p) has been studied for proton bombarding energies between 8.3 MeV and 14 MeV. Excitation functions measured in 30 keV steps at five backward angles showed pronounced fluctuations for the transitions into the different final states. The cross sections for the (p, p 0 ) (p, p 2 ) and (p, p 4 ) reaction have been analysed in terms of the various correlation functions of the statistical theory and compared with statistical-model predictions. Allowance was made for finite range of data errors. In general, the fluctuations were found to be damped by direct reaction contributions, the relative contributions of which were estimated for the elastic scattering by two methods. The first method used the variance of the fluctuating cross sections, whereas the second one employed an analysis of the energy-averaged angular distributions by means of the optical model plus Hauser-Feshbach estimates for the compound nucleus cross sections.

Coupled channel analysis of proton scattering from 19F

Abstract Elastic and inelastic differential cross sections measured for protons of incident energies 4.26, 5.96 and 6.87 MeV scattered from 19F are analysed using the adiabatic coupled channel (ACC) approximation. The scattering to the first two, positive-parity states ( 1 2 + and 5 2 + ) of the ground state rotational band are considered, the excitation of negative-parity states being negligibly weak. Using a quadrupole deformation β=0.37 determined from Coulomb excitation measurements, good fits to the 1 2 + and 5 2 + state differential cross sections are obtained by varying only the surface absorption potential with energy, all other parameters being fixed. Comparison with a spherical, optical-model analysis of the same data shows that the latter model overestimates the spin-orbit potential by a factor of 3 compared with the value obtained from the ACC analysis. The effect is related to the large deformation.

Angular correlation studies for α-particle excitation of the 1.78 MeV 2+ state in 28Si

Abstract The α-γ in-plane angular correlations of the reaction 28 Si(α, α 1 γ) 28 Si have been measured at 10, 12, 14 and 18 MeV. Correlations were obtained for c.m. scattering angles from 20° to 170° in 3° steps. Extracted angular-correlation parameters show a strong energy dependence, with a more rapid variation of the correlation pattern as a function of scattering angle with bombarding energy increase. Detailed coupled-channels analyses of the 18 MeV data with coupling of the first three excited states to the ground state of 28 Si were performed and a prolate deformation β R = 0.3 was deduced.

Dissipative forces and quantum mechanics

The dissipative forces of classical mechanics can be included in quantum mechanics by the use of non‐Hermitian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. The viscosity coefficient for a nuclear collision is estimated.

Optical‐model and coupled‐channels calculations in quantum‐mechanical scattering

Non‐Hermitian Hamiltonians are used in many research areas as approximate models of physical systems, for example, the optical‐model potential in nuclear physics. Such Hamiltonians are rarely treated in introductory quantum mechanics. Here the quantum scattering problem of a two‐state system is treated exactly for the case of one‐dimensional square‐well potentials. By introducing an appropriate optical‐model potential, an approximate solution for one of the two states is obtained. The exact and approximate solutions are compared for a realistic example.

Reaction-plane and spin-flip angular correlations in the reactions 12C(τ, τ1γ4.43)12C and 12C(α, α1γ4.43)12C

Abstract Reaction-plane particle-γ angular correlations were measured in the reaction 12 C(τ,τ 1 γ) 12 C at 17 MeV as a function of the γ-ray angle for forty-three τ (lab) scattering angles from 13.5° to 170°. The τ 1 -γ angular correlation function with the γ-ray detector at 90° to the reaction plane was measured for twenty τ (lab) angles from 19° to 114° and the spin-flip probability P 1 was extracted. For comparison of τ and α interactions, reaction-plane correlations were obtained for the 12 C(α, α 1 γ) 12 C reaction at 19 MeV for fifty-five α (lab) scattering angles from 9° to 171°. A coupled-channels analysis of the τ data assuming quadrupole-deformed collective states in 12 C with deformation β 2 = −0.60 was made. Spin-orbit depth V s.o. and β 2 are shown to be strongly correlated in determining P 1 , indicating the inadequacy of DWBA calculations.

Nuclear shapes of /sup 24/Mg and /sup 28/Si by inelastic scattering of /sup 12/C and /sup 16/ /sup 18/O

The measurement and analysis of the differential cross sections for the elastic and inelastic scattering to the lowest 2/sup +/ states of /sup 24/Mg and /sup 28/Si in the scattering of /sup 12/C at bombarding energies of 25 and 30 MeV are reported. In addition, elastic and inelastic scattering for /sup 16/O + /sup 24/Mg, /sup 16/O + /sup 28/Si, and /sup 18/O + /sup 28/Si, which had been measured previously, are reanalyzed. The analyses are carried out utilizing a coupled-channels code, and deformation lengths for /sup 24/Mg and /sup 28/Si are determined from the scattering of the different projectiles. The deformation lengths extracted from these analyses are compared with each other and with the results of a recently reported systematic investigation of deformation lengths in light nuclei.