The Li6(a,2a)d Reaction at 50 to 80 MeV

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Watson, John W.
Pugh, Howel G.
The Li6(a,2a)d reaction was studied at 50.4, 59.0, 60.5, 70.3 and 79.6 MeV bombarding energy. For each bombarding energy, several coincident energy spectra of the two emitted a-particles were measured. Special emphasis was placed on measuring spectra at pairs of angles where zero momentum (in the laboratory frame of reference) was possible for the residual deuteron. Using the constraints on three body kinematics, events corresponding to an a+ a+ d final state were selected from the coincident energy spectra. The cross section for these events was projected onto the E1 energy axis of the coincident spectra. The projected energy spectra were analyzed with the Plane Wave Impulse Approximation. From those points in the projected spectra which corresponded to zero deuteron recoil momentum, off-mass-shell a-a scattering cross sections were extracted. These were found to be in excellent agreement with free a-a scattering cross sections, if free cross sections for the final state center of mass energy of the two a's in the Li6 (a,2a)d reaction were chosen for the comparison. Off- mass-shell a-a cross sections were also extracted for data where the residual deuteron had a momentum of 30 MeV/c. These cross sections were also found to agree with free a-a scattering, but it was necessary to introduce an ad hoc shift in the a-a scattering angle to produce this agreement. Predictions of off-mass-shell a-a cross sections were made using a potential model. These indicate that the off-mass-shell cross section should indeed be very similar to the on-mass-shell cross section at the final state energy. Using the Plane Wave Impulse Approximation a momentum distribution for a's in Li6 was extracted from the experimental data. A cluster model for Li6 was devised to fit the binding energy and r.m.s. charge radius of Li6, as well as the 3s1 a-d scattering phase shift. For comparison with the experimental data, the momentum wave function of the a-particle in Li6 was calculated by taking the Fourier transform of the a-d relative motion. The theoretical and experimental momentum distributions were found to be in serious disagreement, both in magnitude and width at half maximum. By introducing a cut-off radius into the theoretical wave function, the discrepancies between theory and experiment were accounted for. It was also found, that if the cut-off radius is used as an adjustable parameter, then this Li6 wave function and reaction model explains the magnitudes and widths of the a-d relative momentum distributions determined from a wide variety of other reactions.