Inelastic electron scattering from the alpha particle☆

We consider the problem of quantizing a Skyrmion which is allowed to vibrate, rotate and isorotate. Previous approaches have neglected the interactions between vibrations and zero modes (analogous to so-called Coriolis terms in the molecular physics literature). A new formalism incorporating these interactions is introduced, inspired by a principal bundle approach to deformable-body dynamics. We quantize the $B=4$ and $B=7$ Skyrmions and compare the results to observed nuclear properties of Helium-4 and the Lithium-7/Beryllium-7 isospin doublet.

The cross sections of inelastic electron scattering on ⁴He leading to the quasi-bound state (0⁺, ε = 20.1 MeV) were measured in the momentum transfer range 0.8 fm⁻² < q² < 2.4 fm⁻². We found it to be a pure longitudinal transition and give the form factor of this C0transition.

The three-particle reactions ⁴He(d, d' t)¹H and ⁴He(d, d' d)²H were investigated at an incident energy of 52 MeV. The energy spectra of tritons and deuterons were measured simultaneously with inelastically scattered deuterons with two detectors, one at a fixed angle of 31° lab and the other at varied angles ranging from 20° to 38° lab. The data are interpreted in terms of six resonances arising in final-state interaction through T = 0 excited states of ⁴He. Only the lower three resonances are prominent in the data.

The extracted resonance parameters (energies and widths) are consistent with those obtained from measurements of similar reactions in two other different entrance channels. A summary of results from the present measurement and the two others is presented and compared with results from the phase-shift analysis. Singles spectra from the ⁴He(d, d')⁴He∗ reaction were also obtained and used in addition to the coincidence data in the analysis. The validity of the sequential reaction mechanism is examined.

The reaction ²⁰⁵Tl(α,t) ²⁰⁶Pb(g.s.) has been measured between 20 and 25 MeV α-energy, i.e. below and near the Coulomb barrier. It was possible to calculate the absolute experimental cross sections using a DWBA code with finite-range corrections provided that the (t+p) relative motion in the projectile is described by a Hulthén potential with $\text{β}\text{α}\text{= 1.55 ± 0.14}$. This leads to an experimental normalization of $\text{D}{}_0{}^{\mathrm{<mtext>exp</mtext>}}\text{(α,}\text{t}\text{) = −(272 ± 14)}\text{MeV}\text{·}\text{fm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, where the errors are due to uncertainties in the proton bound state potential parameters. A calculation of the theoretical normalization using only known properties of the α-particle leads to $\text{β}\text{α}\text{= 1.57 ± 0.02}$ and $\text{D}{}_0{}^{\mathrm{<mtext>th</mtext>}}\text{(α,}\text{t}\text{) = −(269 ± 2)}\text{MeV}\text{·}\text{fm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$. Using this value we deduce a proton bound state potential for the lead region of Woods-Saxon type with r₀ = 1.27 fm and a = 0.71 fm.

A possible extension of the general results of this analysis to all transfer reactions from projectiles with A ≦ 4 is discussed.

Excitation of the α-particle by inelastic electron scattering was studied at momentum transfers q < 0.5 fm¹. The assignment 0⁺ for the state at 20.10 ± 0.05 MeV (measured excitation energy) has been definitely established. The total width is 270 ± 50 keV, and the monopole matrix element 1.10 ± 0.16 fm². Evidence for the M2 resonance at 24 MeV is presented.