Large Longitudinal Spin Alignment of Excited Projectiles in Intermediate Energy Inelastic Scattering

We study the sequential breakup of $E/A=24.0\mathrm{MeV}$ ${}^7\mathrm{Li}$ projectiles excited through inelastic interactions with C, Be, and Al target nuclei. For peripheral events that do not excite the target, we find very large spin alignment of the excited ${}^7\mathrm{Li}$ projectiles longitudinal to the beam axis. This spin alignment is independent of the target used, and we propose a simple alignment mechanism that arises from an angular-momentum-excitation-energy mismatch. This mechanism is independent of the potential used for scattering and should be present in many scattering experiments.

Figure 1

Experimental distributions of excitation energy for the (a) ${}^7\mathrm{Li}$ projectile and (b) the ${}^{12}\mathrm{C}$ target.

Figure 2

(a) The efficiency-corrected angular correlations from the data for the entire angular range measured. (b) The definitions of angles $\psi$ and $\chi$ in the rest frame of ${}^7\mathrm{Li}$. (c) The Legendre polynomial contributions from the fit to the angular correlations projected onto the $\cos (\psi )$ axis. (d) The resulting extracted magnetic-substate distribution.

Figure 3

Equation (4) is plotted for $E^{*}=4.6\mathrm{MeV}$ and $R=5\mathrm{fm}$ (red dot-dash line). The predicted alignment from the cluster-model calculations in the angular range $5°<{\theta }_{\mathrm{CM}}<15°$ as a function of beam energy is also shown (black solid line). When $\mathrm{\Delta }L=2\hslash$ is allowed, the alignment disappears completely ($A=0$), corresponding to no tilting (left). For larger energies only tilting is allowed (right).

Figure 4

The most prominent Clebsch-Gordan coefficients from angular-momentum conservation in the squared transition amplitude, $|T_{m_i,m_f}{|}^2$, come from (a) exciting the internal motion of the $\alpha +t$ and (b) the relative angular momentum of ${}^7\mathrm{Li}+{}^{12}\mathrm{C}$. Results are shown for grazing $L_{\mathrm{in}}=L_{\mathrm{out}}=L_{\mathrm{graz}}=35$. Panel (c) shows the multiplication of the two. (d) The squared transition amplitude calculated by the cluster model normalized to the scale of panel (c). (e) The predicted alignment, as a function of angle, from cluster-model calculations for all $\mathcal{J}$ (red solid line) and for a single $\mathcal{J}=35.5$ (blue dashed line), as well as the data (circles). Panels (f) and (g) are normalized projections of panels (c) and (d), respectively, showing the predicted magnetic-substate distributions.