Rapid fluctuation of the tensor polarization of deuteron beams behind carbon foils and their relation to the resonances in the isospin-breaking ¹²{rm C}(d,α₂)¹⁰{rm B}^(*) reaction

Rapid fluctuations are observed in the tensor-polarization $p_{zz}$ of deuteron beams forward-transmitted through graphite targets. Unpolarized 9.50 to 18.60\,MeV beams from the K\"oln tandem accelerator were utilized, and the polarization behind seven 36 to 188\,mg/cm$^{2}$ targets was measured with a polarimeter based on the $^{3}{\rm He}(\vec{d},p)^{4}{\rm He}$ reaction. Due to the chosen relation between the areal target densities and the initial beam energies $E_{\rm in}$, the seven sets of $p_{zz}(E_{\rm in})$ can be combined in a common plot as a function of $E_{\rm in}$. This allows one to understand $p_{zz}$, measured behind the 188\,mg/cm$^{2}$ target at $E_{\rm in}$=18.6\,MeV, as resulting from the sequence of differential polarization production $\Delta p_{zz}(E)/\Delta E$ during energy degradation in the target from $E$=18.60 to 9.50\,MeV. The rapid fluctuations of $\Delta p_{zz}(E)/\Delta E$$p_{zz}$ are described by 51 Gaussian-distributed cross-sections removing deuterons either in the $m=0$ or in the $m=\pm 1$ state from the beam. The 51 fitted central energies $E_{0}$ with a single exception agree with the energies of the narrow peaks in the excitation functions of the weak, isospin-breaking $^{12}{\rm C}(d,\alpha_{2})^{10}{\rm B}^{*}(1.74\,{\rm MeV},J^{\pi}=0^{+},T=1)$ reaction with population of the second excited $^{10}{\rm B}$ state via intermediate excited $^{14}$N states. Strong evidence is found that removal of deuterons in the $m=0$ ($m=\pm 1$) state from the beam leads to the formation of $^{14}$N states of established positive (negative) parity. As an application, the removal cross-section functions allow to calculate $p_{zz}$ achievable with carbon targets for initial beam energies $E_{\rm in}$ between 18.60 and 9.50\,MeV and $E_{\rm out}$ given by the areal target density. Carbon layers in a sandwich technique would enable $p_{zz}$ between -0.4 and +0.3.