Potential absence of observed $π^2$ linear-chain structures in $^{14}$O via $^{10}$C($α,α$) resonant scattering

TL;DR

This study tests the existence of a $\pi^2$ linear-chain rotational band in the mirror nucleus $^{14}$O by examining $^{10}$C($\alpha,\alpha$) elastic scattering in inverse kinematics using the TexAT active-target TPC. An $\mathcal{R}$-matrix analysis, incorporating mirror-shifted resonances from $^{14}$C and a Gaussian energy resolution, shows that the previously claimed $\pi^2$ chain states in $^{14}$C do not translate cleanly to $^{14}$O; notably, a strong $4^{+}$ state around 16.3 MeV would produce cross sections exceeding measurements unless its width is narrower than $\sim$10 keV, which is inconsistent with a highly clustered configuration. The results highlight potential spin-assignment ambiguities in non-zero-spin reactions and possible mirror-symmetry breaking or alternative explanations, emphasizing the difficulties in identifying broad, highly-deformed linear-chain states in high-level-density systems. The work suggests further experiments with spin-zero targets or a $^{14}$O beam to robustly test the mirror symmetry of such cluster configurations.

Abstract

Background: The preference for light nuclear systems to coagulate into $α$-particle clusters has been well-studied. The possibility of a linear chain configuration of $α$-particles would allow for a new way to study this phenomenon. Purpose: A rotational band of states in $^{14}$C has been claimed showing a $π^2$ linear chain structure. The mirror system, $^{14}$O, has been studied here to examine how this linear chain structure is affected by replacing the valence neutrons with protons. Method: A beam of $^{10}$C was incident into a chamber filled with He:CO$_2$ gas with the tracks recorded inside the TexAT Time Projection Chamber and the recoil $α$-particles detected by a silicon detector array to measure the $^{10}\mathrm{C}(α,α)$ cross section. Results: The experimental cross section was compared with previous studies and fit using R-Matrix theory with the previously-observed $^{14}$O states being transformed to the $^{14}$C using mirror symmetry. The measured cross section does not replicate the claimed states, with the predicted cross section exceeding that observed at several energies and angles. Conclusion: A series of possibilities are highlighted with the most likely being that the originally-seen $^{14}$C states did not constitute a $π^2$ rotational band with a potentially incorrect spin assignment due to the limitations of the angular correlation method with non-zero spin particles. The work highlights the difficulties in measuring broad resonances corresponding to a linear chain state in a high level density.

Figures (11)

• Figure 1: (Top) Schematic of the detector setup with distances between the window, active region of the TPC and the silicon forward wall denoted. (Bottom) Layout of the forward wall of detectors showing their horizontal and vertical offset with respect to the beam. Quadrants which were not used for data analysis (primarily due to detector issues) are indicated with an "X". The five colored regions (color online) show the separation of different detector quadrants to form five different angular ranges.
• Figure 2: Ionization chamber (IC) energy versus time plot showing the $^{10}$C coincident peak within the 2D gate (red dotted line). A small contaminant ($^{7}$Be) can be seen around an energy of 200 (arbitrary units) that is hence excluded.
• Figure 3: Identification of the charge of the recoil particle detected in the silicon detectors. The average energy loss in the Micromegas is compared to the energy deposited in the silicon detector. The band for Z=2 can clearly be seen against the Z=1 band as well as a weaker Z=3 band. The gate to select Z=2 is overlaid by a red dotted line.
• Figure 4: Top down (top panel) and side view (bottom panel) of a single $^{10}\mathrm{C}(\alpha,\alpha)$ scattering event with the interaction vertex inside of the Micromegas active region. The upright red triangle points (color online) show the fitted interaction vertex from the RANSChiSM algorithm and the silicon hit location is shown as an upside-down magenta triangle. The color scale denotes the energy deposition in the Micromegas with the lower dE/dx of the $\alpha$ (travelling left and down relative to the beam) being apparent.
• Figure 5: Channel selection plot for the elastic channel (red) versus the first-excited state (magenta) identified by analysing the interaction vertex location inside TexAT (relative to the start of the Micromegas) versus the energy of the $\alpha$-particle at the vertex for the outer detectors. An energy loss correction through the gas is applied to reconstruct the energy at the vertex. The solid lines show the expected behavior from kinematics for an $\alpha$-particle scattering at zero degrees with the dashed lines showing the 2D cuts that were applied to the data.