Search for the high-spin members of the $\alpha :2n:\alpha$ band in ${}^{10}\mathrm{Be}$

Background: Clustering plays an important role in the structure of ${}^{10}\mathrm{Be}$. Exotic molecular-like configurations, such as $\alpha$:$2n$:$\alpha$, have been suggested at relatively low excitation energies.

Purpose: To search for the high-spin states that may belong to the molecular-like $\alpha$:$2n$:$\alpha$ configuration in ${}^{10}\mathrm{Be}$.

Method: Measuring excitation functions for ${}^6\mathrm{He}+\alpha$ scattering, populating states in the excitation energy range from 4.5 MeV to 8 MeV in ${}^{10}\mathrm{Be}$ using a ${}^6\mathrm{He}$ rare-isotope beam and a thick helium gas target.

Results: No new excited states in ${}^{10}\mathrm{Be}$ have been observed. Stringent limits on the possible degree of $\alpha$-clustering of the hypothetical yrast $6^{+}$ state have been obtained.

Conclusions: The high-spin members of the $\alpha$:$2n$:$\alpha$ molecular-like rotational band configuration, that is considered to have a $0^{+}$ band head at 6.18 MeV, either do not exist or have small overlap with the ${}^6\mathrm{He}$(g.s.)$+\alpha$ channel.

Figure 1

The energy-spin systematics for states in the $K^{\pi }=0_1^{+}$ and $K^{\pi }=0_2^{+}$ rotational band. The excitation energies are plotted as a function of the angular momentum $J(J+1)$.

Figure 2

(a) CAD rendering of the scattering chamber and detector set up. (b) Cross-sectional view of the set up. The silicon detectors plane, the beam stopper “Lollipop”, the proportional counter cells (indicated by numbers), the ionization chamber “IC”, and the scintillator are shown.

Figure 3

Scatter plot of the secondary beam energy deposition in the scintillator foil vs energy deposition in the ionization chamber. The region enclosed within the red contour represents the ${}^6\mathrm{He}$ ions. Tritium, the main contaminant in the secondary beam, can be observed at the bottom left.

Figure 4

Scatter plot of energy losses of the recoils in the proportional counter layers as a function of energy deposited in the Si detector. The first layer (a) of the proportional counter wires is used for an antigate (red contour) on the events associated with the ${}^6\mathrm{He}$ ions in the proportional counter cell. The antigated scatter plot for the second layer of the proportional counter wires is shown in (b). The events selected with the red contour in the second layer (b) are the recoil $\alpha$ particles.

Figure 5

$\alpha$-particle spectra for regions (a) and (b) of the silicon detectors. Region (a) corresponds to the inside quadrants of the outside two detectors, and region (b) corresponds to the outside quadrants of the outside detectors.

Figure 6

Total cross section for inelastic scattering (dash-dotted curve) and 90–180 ${}^{\circ }$ c.m. angle integrated cross section for elastic scattering (solid curve) produced by MinRMatrix calculations using the partial widths for the hypothetical $6^{+}$ state from Ref. [17] (Kuchera 2013).

Figure 7

Angular distribution for inelastic scattering (dash curve) and elastic scattering (solid curve) produced by MinRMatrix calculations using the partial widths for the hypothetical $6^{+}$ state from Ref. [17] (Kuchera 2013). This plot shows a prominent feature at angles close to ${180}_{\mathrm{c}.\mathrm{m}.}^{\circ }$.

Figure 8

Geant4 Monte Carlo simulations with parameters from Ref. [17] for the elastic (dashed red) and inelastic channels (dashed green), overlaid with this work's experimental spectrum (solid blue) shown in Fig. 5. The sum of the elastic and inelastic spectrum is represented by the dashed black curve. (a) Experimental, elastic, inelastic, and total spectra for region (a). (b) Experimental, elastic, inelastic, and total spectra for region (b).

Figure 9

MinRMatrix calculations using the spectroscopic factors provided by Kravvaris 2018, [24] to give the total cross sections of the elastic and inelastic channels. In the case of the elastic channel, forward angles were excluded from the calculations to omit the Rutherford contribution. These cross sections were fed into the Geant4 simulations, resulting in Fig. 10.

Figure 10

Geant4 Monte Carlo simulations with parameters from Ref. [24], overlayed with this work's experimental spectrum shown in Fig. 5. While the Geant4 simulations with parameters provided by Ref. [24] still far exceed the expected yield in this work's experimental spectra as shown here, this setup is still sensitive to the elastic and inelastic channel of the $6^{+}$ state. (a) Experimental (solid blue), elastic (dashed red), inelastic (dashed green), and total spectra (dashed black) for region (a). (b) Experimental (solid blue), elastic (dashed red), inelastic (dashed green), and total spectra (dashed black) for region (b).

Figure 11

Geant4 Monte Carlo simulations overlaid with this work's experimental spectra. The parameters used for the Geant4 simulations are consistent with the absence of the $6^{+}$ resonance. (a) Experimental (solid blue), elastic (dashed red), inelastic (dashed green), and total spectra (dashed black) for region (a). (b) Experimental (solid blue), elastic (dashed red), inelastic (dashed green), and total spectra (dashed black) for region (b).

Figure 12

Geant4 Monte Carlo simulations overlaid with this work's experimental spectra. The parameters used for the Geant4 simulations are ${\mathrm{\Gamma }}_{\alpha }/{\mathrm{\Gamma }}_{{\alpha }^{\prime }}=0.017$. This plot shows the experimental (solid blue), elastic (dashed red), inelastic (dashed green), and total spectra (dashed black) for region (a).