Resonant $\alpha$ scattering of ${}^6$He: Limits of clustering in ${}^{10}$Be

The structure of ${}^{10}$Be was studied via resonant $\alpha$-particle scattering of a neutron-rich ${}^6$He beam. A time projection chamber, PAT-TPC, was operated in an active-target mode to provide a gaseous ${}^4$He target and trace the beam and reaction products traversing its active tracking volume. This significantly lowered the detection threshold of reaction products at low energies. Elastic scattering, inelastic scattering to the ${}^6$He 2${}^{+}$ state, and the ${}^6$He($\alpha$, 2$n$)${}^8$Be reaction were measured below an energy of 6 MeV in the center-of-mass frame. Continuous spectra of excitation functions and angular distributions were obtained from unambiguously-identified recoiling $\alpha$ particles for the elastic and inelastic channels. While a resonance of the 4${}^{+}$ state at 10.15 MeV in ${}^{10}$Be previously reported was confirmed, no other resonances were identified in the elastic channel over the measured energy region. The results are in line with antisymmetric molecular dynamics calculations that predict the limits of $\alpha$ clustering in high-spin states due to a spin-orbit force.

Figure 1

Schematic drawing of the experimental setup of the PAT-TPC. The inset is a magnified view of the segmented anode pad plane of the Micromegas detector near the beam axis.

Figure 2

Identification of the secondary beam particles. (a) Scatter plot between the energy loss per unit length of beam path $dE/dz$ and the reaction position $z_{\mathrm{reac}}$. (b) Scatter plot between $dE/dz$ and the opening angle of reaction products ${\theta }_{\mathrm{lab}}^{\left(1\right)}+{\theta }_{\mathrm{lab}}^{\left(2\right)}$ for the events at $z_{\mathrm{reac}}<50$ mm. The gate to select ${}^6$He scattering is indicated.

Figure 3

TKE/nucleon vs ${\theta }_{\mathrm{lab}}$ plot for ${}^6$He $+$ $\alpha$ scattering at 15 MeV. Elastic scattering and inelastic scattering to the first 2${}^{+}$ state of ${}^6$He are denoted by the solid and dashed lines, respectively. Calculated curves are shown both for the recoiling $\alpha$ (thick blue) and scattered ${}^6$He (thin magenta) particles.

Figure 4

Scatter plot between $E_x^{\left(1\right)}$ and $E_x^{\left(2\right)}$. The events to the left of the solid lines were excluded from the analysis. The contents of the region inside the dashed lines are weighted by a factor of 3 for presentation purposes.

Figure 5

(a) Excitation-energy spectrum of ${}^6$He (unshaded histogram). The best-fit result (thin red line) is shown together with the contribution of the background from the ${}^6$He breakup reaction (thick green line). The spectrum in the shaded histogram was made by selecting backward scattering (${\theta }_{\mathrm{c}.\mathrm{m}.}>{90}^{\circ }$) with particle escape from the TPC. (b) Scatter plot of $E_x$ and $E_x^{\theta }$. $E_x^{\theta }$ is the excitation energy of ${}^6$He obtained from the angles of the two reaction products.

Figure 6

Total charge collected $Q_{\mathrm{total}}$ as a function of the location of the reaction vertex $z_{\mathrm{reac}}$. (a) Experimental data. The elastic events are clearly distinguishable near $Q_{\mathrm{total}}$ $=$ 15 MeV. Events above the locus of elastic scattering indicate pile up of beam particles. Only events inside the contour line were used in calculating the excitation function. (b) Simulated results for the decay into the $0^{+}$ ground state and (c) the 2${}^{+}$ state at 3.03 MeV of ${}^8$Be.

Figure 7

Excitation functions of ${}^6$He $+$ $\alpha$ scattering: (a) angle-integrated spectrum over ${\theta }_{\mathrm{c}.\mathrm{m}.}$ $=$ 65${}^{\circ }$–135${}^{\circ }$, and (b)–(h) spectra for 10${}^{\circ }$ angular bins. The data for elastic scattering are shown by the filled circles, while those for inelastic scattering to the 2${}^{+}$ state are shown by the open circles. The inelastic scattering data are scaled by a factor of 1.5. The dashed and dotted lines denote $E_{\mathrm{c}.\mathrm{m}.}$ $=$ 2.7 and 4.4 MeV, respectively.

Figure 8

Angular distributions of elastic ${}^6$He $+$ $\alpha$ scattering. The results of CRC calculations (solid lines) are compared to the data. The CRC results at the higher energy bins are also shown for reference with the dashed lines. The blue shaded areas denote the systematic errors from the ambiguities in the beam angle. The inset of (h) shows the data at $E_{\mathrm{c}.\mathrm{m}.}$ $=$ 2.7 (full circles) and 3.3 MeV (open circles) on a linear scale. The angles where the Legendre polynomials $P_L\left(\cos {\theta }_{\mathrm{c}.\mathrm{m}.}\right)$ for $L$ $=$ 4 and 6 become zero are denoted by the solid and dashed lines, respectively.

Figure 9

Angular distributions of inelastic ${}^6$He $+$ $\alpha$ scattering to the ${}^6$He 2${}^{+}$ state. The results of CRC calculations (solid lines) are compared with the data. The blue shaded areas denote the systematic errors from the ambiguities of the beam angle.

Figure 10

Angle-integrated excitation function for the ${}^6$He($\alpha$, 2$n$)${}^8$Be channel.

Figure 11

Plot of $E_x$ vs $J(J+1)$ for ${}^{10}$Be. The band members of the ground and the second 0${}^{+}$ states are shown by the circles and squares, respectively. The linear extrapolation using the 0${}^{+}$ and 2${}^{+}$ states is shown for each band. The horizontal lines at $J$ $=$ 4 denote predicted level energies of the 4${}^{+}$ member of the ground state band from the $\beta$-$\gamma$ constraint AMD method [24] (solid line), the variational AMD method [15] (dashed line), the four-body cluster model [21] (dotted line), the molecular orbital model [16] (dot-dashed line), the semimicroscopic algebraic cluster model [18], (double-dot-dashed line), and the multicluster generator coordinate method [19] (triple-dot-dashed line). The data of Refs. [16, 21] were obtained from the calculated values with respect to the threshold energy of 2$\alpha$ $+$ 2$n$ at 8.386 MeV. The shaded area denotes the energy domain covered by the present study.