Searching for states analogous to the ${}^{12}\mathrm{C}$ Hoyle state in heavier nuclei using the thick target inverse kinematics technique

Identification of α-cluster states analogous to the ${}^{12}\mathrm{C}$ Hoyle state in heavier α-conjugate nuclei can provide tests of the existence of α condensates in nuclei. Such states are predicted for ${}^{16}\mathrm{O}$, ${}^{20}\mathrm{Ne}$, ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, etc., at excitation energies slightly above the multi- α-particle decay threshold but have not yet been experimentally identified. The thick target inverse kinematics (TTIK) technique can be used to study the breakup of excited self-conjugate nuclei into many α particles. The reaction ${}^{20}\mathrm{Ne}+\alpha$ was studied using a ${}^{20}\mathrm{Ne}$ beam at 12 MeV/nucleon from the K150 cyclotron at Texas A&M University. The TTIK method was used to study both single α-particle emission and multiple α-particle decays. Events with α multiplicity up to four were analyzed. The analysis of the three α-particle emission data allowed the identification of the Hoyle state and other ${}^{12}\mathrm{C}$ excited states decaying into three α particles. The results are shown and compared with other data available in the literature. Although the statistics for events with α-multiplicity four is low, the data show a structure at about 15.2 MeV that could indicate the existence in ${}^{16}\mathrm{O}$ of a state analogous to the ${}^{12}\mathrm{C}$ Hoyle state. Moreover, the reconstructed excitation energy of ${}^{24}\mathrm{Mg}$ for these events peaks at around 34 MeV, very close to the predicted excitation energy for an excited state analogous to the ${}^{12}\mathrm{C}$ Hoyle state in ${}^{24}\mathrm{Mg}$. The structure is further confirmed by the reanalysis of α-multiplicity-four events from a previous experiment performed at 9.7 MeV/nucleon with a similar, but lower granularity, experimental setup.

Figure 1

(a) Experimental setup. (b) Typical DE-E plot recorded during the experiment from the strip placed at 1.3° from the center of the entrance window. α particles were selected with a two-dimensional gate around the α-particle locus.

Figure 2

α-particle energy spectra measured per telescope. PACE4 and HIPSE calculations are also shown. Note that one of the quadrants in the E detector of the telescope placed at 11° was not working, so the counts in this telescope (d) are less than those in the telescope at −12° (a).

Figure 3

Differential cross section for resonant scattering in the center of mass frame. The black line shows the result of this work, the red line is from Ref. [26].

Figure 4

Correlation between kinetic energies of the two detected α-particles. Panel (a) shows the experimental data; panel (b) shows results of the HIPSE calculation after correcting for the energy loss in the gas; panel (c) shows the remainder when the events in panel (b) are subtracted from the data.

Figure 5

Distribution of relative energy of two detected α particles. The background estimates obtained by HIPSE, by PACE4, and by randomly mixing two α particles from different multiplicity-two events are also shown.

Figure 6

Relative energy of two α particles. Black solid line: Interaction point obtained from the reconstruction code. Red dashed line: Fixed interaction point at 27 cm from the window, corresponding to beam energy of 6 AMeV.

Figure 7

Relative energy of two α particles after background subtraction.

Figure 8

(a, c) $E1$ vs. $E2$ plot obtained after selecting the events corresponding to the decay of the ${}^8\mathrm{Be}$ in the ground state (a) and in the $2^{+}$ state at 2.9 MeV (c). (b, d) Kinetic energy of the ${}^8\mathrm{Be}$ in the ground state (b) and in the $2^{+}$ state at 2.9 MeV (d); background estimates from mixed events, PACE4, and HIPSE are also shown.

Figure 9

Excitation energy of ${}^{12}\mathrm{C}$ obtained from the α-multiplicity-three events. The backgrounds estimated by HIPSE, PACE4, and mixed events are also plotted.

Figure 10

Excitation energy of ${}^{12}\mathrm{C}$ obtained from the α-multiplicity-three events obtained after subtracting the background from the mixed events.

Figure 11

Experimental data. (a, c) Dalitz plots for the Hoyle state (a) and the ($3^{-}$) state (c) after background subtraction. (b, d) Relative energies of the three possible couples of α particles for the Hoyle state (b) and the ($3^{-}$) state (d). The blue solid line shows the smallest value of the relative energy, the green dotted line shows the biggest value and the red dashed line shows the middle value.

Figure 12

Monte Carlo simulation of the Hoyle state and the ($3^{-}$) state sequentially decaying through the ground state of ${}^8\mathrm{Be}$. The energy resolution of the relative energy is 50 keV. Panels same as for Fig. 11.

Figure 13

Reconstructed excitation energy of ${}^{16}\mathrm{O}$ obtained from the events with α-multiplicity four after subtracting the background estimated by mixing α particles from different events with multiplicity four. States measured by Freer et al. (Refs. [14, 32]) are also reported.

Figure 14

Reconstructed excitation energy of ${}^{16}\mathrm{O}$ obtained from the events with multiplicity four in the run with maximum beam energy 9.7 MeV/nucleon. States measured by Freer et al. (Refs. [14, 32]) are also reported.

Figure 15

Sum of the energies of the four detected α particles as a function of the reconstructed scattering angle of ${}^{16}\mathrm{O}$ in the laboratory frame.

Figure 16

Reconstructed excitation energy of ${}^{24}\mathrm{Mg}$ for the events in the 15.2 MeV peak with total kinetic energy less than 120 MeV.