Resonances in ${}^{14}\mathrm{C}$ observed in the ${}^4\mathrm{He}\left({}^{10}\mathrm{Be},\alpha \right){}^{10}\mathrm{Be}$ reaction

The $\alpha ({}^{10}\mathrm{Be},\alpha ){}^{10}\mathrm{Be}$ resonant scattering reaction has been measured at nine ${}^{10}\mathrm{Be}$ beam energies from 25 to 48 MeV, scanning out resonances in ${}^{14}\mathrm{C}$ from excitation energies of 13 to 24 MeV. Angular distribution measurements were used to assign the spin and parity of $5^{-}$ to resonances at $E_x=18.82\left(2\right)$ and 19.67(2) MeV and $6^{+}$ at $E_x=20.80\left(2\right)$ MeV. The data also strongly indicate a $3^{-}$ resonance at 17.32(2) MeV. The systematic uncertainty on the excitation energies is 175 keV. An $R$-matrix analysis has been performed for the excitation energy range 16.5 to 22 MeV. The data are discussed in terms of cluster bands in ${}^{14}\mathrm{C}$.

Figure 1

Experimental arrangement used in the measurements.

Figure 2

Resonant scattering yields for the nine different beam energies, following the correction for detection efficiency and normalization.

Figure 3

Excitation function averaged over all of the beam energies. The error bars reflect the standard deviations between the measurements that overlap in excitation energy.

Figure 4

Energy and angle of events in the second Lamp2 detector array for 32-MeV beam energy. The resonances at the excitation energies of 18.8 and 19.8 MeV are indicated for the case when the $\alpha$ particles are detected.

Figure 5

Energy and angle of simulated events in the second Lamp detector array for 32-MeV beam energy for the 18.8- and 19.8-MeV resonances, with $J^{\pi }=5^{-}$, showing (a) the locus for ${}^4\mathrm{He}$ nuclei and (b) that for ${}^{10}\mathrm{Be}$ nuclei.

Figure 6

Angular distributions for the peak at $E_x=18.8$ MeV for beam energies of 32 MeV (top) and 34 MeV (bottom). The experimental data (filled circles) are compared with simulated angular distributions for spins 4, 5, and 6. The experimental data are consistent with a spin of 5.

Figure 7

Angular distributions for the peak at $E_x=20.9$ MeV for a beam energy of 40 MeV. The experimental data (filled circles) are compared with simulated angular distributions for spins 4, 5, and 6. The experimental data are consistent with a spin of 6.

Figure 8

Angular distributions for the peak at $E_x=17.2$ MeV for a beam energy of 29 MeV. The experimental data (filled circles) are compared with simulated angular distributions for spins 2, 3, and 4. The data are most consistent with a spin of 3.

Figure 9

Angular distributions for the peak at $E_x=16.2$ MeV for a beam energy of 29 MeV. The experimental data (filled circles) are compared with simulated angular distributions for spins 1, 2, and 3. The data are most closely consistent with a spin of 1, though clearly other contributions are included.

Figure 10

Angular distributions for the peak at $E_x=15.4$ MeV for a beam energy of 29 MeV. The experimental data (filled circles) are compared with simulated angular distributions for spins 2, 3, and 4. The data are most closely consistent with a spin of 4, as indicated by the peak close to $7^{\circ }$.

Figure 11

$R$-matrix fit to the data in the region between $E_x=16.5$ and 22 MeV (red-solid and blue-dashed lines). The difference between the two fits is the inclusion of an additional $4^{+}$ state in the calculation shown by the red line. See Table 1 for the parameters of fits 1 and 2.

Figure 12

Energy spin systematics of resonances observed in the present measurements. Solid circles correspond to firm spin assignments, whereas open circles are tentative. The linear fit is to the solid points. The gradient and intercept are 116 keV and 15.84 MeV, respectively.