Experimental study of high-lying states in ${}^{28}\mathrm{Mg}$ using the resonant elastic scattering of $\alpha$ particles

The excitation function of ${}^{28}\mathrm{Mg}$ above the $\alpha$-decay threshold has been measured for the first time using the resonant scattering of $\alpha$ particles with the technique of a thick target in inverse kinematics. Thirteen new states are reported between $E_x=15.5$ and $E_x=20.5$ MeV, and suggestions for spin-parity assignments are given for two of these. Calculations of the branching ratio to $\alpha$ decay for these states as well as comparison of the measured cross sections to calculations suggest that $\alpha +{}^{24}\mathrm{Ne}_{\mathrm{g.s.}}$ clustering is not dominant in this energy regime.

Figure 1

Schematic of the experimental chamber.

Figure 2

Comparison of the excitation function of ${}^{24}\mathrm{Mg}$ measured in this work at ${180}^{\circ }$ and of Ref. [25] measured at ${168}^{\circ }$. The latter is shown (a) unaltered and (b) after convolution with a resolution of 60 keV FWHM.

Figure 3

Excitation energy in ${}^{28}\mathrm{Mg}$, showing the calculated Rutherford cross section (green dashed line) that has been used for normalization. The inset shows detail of the resonances with a fit using overlaid Gaussian peak shapes (red solid line). The three regions that were used for normalization of the data are indicated with yellow shading. See text for details.

Figure 4

Comparison of excitation functions for ${}^{28}\mathrm{Mg}$ measured with four different beam energies, showing (a) the spectra normalized to each other using the Rutherford cross section between 13.1 and 14.0 MeV and (b) the differences between each of the lower beam energy spectra (green with dashed line, red with dot-dashed line, magenta with dotted line) and the spectrum with the highest beam energy (blue with solid line). For each spectrum, the highest available excitation energy is marked.

Figure 5

Energy of all $\alpha$ particles from ${}^{28}\mathrm{Mg}$ plotted against angle, measured with the coordinate origin placed at the entrance window. The data in the left-hand block are from the zero-degree detector, and those in the right-hand block are from the lamp-shade array. The software gates used to obtain angular distributions are shown; see text for details of the gating procedure.

Figure 6

Angular distribution for the state at 19.14 MeV (points with error bars), with simulated distributions (lines).

Figure 7

Angular distribution for the state at 18.14 MeV (points with error bars), with simulated distributions (lines).

Figure 8

$R$-matrix fit (red line) to the state (blue circles) at 19.14 MeV with $J^{\pi }=4^{+}$. A clear shoulder on the high energy side of the peak has been ignored in the fit. In the fitting region $(E_x=18.9–19.3$ MeV) ${\chi }^2/\text{d.o.f}=1.22.$

Figure 9

Calculated widths for the $\alpha$ and neutron channels, (a) ${\mathrm{\Gamma }}_{\alpha }$ and (b) ${\mathrm{\Gamma }}_n$, using the code gamow, as a function of the radius and diffuseness parameters $r_0$ and $a$. A horizontal red line shows the experimental value of ${\mathrm{\Gamma }}_{\alpha }$ (90 keV); the corresponding value for ${\mathrm{\Gamma }}_n$ found using an $R$-matrix calculation (150 keV) is not visible on this scale.