${}^{21}\mathrm{Ne}$ energy levels approaching the $\alpha$-particle threshold

Background: Nuclei around ${}^{20}\mathrm{Ne}$ exhibit an interplay of different excitations caused by different aspects of nuclear structure, including single-particle and multiparticle configurations and collective rotations. One-nucleon transfer reactions selectively probe single-particle structures in these nuclei. These nuclei are also important to astrophysics, with a number of important reactions proceeding through this mass region.

Purpose: Energy levels approaching the $\alpha$-particle threshold in ${}^{21}\mathrm{Ne}$ are of importance to nuclear structure. The ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction was measured and the corresponding spectroscopic nuclear information was extracted.

Method: States in ${}^{21}\mathrm{Ne}$ were populated using the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction in forward kinematics. Protons were identified in the Triangle Universities Nuclear Laboratory (TUNL) Enge split-pole spectrograph and angular distributions were extracted. Spin-party assignments were made and neutron partial widths were determined based on distorted-wave Born approximation (DWBA) analysis.

Results: Several new energy levels were observed at energies of 7176, 7235, 7250, and 7337 keV, and spin-parities are reported which generally agree with previous results where literature was available. Spin and parity assignments are reported for several energy levels along with estimated neutron widths for those states above the neutron threshold ($S_n=6761\mathrm{keV}$).

Conclusions: Results from this study are placed in context with a review of the available literature on all known states in this energy region of ${}^{21}\mathrm{Ne}$.

Figure 1

Energy deposited in $\mathrm{\Delta }E$ against front position on the focal plane detector for laboratory angle ${20}^{\circ }$.

Figure 2

Energy deposited in $\mathrm{\Delta }E$ detector against energy deposited in $E$ detector at a laboratory angle of ${20}^{\circ }$, ungated but with $\mathrm{\Delta }E\text{−}E$ gate shown.

Figure 3

Focal plane spectrum for protons at ${\theta }_{\mathrm{lab}}={10}^{\circ }$. Red indicates the carbon spectrum.

Figure 4

Focal plane spectrum for protons at ${\theta }_{\mathrm{lab}}={15}^{\circ }$. Red indicates the carbon spectrum.

Figure 5

Focal plane spectrum for protons at ${\theta }_{\mathrm{lab}}={20}^{\circ }$. Red indicates the carbon spectrum.

Figure 6

Focal plane spectrum for protons at ${\theta }_{\mathrm{lab}}={25}^{\circ }$. Note the contamination occurring from the $p(d,p)d$. Red indicates the carbon spectrum.

Figure 7

Focal plane spectrum for protons at ${\theta }_{\mathrm{lab}}={38}^{\circ }$. Red indicates the carbon spectrum.

Figure 8

A comparison of DWBA predictions for the 6609-keV state (assuming $2J^{\pi }=3^{-}$), made by varying the global nucleon potential [20] by $\pm 10\%$.

Figure 9

The differential cross section of the $E_{\mathrm{x}}=5.994$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=27.18$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=33.58$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=92.56$. The best fit for this energy level was $\ell =1$.

Figure 10

The differential cross section of the $E_{\mathrm{x}}=6.609$-MeV populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=99.11$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=11.64$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=46.78$. The best fit for this energy level was $\ell =2$. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.

Figure 11

The differential cross section of the $E_{\mathrm{x}}=6.753$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=95.05$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=19.94$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=2.54$. The best fit for this energy level was $\ell =3$. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.

Figure 12

The differential cross section of the $E_{\mathrm{x}}=6.901$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=15.08$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=1.27$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=4.79$. The best fit for this energy level was $\ell =2$. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.

Figure 13

The differential cross section of the $E_{\mathrm{x}}=7.108$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=130.90$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=0.9$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=1.42$. The best fit for this energy level was either $\ell =2$ or $\ell =3$, which could not be discriminated between. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.

Figure 14

The differential cross section of the $E_{\mathrm{x}}=7.176$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=82.02$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=9.67$, and (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=5.79$. The best fit for this energy level was $\ell =2$. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.

Figure 15

The differential cross section of the $E_{\mathrm{x}}=7.337$ MeV state populated in the ${}^{20}\mathrm{Ne}(d,p){}^{21}\mathrm{Ne}$ reaction. The displayed curves are (black) $\ell =1$ to populate a $J^{\pi }={\frac{3}{2}}^{-}$ state, with ${\chi }^2=77.27$, (green) $\ell =2$ to populate a $J^{\pi }={\frac{5}{2}}^{+}$ state, with ${\chi }^2=5.37$, (blue) $\ell =3$ to populate a $J^{\pi }={\frac{7}{2}}^{-}$ state, with ${\chi }^2=53.45$. The best fit for this energy level was $\ell =2$. The ${38}^{\circ }$ data point has been included in this plot but was not used in DWBA analysis.