Invariant-mass spectroscopy of ${}^{10}\mathrm{B}, {}^{11}\mathrm{C}, {}^{14}\mathrm{F}, {}^{16}\mathrm{F}$, and ${}^{18}\mathrm{Na}$

The invariant-mass method is used to study the structure of a number of light proton-rich isotopes utilizing fast beams. Reactions where the projectile picks up a proton have been used to study $d$-wave resonances in ${}^{14}\mathrm{F}, {}^{16}\mathrm{F}$, and ${}^{18}\mathrm{Na}$. While the ${}^{16}\mathrm{F}$ and ${}^{18}\mathrm{Na}$ results are consistent with previous studies, the ${}^{14}\mathrm{F}$ results are not consistent with the only previous work. We have tentatively identified the $4^{+}$ member of a rotational band in ${}^{10}\mathrm{B}$, which is the analog of well-known states with strong $\alpha$-cluster structure in ${}^{10}\mathrm{Be}$ and ${}^{10}\mathrm{C}$. Finally, spin and parities of newly observed states in ${}^{11}\mathrm{C}$ which decay sequentially into three-body exit channels have been determined or restricted.

Figure 1

Results from an invariant-mass study of ${}^{15}\mathrm{O}+p$ events produced with the mixed ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beam. (a) Laboratory velocity distribution of the reconstructed ${}^{16}\mathrm{F}$ parents. For comparison, the arrows show the velocities of the two beam components taking into account their energy loss in traversing 1/2 the target thickness. (b, c) Distributions of the ${}^{16}\mathrm{F}$ excitation-energy quantity $E_{n\gamma }^{*}$ gated on the two beam components. To improve resolution only $|cos{\theta }_H|<0.2$ events are histrogrammed. Red curves show joint fits to these distribution including contributions from the four low-lying states at their tabulated widths (dotted green curves). The dotted magenta curve in (b) shows the contribution from inelastically scattered ${}^{17}\mathrm{Ne}$ fragments ($E^{*}=1.749$ and 2.65 MeV) that undergo sequential two-proton decay. Appropriately scaled components with $\approx 5.2$-MeV $\gamma$ rays in the exit channel are shown in (b) and (c) (cyan curves). For these components the invariant-mass deduced energy $E_{n\gamma }^{*}$ is less than the total excitation energy by the $\gamma$-ray energy. The dashed blue curve in (c) is the background from promptly emitted protons and the dotted green curves show contributions from individual levels.

Figure 2

(a) Doppler-corrected spectrum of $\gamma$-ray energies found in coincidence with the ${}^{15}\mathrm{O}+p$ events from both beam components. The location of some known ${}^{15}\mathrm{O}\gamma$ rays are indicated with the arrows. The gate used to select events associated with the $E_{\gamma }=5.183/5.241$-MeV doublet is indicated. (b) Spectrum of the ${}^{16}\mathrm{F}$ excitation-energy quantity $E_{n\gamma }^{*}$ in coincidence with the $E_{\gamma }=5.183/5.241$-MeV $\gamma$-ray doublet and for $|cos{\theta }_H|<0.2$ is shown by the red data points. The blue data points are an estimate of the background obtained from downscaling the ungated excitation spectrum.

Figure 3

Distributions of the background-subtracted excitation-energy quantity $E_{n\gamma }^{*}$ for events in coincidence with the $E_{\gamma }=5.183/5.241$-MeV $\gamma$-ray doublet and for $|cos{\theta }_H|<0.2$. (a) is associated with reactions produced by the ${}^{17}\mathrm{Ne}$ beam component while (b) is for the ${}^{15}\mathrm{O}$ beam component.

Figure 4

Comparison of reconstructed velocity distributions of the ${}^{16}\mathrm{F}$ parent for $d_{5/2}$-wave resonances ($2^{-}$ and $3^{-}$, red curve) to that for the newly observed level at $E_{n\gamma }^{*}=0.249$ MeV (black data points). The latter is background subtracted and corrected for the $\gamma$-ray efficiency. The arrow indicates the velocity of the ${}^{17}\mathrm{Ne}$ beam component.

Figure 5

Comparison of levels of interest in the mirror pair ${}^{16}\mathrm{F}$ and ${}^{16}\mathrm{N}$ including daughter levels associated with their decay. In order to highlight Thomas-Erhman shifts, the zero energy on the $y$ axis is based on the average of the $2^{-}$ and $3^{-}$ states, both of which lack significant proton (neutron) $s_{1/2}$ strength in ${}^{16}\mathrm{F}$ (${}^{16}\mathrm{N}$). The two new states observed in this work have arrows showing their proton decay to the $E^{*}=5.183/5.241$-MeV doublet in ${}^{15}\mathrm{O}$.

Figure 6

Results from the invariant-mass study of ${}^{17}\mathrm{Ne}+p$ events produced with the mixed ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beam. (a) Laboratory velocity distribution of the reconstructed ${}^{18}\mathrm{Ne}$ parents. For comparison, the arrows show the velocities of two beam components in the center of the target. (b) ${}^{18}\mathrm{Na}$ decay-energy distributions. To improve resolution only $|cos{\theta }_H|<0.2$ events are histrogrammed. The red curve is a fit to this distribution with two levels of Breit-Wigner intrinsic line shape (dotted curved curves) plus a smooth background component (dashed blue curve). The arrows indicate the energies of the $2_1^{-}$ and $3_1^{-}$ states from Assié et al. [33].

Figure 7

Results from an invariant-mass study of ${}^{13}\mathrm{O}+p$ events produced with the ${}^{13}\mathrm{O}$ beam. (a) Laboratory velocity distribution of the reconstructed ${}^{14}\mathrm{F}$ parents. For comparison the arrow shows the velocity the beam after traversing 1/2 the target thickness. (b, c) Experimental ${}^{14}\mathrm{F}$ decay-energy distributions are given by the data points. To improve resolution only $|cos{\theta }_H|<0.5$ events are used to construct these distributions. The red curves show fits to this distribution including only contributions from (b) three and (c) five levels. Fitted contributions from individual levels are shown by the dotted green curves and in (c) a smooth background (dashed blue curve) was necessary to improve the fit at the largest $Q_p$ values. The deduced states from the proton scattering study [6] are indicated by arrows in (b).

Figure 8

Results from an invariant-mass study of ${}^6\mathrm{Li}+\alpha$ events produced with the mixed ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beam. (a) Spectrum of $\gamma$-ray energies recorded in coincidence with these events which have been Doppler corrected relative to the measured ${}^6\mathrm{Li}$ velocity vector and addback from neighboring crystals has been implemented. The gate on the 3.563-MeV $\gamma$ ray is indicated. (b) Distribution of the excitation-energy quantity $E_{n\gamma }^{*}$ with this $\gamma$-ray gate (black histogram). The contribution from the background events is shown as the green histogram. The background-subtracted spectrum is given by the red histogram. These excitation-energy spectra were produced with no gate on $cos{\theta }_H$. The black arrows locate peaks associated with proton decay of known ${}^{10}\mathrm{B}$ states to the ground state of ${}^6\mathrm{Li}$. The red arrows locate the peaks remaining after the background is subtracted.

Figure 9

Background-subtracted ${}^6\mathrm{Li}+\alpha +\gamma$ invariant-mass spectrum. The red curve shows the fit which contains two levels (green dotted curves) plus a smooth background (dashed blue curve).

Figure 10

Histogram shows the excitation-energy distribution determined from the invariant mass of ${}^9\mathrm{Be}+p$ events. If the two peaks in our ${}^6\mathrm{Li}+\alpha +\gamma$ distributions are $2^{+}$ and $1^{-}$ states, then from the branching ratios of [40] and our simulated detection efficiencies, their expected yields in the ${}^9\mathrm{Be}+p$ channel are shown by the solid curves. The dashed red curve shows the maximum yield possible for the possible $1^{-}$ state.

Figure 11

Comparison of analog rotational bands in ${}^{10}\mathrm{C}, {}^{10}\mathrm{B}$, and ${}^{10}\mathrm{Be}$. The quantity $\mathrm{\Delta }{E}^{*}$ is the excitation energy relative to the first $T=1, J^{\pi }=0^{+}$ state. The rotational bands built on these states have smaller moments of inertia compared to that for the second $0^{+}$ states.

Figure 12

Excitation-energy distributions obtained for intermediate states in the decay of ${}^{11}\mathrm{C}$ parent states. (a) is obtained from the ${}^6\mathrm{Li}+\alpha$ subevents of detected ${}^6\mathrm{Li}+\alpha +p$ events while (b) is for the two $\alpha +{}^3\mathrm{He}$ subevents of detected $2\alpha +{}^3\mathrm{He}$ events. These data were obtained from the experiment with the ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beam. Gates are shown for which projected ${}^{11}\mathrm{C}$ spectra are presented in Figs. 13, 15, and 16.

Figure 13

Excitation-energy spectra for ${}^6\mathrm{Li}+\alpha +p$ events where there is a ${}^{10}\mathrm{B}(3^{-}$) intermediate state. Results shown were obtained with (a) ${}^{13}\mathrm{O}$ and (b) ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beams. Fits to these data (solid red curves) are shown where the smooth fitted backgrounds are given by the dashed blue curves.

Figure 14

Level scheme of ${}^{11}\mathrm{C}$ showing the states observed in this work and their decay paths.

Figure 15

Excitation-energy spectra for ${}^6\mathrm{Li}+\alpha +p$ events where there is a ${}^{10}\mathrm{B}(2^{\pm }$) intermediate state. Results shown were obtained with (a) ${}^{13}\mathrm{O}$ and (b) ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beams. Fits to these data (solid red curves) are shown where the fitted backgrounds are given by the dashed blue curves.

Figure 16

Excitation-energy spectra for $2\alpha +{}^3\mathrm{He}$ events where there is a ${}^7\mathrm{Be}(5/2^{-}$) intermediate state. Results shown were obtained with the (a) ${}^{13}\mathrm{O}$ and (b) ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ beams. Fits to these data (solid red curves) are shown where the fitted smooth backgrounds are given by the dashed blue curves.

Figure 17

Distributions of the angle between the two decay axes in the sequential decay for the (a) 14.1-MeV and (b) 16.1-MeV states observed in the ${}^6\mathrm{Li}+\alpha +p$ channel. Black circular data points were obtained for the ${}^{13}\mathrm{O}$ data set while the square magenta ones are from the ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ data set. The curves show examples of fits to these correlations. The solid and dashed curves in (a) show the best reproduction assuming the parent state has positive and negative parity, respectively, with the parent spins shown. In (b) the best reproduction is produced with a flat isotropic distribution (solid red horizontal line).

Figure 18

Distributions of the angle between the two decay axes in the sequential decay of the 14.1-MeV state observed in the $2\alpha +{}^3\mathrm{He}$ channel. Circular black data points were obtained for the ${}^{13}\mathrm{O}$ data set while the square magenta ones are from the ${}^{15}\mathrm{O}/{}^{17}\mathrm{Ne}$ data set. The curve shows the reproduction of the experimental correlation for a parent state of $J^{\pi }=7/2^{+}$.