Invariant-mass spectroscopy of ${}^{14}\mathrm{O}$ excited states

Excited states in ${}^{14}\mathrm{O}$ have been investigated both experimentally and theoretically. Experimentally, these states were produced via neutron-knockout reactions with a fast ${}^{15}\mathrm{O}$ beam and the invariant-mass technique was employed to isolate the $1p$ and $2p$ decay channels and determine their branching ratios. The spectrum of excited states was also calculated with the shell model embedded in the continuum that treats bound and scattering states in a unified model. By comparing energies, widths, and decay branching patterns, spin and parity assignments for all experimentally observed levels below 8 MeV are made. This includes the location of the second $2^{+}$ state that we find is in near degeneracy with the third $0^{+}$ state. An interesting case of sequential $2p$ decay through a pair of degenerate ${}^{13}\mathrm{N}$ excited states with opposite parities was found where the interference between the two sequential decay pathways produces an unusual relative-angle distribution between the emitted protons.

Figure 1

Simulated invariant-mass resolution for $1p$ and $2p$ emissions from ${}^{14}\mathrm{O}$. Panel(a) shows the dependence of the resolution on the emission angle ${\theta }_C$ of the heavy core in the ${}^{14}\mathrm{O}^{*}$ center-of-mass frame. Dependence of the (b) resolution and (c) detection efficiency on the ${}^{14}\mathrm{O}^{*}$ excitation energy for all and only transverse emissions of the core. Note that the efficiency for transverse emissions has been multiplied by a factor of 4 for display purposes.

Figure 2

Comparison of the experimental and SMEC level schemes for ${}^{14}\mathrm{O}$. The experimental level scheme is derived from the most recent evaluation [10] and from the states observed in this work and Refs. [16, 17]. Observed proton decay branches are indicated by the arrows. The width of the arrows is roughly proportional to relative intensity of the decay branch. The excitation energies of the levels are given in MeV. Note it is possible that some of the higher-lying states have significant unobserved decay branches to ${}^{13}\mathrm{N}_{\text{g.s.}}$ (see Table 1). The SMEC results are obtained using the modified YSOX interaction [18] and the Wigner-Bartlett continuum-coupling interaction with the continuum-coupling strength $V_0=-350\mathrm{MeV}{\mathrm{fm}}^3$. For details of the calculation, see Sec. 5. The experimental levels whose spin and party were assigned before this work are connected by dotted blue lines to their theoretical partners while the assignments made or confirmed in this work are connected by the dashed green lines.

Figure 3

Laboratory velocity distribution of the parent ${}^{14}\mathrm{O}^{*}$ fragments reconstructed from the detected $p+{}^{13}\mathrm{N}$ and $2p+{}^{12}\mathrm{C}$ events. Values of the velocities of the ${}^{15}\mathrm{O}$ and ${}^{17}\mathrm{Ne}$ beam particles are indicated for comparison. Gates $G17$, $G{15}_{\text{peak}}$, and $G{15}_{\text{low}}$ used to examine the $p+{}^{13}\mathrm{N}$ events are indicated.

Figure 4

${}^{14}\mathrm{O}$ excitation-energy distributions from detected $p+{}^{13}\mathrm{N}$ events. Solid red histograms are where the ${}^{13}\mathrm{N}$ fragment is emitted transversely from the parent ${}^{14}\mathrm{O}^{*}$ system while the dotted blue histograms are for all events scaled by the factor 0.3. (a) gated on the ${}^{17}\mathrm{Ne}$ beam (gate $G17$), (b,c) on the ${}^{15}\mathrm{O}$ beam. (b) is for ${}^{14}\mathrm{O}$ velocity gate $G{15}_{\text{peak}}$ around the peak, while (c) is for the $G{15}_{\text{low}}$ gate containing the low-velocity tail. The arrows in (a) show the locations of states listed in the most recent evaluation [10] and from Refs. [16, 17].

Figure 5

Fit to the excitation-energy distribution for transverse $p+{}^{13}\mathrm{N}$ events with the combined $G{15}_{\text{peak}}$ and $G{15}_{\text{low}}$ gates. Individual curves (dotted) are shown for each state included in the fit and the fitted background distribution is shown as the dashed blue curve. Arrows indicate the locations of states listed in the most recent evaluation [10] and from Refs. [16, 17].

Figure 6

Fits to the peak near the location of the known $2_2^{+}$ state. The solid red curve in (a) is a fit with a single Breit-Wigner intrinsic line shape where the centroid and width are allowed to vary. The dot-dashed magenta curve was obtained when the centroid and width are constrained to the known values for the $2_2^{+}$ state. Panel (b) shows a fit assuming the observed peak is a doublet. The individual peaks are indicated by the dashed lines. The higher-energy peak has its centroid and width constrained to the values for the $2_2^{+}$ state. The smooth dashed blue curve in both panels is the fitted background.

Figure 7

Reconstructed ${}^{14}\mathrm{O}^{*}$ parent velocity distributions in the laboratory frame determined for the indicated peaks. For reference, the two beam velocities are shown by the arrows.

Figure 8

${}^{14}\mathrm{O}$ excitation-energy distributions from detected $2p+{}^{12}\mathrm{C}$ events. (a) Distribution for all events where the ${}^{12}\mathrm{C}$ fragment is emitted transversely. (b) Distribution of all events for the gate on the $J^{\pi }=1/2^{-}$ intermediate state of ${}^{13}\mathrm{N}$. (c) Distribution of transversely emitted events for the gate on the $J^{\pi }$=$3/2^{-}$ and $5/2^{+}$ intermediate states of ${}^{13}\mathrm{N}$. Curves shows fits to these distribution with the fitted background given by the dashed blue curves and the contribution from the individual states is also shown. The arrows in (a) show the energies of ${}^{14}\mathrm{O}$ levels in the most recent evaluation [10]. The labels associated with these indicate the spin and parity assigned in this evaluation when known. The level associated with the question mark was not considered firmly established in the evaluation.

Figure 9

Schematic showing the definition of the angle ${\theta }_k$ used in the Jacobi Y correlation plots. ${\mathit{V}}_{p\text{-core}}$ is the relative velocity between proton “2” and the core while ${\mathit{V}}_1$ is the relative velocity between proton “1” and the center of mass of the other two particles. Also shown is the relationship of ${\theta }_k$ to the relative angle ${\theta }_{pp}$.

Figure 10

Jacobi Y correlation plots for the $2p$ decay of the 8.79-MeV and 9.78-MeV peak in the $2p+{}^{12}\mathrm{C}$ excitation energy distributions. Panels (a) and (c) are from experimental data while (b) and (d) are the corresponding simulated distributions. Curves in (b) and (d) identify the ridge tops associated with different decays. Solid curves are for decay through the $3/2^{-}$, $5/2^{+}$ doublet, while dotted curves are for decays through the $1/2^{+}$ singlet.

Figure 11

The black circular data points give the distribution of relative-angle ${\theta }_{pp}$ between the two emitted protons in the sequential decay of the 9.78-MeV state. The dashed curves shows a calculation for isotropic proton emission including the Coulomb final-state interaction between the protons. The red square data points have been corrected to remove this final-state interaction and also the effects of the detector resolution. The solid curve is a fit with a quartic function in $cos{\theta }_{pp}$.

Figure 12

Results for the $2_2^{+}$ and $0_3^{+}$ levels in the SMEC as a function of the continuum coupling strength $V_0$. Panel (a) shows the eigenenergies and panel (b) the widths of SMEC eigenstates which form a doublet of resonances in the interval $-450\le V_0\le -330\mathrm{MeV}{\mathrm{fm}}^3$. The dotted vertical line shows the value of $V_0=-350\mathrm{MeV}{\mathrm{fm}}^3$ which gives an overall reasonable reproduction of the resonances reported in this work; see Fig. 2.

Figure 13

The SMEC spectrum of $2_i^{+}$ eigenstates ($i=1,2,3,4$) in ${}^{14}\mathrm{O}$ is shown as a function of the (real) continuum coupling strength $V_0$. Panel (a) presents the eigenenergies and panel (b) the widths of $2_3^{+}$ and $2_4^{+}$ SMEC eigenstates, the states that are involved in the avoided crossing at $V_0\approx -280\mathrm{MeV}{\mathrm{fm}}^3$; see vertical arrows. The dotted vertical line shows the value of $V_0=-350\mathrm{MeV}{\mathrm{fm}}^3$ which gives an overall reasonable reproduction of the resonances reported in this work. For more details, see the text.

Figure 14

The branching fractions, as a function of the continuum-coupling strength $V_0$, for the one-proton decay of $2_3^{+}$ and $2_4^{+}$ resonances either to (a) the doublet of resonances $3/2_1^{-}-5/2_1^{+}$ or (b) the first-excited state $1/2_1^{+}$ in ${}^{13}\mathrm{N}$. The arrows show the location of the avoided crossing and the dotted vertical line is at $V_0=-350\mathrm{MeV}{\mathrm{fm}}^3$, the value of the $V_0$ that gives a satisfactory reproduction of the observed ${}^{14}\mathrm{O}$ spectrum.

Figure 15

Exceptional threads for $2^{+}$ eigenstates of SMEC in ${}^{14}\mathrm{O}$ are shown as a function of the real and imaginary parts of the continuum coupling strength $V_0$. Negative (positive) imaginary values of $V_0$ correspond to outgoing, i.e., decaying, (ingoing, i.e., capturing) asymptotics. Different points on these ETs correspond to different excitation energies. The filled circle points to the threshold energy of the lowest decay channel (the elastic reaction channel). Open circles denote excitation energies at which subsequent (inelastic) channels open. The open double circle corresponds to the opening of two nearly-degenerate decay channels at 8.129 and 8.174 MeV. Arrows indicate the direction of increasing excitation energy along each ET.

Figure 16

Exceptional threads for $2^{+}$ eigenstates are displayed in the $\mathcal{I}m\left(V_0\right)-E$ plane. The thick red curve is the exceptional thread responsible for the avoided crossing.

Figure 17

SMEC spectrum of $1^{-}$ eigenstates in ${}^{14}\mathrm{O}$ is shown as a function of the continuum coupling strength $V_0$. For more details see the caption of Fig. 13 and the discussion in text.

Figure 18

Exceptional threads for $1^{-}$ eigenstates of SMEC in ${}^{14}\mathrm{O}$ are shown as a function of the real and imaginary parts of the continuum coupling strength $V_0$. The circles on each curve denote where the excitation energies corresponding to the thresholds for the elastic (solid) and inelastic (open) channels are located. Arrows indicate the direction of increasing excitation energy along each ET.

Figure 19

The SMEC spectrum of $0^{+}$ eigenstates in ${}^{14}\mathrm{O}$ is shown as a function of the continuum coupling strength $V_0$. For more details see the caption of Fig. 13 and the discussion in text.

Figure 20

Exceptional threads for $0^{+}$ eigenstates of the SMEC in ${}^{14}\mathrm{O}$ are shown as a function of the real and imaginary parts of the continuum coupling strength $V_0$. The circles on each curve denote where the excitation energies corresponding to the thresholds for the elastic (solid) and inelastic (open) channels are located. Arrows indicate the direction of increasing excitation energy along each ET.