Cluster structure of $3\alpha +p$ states in ${}^{13}\mathrm{N}$

Background: Cluster states in ${}^{13}\mathrm{N}$ are extremely difficult to measure due to the unavailability of ${}^9\mathrm{B}+\alpha$ elastic-scattering data.

Purpose: Using $\beta$-delayed charged-particle spectroscopy of ${}^{13}\mathrm{O}$, clustered states in ${}^{13}\mathrm{N}$ can be populated and measured in the $3\alpha +p$ decay channel.

Methods: One-at-a-time implantation and decay of ${}^{13}\mathrm{O}$ was performed with the Texas Active Target Time Projection Chamber. $149\beta 3\alpha p$ decay events were observed and the excitation function in ${}^{13}\mathrm{N}$ reconstructed.

Results: Four previously unknown $\alpha$-decaying excited states were observed in ${}^{13}\mathrm{N}$ at an excitation energy of 11.3, 12.4, 13.1, and 13.7 MeV decaying via the $3\alpha +p$ channel.

Conclusions: These states are seen to have a ${[}^9\mathrm{B}(\mathrm{g}.\mathrm{s})⨂\alpha /p+{}^{12}\mathrm{C}\left(0_2^{+}\right)], {[}^9\mathrm{B}\left({\frac{1}{2}}^{+}\right)⨂\alpha ], {[}^9\mathrm{B}\left({\frac{5}{2}}^{+}\right)⨂\alpha ]$, and ${[}^9\mathrm{B}\left({\frac{5}{2}}^{+}\right)⨂\alpha ]$ structure, respectively. A previously seen state at 11.8 MeV was also determined to have a $[p+{}^{12}\mathrm{C}(\mathrm{g}.\mathrm{s}.)/p+{}^{12}\mathrm{C}\left(0_2^{+}\right)]$ structure. The overall magnitude of the clustering is not able to be extracted, however, due to the lack of a total width measurement. Clustered states in ${}^{13}\mathrm{N}$ (with unknown magnitude) seem to persist from the addition of a proton to the highly $\alpha$-clustered ${}^{12}\mathrm{C}$. Evidence of the ${\frac{1}{2}}^{+}$ state in ${}^9\mathrm{B}$ was also seen to be populated by decays from ${}^{13}\mathrm{N}^{★}$.

Figure 1

An overview of the experimental setup showing how the K500 Cyclotron phase shifter inhibits the ${}^{14}\mathrm{N}$ primary beam following an implantation event from the ${}^{13}\mathrm{O}$ secondary beam (L1A). Following this, for a fraction of events a subsequent decay (within 30 ms) of the ${}^{13}\mathrm{N}\to 3\alpha +p$ (or more-likely, a single proton) provides a second L1B (decay) trigger and the decay products from can be reconstructed inside the TPC. A silicon detector at zero degrees was used for tuning the radioactive beam and providing a veto signal for beam events that do not stop inside of the TexAT active region.

Figure 2

Energy deposition ($dE$) within the MM Jr detector to differentiate the beam species. The contaminants to the ${}^{13}\mathrm{O}$ were dominated by ${}^7\mathrm{Be}$ and they total $\approx 28\%$ of the total beam intensity of 5 pps.

Figure 3

Decay time between the implant of ${}^{13}\mathrm{O}$ and proton or $\alpha$ decay overlaid with a background-free exponential fit yielding a value of $t_{1/2}=8.55\pm 0.09$ (stat.) ms compared with the adopted value of $8.58\pm 0.05$ ms [11]. ${\tilde{\chi }}^2=1.26$ from log-likelihood minimization.

Figure 4

Selection of (${}^{13}\mathrm{N},p_{0,1})$ events. (top) Experimental data of ${}^{12}\mathrm{C}$ recoil range in TPC versus energy. The expected result from trim [12] is overlaid as a dotted red line. (bottom) Proton energy spectrum from these data obtained from the ${}^{12}\mathrm{C}$ recoil (red histogram). The expected yield using previously obtained branching ratios [13] is overlaid as a black solid line after being convoluted with a Gaussian profile to best replicate the data.

Figure 5

Schematic showing the basis of the RANSChiSM fit by selection of five points to parametrize the four-track fit. Any points in the point cloud more than 10 mm from the nearest track line are counted as if they are 10 mm away to reduce the influence of outliers.

Figure 6

Relative energy spectrum for pairs of $\alpha$ particles (taking the smallest relative energy) showing the ${}^8\mathrm{Be}$(g.s.) energy of 92 keV (represented by the red dashed vertical line) is well-reproduced in our data.

Figure 7

For events that do not decay via the Hoyle state ($E_x<8.1$ MeV), the relative energy spectrum is shown here which is generated by selecting the two $\alpha$ particles that produce the ${}^8\mathrm{Be}$(g.s.) and then reconstructing the ${}^9\mathrm{B}$ relative energy with the proton. Overlaid in dashed red are simulated data for the ground-state contribution ($E_{\mathtt{rel}}=186$ keV, $\mathrm{\Gamma }=0.54$ keV) and in solid red are the ${\frac{1}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ states from single channel $R$-matrix calculations convoluted with a Gaussian with $\sigma =0.23$ MeV. The ${\frac{1}{2}}^{+}$ parameters are those obtained by Wheldon [15] and show excellent agreement.

Figure 8

Invariant-mass spectrum for ${}^{12}\mathrm{C}$ from $3\alpha$ particles. A peak at 7.65 MeV is seen, well reproducing the Hoyle state energy (denoted by a red dashed vertical line) and a broad peak is seen at higher excitation energies which correspond to events that decay via ${}^9\mathrm{B}+\alpha$.

Figure 9

An example $p_2 [{}^{12}\mathrm{C}\left(0_2^{+}\right)+p]$ event where the energy deposition as a function of distance in the TPC is shown projected in 2D.

Figure 10

An example ${\alpha }_0 \left[{}^9\mathrm{B}\right(\mathrm{g}.\mathrm{s}.)+\alpha ]$ event where the energy deposition as a function of distance in the TPC is shown projected in 2D. The track going downwards can be identified as the proton by its lower energy deposition. Also shown in Ref. [5].

Figure 11

Excitation spectrum in ${}^{13}\mathrm{N}$ for $3\alpha +p$ separated by channels: (a) The sum of all channels, (b) $p_2$, (c) ${\alpha }_0$, (d) ${\alpha }_1$, and (e) ${\alpha }_3$. Dashed vertical arrows show the position of observed states populated by $\beta$ decay while, in the top panel, black solid arrows note the location of previously observed states [13].

Figure 12

Variation of experimental resolution from a geant4 simulation of infinitely narrow states decaying via ${}^9\mathrm{B}\left(\text{g.s.}\right)+\alpha$ as a function of excitation energy. The statistical error bars are not shown as the error for each point is dominated by systematic errors via the stopping power uncertainties for $\alpha$ particles and may be as large as 0.1 MeV (towards larger peak $\sigma$ values).

Figure 13

Level scheme of measured $3\alpha +p$ states in ${}^{13}\mathrm{N}$ in the central column with the proposed spin-parity assignments. The location of the thresholds for proton and $\alpha$ decay are shown in red with the equivalent excitation energy shown. The corresponding states in the daughter nuclei (${}^{12}\mathrm{C}$ and ${}^9\mathrm{B}$) are similarly displayed. Also shown in Ref. [5].