Structure of ${}^9\mathrm{C}$ through proton resonance scattering with the Texas Active Target detector

Background: Level structure of the most neutron-deficient nucleon-bound carbon isotope, ${}^9\mathrm{C}$, is not well known. Definitive spin-parity assignments are only available for two excited states. No positive-parity states have been conclusively identified so far and the location of the $sd$ shell in the $A=9, T=3/2$ isospin quadruplet is not known.

Purpose: We have studied the level structure of exotic nucleus ${}^9\mathrm{C}$ at excitation energies below 6.4 MeV.

Methods: Excited states in ${}^9\mathrm{C}$ were populated in ${}^8\mathrm{B}+p$ resonance elastic scattering and excitation functions were measured using the active target approach.

Results: Two excited states in ${}^9\mathrm{C}$ were conclusively observed, and $R$-matrix analysis of the excitation functions was performed to make the spin-parity assignments. The first positive-parity state in the $A=9, T=3/2$ nuclear system, the $5/2^{+}$ resonance at 4.3 MeV, has been identified.

Conclusions: The new $5/2^{+}$ state at 4.3 MeV in ${}^9\mathrm{C}$ is a single-particle $\ell =0$ broad resonance and it determines the energy of the $2s$ shell. The $2s$ shell in this exotic nucleus appears well within the region dominated by the $p$-shell states.

Figure 1

TexAT Assembly with one side removed. The top part is the Micromegas where the red portion depicts the central pads and the green are the side regions. The Si detectors (yellow) are each backed by a CsI (turquoise) detector. The beam travels from right to left along the central pads [20].

Figure 2

The energy deposited in each of the central region pads. The Bragg peak occurs around row number 90.

Figure 3

Energy deposition in the ionization chamber at the entrance of TexAT. A peak at channel 1700 corresponds to the ${}^8\mathrm{B}$ beam ions. The red lines show the energy gate that was applied to select events associated with ${}^8\mathrm{B}$.

Figure 4

Scatter plot of the specific energy loss per unit pad in the Micromegas detector ($\mathrm{\Delta }E$/pad) vs the sum of energies deposited in the Si and CsI(Tl) detectors for detectors with a c.m. angle of 100–${145}^{\circ }$. The red band shows the “proton” cut.

Figure 5

Energy in the CsI plotted vs energy deposited in the Si detector for proton events that punch through the Si detectors and above the threshold in the CsI for detectors with a c.m. angle of 155–${175}^{\circ }$.

Figure 6

A two-dimensional (2D) projection onto the Micromegas plane for a typical ${}^8\mathrm{B}+p$ elastic scattering event. The ${}^8\mathrm{B}$ projectile and recoil tracks are shown in black. The proton track, produced by matching strips and chains in the multiplexed high-gain side region of the Micromegas detector, is shown in red. Active area of the Micromegas detector is shown by the dashed lines and the location of the $\mathrm{Si}+\text{CsI(Tl)}$ telescopes is shown with bold solid lines. Note that proton track is not visible until it gets to the high-gain region of the Micromegas; this is why the proton track does not start at the reaction vertex location.

Figure 7

Vertex location plotted against the proton energy as measured by Si and CsI(Tl) detectors. Vertex location is measured relative to the start of the Micromegas detector (0 mm) where positive vertex positions are further downstream toward the forward Si detectors and negative vertex positions occur further upsteam of the Micromegas detector, outside of the active region of the TPC. The top panel (a) corresponds to the events that produce a proton track in the central region of the micromegas only, and the bottom panel (b) are the events that produce a proton track in the side regions.

Figure 8

The vertex location distribution for events with a c.m. energy between 2.4 and 2.5 MeV for events in the detectors located at c.m. angles 100–${145}^{\circ }$. The vertex is relative to the start of the Micromegas detector (0 mm), where positive vertex positions are further downstream.

Figure 9

Excitation function for ${}^8\mathrm{B}+p$ elastic scattering in the angular range of ${157–172}^{\circ }$ (a) and 100–${145}^{\circ }$ (b) in c.m. The red dashed curve is the $R$-matrix calculations using the phase shifts shown in Fig. 11. The blue short-dashed curve includes the $1/2^{-}, 5/2^{-}$, and $5/2^{+}$ states while the black solid curves includes a $7/2^{-}$ on top of the $1/2^{-}, 5/2^{-}$, and $5/2^{+}$ states.

Figure 10

A 2D projection onto the Micromegas plane for a typical ${}^8\mathrm{B}+p$ inelastic scattering event, with subsequent proton decay of a ${}^8\mathrm{B}$ excited state. The ${}^7\mathrm{Be}$ recoil track is shown in black. The proton tracks, produced by matching strips and chains in the multiplexed high-gain side region of the micromegas detector, are shown in red. Active area of the micromegas detector is shown by the dashed lines and the location of the $\mathrm{Si}+\text{CsI(Tl)}$ telescopes is shown with bold solid lines. For this event, the reaction vertex is located outside of the active region of Micromegas (negative $Y$ values). It is not shown but it can be easily reconstructed. The proton to the right of the ${}^7\mathrm{Be}$ recoil track produced a trigger in a Si detector. The proton to the left of the ${}^7\mathrm{Be}$ recoil track did not make it to the Si array.

Figure 11

The dashed black curves are the phase shifts for the $3/2^{-}$ and $1/2^{-}$ partial waves calculated using Woods-Saxon potentials that reproduce the binding energy of the ${}^9\mathrm{C}3/2^{-}$ ground state (1.3 MeV) and the c.m. energy of the $1/2^{-}$ first excited state (0.92 MeV). The $R$-matrix phase shifts are shown as red solid curves.

Figure 12

Square of the amplitude of the proton wave function (arbitrary units) at 1.00 fm for the $s$-wave states in ${}^8\mathrm{B}$ (short-dashed curve), ${}^9\mathrm{C}$ (dashed curve), and ${}^{10}\mathrm{N}$ (solid curve) calculated using the Woods-Saxon potential with $V=-58.0$ MeV, $R=1.2\sqrt[3]{A}$ fm, $a=0.65$ fm, and the Coulomb potential due to the uniformly charged sphere of radius $1.3\sqrt[3]{A}$, where $A=7$, 8, and 9 for the ${}^8\mathrm{B}, {}^9\mathrm{C}$, and ${}^{10}\mathrm{N}$, respectively.