Structure of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{B}$ from the ${}^{14,15}\mathrm{C}(d,{}^3\mathrm{He}){}^{13,14}\mathrm{B}$ reactions

We have studied the ${}^{14,15}\mathrm{C}(d,{}^3\mathrm{He}){}^{13,14}\mathrm{B}$ proton-removing reactions in inverse kinematics. The $\left(d,{}^3\mathrm{He}\right)$ reaction probes the proton occupation of the target ground state, and also provides spectroscopic information about the final states in ${}^{13,14}\mathrm{B}$. The experiments were performed using ${}^{14,15}\mathrm{C}$ beams from the ATLAS accelerator at Argonne National Laboratory. The reaction products were analyzed with the HELIOS device. Angular distributions were obtained for transitions from both reactions. The ${}^{14}\mathrm{C}$-beam data reveal transitions to excited states in ${}^{13}\mathrm{B}$ that suggest configurations with protons outside the $\pi \left(0p_{3/2}\right)$ orbital, and some possibility of proton cross-shell $0p\text{−}1s0d$ excitations, in the ${}^{14}\mathrm{C}$ ground state. The ${}^{15}\mathrm{C}$-beam data confirm the existence of a broad $2^{-}$ excited state in ${}^{14}\mathrm{B}$. The experimental data are compared to the results of shell-model calculations.

Figure 1

Schematic diagram of the experimental setup.

Figure 2

Silicon-detector telescope particle-identification spectrum obtained with the ${}^{14}\mathrm{C}$ beam incident on the $({\mathrm{CD}}_2{)}_n$ target. The heavy particles are in coincidence with a particle in the HELIOS PSD array. The groups labeled ${}^{13}\mathrm{B}$ and $\stackrel{b}{{}^{12}\mathrm{B}}$ are from particle-bound and unbound states in ${}^{13}\mathrm{B}$; the groups labeled $\stackrel{a}{{}^{12}\mathrm{B}}$ and ${}^{11}\mathrm{B}$ are from particle-bound and unbound states in ${}^{12}\mathrm{B}$ from the $(d,\alpha )$ reaction.

Figure 3

Energy-versus-position spectra for ${}^3\mathrm{He}$ particles from the ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ reaction. (a) Data for ${}^3\mathrm{He}+{}^{13}\mathrm{B}$ coincidence events. (b) Data for ${}^3\mathrm{He}+{}^{12}\mathrm{B}$ coincidence events. Further analysis on the unbound states includes only data taken for $z>1180$ mm.

Figure 4

Monte Carlo simulations of energy-versus-position spectra for ${}^3\mathrm{He}$ particles from the ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ reaction. (a) Simulated data for ${}^3\mathrm{He}+{}^{13}\mathrm{B}$ coincidence events. (b) Simulated data for ${}^3\mathrm{He}+{}^{12}\mathrm{B}$ coincidence events. The excitation energies used in the calculations are indicated on the figure.

Figure 5

Energy-versus-position spectra for ${}^3\mathrm{He}$ particles from the ${}^{15}\mathrm{C}(d,{}^3\mathrm{He}){}^{14}\mathrm{B}$ reaction. The black circles and red squares correspond to ${}^3\mathrm{He}+{}^{14}\mathrm{B}$ and ${}^3\mathrm{He}+{}^{13}\mathrm{B}$ coincidence events, respectively.

Figure 6

${}^{13}\mathrm{B}$ excitation-energy spectra from the ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ reaction. (a) Events in coincidence with identified ${}^{13}\mathrm{B}$ ions with the open histogram displaying the same data multiplied by a factor of 8 to enhance weak transitions. (b) Events in coincidence with identified ${}^{12}\mathrm{B}$ ions.

Figure 7

${}^{14}\mathrm{B}$ excitation-energy spectra from the ${}^{15}\mathrm{C}(d,{}^3\mathrm{He}){}^{14}\mathrm{B}$ reaction. (a) and (b) Particle-bound (unbound) states obtained in coincidence with identified ${}^{14}\mathrm{B} \left({}^{13}\mathrm{B}\right)$ ions.

Figure 8

Correlation between boron recoil energy and reconstructed ${}^{13}\mathrm{B}$ excitation energy. (a) Data (b) Monte Carlo simulation. The polygons illustrate the regions corresponding to bound and unbound states in ${}^{13}\mathrm{B}$ and are not used as event-selection criteria in the analysis. The labels (0)–(4) correspond to excitations in ${}^{13}\mathrm{B}$ listed in Table 1.

Figure 9

Angular-distribution data for the ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}\left(3/2^{-}\right)$ ground-state transition from Ref. [6]. The curve represents a DWBA calculation described in the text.

Figure 10

Angular distributions for the (a) 0.0-, (b) 3.8-, and (c) 4.8-MeV transitions in ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$. The curves represent DWBA calculations discussed in the text. For (a) and (b) the transitions are $\ell =1$; for (c) the solid curve corresponds to $\ell =0$. The dashed curve in (c) represents an $\ell =1$ transition for comparison. When not visible, the vertical error bars are smaller than the plotting symbols. The horizontal error bars show the angular range for each point.

Figure 11

Angular distributions for the (a) 5.3- and (b) 6.3-MeV transitions in ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$. The curves represent DWBA calculations discussed in the text. The horizontal error bars show the angular range for each point. In (a) the solid and dot-dashed curves correspond to $\ell =1$ with $J^{\pi }=1/2^{-}$ or $3/2^{-}$. In (b), the solid and dashed curves represent $\ell =0$ and 1 transitions, respectively. The DWBA curves in (b) are for illustration only.

Figure 12

Angular distribution for the (a) $2_1^{-}-1{}_1^{-}$ doublet and (b) 1.8-MeV state in ${}^{14}\mathrm{B}$. The horizontal error bars show the angular range for each point. The DWBA curves represent $\ell =1$ transitions as described in the text.