Structure of ${}^{13}\mathrm{Be}$ studied in proton knockout from ${}^{14}\mathrm{B}$

The neutron-unbound isotope ${}^{13}\mathrm{Be}$ has been studied in several experiments using different reactions, different projectile energies, and different experimental setups. There is, however, no real consensus in the interpretation of the data, in particular concerning the structure of the low-lying excited states. Gathering new experimental information, which may reveal the ${}^{13}\mathrm{Be}$ structure, is a challenge, particularly in light of its bridging role between ${}^{12}\mathrm{Be}$, where the $N=8$ neutron shell breaks down, and the Borromean halo nucleus ${}^{14}\mathrm{Be}$. The purpose of the present study is to investigate the role of bound excited states in the reaction product ${}^{12}\mathrm{Be}$ after proton knockout from ${}^{14}\mathrm{B}$, by measuring coincidences between ${}^{12}\mathrm{Be}$, neutrons, and $\gamma$ rays originating from de-excitation of states fed by neutron decay of ${}^{13}\mathrm{Be}$. The ${}^{13}\mathrm{Be}$ isotopes were produced in proton knockout from a 400 MeV/nucleon ${}^{14}\mathrm{B}$ beam impinging on a ${\mathrm{CH}}_2$ target. The ${}^{12}\mathrm{Be}\text{−}n$ relative-energy spectrum $d\sigma /d{E}_{fn}$ was obtained from coincidences between ${}^{12}\mathrm{Be}$(g.s.) and a neutron, and also as threefold coincidences by adding $\gamma$ rays, from the de-excitation of excited states in ${}^{12}\mathrm{Be}$. Neutron decay from the first $5/2^{+}$ state in ${}^{13}\mathrm{Be}$ to the $2^{+}$ state in ${}^{12}\mathrm{Be}$  at 2.11 MeV is confirmed. An energy independence of the proton-knockout mechanism is found from a comparison with data taken with a 35 MeV/nucleon ${}^{14}\mathrm{B}$ beam. A low-lying $p$-wave resonance in ${}^{13}\mathrm{Be}\left(1/2^{-}\right)$ is confirmed by comparing proton- and neutron-knockout data from ${}^{14}\mathrm{B}$ and ${}^{14}\mathrm{Be}$.

Figure 1

Schematic view of the experimental setup. The square-shaped plastic scintillator (POS) is used as the start signal of the time-of-flight measurements and gives also information about the energy loss of the beam particles. The position sensitive silicon pin diode (PSP) detectors are used for tracking of the beam position and for determining the charge of the isotopes from their energy loss. The ROLU is a set of scintillators, which allows one to restrict the active beam size. Any particle that does not pass through the hole defined by the position of the four scintillators gives a signal, which is used as a veto trigger for the data acquisition system. Double-sided silicon strip detectors (DSSDs) in front of and behind the reaction target are used for separating the charge and tracking of the emerging fragments. The two fiber detectors (GFIs) are used for tracking the fragment trajectories. A set of scintillators, the time-of-flight wall (TFW), is used to provide a stop signal for the time-of-flight measurement and as an energy loss detector. The LAND neutron detector and the Crystal Ball, surrounding the target, are discussed in the text. Figure from Ref. [43].

Figure 2

Fragment identification data of the incoming beam. The ordinate corresponds to the charge $\left(Z\right)$ of the incoming isotopes whereas the abscissa is the ratio between mass and charge $\left(A/Z\right)$.

Figure 3

Contour plot of $E_{\gamma }$ as function of $E_{fn}$ after multi-quadratic smoothing of the triple-coincidence data. The maximal intensity is found in the energy region $E_{\gamma }\sim 2$ MeV and $E_{fn}$ less than 0.5 MeV (hatched area). Note also the events at $E_{\gamma }\sim 2$ MeV and $E_{fn}\sim 2$ MeV.

Figure 4

(a) Doppler-corrected $\gamma$ spectrum measured with the Crystal Ball detector in coincidence with ${}^{12}\mathrm{Be}$ and a neutron obtained from a projection of the two-dimensional distribution $E_{\gamma }\left(E_{fn}\right)$ in Fig. 3. The centroid of the Gaussian-shaped peak was found to be 2.16(4) MeV with width $\sigma =168\left(50\right)\mathrm{keV}$ on the top of a smooth background. This confirms the presence of neutron decay from ${}^{13}\mathrm{Be}$ to the $2^{+}$ state in ${}^{12}\mathrm{Be}$. (b) $\gamma$ spectrum after background subtraction.

Figure 5

Experimental spectrum of the relative ${}^{12}\mathrm{Be}\text{−}n$ energy, $d\sigma /d{E}_{fn}$, obtained in proton knockout from ${}^{14}\mathrm{B}$ at (a) 400 MeV/nucleon (present data) and (b) 35 MeV/nucleon energies (Ref. [36]). The data are corrected for overall efficiency and normalized to the same integral value. The contributions from the threefold ${}^{12}\mathrm{Be}+n+\gamma$ coincidences are shown by $▴$. The data are corrected for the efficiency of $\gamma$ detection, 40%. Overlaid on the experimental points, the fit to three Breit-Wigner resonances (thin solid lines: black, pink, red, and blue) and their decay branches to the $\gamma$-decaying ${}^{12}\mathrm{Be}\left(2^{+}\right)$ state (dashed lines). The thick solid black lines show a global fit to the data: (a) ${\chi }^2/N=1.0$ and (b) ${\chi }^2/N=1.8$. See text for details.

Figure 6

Proposed level scheme of ${}^{13}\mathrm{Be}$ together with the neutron decay channels to the ground state and excited states in ${}^{12}\mathrm{Be}$. The energies for the positive-parity states are from the present paper, while the low-energy negative-parity state is from neutron-knockout data from ${}^{14}\mathrm{Be}$ [35, 51].

Figure 7

(a) Relative-energy spectra ${}^{12}\mathrm{Be}\text{−}n$ obtained in proton knockout from ${}^{14}\mathrm{B}$ at 400 MeV/nucleon $(▾$, present data), and 35 MeV/nucleon $(▴$, Ref. [36]), and in neutron knockout from 360 MeV/nucleon ${}^{14}\mathrm{Be}(\diamond$, Ref. [51]). (b) Relative-energy spectra ${}^{12}\mathrm{Be}\text{−}n$ in nucleon exchange with a ${}^{13}\mathrm{B}$ beam $(•$, Ref. [37]), and in neutron knockout from ${}^{14}\mathrm{Be}(\diamond$, Ref. [51]; $\times$, Ref. [35]). All spectra were corrected for overall efficiencies of the experimental setup and normalized to the same integral in the relative-energy region 0–5 MeV.