Search for the missing $d$-wave neutron excitation states in ${}^{13}\mathrm{B}$

A ${}^{13}\mathrm{B}(d,d^{\prime })$ inelastic scattering experiment was carried out using a 23 MeV/nucleon ${}^{13}\mathrm{B}$ beam in order to search for the missing positive parity state with a configuration of ${}^{12}{\mathrm{B}}_{\mathrm{g}.\mathrm{s}.}\otimes d_{5/2}$ in the $N=8$ neutron-rich nucleus ${}^{13}\mathrm{B}$, referred to as the $d$-wave neutron excitation state. Several states at excitation energies of 3.6(1), 4.2(1), 5.4(2), and 6.5(2) MeV in ${}^{13}\mathrm{B}$ were observed in its excitation energy spectra, which were derived from the energies and angles of the scattered deuterons from ${}^{13}\mathrm{B}$ using the missing mass method. To determine the parity of each populated state, the inelastic scattering differential cross sections (DCSs) were compared to the distorted wave Born approximation (DWBA) calculations. The 5.4- and 6.5-MeV states were inferred to be positive parity states and considered as potential candidates for the missing $d$-wave neutron excitation state. The gap between $s$ and $d$ shells in ${}^{13}\mathrm{B}$ and the systematic behavior of neutron-rich Boron isotopes were also investigated based on the experimental findings.

Figure 1

Energy-level scheme of ${}^{13}\mathrm{B}$ up to an excitation energy of 7 MeV, obtained from ${}^{11}\mathrm{B}(t,p){}^{13}\mathrm{B}$ [20, 21], ${}^7\mathrm{Li}({}^7\mathrm{Li},p){}^{13}\mathrm{B}$ [8, 22, 23], ${}^{13}\mathrm{C}(t,{}^3\mathrm{He}){}^{13}\mathrm{B}$ [24], ${}^4\mathrm{He}({}^{12}\mathrm{Be},t){}^{13}\mathrm{B}$ [9], $d({}^{14}\mathrm{C},{}^3\mathrm{He}){}^{13}\mathrm{B}$ [25, 26], and $d({}^{12}\mathrm{B},p){}^{13}\mathrm{B}$ [18, 19] reactions, as well as the present inelastic scattering of ${}^{13}\mathrm{B}+d$. The red, blue, and black lines represent positive, negative, and unassigned spin-parity states, respectively.

Figure 2

The energies of [(a) and (b)]${}^{13}\mathrm{B}$ and [(c) and (d)]${}^{12}\mathrm{B}$ as a function of their angles in the laboratory frame, which were measured by telescope T0. Panels (a) and (c) were obtained from the coincidence data of ${}^{12,13}\mathrm{B} + d$, while (b) and (d) were drawn from the geant4 simulation data using the real experimental setup. The red solid and blue dotted curves represents the calculated functions for elastic scattering of ${}^{13}\mathrm{B}+d$ and inelastic scattering to unbound states in ${}^{13}\mathrm{B}$.

Figure 3

The excitation energy spectra of ${}^{13}\mathrm{B}$ reconstructed from the energies and angles of the scattering deuterons in coincidence with ${}^{12,13}\mathrm{B}$. Panel (a) represents the experimental data and (b) represents the results obtained from simulations. The inset in (a) shows the entire excited energy spectrum, including both elastic and inelastic scattering events. The red and blue curves, each with different styles, depict the fitted peaks corresponding to different excited states. The purple solid curve represents the total fit, which is the sum of the red and blue curves. The yellow vertical line shows the 4.87-MeV one-neutron separation threshold of ${}^{13}\mathrm{B}$.

Figure 4

Differential cross sections of ${}^{13}\mathrm{B}+d$ inelastic scattering to the peaks at (a) 3.6(1), (b) 4.2(1), (c) 5.4(2), and (d) 6.5(2) MeV in the excited energy spectrum, compared with the DWBA calculations using various orbital angular momenta $\mathrm{\Delta }l$. See text for mote details.

Figure 5

Effective single particle energy for ${\varepsilon }_0\left(s_{1/2}\right)$ and ${\varepsilon }_0\left(d_{5/2}\right)$ of ${}^{12,13,14}\mathrm{B}$ determined from several experiments. In the case of ${}^{13}\mathrm{B}$, the dashed and solid blue lines represent the assumption that the 6.5- or 5.4-MeV state corresponds to the missing $d$-wave neutron excited state, respectively. See more details in the text.