$s$- and $d$-wave intruder strengths in ${}^{13}\mathrm{B}_{\mathrm{g}.\mathrm{s}.}$ via the ${}^1\mathrm{H}({}^{13}\mathrm{B},d){}^{12}\mathrm{B}$ reaction

Experimental results of the ${}^1\mathrm{H}({}^{13}\mathrm{B},d){}^{12}\mathrm{B}$ transfer reaction to the low-lying states in ${}^{12}\mathrm{B}$ are reported. The optical potential parameters for the entrance channel are extracted from the elastic scattering ${}^1\mathrm{H}({}^{13}\mathrm{B},p)$ measured in the same experiment, while those for the exit channel are global ones. Spectroscopic factors associated with the $p$-, $s$-, and $d$-wave neutron transfer to the known ${}^{12}\mathrm{B}$ states are extracted by comparing the deuteron angular distributions with the calculation results. The separated $s$- and $d$-wave intruder strengths in ${}^{13}\mathrm{B}_{\mathrm{g}.\mathrm{s}.}$ were determined to be $5\left(2\right)\%$ and $12\left(2\right)\%$, respectively, which follow roughly the systematics for the $N=8$ neutron-rich isotones and shell model calculations with YSOX interaction. The sudden change of the intruder $sd$-wave intensity between ${}^{13}\mathrm{B}$ and ${}^{12}\mathrm{Be}$ needs further theoretical interpretation.

Figure 1

Schematic view of the experimental setup.

Figure 2

Protons elastically scattered from ${}^{13}\mathrm{B}$ in the particle identification (PID) spectrum measured by T2. The inset figure shows the PID spectrum measured by T0, where the Boron isotopes are shown in coincidence with protons.

Figure 3

The PID spectrum of boron isotopes detected by T0 in coincidence with T1. The inset shows the PID spectrum measured by T1.

Figure 4

Bi-dimensional plot of energy vs angle for recoiling protons in coincidence with ${}^{13}\mathrm{B}$ at forward angles. The red solid curve stands for the kinematic loci of the elastic scattering.

Figure 5

Excitation energy spectrum of ${}^{13}\mathrm{B}$ reconstructed from the energies and angles of the scattered protons measured by T2. The inset figure shows the energy spectrum for inelastic scattering.

Figure 6

Elastic scattering differential cross sections, relative to the Rutherford cross sections. Theoretical calculations using the normalized WSS potential (red dashed curve) reproduce the experimental data. See text for more details.

Figure 7

The deuteron energies versus outgoing angles in laboratory frame, gated on the boron isotopes measured by T0. The red lines stand for the calculated kinematics of the ${}^1\mathrm{H}({}^{13}\mathrm{B},d){}^{12}\mathrm{B}$ transfer reaction to the states of interests in ${}^{12}\mathrm{B}$.

Figure 8

Excitation energy spectra of ${}^{12}\mathrm{B}$ reconstructed from the energies and angles of deuterons at (a) $23–{27}^{\circ }$, (b) $27–{31}^{\circ }$, (c) $31–{35}^{\circ }$, and (d) $35–{39}^{\circ }$. The blue solid lines show the fitted spectrum for each state, and the red solid curves show the total fits, i.e., sums of blue solid curves. Note that the amplitudes for states above 3 MeV are zero in (d). The number of degrees of freedom (ndf) corresponds to the number of points used in the fit minus the number of free parameters.

Figure 9

Differential cross sections of ${}^1\mathrm{H}({}^{13}\mathrm{B},d)$ to the excited states at (a) 0.00, (b) 0.953, (c) 1.674, (d) 2.261 and 2.723, (e) $3.389$, (f) 4.523 MeV. The excitation energy, the spin parity, and the transferred orbital angular momentum $l$, are given in the figure. The red dashed curves are the calculated differential cross sections for each state, multiplied by the corresponding SFs. The 2.621-MeV state could not be separated from the 2.723-MeV state in this experiment, so it was fitted as one peak in Fig. 8 and decomposed by two components in (d).

Figure 10

(a) Individual $p$-, $s$-, and $d$-wave intensities in the ground state of ${}^{12}\mathrm{Be}$ [5], ${}^{13}\mathrm{B}$ (this work), and ${}^{14}\mathrm{C}$ [17]. (b) Shell model calculations with YSOX interaction in full $p\text{−}sd$ model space. The results for ${}^{12}\mathrm{Be}$ are from Ref. [5].