Neutron halos in the excited states of ${}^{12}\mathrm{B}$

The differential cross sections of the ${}^{11}\mathrm{B}(d,p){}^{12}\mathrm{B}$ reaction leading to formation of the $1^{+}$ ground state and the 0.95-MeV $2^{+}$, 1.67-MeV $2^{-}$, 2.62-MeV $1^{-}$, 2.72-MeV $0^{+}$, and 3.39-MeV $3^{-}$ excited states of ${}^{12}\mathrm{B}$ are measured at $E_d$ = 21.5 MeV. The analysis of the data is carried out within the coupled-reaction-channels method for the direct neutron transfer and the Hauser-Feshbach formalism of the statistical compound-nucleus model. The spectroscopic factors, asymptotic normalization coefficients, and rms radii of the last neutron in all states studied are deduced. The existence of the neutron halos in the 1.67-MeV $2^{-}$ and 2.62-MeV $1^{-}$ states is found, consistent with the earlier published data. New information about the enlarged rms radii of the last neutron in the 2.72-MeV $0^{+}$ (5.7 fm) and the unbound 3.389-MeV $3^{-}$ (5.9 fm) states of ${}^{12}\mathrm{B}$ was obtained, resulting in the possible existence of neutron halo-like states in ${}^{12}\mathrm{B}$.

Figure 1

A proton spectrum from the ${}^{11}\mathrm{B}(d,p){}^{12}\mathrm{B}$ reaction at $18{}^{\circ }$ (c.m.) with the excitation of ${}^{12}\mathrm{B}$ states up to $E_x\approx 3.5$ MeV.

Figure 2

Deuteron elastic-scattering CRC calculation (solid line) compared with the $d+{}^{11}\mathrm{B}$ elastic scattering cross section at 21.5 MeV measured in the present work (points).

Figure 3

Proton angular distributions from the ${}^{11}\mathrm{B}(d,p){}^{12}\mathrm{B}$ reaction populated the $1^{+}$ ground state and the first excited 0.95-MeV $2^{+}$ state of ${}^{12}\mathrm{B}$ at $E_d=21.5$ MeV (points). The curves corresponds to the CRC (dotted lines) and CN (dashed lines) calculations, and their incoherent sum (solid lines).

Figure 4

The same as in Fig. 3, but for the second excited 1.67-MeV $2^{-}$ state and the third excited 2.62-MeV $1^{-}$ state of ${}^{12}\mathrm{B}$. The dash-dotted lines correspond to the CRC calculations with the standard geometric parameters $r_0=1.35$ fm and $a_0=0.65$ fm.

Figure 5

The same as in Fig. 3, but for the fourth excited 2.72-MeV $0^{+}$ state and the fifth excited 3.39-MeV $3^{-}$ state of ${}^{12}\mathrm{B}$. The dash-dotted lines correspond to the CRC calculations with the standard geometric parameters $r_0=1.35$ fm and $a_0=0.65$ fm.

Figure 6

Examples of the radial sp neutron wave functions ${\phi }_{n_2{l}_2}\left(r\right)$ multiplied by ${\left(S^{\text{expt}}\right)}^{1/2}$ for the $1^{+}$ g.s., the first excited 0.95-MeV $2^{+}$ state, and the second excited 1.67-MeV $2^{+}$ state of ${}^{12}\mathrm{B}$ (solid and dashed lines) in comparison with the asymptotic parts of the corresponding Hankel functions $i{k}_{{}^{11}\mathrm{B}n}{h}_l\left(i{k}_{{}^{11}\mathrm{B}n}r\right)$ multiplied by $C_{{}^{11}\mathrm{B}n}^{\text{expt}}$ (dotted lines).

Figure 7

The same as in Fig. 6, but for the third excited 2.62-MeV $1^{-}$ state, the fourth excited 2.72-MeV $0^{+}$ state, and the fifth excited 3.39-MeV $3^{-}$ state of ${}^{12}\mathrm{B}$.