Dipole excitation and geometry of Borromean nuclei

We analyze the Coulomb breakup cross sections of ${}^{11}\mathrm{Li}$ and ${}^6\mathrm{He}$ nuclei using a three-body model with a density-dependent contact interaction. We show that the concentration of the $B(E1)$ strength near the threshold can be well reproduced with this model. With the help of the calculated $B(E1)$ value, we extract the root-mean-square (rms) distance between the core nucleus and the center-of-mass of two valence neutrons without resorting to the sum rule, which may suffer from unphysical Pauli forbidden transitions. Together with the empirical rms distance between the neutrons obtained from the matter radius study and also from the three-body correlation study in the breakup reaction, we convert these rms distances to the mean opening angle between the valence neutrons from the core nucleus. We find that the obtained mean opening angles in ${}^{11}\mathrm{Li}$ and ${}^6\mathrm{He}$ agree with the three-body model predictions.

Figure 1

The $B(E1)$ distribution for the ${}^6\mathrm{He}$ and ${}^{11}\mathrm{Li}$ nuclei. The solid curve is obtained with a smearing procedure with $\Gamma =0.2$ MeV.

Figure 2

Coulomb breakup cross sections for ${}^6\mathrm{He}+\mathrm{Pb}$ at 240 MeV/nucleon. The solid line is the result of the full three-body calculations, while the dashed line is obtained by neglecting the off-diagonal component of the recoil kinetic energy in the excited states. The dotted line is obtained by neglecting the off-diagonal recoil term both in the ground and the excited states. These results are smeared with an energy-dependent width of $\Gamma =0.15·\sqrt{E_{\mathrm{rel}}}$ MeV. The experimental data are taken from Ref. [7].

Figure 3

Coulomb breakup cross sections for the ${}^{11}\mathrm{Li}+\mathrm{Pb}$ at 70 MeV/nucleon. The meaning of each line is the same as described in Fig. 2. The calculated results are smeared with an energy-dependent width of $\Gamma =0.25·\sqrt{E_{\mathrm{rel}}}$ MeV. The experimental data are taken from Ref. [6].

Figure 4

Geometry of a 2n halo nucleus consisting of a core nucleus and two valence neutrons.