Two-particle correlations in continuum dipole transitions in Borromean nuclei

We study the energy and angular distributions of two emitted neutrons from the dipole excitation of two typical, weakly bound Borromean nuclei, ${}^{11}\mathrm{Li}$ and ${}^6\mathrm{He}$, by using a three-body model. Our calculation indicates that those distributions are considerably different between the two nuclei, even though both the nuclei exhibit similar strong dineutron correlations in the ground state to each other. We point out that this different behavior primarily reflects the interaction between the neutron and the core nucleus, especially the $s$-wave virtual state in ${}^{10}\mathrm{Li}$, rather than the interaction between the valence neutrons.

Figure 1

The dipole strength distributions, $d^{2}B(E1)/{\mathit{de}}_1{\mathit{de}}_2$, of ${}^{11}\mathrm{Li}$ as a function of the energies of the two emitted neutrons relative to the core nucleus. They are plotted in units of $e^2$ ${\mathrm{fm}}^2$/M${\mathrm{eV}}^2$. Panel (a) shows the correlated response, which fully takes into account the final state interaction between the two neutrons, while panel (b) shows the unperturbed response, obtained by neglecting the neutron-neutron interaction in the final states. Panels (c) and (d) are obtained by neglecting the neutron-core interaction, without and with the final state interaction between the two neutrons, respectively. The difference between neighboring contour levels is 0.2 $e^2$ ${\mathrm{fm}}^2$/M${\mathrm{eV}}^2$ for panels (a) and (b), while it is 0.1 $e^2\hspace{0.5em}{\mathrm{fm}}^2/{\mathrm{MeV}}^2$ for panels (c) and (d).

Figure 2

Same as Fig. 1, but for ${}^6\mathrm{He}$. The difference between neighboring contour levels is 0.02 $e^2\hspace{0.5em}{\mathrm{fm}}^2/{\mathrm{MeV}}^2$ for Figs. 2a and 2b, while it is 0.005 and 0.01 $e^2\hspace{0.5em}{\mathrm{fm}}^2/{\mathrm{MeV}}^2$ for Figs. 2c and 2d, respectively.

Figure 3

(Top) The dipole strength distribution for ${}^{11}\mathrm{Li}$ as a function of $E=e_1+e_2$. The thick solid, dashed, dotted, and dot-dashed lines were obtained under the same assumptions as for Figs. 1a, 1b, 1c, and 1d, respectively. These curves are smeared with the experimental energy resolution. The thin solid line is the same as the thick solid line, but without the smearing. The experimental data are taken from Ref. [6]. (Bottom) The same as the top panel, but for ${}^6\mathrm{He}$. The shaded area shows the experimental data, taken from Ref. [7].

Figure 4

Angular distributions of the two valence neutrons in ${}^{11}\mathrm{Li}$ and ${}^6\mathrm{He}$ emitted in the rest frame of the corresponding nuclei. These are calculated for the configuration in which the two neutrons are emitted in the same reaction plane (i.e., ${\varphi }_1={\varphi }_2$) by the longitudinal component of the $E1$ operator. Panel (a) shows the angular distribution for ${}^{11}\mathrm{Li}$ at $e_1=0.375$ MeV and $e_2=0.075$ MeV, while panels (b) and (c) are for $e_1=e_2=0.225$ MeV and $e_1=e_2=0.5$ MeV, respectively. Panel (d) shows the angular distribution for ${}^6\mathrm{He}$ at $e_1=e_2=0.7$ MeV. The difference between neighboring contour levels is 0.03.