Continuum spectroscopy of Borromean two-neutron halo nuclei

Energy and angular correlation distributions of the three fragments in ${}^6\mathrm{He}$ breakup on ${}^{208}\mathrm{Pb}$ at a collision energy of 240 MeV/nucleon are discussed within the microscopic four-body distorted wave model and compared with experimental data. The nuclear structure of the ground state and low-energy three-body continuum of ${}^6\mathrm{He}$ is calculated by the method of hyperspherical harmonics within the three-body cluster model. Reflections of the fundamental permutation symmetry of the halo neutrons in angular and energy correlations are pointed out. The calculations describe the experimental data for fragment correlations near breakup threshold rather well, and the physics is contained in a few elementary modes; but with increasing excitation energy of ${}^6\mathrm{He}$, some striking deviations from experimental distributions are encountered. Possible reasons for this are discussed.

Figure 1

$T$ and $Y$ Jacobi coordinate systems for two-neutron halo nucleus.

Figure 2

Energy correlations of elementary modes of $2^{+}$ excitation with hypermoment $K=2$. (a) $T$ system: dashed, dotted, and thin solid lines marked by the 1, 2, and 3 show correlations of modes with quantum numbers ($L,S,l_x^T,l_y^T$) as (2, 0, 0, 2), (2, 0, 2, 0), and (1, 1, 1, 1), respectively. (b),(c), and (d) show decompositions in the $Y$ system of modes 1, 2, and 3, respectively. Thick solid line is for total correlation; dashed, dotted, and thin solid lines show the partial content with quantum numbers ($L,S,l_x^Y,l_y^Y$) as (2, 0, 0, 2), (2, 0, 2, 0), and (2, 0, 1, 1), respectively.

Figure 3

Energy correlations for $2^{+}$ resonance in ${}^6\mathrm{He}$ in the (a) $T$ and (b) $Y$ coordinate systems. Dashed, dotted, and dashed-dotted lines show contributions from elementary modes marked by the quantum numbers ($L,S,l_x,l_y$).

Figure 4

Comparison of theoretical ${}^6\mathrm{He}$ excitation spectrum (thick solid line) for ${}^6\mathrm{He}$$+{}^{208}\mathrm{Pb}$ breakup at 240 MeV/nucleon with experimental data [4]. Thin solid, dashed, and dotted lines show the dipole $1^{-}$, quadrupole $2^{+}$, and monopole $0^{+}$ contributions.

Figure 5

Energy (a) and (b) and angular (c) and (d) fragment correlations (solid line) in the ${}^6\mathrm{He}$$+{}^{208}\mathrm{Pb}$ breakup at 240 MeV/nucleon for excitation energy region $0<E_{\kappa }<1$ MeV. (a) and (c) are shown in Jacobi configuration $T$; (b) and (d) in configuration $Y$. Dashed, dotted, and dash-dotted lines show the dipole $1^{-}$, monopole $0^{+}$, and quadrupole $2^{+}$ contributions, respectively.

Figure 6

Same as Fig. 5, but for excitation energy region $1<E_{\kappa }<3$ MeV.

Figure 7

Same as Fig. 5, but for excitation energy region $3<E_{\kappa }<6$ MeV.

Figure 8

Same as Fig. 5, but for excitation energy region $6<E_{\kappa }<9$ MeV.

Figure 9

Neutron-neutron energy correlations in ${}^6\mathrm{He}$+${}^{208}\mathrm{Pb}$ breakup at 240 MeV/nucleon. Dashed, dash-dotted, and solid lines show calculations with only Coulomb, only nuclear, and full (nuclear + Coulomb) interactions, respectively.