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Register a new userCorrelations in a Many-Body Calculation of $^{bf 11}$Li
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A many-body calculation of $^{11}$Li is presented where the only input is the well-tested, finite-range {it D1S} effective interaction of {it Gogny}. Pairing correlations are included in a constrained Hartree-Fock-Bogolyubov calculation, while long-range collective correlations are introduced using a GCM derived calculation. Correlations are found to play an important role in describing $^{11}$Li. A substantive underlying $^9$Li core of $^{11}$Li is found, which has a different density profile than a free $^9$Li nucleus. This may have significant implications in the use of a three-body framework in studies of $^{11}$Li.
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We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in $^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.
We present calculations of ground state properties of spherical, doubly closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of many-body perturbation theory using a separable density dependent monopole interaction. The model gives results in Hartree-Fock order which are of similar quality to other effective density-dependent interactions. In addition, second and third order perturbation corrections to the binding energy are calculated and are found to contribute small, but non-negligible corrections beyond the mean-field result. The perturbation series converges quickly, suggesting that this method may be used to calculate fully correlated wavefunctions with only second or third order perturbation theory. We discuss the quality of the results and suggest possible methods of improvement.
The Borromean $^6$He nucleus is an exotic system characterized by two `halo neutrons orbiting around a compact $^4$He (or $alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for self-bound systems. In a similar way that there is a unique relation between the one-body density and the external potential that gives rise to it, we demonstrate that there is a unique relation between that particular many-body density and a definite many-body potential. The energy is then a functional of this density and its minimization leads to the ground-state energy of the system. As a proof of principle, the analogous of the Kohn-Sham equation is solved in the specific case of $^4$He atomic clusters, to put in evidence the advantages of this new formulation in terms of physical insights.
Coincidences between charged particles emitted in the $beta$-decay of $^{11}$Li were observed using highly segmented detectors. The breakup channels involving three particles were studied in full kinematics allowing for the reconstruction of the excitation energy of the $^{11}$Be states participating in the decay. In particular, the contribution of a previously unobserved state at 16.3 MeV in $^{11}$Be has been identified selecting the $alpha$ + $^7$He$toalpha$ + $^6$He+n channel. The angular correlations between the $alpha$ particle and the center of mass of the $^6$He+n system favors spin and parity assignment of 3/2$^-$ for this state as well as for the previously known state at 18 MeV.
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