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Register a new userA multi-channel model for an {alpha} plus $^6$He nucleus cluster
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A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the $alpha$+${}^6$He cluster system, so finding a model spectrum for ${}^{10}$Be to more than 10 MeV excitation. Three states of ${}^6$He are included and the resonance character of the two excited states taken into account in finding solutions. A model Hamiltonian has been found that gives very good agreement with the known bound states and with some low-lying resonances of ${}^{10}$Be. More resonance states are predicted than have as yet been observed. The method also yields $S$-matrices which we have used to evaluate low-energy ${}^6$He-$alpha$ scattering cross sections. Reasonable reproduction of low-energy differential cross sections and of energy variation of cross sections measured at fixed scattering angles is found.
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Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is derived describing $^6$He in terms of a $^4$He-core and two neutrons. The Watson first order multiple scattering ansatz is extended to accommodate the internal dynamics of a composite cluster model for the $^6$He nucleus scattering from a nucleon projectile. The calculations are compared with the recent experiments at the projectile energy of 71 MeV/nucleon. In addition, differential cross sections and analyzing powers are calculated at selected higher energies.
The $beta$-decay process of the $^6$He halo nucleus into the $alpha+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $alpha+n+n$ system in hyperspherical coordinates on a Lagrange-mesh. The shape and absolute values of the transition probability per time and energy units of new experiments are reproduced with a modified $alpha+d$ potential. The obtained total transition probabilities are $2.48 times 10^{-6}$ s$^{-1}$ for the full energy region and $2.40 times 10^{-6}$ s$^{-1}$ for the cut-off $E>150$ keV. The strong cancellation between the internal and halo parts of the $beta$ decay matrix element is a challenge for future {it ab initio} calculations.
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 bound state of uclide[6][LambdaLambda]{He} is studied as a three-body ($LambdaLambdaalpha$) system in a cluster effective field theory at leading order (LO). We find that the system exhibits the limit cycle which is associated with the formation of bound states called the Efimov states. This implies that the three-body contact interaction should be promoted to LO. The relationship of the binding energy and the $LambdaLambda$ scattering length is discussed as well as the role of the scale in this system.
We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of the Hamiltonian within the harmonic-oscillator expansion of the no-core shell model are coupled with continuous microscopic three-cluster states to correctly describe the nuclear wave function both in the interior and asymptotic regions. We discuss the formalism in detail and give algebraic expressions for the case of core+$n$+$n$ systems. Using similarity-renormalization-group evolved nucleon-nucleon interactions, we analyze the role of $^4$He+$n$+$n$ clustering and many-body correlations in the ground and low-lying continuum states of the Borromean $^6$He nucleus, and study the dependence of the energy spectrum on the resolution scale of the interaction. We show that $^6$He small binding energy and extended radii compatible with experiment can be obtained simultaneously, without recurring to extrapolations. We also find that a significant portion of the ground-state energy and the narrow width of the first $2^+$ resonance stem from many-body correlations that can be interpreted as core-excitation effects.
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