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Register a new userContainer structure of alpha alpha Lambda clusters in $_Lambda^9$Be
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New concept of clustering is discussed in $Lambda$ hypernuclei using a new-type microscopic cluster model wave function, which has a structure that constituent clusters are confined in a container, whose size is a variational parameter and which we refer to as Hyper-Tohsaki-Horiuchi-Schuck-Ropke (Hyper-THSR) wave function. By using the Hyper-THSR wave function, $2alpha + Lambda$ cluster structure in ${^{9}_Lambda{rm Be}}$ is investigated. We show that full microscopic solutions in the $2alpha + Lambda$ cluster system, which are given as $2alpha + Lambda$ Brink-GCM wave functions, are almost perfectly reproduced by the single configurations of the Hyper-THSR wave function. The squared overlaps between the both wave functions are calculated to be $99.5$%, $99.4$%, and $97.7$% for $J^pi=0^+$, $2^+$, and $4^+$ states, respectively. We also simulate the structural change by adding the $Lambda$ particle, by varying the $Lambda N$ interaction artificially. As the increase of the $Lambda N$ interaction, the $Lambda$ particle gets to move more deeply inside the core and invokes strongly the spatial core shrinkage, and accordingly distinct localized $2alpha$ clusters appear in the nucleonic intrinsic density, though in ${^{8}{rm Be}}$ rather gaslike $2alpha$-cluster structure is shown. The origin of the localization is associated with the strong effect of Pauli principle. We conclude that the container picture of the $2alpha$ and $Lambda$ clusters is essential in understanding the cluster structure in ${^{9}_Lambda{rm Be}}$, in which the very compact spatial localization of clusters is shown in the density distribution.
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We study the structure of $^9_Lambda$Be in the framework of three body $alpha+alpha+Lambda$ cluster model using YNG-NF interaction with the Gaussian expansion method. Employing the complex scaling method, we obtain the energies of bound states as well as energies and decay widths of the resonant states. By analyzing our wave functions of bound states and resonant states, we confirm three analogue states of $^9_Lambda$Be pointed out by Band${rm bar{o}}$ and Motoba {it et al.} cite{motoba1983,motoba1985,bando1983}, $^8$Be analogue states, $^9_{Lambda}$Be genuine states and $^9$Be analogue states. The new states of $^9_Lambda$Be are also obtained at a high energy region with broader decay widths.
We investigate properties of bound and resonance states in the $_{Lambda}^{9}$Be nucleus. To reveal the nature of these states, we use a three-cluster $2alpha+Lambda$ microscopic model. The model incorporates Gaussian and oscillator basis functions and reduces a three-cluster Schr{o}dinger equation to a two-body like many-channel problem with the two-cluster subsystems ($_{Lambda}^{5}$He and $^8$Be) being in a bound or a pseudo-bound state. Influence of the cluster polarization on the energy and widths of resonance states in $_{Lambda}^{9}$Be and on elastic and inelastic $_{Lambda}^{5}$He+$alpha$ scattering is analyzed.
We propose a new approach to probe the spatial extension of the valence neutron orbital in the $^{9}$Be nucleus via the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction. This property of the nuclear molecular orbital has not been established in previous experimental studies and divergence exists between the theoretical descriptions of ${}^{9}$Be from different perspectives, textit{i.e.}, the antisymmetrized molecular dynamics and the container pictures of cluster dynamics. These pictures are represented by two different well-proven microscopic models, the antisymmetrized molecular dynamics (AMD) and Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave functions. The corresponding reduced width amplitudes (RWAs) in the $^{8}$Be$+n$ channel are extracted from both the AMD and THSR wave functions, and they are found to describe drastically different valence-nucleon motion, which shows the theoretical ambiguity in describing the $pi$-orbitals in $^{9}$Be. Using the RWAs as input, the physical observables of the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction are predicted by the distorted-wave impulse approximation (DWIA) framework. The magnitudes of the triple-differential cross sections (TDX) are found to be highly sensitive to the RWA input. It is concluded that the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction could provide a feasible probing for the subtle differences between several structure models manifesting through the spatial extension of the $pi$-orbital in the $^{9}$Be nucleus.
We carry out Faddeev calculations of three-alpha (3 alpha) and two-alpha plus Lambda (alpha alpha Lambda) systems, using two-cluster resonating-group method kernels. The input includes an effective two-nucleon force for the alpha alpha resonating-group method and a new effective Lambda N force for the Lambda alpha interaction. The latter force is a simple two-range Gaussian potential for each spin-singlet and triplet state, generated from the phase-shift behavior of the quark-model hyperon-nucleon interaction, fss2, by using an inversion method based on supersymmetric quantum mechanics. Owing to the exact treatment of the Pauli-forbidden states between the clusters, the present three-cluster Faddeev formalism can describe the mutually related, alpha alpha, 3 alpha and alpha alpha Lambda systems, in terms of a unique set of the baryon-baryon interactions. For the three-range Minnesota force which describes the alpha alpha phase shifts quite accurately, the ground-state and excitation energies of 9Be Lambda are reproduced within 100 - 200 keV accuracy.
We investigate the linear-chain configurations of four-$alpha$ clusters in $^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum (13-18 $hbar$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia ($hbar^2/2Theta$ $sim$ 0.06-0.08 MeV) can exist.
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