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Register a new userResonance structure of $^{8}$Be with the two-cluster resonating group method
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A two-cluster microscopic model is applied to study elastic alpha-alpha scattering and resonance structure of $^{8}$Be. The model is an algebraic version of the Resonating Group Method, which makes use complete set of oscillator functions to expand wave function of two-cluster system. Interaction between clusters is determined by well-known semi-realistic nucleon-nucleon potentials of Hasegawa-Nagata, Minnesota and Volkov. Detail analysis of resonance wave functions is carried out in oscillator, coordinate and momentum spaces. Effects of the Pauli principle on wave functions of the $^{8}$Be continuous spectrum states are thoroughly studied.
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How the nuclear force behaves in cluster states, in particular those consisting of the $alpha$ clusters, has been investigated so far, but not yet elucidated. Today the chiral effective field theory is established and it would shed new light on the microscopic understanding of the cluster states. We aim to address a possible source of the attraction in the cluster states of $^8mathrm{Be}$ in view of the pion exchange. Namely, we investigate whether the two-pion-exchange interaction acts as a dominant attraction in the $alpha+alpha$ system as predicted by a previous work. We describe theoretically the cluster structure of $^8mathrm{Be}$ by the Brink model, for which the effective interaction is designed from the realistic nuclear force derived through the chiral effective field theory. The two-body matrix elements of the chiral interaction with the local-Gaussian bases are formulated within the approximation of the spin-isospin saturation forming an $alpha$ particle. Introducing a global prefactor to the chiral interaction phenomenologically, the ground and low-lying excited states of $^8mathrm{Be}$, the scattering phase shift of the $alpha$-$alpha$ system as well, are satisfactorily depicted. The attraction in the cluster states is found to be stemming from the two-pion-exchange contributions dominantly, along with nonnegligible short-range terms. The present work can be the foundation towards constructing realistic cluster models, by which the cluster states will be revealed microscopically in the next step.
The G-matrix equation is most straightforwardly formulated in the resonating-group method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energy-dependence involved in the exchange term of the normalization kernel plays the essential role to define the off-shell T-matrix uniquely when the complete Pauli-forbidden state exists. We analyze this using a simple solvable model with no quark-quark interaction, and calculating the most general T-matrix in the formulation developed by Noyes and Kowalski. This formulation gives a certain condition for the existence of the solution in the Lippmann-Schwinger resonating-group method. A new procedure to deal with the corrections for the reduced masses and the internal-energy terms in the Lambda N - Sigma N coupled-channel resonating-group equation is proposed.
In this paper, we extend the framework of improved version of simplified method to take into account the tensor contribution ($i$SMT) and propose AQCM-T, tensor version of antisymmetrized quasi cluster model (AQCM). Although AQCM-T is phenomenological, we can treat the $^3S$-$^3D$ coupling in the deuteron-like $T=0$ $NN$-pair induced by the tensor interaction in a very simplified way, which allows us to proceed to heavier nuclei. Also we propose a new effective interaction, V2m, where the triplet-even channel of the Volkov No.2 interaction is weakened to 60% so as to reproduce the binding energy of $^4$He after including the tensor term of a realistic interaction. Using AQCM-T and the new interaction, the significant tensor contribution in $^4$He is shown, which is almost comparable the central interaction, where $D$-state mixes by 8% to the major $S$-state. The AQCM-T model with the new interaction is also applied to $^8$Be. It is found that the tensor suppression gives significant contribution to the short-range repulsion between two {alpha} clusters.
We investigate the evolution of clustering structure through the momentum distributions in the $^{8-10}$Be isotopes. The nucleon dynamics within the inter-cluster antisymmetrization are discussed via the momentum distribution of a Brink type $alpha$-$alpha$ wave function. For the state with a small $alpha$-$alpha$ distance, we observe a significant depression with a dip structure at zero-momentum and an enhanced tail at relatively higher momentum region. In addition, we find the cluster structure in the intrinsic frame of momentum space, which is complementary to its significant $alpha$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8-10}$Be isotopes, the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at the zero-momentum of nucleon distribution for the two $alpha$-clusters within $^{8-10}$Be isotopes. For the compact $^{10}$Be nucleus, the momentum distribution of all nucleons shows significant depression at zero-momentum with a dip structure, which is found to be contributed by both the inter-cluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $alpha$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.
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.
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