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Register a new userTowards modeling cluster structure of $^8$Be with chiral interaction
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Authors
Tokuro Fukui
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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.
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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.
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.
Background: Recent theoretical and experimental researches using proton-induced $alpha$-knockout reactions provide direct manifestation of $alpha$-cluster formation in nuclei. In recent and future experiments, $alpha$-knockout data are available for neutron-rich beryllium isotopes. In $^{12}$Be , rich phenomena are induced by the formation of $alpha$-clusters surrounded by neutrons, for instance, breaking of the neutron magic number $N=8$. Purpose: Our objective is to provide direct probing of the $alpha$-cluster formation in the $^{12}$Be target through associating the structure information obtained by a microscopic theory with the experimental observables of $alpha$-knockout reactions. Method: We formulate a new wave function of the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) type for the structure calculation of ${}^{12}$Be nucleus and integrate it with the distorted wave impulse approximation framework for the $alpha$-knockout reaction calculation of $^{12}$Be$(p,palpha)^{8}$He. Results: We reproduce the low-lying spectrum of the $^{12}$Be nucleus using the THSR wave function and discuss the cluster structure of the ground state. Based on the microscopic wave function, the optical potentials and $alpha$-cluster wave function are determined and utilized in the calculation of ${}^{12}$Be($p,palpha$)${}^{8}$He reaction at 250 MeV. The possibility of probing the clustering state of $^{12}$Be through this reaction is demonstrated by analysis of the triple differential cross sections that are sensitively dependent on the $alpha$-cluster amplitude at the nuclear surface. Conclusions: This study provides a feasible approach to validate directly the theoretical predictions of clustering features in the $^{12}$Be nucleus through the $alpha$-knockout reaction.
The study of inelastic scattering and multi-nucleon transfer reactions was performed by bombarding a $^{9}$Be target with a $^3$He beam at an incident energy of 30 MeV. Angular distributions for $^9$Be($^3$He,$^3$He)$^{9}$Be, $^9$Be($^3$He,$^4$He)$^{8}$Be, $^9$Be($^3$He,$^5$He)$^{7}$Be, $^9$Be($^3$He,$^6$Li)$^6$Li and $^9$Be($^3$He,$^5$Li)$^7$Li reaction channels were measured. Experimental angular distributions for the corresponding ground states (g.s.) were analysed within the framework of the optical model, the coupled-channel approach and the distorted-wave Born approximation. Cross sections for channels leading to unbound $^5$He$_{g.s.}$, $^5$Li$_{g.s.}$ and $^8$Be systems were obtained from singles measurements where the relationship between the energy and the scattering angle of the observed stable ejectile is constrained by two-body kinematics. Information on the cluster structure of $^{9}$Be was obtained from the transfer channels. It was concluded that cluster transfer is an important mechanism in the investigated nuclear reactions. In the present work an attempt was made to estimate the relative strengths of the interesting $^8$Be+$n$ and $^5$He+$alpha$ cluster configurations in $^9$Be. The branching ratios have been determined confirming that the $^5$He+$alpha$ configuration plays an important role. The configuration of $^9$Be consisting of two bound helium clusters $^3$He+$^6$He is significantly suppressed, whereas the two-body configurations ${}^{8}$Be+$n$ and ${}^{5}$He+$alpha$ including unbound $^8$Be and $^5$He are found more probable.
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