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.
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 …
A practical method to solve cut-off Coulomb problems of two-cluster systems in the momentum space is given. When a sharply cut-off Coulomb force with a cut-off radius $ρ$ is introduced at the level of constituent particles, two-cluster direct potential of the Coulomb force becomes in general a local screened Coulomb potential. The asymptotic Hamiltonian yields two types of asymptotic waves; one is an approximate Coulomb wave with $ρ$ in the middle-range region, and the other a free (no-Coulomb) wave in the longest-range region. The constant Wronskians of this Hamiltonian can be calculated in e…
We calculate n alpha phase-shifts and scattering observables in the resonating-group method, using the nuclear-matter G-matrix of an SU_6 quark-model NN interaction. The G-matrix is generated in the recent energy-independent procedure of the quark-model NN interaction with the continuous prescription for intermediate spectra, by assuming an appropriate Fermi momentum k_F=1.2 fm^-1. The n alpha RGM interaction kernels are evaluated with explicit treatments of the nonlocality and momentum dependence of partial-wave G-matrix components. The momentum dependence of the G-matrix components is differ…
The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.
We investigate colorless (mesonic) 3q-q qbar components in the nucleon and the Roper resonance N*(1440). Starting from constituent quarks and gluons we estimate the excitation of quark-antiquark pairs in a gluon exchange model with the strong coupling constant extracted from a comparison with a non-perturbative resonating group calculation of the pi, eta, rho and omega content of the nucleon. Applying the same model to the Roper resonance, we find as the most striking result a very strong scalar-isoscalar sigma content of the N*(1440) with a strength of the 3q-q qbar configurations comparable …
We introduce an extension of the ab initio no-core shell model/resonating group method (NCSM/RGM) in order to describe three-body cluster states. We present results for the $^6$He ground state within a $^4$He+n+n cluster basis as well as first results for the phase shifts of different channels of the $^4$He+n+n system which provide information about low-lying resonances of this nucleus.
Quark-model nucleon-nucleon and hyperon-nucleon interactions by the Kyoto- Niigata group are applied to the hypertriton calculation in a new three-cluster Faddeev formalism using the two-cluster resonating-group method kernels. The most recent model, fss2, gives a reasonable result similar to the Nijmegen soft-core model NSC89, except for an appreciable contributions of higher partial waves.
Clustering plays an important role in the structure of nuclei, especially for light nuclei in the $p$-shell. In nuclear cluster models these degrees of freedom are introduced explicitly. In the Resonating Group Method or in the Generator Coordinate Method the clusters are built from individual nucleons interacting via an effective nucleon-nucleon interaction; the total wave function is antisymmetrized. Fermionic Molecular Dynamics (FMD) goes beyond pure cluster models. It is a microscopic many-body approach using a Gaussian wave packet basis that includes the harmonic oscillator shell model an…
We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed to the Faddeev equation which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximat…
A dynamical calculation of pentaquark systems with quark contents $uudd\bar{s}$ is performed in the framework of quark delocalization color screening model with the help of resonating group method. The effective potentials between baryon and meson clusters are given, and the possible bound states or resonances are investigated. The single calculations show that the $NK^{*}$ with $I=0, J^{P}=\frac{1}{2}^{-}$, $ΔK^{*}$ with $I=1, J^{P}=\frac{1}{2}^{-}$, and $ΔK^{*}$ with $I=2, J^{P}=\frac{3}{2}^{-}$ are all bound, but they all turns into scattering states by coupling with the corresponding open …
Within the microscopic model based on the algebraic version of the resonating group method the role of the Pauli principle in the formation of continuum wave function of nuclear systems composed of three identical $s$-clusters has been investigated. Emphasis is placed upon the study of the exchange effects contained in the genuine three-cluster norm kernel. Three-fermion, three-boson, three-dineutron ($3d'$) and $3α$ systems are considered in detail. Simple analytical method of constructing the norm kernel for $3α$ system is suggested. The Pauli-allowed basis functions for the $3α$ and $3d'$ s…
It is found that $α$ cluster structure has the apparently opposing dual property of crystallinity and condensation simultaneously. The mathematical equivalence of the spatially localized Brink $α$ cluster model in the generator coordinate method (GCM) and the nonlocalized cluster model (NCM), which is also called the THSR (Tohsaki-Horiuchi-Schuck-R$\ddot{\rm o}$pke) wave function based on the condensation of $α$ clusters, is shown. The latter is found to be an equivalent representation of the localized cluster model and it is a natural consequence that the many NCM (THSR) calculations reproduc…
Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-Lambda plus alpha system in a new three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-Lambda separation energy Delta B_{Lambda Lambda}=1.41 MeV, which is consistent with the recent empirical value, Delta B^{exp}_{Lambda Lambda}=1.01 +/- 0.20 MeV, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.
We introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method (NCSM/RGM). Energy-independent non-local interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of…
The low-lying continuum spectrum of the $^6{\rm He}$ nucleus is investigated for the first time within an ab initio framework that encompasses the $^4{\rm He}$+$n$+$n$ three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core-shell model combined with the resonating-group method, in which energy-independent non-local interactions among three nuclear fragments can be calculated microscopically starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödi…
We investigate the $α$+\oo\ cluster structure in the inversion-doublet band ($K^π=0_{1}^\pm$) states of \nene\ with an angular-momentum-projected version of the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function, which was successful "in its original form" for the description of, e.g., the famous Hoyle state. In contrast with the traditional view on clusters as localized objects, especially in inversion doublets, we find that these {\it single} THSR wave functions, which are based on the concept of nonlocalized clustering, can well describe the $K^π=0_1^-$ band and the $K^π=0_1^+$ band. For in…
We present explicit analytical formulae for two-body matrix elements between Pauli-projected single-particle orbits generated by gaussians shifted from the centre of a nuclear core, which is populated by nucleons occupying harmonic-oscillator orbits. Such shifted gaussian orbits appear in the generator-coordinate model of two-cluster systems and, as ingredients of generating functions, in the resonating group model as well. A Pauli projection is to be understood as a projection onto the subspace not occupied by the core nucleons. This is an exact procedure to take into account the Pauli princi…
Three-body hadronic models with separable pairwise interactions are formulated and solved to calculate resonance masses and widths of L=0 N-Delta and Delta-Delta dibaryons using relativistic kinematics. For N-Delta, I(JP)=1(2+) and 2(1+) resonances slightly below threshold are found by solving pi-N-N Faddeev equations. For Delta-Delta, several resonances below threshold are found by solving pi-N-Delta Faddeev equations in which the N-Delta interaction is dominated by the 1(2+) and 2(1+) resonating channels. The lowest Delta-Delta dibaryon resonances found are for I(JP)=0(3+) and 3(0+), the for…
The resonance states of $^{4}H$, $^{4}He$ and $^{4}Li$, embedded in the three-cluster $d+N+N$ continuum, are investigated within a three-cluster model. The model treats the Pauli principle exactly and incorporates the Faddeev components for proper description of the boundary conditions for the two- and three-body continua. The hyperspherical harmonics are used to distinguish and numerate channels of the three-cluster continuum. It is shown that the effective barrier, created by three-cluster configuration $d+N+N$, is strong enough to accommodate two resonance states.
We study nature of the low-lying resonance states in mirror nuclei $^{9}$Be and $^{9}$B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides convenient description of three-cluster continuum. The dominant three-cluster configurations $α+α+n$ and $α+α+p$ in $^{9}$Be and $^{9}$B, respectively, are taken into account. Dominant decay channels for all resonance states in $^{9}$Be and $^{9}$B are explored. Much attention is paid to the controversial $1/2^{+}$ resonance states in both nuclei. We study effects of the Coulomb in…
We theoretically investigate the possibility for a tetraneutron to exist as a low-energy resonance state. We explore a microscopic model based on the assumption that the tetraneutron can be treated as a compound system where $^3$n+n and $^2$n+$^2$n coupled cluster configurations coexist. The influence of the Pauli principle on the kinetic energy of the relative motion of the neutron clusters is shown to result in their attraction. The strength of such attraction is high enough to ensure the existence of a low-energy resonance in the tetraneutron, provided that the oscillator length is large en…
With a view toward describing reactions of intermediate-mass nuclei from first principles, we present first results for the norm and Hamiltonian overlaps (kernels) for the p-α, p-16O and p-20Ne cluster systems using realistic nucleon-nucleon interactions. This is achieved in the framework of a new ab initio approach that combines the symmetry-adapted no-core shell model (SA-NCSM) with the resonating group method (RGM). In this model, a physically relevant basis based on the SU(3) symmetry is used. The structure of the clusters is provided by the ab initio SA-NCSM, which enables the description…
We extend the ab initio no-core shell model/resonating-group method (NCSM/RGM) to projectile-target binary-cluster states where the projectile is a deuteron. We discuss the formalism in detail and give algebraic expressions for the integration kernels. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we calculate deuteron-4He scattering and investigate 6Li bound and unbound states. Virtual three-body breakup effects are obtained in an approximated way by including excited pseudo-states of the deuteron in the calculation. We compare our results to experime…
We analyze the possible existence of a resonance in the $J^P=0^-$ channel with isospin two by means of nucleon-$Δ$ interactions based on the constituent quark model. We solve the bound state and the scattering problem using two different potentials, a local and a non-local one. The non-local potential results to be the more attractive, although not enough to generate the experimentally predicted resonance.
We investigate how the Coulomb interaction affects the energy $E$ and width $Γ$ of resonance states in mirror nuclei. We employ a three-cluster microscopic model to determine position of resonance states in two- and three-body continua. Two parameters are introduced to quantify effects of the Coulomb interactions. As the energy and width of the corresponding resonance states of mirror nuclei are displayed on an $E$-$Γ$ plane, these parameters determine a rotation and a dilatation. With the help of these parameters we found resonance states with strong, small and medium effects of the Coulomb i…
We discuss resonance properties in three-body systems, with examples on $^{12}{\rm C}$ and $^{24}{\rm Mg}$. We use a microscopic cluster model, where the generator coordinate is defined in the hyperspherical formalism. The $^{12}{\rm C}$ nucleus is described by an $α+α+α$ structure, whereas $^{24}{\rm Mg}$ is considered as an $^{16}{\rm O}+α+α$ system. We essentially pay attention to resonances. We review various techniques which may extend variational methods to resonances. We consider $0^+$ and $2^+$ states in $^{12}{\rm C}$ and $^{24}{\rm Mg}$. We show that the r.m.s. radius of a resonance …
A microscopic model for three-cluster configurations in light nuclei is presented. It uses an expansion in terms of Faddeev components for which the dynamic eqations are derived. The model is designed to investigate binary channel processes in a compound system. Gaussian and oscillator bases are used to expand the wave function and to represent appropriate boundary conditions. We study the effect of cluster polarization on ground and resonance states of 7Be, and on the astrophysical S-factor of the reaction 6Li(p,3He)4He.
We investigate resonances in light halo nuclei using a fully microscopic cluster model and the complex scaling method. We make use of the hermitian representation of the complex scaling method. The general structure of the cluster model is that of a correlation operator acting on a starting function that describes a number of neutrons relative to an alpha-particle. The correlation operator is expanded in terms of a small non-orthogonal set of Gaussian basis states and we make use of a simplified, central but state-dependent, interaction. The many-body integrals required for the computation are…
The fundamental description of both structural properties and reactions of light nuclei in terms of constituent protons and neutrons interacting through nucleon-nucleon and three-nucleon forces is a long-sought goal of nuclear theory. I will briefly present a promising technique, built upon the {\em ab initio} no-core shell model, which emerged recently as a candidate to reach such a goal: the no-core shell model/resonating-group method. This approach, capable of describing simultaneously both bound and scattering states in light nuclei, complements a microscopic cluster technique with the use…
The antisymmetrization of the composite particles in cluster model calculations manifests itself in Pauli forbidden states (ghost states), if one restricts oneself on undeformed cluster in the low energy region. The resonating group method and the generating coordinate method rely on a property of the norm kernel, which introduces some of the ghost states. The norm kernel has been usually calculated under the assumption that the inner wavefunctions have a simple Gaussian form. It is the first time that this assumption is tested by the rigorous way. In the 4He+N system, we demonstrate a ghost s…
We compute energy distributions of three $α$-particles emerging from the decay of $^{12}$C resonances by means of the hyperspherical adiabatic expansion method combined with complex scaling. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. The substantial changes from small to large distances determine the decay mechanisms. We illustrate by computing the energy distributions from decays of the $1^{+}$ and $3^-$-resonances in $^{12}$C. These states are dominated by direct and sequential decays into the three-body continuum respectively…
We study the nonresonant part of the $^7$Be($p,γ$)$^8$B reaction using a three-cluster resonating group model that is variationally converged and virtually complete in the $^4$He+$^3$He+$p$ model space. The importance of using adequate nucleon-nucleon interaction is demonstrated. We find that the low-energy astrophysical $S$-factor is linearly correlated with the quadrupole moment of $^7$Be. A range of parameters is found where the most important $^7$Be and $^7$Li properties are reproduced simultaneously; the corresponding $S$-factor at $E_{\rm cm}=20$ keV is $24.6-26.1$ eV$\cdot$b.
It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003)) that the widths of narrow proton resonances are related to neutron Asymptotic Normalization Coefficients (ANCs) of their bound mirror analogs because of charge symmetry of nucleon-nucleon interactions. This relation is approximated by a simple analytical formula which involves proton resonance energies, neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. In the present paper, we perform microscopic-cluster model calculations for the ratio of proton widt…
We discuss the degree of anharmonicity of dipole plasmon resonances in metal clusters. We employ the time-dependent variational principle and show that the relative shift of the second phonon scales as $N^{-4/3}$ in energy, $N$ being the number of particles. This scaling property coincides with that for nuclear giant resonances. Contrary to the previous study based on the boson-expansion method, the deviation from the harmonic limit is found to be almost negligible for Na clusters, the result being consistent with the recent experimental observation.
The mass and wave function of a six-quark system with quantum numbers J^P=0^-, T=0, called d', are calculated. We use a colored diquark-tetraquark cluster model for the six-quark wave function. A constituent quark model Hamiltonian with a two-body confinement potential, and residual one-gluon, one-pion, and one-sigma exchange interactions is used. The complications due to the quark exchange interactions between tetraquark and diquark clusters (Pauli principle) are taken into account within the framework of the Resonating Group Method. The calculated d' mass is some 350 MeV above the empirical …
Motivation: Detailed experimental knowledge of the level structure of light weakly bound nuclei is necessary to guide the development of new theoretical approaches that combine nuclear structure with reaction dynamics. Purpose: The resonant structure of 8B is studied in this work. Method: Excitation functions for elastic and inelastic 7Be+p scattering were measured using a 7Be rare isotope beam. Excitation energies ranging between 1.6 and 3.4 MeV were investigated. An R-matrix analysis of the excitation functions was performed. Results: New low-lying resonances at 1.9, 2.5, and 3.3 MeV in 8B a…
It is studied how the $α$ cluster degrees of freedom, such as $α$ clustering configurations close to the $α$ decay threshold in $^{12}$C and $^{16}$O, including the linear chain, triangle, square, kite, and tetrahedron, affect nuclear collective vibrations with a microscopic dynamical approach, which can describe properties of nuclear ground states well across the nuclide chart and reproduce the standard giant dipole resonance (GDR) of $^{16}$O quite nicely. It is found that the GDR spectrum is highly fragmented into several apparent peaks due to the $α$ structure. The different $α$ cluster co…
There is a deep astrophysical interest in the structure of $^{19}$F states close to the alpha decay threshold. The nuclear structure of these states is important for understanding of the development of $α$ clustering in the $^{20}$Ne region. Emergence of clustered states and generally states that favor coupling to reaction channels near the corresponding decay thresholds is currently of special interest in theoretical physics. Excitation function for $^{15}$N($α$,$α$) elastic scattering was measured by the TTIK method. These new data together with old, high energy resolution data, were analyze…
The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius …
