Shigeyoshi Aoyama

The complex scaling method for many-body resonances and its applications to three-body resonances

Resonance phenomena in quantum physics are very familiar in many fields of physics, but we have not yet obtained a complete physical understanding, mathematical description or computational treatment, especially in the case of many-body resonances. Recently, in experimental developments concerning unstable nuclear physics and heavy-ion nuclear reactions, much interest has been concentrated on many-body resonance problems. In the last quarter century, theoretical and mathematical treatments of many-body resonances have experienced great development through application of the complex scaling method (CSM). We can now treat resonant states of three-body systems in the same way as those of twobody systems. In this article, starting from the definition of a resonant state and discussion of its norm, we present a summary of recent studies of CSM to treat many-body resonances and applications to three-body resonant states in two-neutron halo nuclei and three-cluster systems.

Partial Decay Widths in Coupled-Channel Systems with the Complex-Scaled Jost Function Method

Partial decay widths of resonant states in a coupled-channel system are studied by using the complex-scaled Jost function method (CSJFM). With CSJFM, we use the ratio of the S-matrices to calculate partial decay widths, and then we need not introduce any “channel radius”, which is used in standard scattering theory. Combining the Jost function method (JFM) and the complex scaling method (CSM), we can easily obtain many resonant states even for a large total width and partial decay widths simultaneously. Several methods to calculate partial decay widths in CSM are also discussed and are shown to give the same values in CSJFM.

Three-body Coulomb breakup of 11Li in the complex scaling method

Abstract Coulomb breakup strengths of 11Li into a three-body 9 Li +n+n system are studied in the complex scaling method. We decompose the transition strengths into the contributions from three-body resonances, two-body “ 10 Li +n ” and three-body “ 9 Li +n+n ” continuum states. In the calculated results, we cannot find the dipole resonances with a sharp decay width in 11Li. There is a low energy enhancement in the breakup strength, which is produced by both the two- and three-body continuum states. The enhancement given by the three-body continuum states is found to have a strong connection to the halo structure of 11Li. The calculated breakup strength distribution is compared with the experimental data from MSU, RIKEN and GSI.

Extended 9Li+n+n three-body model of 11Li with a pairing correlation in 9Li

We investigate the binding mechanism of 11 Li on the basis of an extended three-body model of 9 Li+n+n. In the model, we take into account the pairing correlation of p-shell neutrons in 9 Li, in addition to that of valence neutrons outside the 9 Li nucleus, and solve the coupled-channel two- and three-body problems of 10 Li and 11 Li, respectively. The results show that the degrees of freedom of the pairing correlation in 9 Li play an important role in the structure of 10 Li and 11 Li. In 10 Li, the pairing correlation in 9 Li produces a socalled pairing-blocking effect due to the presence of a valence neutron, which causes the sand p-wave neutron orbits to become energetically degenerate. In 11 Li, contrastingly, the pairing-blocking effect is overwhelmed by the core-n interaction due to the two degrees of freedom of the two valence neutrons surrounding 9 Li, and as a result, the ground state is dominated by the p-shell closed configuration and does not exhibit spatial extension with a large r.m.s. radius. These results indicate that the pairing correlation is realized differently in odd- and even-neutron systems of 10 Li and 11 Li. In addition, we further improve the tail part of the 9 Li-n interaction, which yields reasonable reproductions of the observed large r.m.s. radius in 11 Li.

Four-Nucleon Scattering with a Correlated Gaussian Basis Method

Elastic-scattering phase shifts for four-nucleon systems are studied in an ab-initio type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy d+d and t+p scattering. In the present method, the description of the cluster wave function is extended from (0s) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave functions of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8′ potential + a three nucleon force as a realistic interaction and the Minnesota potential as an effective interaction. Especially for 1S0, the calculated phase shifts show that the t+p and h+n channels are strongly coupled to the d+d channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of 4He consistent with experiments. No such splitting is however reproduced with the effective interaction.

The Binding Mechanism and a Low-Lying Resonance in 11Li

Using a new 9 Li-n interaction taking into account the 9 Li-core excitation, it is shown that the 9 Li+n+n model reproduces the observed binding energy of 11 Li. This 9 Li-n interaction naturally explains the degeneracy of single particle s1/2- and p1/2-orbital states above the 9 Li+n threshold. Furthermore, by using the 9 Li-n interaction, a low-lying excited resonant state is obtained in 11 Li together with the ground state, and they are found to be partners in mixed configurations of (0p1/2) 2 and (1s1/2) 2 .

Study of virtual states in 5He and 10Li with the Jost function method

Abstract We study virtual states in 5 He and 10 Li by using the Jost function method (JFM). In 5 He, we obtained an s -wave pole with the complex energy E=7.50−44.7 i MeV using a 4 He–n potential called KKNN. In 10 Li, we investigated s -wave virtual poles with the 9 Li–n interaction microscopically constructed by taking into account the Pauli-blocking effect. We obtained a virtual state at E=−0.135 MeV ( k=−0.077 i fm −1 ). The attractive property of the s -wave 9 Li–n potential for 10 Li is discussed in comparison with the 5 He ( 4 He + n) system and also calculational results for the 9 Li–n potential of Thompson and Zhukov.

Few-body models for nuclear astrophysics

We present applications of microscopic models to nuclear reactions of astrophysical interest, and we essentially focus on few-body systems. The calculation of radiative-capture and transfer cross sections is outlined, and we discuss the corresponding reaction rates. Microscopic theories are briefly presented, and we emphasize on the matrix elements of four-body systems. The microscopic extension of the R-matrix theory to nuclear reactions is described. Applications to the 2H(d, γ)4He, 2H(d, p)3H and 2H(d, n)3He reactions are presented. We show the importance of the tensor force to reproduce the low-energy behaviour of the cross sections.

Where is the ground state of 10He

Abstract We investigated the ground state of 10He by using the method of analytic continuation in the coupling constant with a 8He+n+n model. We got a solution of a three-body cluster resonance near to the 8He+n+n threshold as the ground state. Its main component is two valence neutrons in the s-orbit ( [s 1 2 s 1 2 ] 0+ ).

Development of a charged-particle nuclear reaction data retrieval system on Intelligent Pad: CONTIP

A newly designed retrieval system of charged-particle nuclear reaction data (CPND) is developed on the IntelligentPad architecture. NRDF (Nuclear Reaction Data File), which is a kind of CPND compilation, is applied as an example. The authors designed the network-based (client-server) retrieval system. The server system is constructed on a UNIX workstation with a relational database; the client system is built on a Microsoft Windows PC using an IntelligentPad software package. The system is called CONTIP, which is an abbreviation of ‘Creative, Cooperative and Cultural Objects for Nuclear data and Tools on IntelligentPad’. CONTIP will be developed to realise effective utilisation of nuclear reaction data: (i) reproduction, re-edit, reuse, (ii) circulation, coordination and evolution and (iii) knowledge discovery.