arXiv subjects

Kazuo Takayanagi

Publications and source records attributed to Kazuo Takayanagi.

5 recordsLinked to original sources

arXiv2024

General theory of constructing potential with bound states in the continuum

We present a general theory of potentials that support bound states at positive energies (bound states in the continuum). On the theoretical side, we prove that, for systems described by nonlocal potentials of the form $V(r,r')$, bound states at positive energies are as common as those at negative energies. At the same time, we show that a local potential of the form $V(r)$ rarely supports a positive energy bound state. On the practical side, we show how to construct a (naturally nonlocal) potential which supports an arbitrary normalizable state at an arbitrary positive energy. We demonstrate our theory with numerical examples both in momentum and coordinate spaces with emphasis on the important role played by nonlocal potentials. Finally, we discuss how to observe bound states at positive energies, and where to search for nonlocal potentials which may support them.

quant-ph↗

arXiv2017

Exotic neutron-rich medium-mass nuclei with realistic nuclear forces

We present the first application of the newly developed EKK theory of the effective nucleon-nucleon interaction to shell-model studies of exotic nuclei, including those where conventional approaches with fitted interactions encounter difficulties. This EKK theory enables us to derive the interaction suitable for several major shells ($sd$+$pf$ in this work). By using such an effective interaction obtained from the Entem-Machleidt QCD-based $χ\mathrm{N}^3\mathrm{LO}$ interaction and the Fujita-Miyazawa three-body force, the energies, E2 properties and spectroscopic factors of low-lying states of neutron-rich Ne, Mg and Si isotopes are nicely described, as the first shell-model description of the "island of inversion" without fit of the interaction. The long-standing question as to how particle-hole excitations occur across the $sd$-$pf$ magic gap is clarified with distinct differences from the conventional approaches. The shell evolution is shown to appear similarly to earlier studies.

nucl-th↗

arXiv2013

Multi-shell effective interactions

Background: Effective interactions, either derived from microscopic theories or based on fitting selected properties of nuclei in specific mass regions, are widely used inputs to shell-model studies of nuclei. Until recently, most shell-model calculations have been confined to a single oscillator shell. Recent interest in nuclei away from the stability line, requires however larger shell-model spaces. Since the derivation of microscopic effective interactions has been limited to degenerate model spaces, there are both conceptual and practical limits to present shell-model calculations that utilize such interactions. Purpose: The aim of this work is to present a novel microscopic method to calculate effective interactions for the nuclear shell model. Its main difference from existing theories is that it can be applied not only to degenerate model spaces but also to non-degenerate model spaces. Methods: The formalism is presented in the form of many-body perturbation theory based on the recently developed Extended Kuo-Krenciglowa method. Our method enables us to microscopically construct effective interactions not only in one oscillator shell but also for several oscillator shells. Results: We present numerical results using effective interactions within (i) a single oscillator shell like the sd-shell and the pf-shell, and (ii) two major shells like the sdf7p3-shell and the pfg9-shell. We also present energy levels of several nuclei which have two valence nucleons on top of a given closed-shell core. Conclusions: Our results show that the present method works excellently in shell-model spaces that comprise several oscillator shells, as well as in a single oscillator shell. We show in particular that the microscopic inter-shell interactions are much more attractive than has been expected by degenerate perturbation theory. The consequences for shell-model studies are discussed.

nucl-th↗

arXiv1995

Response Function of Asymmetric Nuclear Matter

The charge longitudinal response function is examined in the framework of the random-phase approximation in an isospin-asymmetric nuclear matter where proton and neutron densities are different. This asymmetry changes the response through both the particle-hole interaction and the free particle-hole polarization propagator. We discuss these two effects on the response function on the basis of our numerical results in detail.

nucl-th↗

arXiv1995

Isospin dependent effective interaction in nucleon-nucleus scattering

The isospin-dependent component of the effective nucleon-nucleon interaction that causes the $ΔT=1$ (p, p') and (p, n) reactions off nuclei is studied. It is shown that the corrections to the impulse approximation comes from the $g$-matrix type correction and the rearrangement term. They are numerically estimated with the isospin-asymmetric nuclear-matter reaction matrix approach. The analysis of the isobaric analog transitions ${}^{42}$Ca(p,n)${}^{42}$Sc and ${}^{48}$Ca(p,n)${}^{48}$Sc are presented.

nucl-th↗