Narrow Results

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered (the unitarity regime). The subject has several precursors in the mathematical literature. We proceed through an operator-theoretic construction of the self-adjoint extensions of the minimal operator obtained by restricting the free Hamiltonian to wave-functions that vanish in the vicinity of the coincidence hyperplanes: all extensions thus model an interaction precisely supported at the spatial configurations where particles come on top of each other. Among them, we select the physically relevant ones, by implementing in the operator construction the presence of the specific short-scale structure suggested by formal physical arguments that are ubiquitous in the physical literature on zero-range methods. This is done by applying at different stages the self-adjoint extension schemes à la Kreĭn–Višik–Birman and à la von Neumann. We produce a class of canonical models for which we also analyze the structure of the negative bound states. Bosonicity and zero range combined together make such canonical models display the typical Thomas and Efimov spectra, i.e. sequence of energy eigenvalues accumulating to both minus infinity and zero. We also discuss a type of regularization that prevents such spectral instability while retaining an effective short-scale pattern. Besides the operator qualification, we also present the associated energy quadratic forms. We structured our analysis so as to clarify certain steps of the operator-theoretic construction that are notoriously subtle for the correct identification of a domain of self-adjointness.

A model for the p d→p dη reaction published earlier, including the final state interaction (FSI) of all particles, is revisited to investigate the low energy data on this reaction. The three-body problem of p–d–η scattering in the final state is approximated in terms of pairwise interactions between the three particles in the final state. Apart from a comparison with some preliminary data, two new findings relevant to the near threshold data analysis are reported. The first one points toward the limitations of an FSI factor used conventionally to extract the eta-deuteron scattering length and infer subsequently on the existence of eta-mesic states. The second result emphasizes the role of the p–d FSI and the strong Coulomb repulsion near threshold. Finally, a comparison of the above model calculation with low energy data, excludes very large eta-nucleon scattering lengths.

Large samples of K^± → 3π and K^± → π⁺π^-e^±ν (K_e4) decays have been collected by the NA48/2 experiment at CERN SPS.

At the π⁺π^- threshold, the π⁰π⁰ invariant mass spectrum of the decay K^± → π^±π⁰π⁰ xhibits a Wigner cusp, from which the S-wave ππ scattering lengths are extracted with high precision.

The same scattering lengths are also independently determined from the accurate measurement of the form factors in the K_e4 decay K^± → π⁺π^-e^±ν.

Λ(1405) is investigated as a resonance in a coupled channel baryon-meson scattering with a 'bound state embedded in the continuum' (BSEC). This BSEC is introduced by hand, as a state not originated from a simple baryon-meson system. We assume it comes from the three-quark state.

There appears a resonance of a large width in the Σπ scattering below the threshold by assuming the baryon meson interaction whose channel dependence is (1) flavor-flavor type like the chiral unitary approach, (2) flavor-flavor type with a lower-momentum cut-off, or (3) the same as that of the quark cluster model. It is necessary to introduce a BSEC for the latter two cases in order to reproduce the peak.

The calculation including a BSEC seems to be preferable to reproduce the scattering length. Our calculation gives the observed value when the BSEC contribution to the resonance is roughly half of that of the channel.

Eta-mesic nucleus or the quasibound nuclear state of an eta (η) meson in a nucleus is caused by strong interaction force alone. This new type of nuclear species, which extends the landscape of nuclear physics, has been extensively studied since its prediction in 1986. In this paper, we review and analyze in great detail the models of the fundamental η–nucleon interaction leading to the formation of an η–mesic nucleus, the methods used in calculating the properties of a bound η, and the approaches employed in the interpretation of the pertinent experimental data. In view of the successful observation of the η–mesic nucleus ²⁵Mg_η and other promising experimental results, future direction in searching for more η–mesic nuclei is suggested.

The properties of cold interacting Fermi gases in terms of scattering length are investigated. The scattering length is calculated by exact solution of Schrödinger equation. A Cosine hyperbolic potential with variable strength is employed in this study. The different interaction regimes are provided by choosing different strength of potential, which are characterized by an inverse of S-wave scattering length and Fermi wave number. The energy per particle for ³He system is calculated within the lowest order constrained variational (LOCV) method. It is found that the bound bosonic pairs as well as bound molecules are formed at positive scattering length, only by considering two-body interactions.

We give an updated study on meson-baryon scattering within the framework of unitary chiral perturbation theory. We focus on S-wave scattering with strangeness -1 channel. After fixing the unknown couplings through fitting to experimental data, we then analyze the baryon spectroscopy and the sub-threshold behavior of the amplitude. We end with a summary and a brief outlook.

Λ(1405) is investigated as a resonance in a coupled channel baryon-meson scattering with a 'bound state embedded in the continuum' (BSEC). This BSEC is introduced by hand, as a state not originated from a simple baryon-meson system. We assume it comes from the three-quark state.

There appears a resonance of a large width in the Σπ scattering below the threshold by assuming the baryon meson interaction whose channel dependence is (1) flavor-flavor type like the chiral unitary approach, (2) flavor-flavor type with a lower-momentum cut-off, or (3) the same as that of the quark cluster model. It is necessary to introduce a BSEC for the latter two cases in order to reproduce the peak.

The calculation including a BSEC seems to be preferable to reproduce the scattering length. Our calculation gives the observed value when the BSEC contribution to the resonance is roughly half of that of the channel.

We present preliminary results on the measurement of ɸp scattering length from the ɸ photoproduction near its threshold energy at LEPS/SPring-8.

We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.

We study the Λ(1405), Λ(1670) and the isovector baryon resonances of Σ-type in the pseudo-Goldstone octet and the lightest baryon octet scattering. S-wave scattering is considered by employing unitary chiral perturbation theory. Through fitting various experimental data, such as cross sections, πΣ event distributions, atomic kaon hydrogen data, etc., we determine the free parameters, which are then used in the discussion of the baryon spectroscopy and the scattering lengths.