K. Yazaki

Short Range Part of Baryon-Baryon Interaction in a Quark Model. I —Formulation—

The short range part of the interaction between non-strange baryons (N and Δ) is studied in a nonrelativistic quark model. The mass of a quark is assumed to be about one-third of the nucleon mass and the quark-quark interaction consists of a confinement term and the one gluon exchange potential. Baryons are described as clusters of three quarks and the resonating group method, which has been extensively developed in the nuclear cluster model, is used to treat the bound state and scattering problems of two baryons. This paper discusses the formal aspects of the present approach, while the numerical results will be given in the subsequent paper.

Nuclear force in a quark model

Abstract The problem of the nuclear force in a nonrelativistic quark model is studied by the resonating group method which has been extensively used in treating the interaction between composite particles. The calculated phase shifts for the 3 S 1 and 1 S 0 states of two nucleons indicate the presence of a strong repulsive force at short distance, while an attractive force is predicted for the 7 S 3 (( S , T )=(3,0)) state of two Δs. These features are due to an interplay between the Pauli principle and the spin-spin interaction between quarks.

On the coalescence model for high energy nuclear reactions

Abstract The coalescence model for composite particle spectra from high energy collisions is formulated in a way which clarifies the underlying assumptions and the meaning of the parameters in the model. A density matrix formalism is used to describe a highly excited part formed by a collision and the coalescence volume is found to be related to the internal wave function of the composite particle and the spatial distribution of nucleons in the highly excited part.

Hyperon-nucleon and hyperon-hyperon interaction in a quark model

Abstract The non-relativistic quark cluster model is employed to describe the two-baryon systems including hyperons such as Λ, Σ and Ξ. Qualitative discussions about the role of the Pauli principle for quarks and the color magnetic interaction in the baryon-baryon scattering are given. Results of the resonating group method (RGM) calculation show a repulsive interaction at short distances in most of the two-baryon systems with strangeness S = −1 and −2. There appears, however, a sharp resonance in the 1 S 0 ΛΛ scattering at E = 26.3 MeV, which may correspond to the di-hyperon state.

Baryon-baryon spin-orbit interaction in a quark model

Abstract The baryon-baryon spin-orbit interactions are studied within the framework of a nonrelativistic quark-cluster model. The origin of the spin-orbit interactions is taken to be the Galilei-invariant part of the spin-orbit term in the one-gluon-exchange potential between quarks. It gives, for example, the NN spin-orbit interaction which is qualitatively similar to the empirical ones. The baryon-nucleus spin-orbit interactions are also considered along this line. The N- and Σ-nucleus spin-orbit interactions are of comparable strength, while the Λ-nucleus spin-orbit interaction is weak. The main origin of the difference between the Λ -nucleus and Σ-nucleus spin-orbit interactions is the presence of the comparatively strong antisymmetric LS (ALS) terms for both NΛ and NΣ interactions but with opposite signs. Other sources of the spin-orbit interactions are briefly discussed in connection with the problem of the spin-orbit effect in the excited baryon spectra.

Ward identity in the many-body system and magnetic moments

Abstract We study the role of the electromagnetic Ward identity in the many-body system. A relativistic framework for density-dependent renormalizations is used. We study the constraints imposed by the Ward identity on the renormalization of the angular momentum g-factor gl and work out the connection with traditionally considered core-polarization and exchange-current processes.

Hamiltonian formulation of two-dimensional gauge theories on the light cone

In Quantum Chromodynamics, the theory of strong interactions, gluons and quarks are the microscopic degrees of freedom. Hadrons constitute the effective degrees of freedom in terms of which hadronic and nuclear reactions as well as nuclear structure are traditionally described. The fundamental problem of low energy strong interaction theory is to understand, within the framework of QCD, the transition from microscopic to phenomenological degrees of freedom. Quark models have been important in clarifying this relation between microscopic and effective degrees of freedom as far as the structure of single hadrons is concerned. As the historical development already indicates, compositeness together with a simple picture about the underlying confining dynamics is sufficient for a qualitative understanding of hadronic properties in terms of “constituent” quarks.

A study on the formation of Σ-hypernuclei by (K̄, π) reaction

Abstract The production of Σ-hypernuclear states is studied using the Green function method with both the Σ-escape process and the Λ-conversion process correctly taken into account. Some numerical results are given and discussed for the reaction 12 C(K − , π + ) with stopped K − . The bound state approximation in the calculation of the production rates is also examined.

The formation probabilities oF Σ-hypernuclei and the “unstable bound state”

Abstract A formalism for treating the processes forming unstable states such as Σ-hypemuclear states is given. The formation probabilities are shown to be expressed by the Green function for the Σ in the nucleus. The formalism is used for examining the effects of the “unstable bound state” which has been proposed as a candidate for explaining the observed sharp Σ-hypernuclear states.

The di-hyperon state in the quark cluster model

Abstract The di-hyperon state (DH) predicted by Jaffe in the MIT bag model is studied in the non-relativistic quark cluster model. The resonating group method is applied to the ΛΛ, NΞ and ΣΣ coupled channels problem. No stable bound state is found below the lowest ΛΛ threshold but a sharp resonance with spin-parity 0+ is predicted just below the NΞ threshold. The structure of the state is similar to that of the flavour SU3 singlet state and the attractive nature of the color magnetic interaction in this state is responsible for the appearance of the resonance. The difference between the present model and the bag model which predicted a strongly bound state is attributed to the difference in the mechanism of confinement for these two models.