Excitation Spectrum in the Friedberg-Lee Model

The excitation spectrum of the nucleon with the spin 1/2 is examined by using the Friedberg-Lee model containing the constituent quark and the scalar meson. An appropriate way of quantization for the non-linear meson field is employed by taking account of the non-topological soliton existed in the classical level. Our model space for the nucleon resonances includes the three-quark plus one-meson state in addition to the pure three-quark state. The excitation spectrum in this model space shows that the positive parity state appears as the first excited state associated with the 0s-excitation of the scalar meson. The meson excitation also generates the additional negative parity state apart from the well-known 0p-excitation of the quark.Comment: 12 pages including 4 figures(eps). Prog. Theor. Phys. in pres

Towards understanding the probability of 0+0^+ ground states in even-even many-body systems

For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $\alpha^J_{I(v \beta)} = <nv \beta I |$ $A^{J \dagger} \cdot A^J | n v\beta I>$, where $n$ is the particle number, $v$ is the seniority, $\beta$ is an additional quantum number, and $I$ is the angular momentum of the state. Interesting regularities of the probabilities of $I^+$ ground states are noticed and discussed for 4-particle systems. Several counter examples of the $0^+$ ground state (0GS) predominance are noticed for the first time.Comment: 5 pages, 1 figure. Phys. Rev. C64, in pres

Nucleon resonances in the constituent quark model with chiral symmetry

The mass spectra of nucleon resonances with spin 1/2, 3/2, and 5/2 are systematically studied in the constituent quark model with meson-quark coupling, which is inspired by the spontaneous breaking of chiral symmetry of QCD. The meson-quark coupling gives rise not only to the one-meson-exchange potential between quarks but also to the self-energy of baryon resonances due to the existence of meson-baryon decay channels. The two contributions are consistently taken into account in the calculation. The gross properties of the nucleon resonance spectra are reproduced fairly well although the predicted mass of N(1440) is too high.Comment: 14 pages, 6 figures, Late

Exchange Currents for Hypernuclear Magnetic Moments

The meson(K and $\pi$) exchange currents for the hypernuclear magnetic moments are calculated using the effective Lagrangian method. The seagull diagram, the mesonic diagram and the $\Sigma^0$-excitation diagram are considered. The $\Lambda$-N exchange magnetic moments for the ${}^5_{\Lambda}He$, ${}^6_{\Lambda}He$ and ${}^6_{\Lambda}Li$ are calculated employing the harmonic oscillator shell model. It is found that the two-body correction is about -9% of the single particle value for ${}^5_{\Lambda}He$. The $\pi$ exchange current, induced only in the $\Sigma^0$-excitation diagram, is found to give dominant contribution for the isovector magnetic moments of hypernuclei with A=6.Comment: 11pp, LaTeX, 7 EPS figures, uses epsf.st

Energy Centroids of Spin II States by Random Two-body Interactions

In this paper we study the behavior of energy centroids (denoted as $\bar{E_I}$) of spin $I$ states in the presence of random two-body interactions, for systems ranging from very simple systems (e.g. single-$j$ shell for very small $j$) to very complicated systems (e.g., many-$j$ shells with different parities and with isospin degree of freedom). Regularities of $\bar{E_I}$'s discussed in terms of the so-called geometric chaoticity (or quasi-randomness of two-body coefficients of fractional parentage) in earlier works are found to hold even for very simple systems in which one cannot assume the geometric chaoticity. It is shown that the inclusion of isospin and parity does not "break" the regularities of $\bar{E_I}$'s.Comment: four figures. to appear in Physical Review

Classification of states of single-jj fermions with JJ-pairing interaction

In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum $I$ around the maximum appear as "non-integer" eigenvalues of four fermions when $I$ is around (or larger than) $J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.Comment: to be published in Physical Review

General pairing interactions and pair truncation approximations for fermions in a single-j shell

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

Chiral Symmetry and N*(1440) -> N pi pi Decay

The N*(1440) -> N pi pi decay is studied by making use of the chiral reduction formula. This formula suggests a scalar-isoscalar pion-baryon contact interaction which is absent in the recent study of Hern{\'a}ndez et al. The contact interaction is introduced into their model, and is found to be necessary for the simultaneous description of g_{RN pi pi} and the pi-pi and pi-N invariant mass distributions.Comment: 12 page