Properties of Deuteron Bound State from Meson and Quark Theories for the Nucleon-Nucleon Interaction

The properties of the nucleon-nucleon bound state in the deuteron are considered. Nucleonnucleon interactions of the Yukawa, Reid and Paris potential forms are used to describe the deuteron bound state. Also, the nudeon-nudeon interaction with different meson exchanges derived fiom the meson theory as well as the nudeon-nudeon interaction with quark exchange derived from the quark theory by introducing the quark-quark potential with one gluon exchange are used to investigate the deuteron properties. The deuteron binding energy, quadrupole moment, effective range, root-mean-square radius and the D/S ratio are calculated by using different nucleon-nucleon interactions. The obtained results of the present calculations are in good agreement with the experimental values.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.     

Hyper-radial adiabatic expansion for a muonic molecule dtμ

By using the hyper-radius, adiabatic potential energy curves with correct asymptotic energies are obtained for the Coulomb three-body problem. The bound state energies of the muonic molecules dtμ with total angular momentum J=0 calculated adopting the three lowest adiabatic potential energy curves are −318.72 and −34.36 eV for vibrational quantum numbers ν=0 and 1, respectively.     

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.     

Relativistic effects in neutrino (Antineutrino) disintegration of the deuteron

The cross section of neutrino disintegration of the deuteron with inclusion of relativistic corrections is calculated. The transition only to¹S₀-state is taken into account, so the results are valid for reactor and meson factory energies. Comparison with earlier works is given. It is shown, that accurate choice of bound state wave function is essential for the final results. The relativistic approach developed in this work should be used as a starting point for calculations of meson exchange current corrections.     

He-He-Ba三原子体系弱束缚态计算

本文利用含有绝热近似的超球坐标方法计算了碱土金属原子Ba和氦原子组成的弱束缚三原子分子体系He₂Ba的基态性质. 系统地研究了该系统的道函数和超球势曲线特征, 进而得到体系的束缚能. 研究结果显示, ¹³⁸Ba 与⁴He, ³He 的各种组合⁴He-⁴He-¹³⁸Ba, ⁴He-³He-¹³⁸Ba和³He-³He-¹³⁸Ba都分别只有一个束缚态.     

Three-Body Bound-State Calculations Without Angular-Momentum Decomposition

 The Faddeev equations for the three-body bound state are solved directly as three-dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three-body binding energy is calculated for Malfliet-Tjon-type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three-body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schr?dinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects. Received May 8, 1998; revised October 27, 1998; accepted for publication February 14, 1999     

Density-dependent potential for multi-neutron halo nuclei

We apply a simple density-dependent potential model to the three-body calculation of the groundstate structure of drip-line nuclei with a weakly bound core. The hyperspherical harmonics method is used to solve the Faddeev equations. There are no undetermined potential parameters in this calculation. We find that for the halo nuclei with a weakly-bound core, the calculated properties of the ground-state structure are in better agreement with experimental data than the results calculated from the standard Woods-Saxon and Gauss type potentials. We also successfully reproduce the experimental cross sections by using the density calculated from this method. This may be explained by the fact that the simple Fermi or Gaussian function can not exactly describe the density distribution of the drip-line nuclei.     

P+D radiative capture and mesonic effects

We have measured precise data for the vector- and tensor-analyzing powers of the radiative capture reaction p+d→³He+γ at deuteron energies of 29 MeV and 45 MeV. These data are compared to modern three-body calculations that treat both the bound and the continuum state exactly. We show that the analyzing powers exhibit very large effects of meson exchange currents, despite the fact that the momentum transfers involved are very small. The MEC are well described by theory. We also find that, at extreme angles, relativistic effects are important.     

Structure and Occurrence of Three-Body Halos in Two Dimensions

 The quantum-mechanical three-body problem is reformulated in two dimensions by use of hyperspherical coordinates and an adiabatic expansion of the Faddeev equations. The effective radial potentials are calculated and their large-distance asymptotic behavior is derived analytically for short-range two-body interactions. Energies and wave functions are computed numerically for various potentials. An infinite series of Efimov states does not exist in two dimensions. Borromean systems, i.e. bound three-body systems without bound binary subsystems, can only appear when a short-range repulsive barrier at finite distance is present in the two-body interaction. The corresponding Borromean state is never spatially extended. For a system of three weakly interacting identical bosons we find two bound states with both binding energies proportional to the two-body binding energy. In the limit of small binding these states are spatially located at the very large distances characterized by the scattering length. Their properties are universal and independent of the details of the potential. We compare throughout with the corresponding properties in three dimensions. Received September 25, 1998; accepted for publication January 30, 1999     

Calculation of eta-meson-nucleus quasibound states with optical potentials of the square-well and woods-saxon forms

The results obtained by calculating bound states of eta mesons and nuclei by using a squarewell optical potential are compared with their counterparts based on the use of an optical potential in the Woods-Saxon form. For any reasonable choice of range for a potential that has a sharp boundary, the results for the case of a diffuse boundary demonstrate the need for a greater baryon charge in order that an eta meson form a bound state with nuclei. The dependence of the probability for the formation of etamesonic nuclei on the diffuseness parameter of the optical potential involving the Woods-Saxon radial dependence is revealed.     

Nucleon-nucleon interaction in the three-nucleon system

The three-nucleon system is reconsidered. The Faddeev equations are given leading to a set of integral equations. Solving these integral equations, suitable forms are considered for the nucleon-nucleon interaction. In the bound state of three-nucleon system, the form of the nuclear forces from the nucleon-nucleon interaction is important. In the present calculations, we consider the nuclear forces resulting from the nucleon-nucleon interaction by the exchange of a scalar meson, a pseudoscalar meson, and a massless vector meson. With this different meson exchange nucleon-nucleon interaction, the binding energy of the three-nucleon system is calculated by solving the Faddeev integral equations giving a value of 8.452 MeV.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid methane using two-body and three-body intermolecular potentials from molecular dynamics simulation

Molecular dynamics simulation has been performed to obtain pressure, radial distribution function, and self-diffusion coefficient of fluid methane using one site OPLS (optimized potentials for liquid simulations), five sites OPLS-SITE, and two-body HFD (Hartree-Fock dispersion)-like potentials. To take higher-body forces into account, three-body potential of Hauschild and Prausnitz (1993) has been used with the two-body HFD-like potential. The significance of this work is that the three-body potential of Hauschild and Prausnitz extended as a function of density and temperature and used with the HFD-like potential to improve the prediction of the results of pressure of fluid methane without requiring an expensive three-body calculation. The molecular dynamics simulation of methane has been also used to determine a new equation of state. The results are in a good agreement with experimental and theoretical values.     

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states a0(980), f0(980), κ,σ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the "fall apart" mechanism.