M. Fabre de la Ripelle

A confining potential for quarks

Abstract A q q potential which, used in a Schrodinger equation, generates hadron masses lying along linear Regge trajectories is derived. It contains a Coulomb-like one-gluon-exchange component and an r 2 3 confining part.

A bridge between hyperspherical and integro-differential approaches to the many-body bound states

The solution of the Schrodinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of a system of identical particles governed by two-body central interactions. It is shown that the system of coupled equations can be transformed into an equivalent integro-differential equation. For three bosons inS states this equation is identical to the Faddeev equation as written by Noyes. The integro-differential equations describing the triton for non-central realisticN-N forces are explicitly given.The solution of the Schrödinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of a system of identical particles governed by two-body central interactions. It is shown that the system of coupled equations can be transformed into an equivalent integro-differential equation. For three bosons inS states this equation is identical to the Faddeev equation as written by Noyes. The integro-differential equations describing the triton for non-central realisticN-N forces are explicitly given.

Contribution of two-body correlations to the wave function of many-body systems

Abstract A solution of the Schrodinger equation including the two-body correlations is proposed. The convergence of the polynomial expansion of the wave function is investigated for the self-conjugate closed shell nuclei 4 He, 16 O, 40 Ca. The results obtained for the ground states and first monopole excited states of these nuclei show that the correlations generated by the two-body interaction cannot be neglected.

Model calculations of doubly closed-shell nuclei in the Integro-Differential equation approach

Abstract The binding energies and root mean square radii obtained from the Integro-Differential Equation Approach (IDEA) and from the Weight-Function Approximation (WFA) of the IDEA for an even number of bosons and for 12 C, 16 O and 40 Ca are compared to those recently obtained by the Variational Monte Carlo, Fermi Hypernetted Chain and Coupled Cluster expansion methods with model potentials. The IDEA provides numbers very similar to those obtained by other methods although it takes only two-body correlations into account. The analytical expression of the wave function for the WFA is given for bosons in the ground state when the interacting pair is outside the potential range. Due to its simple structure, the equations of the IDEA can easily be extended to realistic interactions for nuclei as has already been done for the trinucleon and 4 He.

Green function and scattering amplitudes in many-dimensional space

Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.

Effect of a spurious component of the potential in Faddeev-type equations

In the integro-differential-equation approach (IDEA) and its associated hyperspherical-harmonic expansion method (HHEM) terms appear involving the potential for a single pair of particles. This introduces a spurious component in the potential that is eliminated in the Schrödinger equation by summing over all pairs. We calculate the contribution of this spurious potential in the solution of the HHEM for an even number of bosons in the ground state, using the Afnan-Tang S3 and Malfliet-Tjon MT5 interactions.

An adverse effect of the hyperspherical lm approximation:: Application to 6Li

Abstract It is shown in an application of the hyperspherical Lm approximation to 6Li with soft-core two-body potentials that for nuclei with A > 4 it is necessary to replace the Schrodinger equation by at least two coupled equations in order to treat correctly an interaction including a Majorana exchange operator. Binding energies for 6Li even parity states are calculated.

Electric dipole moment of 3He

Abstract The contribution of CP violating nucleon-nucleon interaction to the electric dipole moment of 3 He is evaluated following a recent proposal for its experimental detection. Two models of CP violating interactions are used, namely, the Kobayashi-Maskawa mechanism and the occurrence of the θ term in the QCD lagrangian. These CP violating interactions are combined with realistic strong nucleon-nucleon interactions to induce a CP forbidden component of the 3 He wave function. The matrix element of the electric dipole operator is then evaluated between CP allowed and CP forbidden components yielding the observable electric dipole moment. Using the parameters emerging from the penguin terms in the Kobayashi-Maskawa model we obtain a result much larger than the electric dipole moment of the neutron in the same model. On the other hand, no enhancement is found for the θ-term mechanism. A possible explanation for this difference is discussed. Numerical estimates can be given only in the Kobayashi-Maskawa model, giving d( 3 He ) ≈ 10 −30 e · cm . In the second mechanism, the estimate gives d( 3 He ) ≈ 10 −16 θ .

Integro-Differential Equations for Systems of Three Particles in S-States

Abstract. Integro-differential equations avoiding the ghost contributions occuring in the Faddeev amplitudes are derived for a system of three identical particles in S-states. The equation for the mixed-symmetry state is given for the case of nucleons. Equations for non-identical particles in S-states are also provided.

Nonrelativistic quark-antiquark potential for mesons☆

Abstract A flavour- and nearly model-independent quark-antiquark potential has been determined by fitting the masses of the vector mesons. The uncertainties in the potential, obtained by an error analysis of the fitting procedure, clearly indicate that the spectra of known mesons determine the potential only between r = 0.7 fm and r = 1.8 fm.