Useful Bases for Problems in Nuclear and Particle Physics

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly Fourier-Bessel transformed. The configuration space functions are associated Laguerre polynomials multiplied by an exponential weight, and their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in $\Lambda^2/(k^2 + \Lambda^2)$. A simple model of a meson containing a confined quark-antiquark pair shows that this basis is much better at describing the high-momentum properties of the wave function than the harmonic-oscillator basis.Comment: 12 pages LaTeX/revtex, plus 2 postscript figure

Relativistic Quantum Mechanics - Particle Production and Cluster Properties

This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number of bare-particle degrees of freedom. The focus of this paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late

Nucleon generalized polarizabilities within a relativistic Constituent Quark Model

Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $\beta_{para}(q)$, as a function of the virtual-photon three-momentum transfer $q,$ is explicitly evaluated within a relativistic constituent quark model by adopting transition form factors obtained in the light-front formalism. The discussion is focussed on the role played by the effects due to the relativistic approach and to the transition form factors, derived within different models.Comment: 14 pages and three figures (included), to appear in Phys. Rev. C (May 1998

Relativistic Structure of the Deuteron: 1.Electro-disintegration and y-scaling

Realistic solutions of the spinor-spinor Bethe-Salpeter equation for the deuteron with realistic interaction kernel including the exchange of pi, sigma, omega, rho, eta and delta mesons, are used to systematically investigate relativistic effects in inclusive quasi-elastic electron-deuteron scattering within the relativistic impulse approximation. Relativistic y-scaling is considered by generalising the non relativistic scaling function to the relativistic case, and it is shown that y-scaling does occur in the usual relativistic scaling variable resulting from the energy conservation in the instant form of dynamics. The present approach of y-scaling is fully covariant, with the deuteron being described by eight components, viz. the 3S_1^{++}, 3S_1^{--}, 3D_1^{++}, 3D_1^{--}, 3P_1^{+-}, 3P_1^{-+}, 1P_1^{+-}, 1P_1^{-+} waves. It is demonstrated that if the negative relative energy states 1P_1, 3P_1 are disregarded, the concept of covariant momentum distributions N(p_0,p), with p_0=M_D/2-\sqrt{p^2+m^2}, can be introduced, and that calculations of lectro-disintegration cross section in terms of these distributions agree within few percents with the exact calculations which include the 1P_1, 3P_1 states, provided the nucleon three momentum |p|\<= 1 GeV/c; in this momentum range, the asymptotic relativistic scaling function is shown to coincide with the longitudinal covariant momentum distribution.Comment: 32 LaTeX pages, 18 eps-figures. Final version to appear in Phys. Rev.

Cluster properties and particle production in Poincaré invariant quantum mechanics

I outline the construction of exactly Poincare invariant quantum models that satisfy cluster separa´ bility but do not conserve particle number

Poincaré Invariant Three-Body Scattering at Intermediate Energies

Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincaré invariant quantum mechanics. Based on a Malfliet-Tjon interaction, observables for elastic and breakup scattering are calculated and compared to non-relativistic ones. The convergence of the Faddeev multiple scattering series is investigated at higher energies

Poincaré Invariant Three-Body Scattering at Intermediate Energies

Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincaré invariant quantum mechanics. Based on a Malfliet-Tjon interaction, observables for elastic and breakup scattering are calculated and compared to non-relativistic ones. The convergence of the Faddeev multiple scattering series is investigated at higher energies

Calculations of the Triton Binding Energy with a Lorentz Boosted Nucleon-Nucleon Potential

We study the binding energy of the three-nucleon system in relativistic models that use two different relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that relates the non-relativistic center-of-mass Hamiltonian to the relativistic mass (rest energy) operator and the other uses a non-linear equation that relates the interaction in the relativistic mass operator to the non-relativistic interaction. In both cases Lorentz-boosted interactions are used in the relativistic Faddeev equation to solve for the three-nucleon binding energy. Using the same realistic NN potentials as input, the solution of the relativistic three-nucleon Faddeev equation for 3H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small