Two-body Amplitudes Research Articles

On the analytic properties of non-relativistic two-body off-shell amplitudes: (I). Spectral function methods

Spectral function methods introduced in field theoretic schemes, are used for the study of nonrelativistic two-body off-shell amplitudes taken in a l-wave and generated by Yukawa-type interactions. The analytic properties of the basic components of such amplitudes are specified in a detailed way, which can provide a useful guide line for their parametrisations. Related integral equations are also examined, as well as some discrepancies with independent results concerning the half-shell case. The connections of such an approach with other r- and p-space formalisms are fully recognised in paper II, in which further unitary representations related with this analysis, are also considered.

Some calculations in lattice gauge theory

We look at the action proposed by Wilson on a lattice and calculate static constants like f π and two-body decay amplitudes in a certain approximation. Results are good to factors of four to six. There is good agreement for some of the predicted meson masses.

Diffractive inelastic monopole transitions and the slope-mass relation inπNproduction

The $t$ slope and peripheral structure of the cross sections $\frac{{d}^{2}\ensuremath{\sigma}}{dtd{m}_{\ensuremath{\pi}N}}$ for diffractive $\ensuremath{\pi}N$ production can be understood as a coherent superposition of non-spin-flip ($\ensuremath{\Delta}l = 0$) inelastic two-body amplitudes. Using a wave-function model of nucleon structure, we fit single diffractive production as a function of excitation, and with the parameters so obtained predict the cross sections for double diffractive excitation.

Unified Model for Elastic Scattering and Inclusive Reactions

A unitary model for the particle production is presented on the basis of the eikonal for­ malism and the Regge theory. The elastic and production processes are treated in a unified way and the diffraction in the former is described explicitly as a shadow of the latter. In our model, the exchange of the Regge cut is important in the particle production and the self-consistency is retained between the input and output forward two-body amplitudes. Our model reproduces rising cross sections and the shrinkage effect in the forward slope parameter. As for the production processes, the increasing average multiplicity, the sharp cutoff of the transverse momentum and the wide rapidity plateau with a bump structure in inclusive spectra are reproduced. High energy experiments at FNALn and at CERN-ISR2J have revealed several regularities in hadronic processes. In proton-proton collisions in the range 300<s <3000 Ge V 2 , s being c.m.s. energy squared, rises of total, elastic and inelastic cross sections are observed. In addition, the forward peak in the elastic differential cross section shrinks and the dip position decreases correspondingly. Variations of all these quantities are approximately the same. The forward real to imaginary ratio of the elastic amplitude is positive but close to zero. It follows from these facts that the effective interaction range between hadrons expands at high energies. In other words, the elastic amplitude in the impact parameter space T(b, s) has an asymptotic behavior of the form

Analytic properties of impact parameter amplitudes and geometricals-channel models

In the framework of a recently proposed impact parameter representation a formalism is developed for two-body helicity amplitudes. Its relation withs-channel phenomenological models is examined by generalizing the results obtained with a simple dynamical input. Spin properties of the impact parameter amplitudes are also discussed.

Numerical evaluation of partial-wave born approximations

A method is developed for the numerical evaluation of any term in the Born series for the off shell partial-wave Tmatrix. At negative energies, the integrals may be evaluated by using any appropriate quadrature formula. Numerical analytic continuation of the negative energy results to positive energies is carried out by means of Pad& approximants. The method enables the rate of convergence of eigenfunction expansions for the two-body off-shell amplitude to be accelerated. Numerical results are presented for a Yukawa potential and for a neutron-proton 3S 1 interaction.

Effective channel approach to nuclear scattering at high energies. II. Proton-helium elastic scattering at 1 GeV

The effective channel formulation of high-energy nuclear reactions is applied to the proton-helium system, and the result is compared with experimental data. This formulation provides a consistent procedure for the evaluation of the ground state to effective channel coupling potential, average excitation energy, and the average potential in the effective channel. The effect of coupling to the effective channel as well as the effect of each quantity in that channel are demonstrated. The calculated cross sections were compared to the recent data from Saclay as well as to the earlier Brookhaven data for 1 GeV p-$sup 4$He elastic scattering. The possibility of using proton-nucleus scattering experiments to obtain a refined estimate of the ratio of the real part to the imaginary part of the proton-nucleon elastic scattering amplitude was investigated. The effect on the calculated cross section due to the uncertainty in the input parameters was carefully analyzed and found to be large enough to obscure the nature of any possible dynamical correlation effects and any possible off-shell effect in the two-body amplitude. (AIP)

ω, ρ and A2 exchanges in forward two-body amplitudes at high energy

The total-cross-section differences and forward differential cross-sections for nondiffractive two-body processes (including the new FNAL data) are analysed and compared with the corresponding Reggepole predictions. The method used is devised to detect possible deviations from these predictions: the data are analysed step by step, independent quantities being fitted separately. All ω amplitudes are found in remarkable agreement with the Regge-pole model, with an intercept\(\alpha _\omega \)=0.44 and residues verifying ω universality. The same is not always true for the isospin-one amplitudes, since difficulties arise in the π\(\pi \)N system for the ρ and in theNN system for the A2. These difficulties might be due to new physical effects. Anyway ρ-A2 exchange degeneracy is strongly violated, at the level of both residues and the intercepts (\(\alpha _\rho \)=0.51, αA2=0.37). The ρ residues are compatible with ρ universality, but there is a 20% breaking of theSU3 prediction for the A2 ones.

New amplitudes for data analysis

We propose sets of quasi two-body amplitudes which express the results of an amplitude analysis concisely, and are very simply related to helicity amplitudes. They are particularly suited to meson-baryon scattering with a polarized target or polarization-analysing baryon decay. In this case they can be used to give optimal bounds on moduli and relative phases of helicity amplitudes.

Реджеометрия

We propose a few general empirical laws summarizing our knowledge on two-body hadronic amplitudes. These systematics lead to a simple analytic parametrization of these amplitudes, allowing the reproduction of all the prominent features of the nonvacuum exchange data from 6 to 50 GeV/c. The obtained results, and in particular the ability of describing in a consistent way both meson and baryon exchanges, are encouraging and suggest that a framework may be found for new dynamical approaches.

Quantum number transfer and overlap calculations

The relationship between Regge behaviour of two-body amplitudes and quantum number exchange in multiparticle production is analyzed. An exact bound on the elastic forward peak in terms of inclusive p ⊥ correlations is given. Another result is that one cannot obtain α′ ϱ > α′ P from overlap calculations, using only the present inclusive data as input.

Two-body photodisintegration ofHe3andH3

Cross sections for two-body photodisintegration of $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ are calculated in electric-dipole approximation. The calculation is performed within the context of exact three-body theory with the two-nucleon interactions represented by $s$-wave spin-dependent separable potentials fitted to the low-energy nucleon-nucleon scattering data. The two-body photo-disintegration amplitude is expressed in terms of the half-off-shell nucleon plus correlated-pair amplitudes, a method applicable to any weak-process disintegration amplitude. The numerical results indicate: (1) The $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ 90\ifmmode^\circ\else\textdegree\fi{} photodisintegration cross sections are essentially identical in shape, being only slightly displaced at low energy due to the different thresholds, when both initial and final states are treated consistently. (2) The $^{3}\mathrm{He}(\ensuremath{\gamma}, d)p$ 90\ifmmode^\circ\else\textdegree\fi{} differential cross section has a peak value of approximately 95 \ensuremath{\mu}b/sr.NUCLEAR REACTIONS Photodisintegration of $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$; exact three-body calculation; separable potentials; charge-dependent interactions.

The deuteron breakup reaction induced by protons of 65, 85 and 100 MeV

Coplanar energy sharing spectra for p + d breakup at 65, 85 and 100 MeV proton bombarding energies were measured using the University of Maryland sectored isochronous cyclotron, by measuring the energies of either two protons or one proton and one neutron in coincidence. The detector angles were chosen to enhance either the p-p or p-n quasifree scattering, or the p-n final state interaction. The energy dependence of the peak cross section at equal symmetric quasifree scattering angle pairs was extracted for the 2H(p, 2p)n and 2H(p, pn)p reactions. Quasifree angular distributions were obtained for the reaction 2H(p, 2p)n at 65 MeV and for the reaction 2H(p, pn)p at 65, 85 and 100 MeV. The plane wave impulse approximation theory can only qualitatively reproduce the shape of the quasifree scattering peak in the energy sharing spectra and the shape of the p-p quasifree angular distribution. The discrepancies observed between the plane wave impulse approximation theory and the experimental data imply that the presence of the spectator particle (i.e., the multiple scattering effects) has a strong influence on the magnitude and the shape of the experimental results. Multiple scattering calculations were carried out in the three-body model of Aaron, Amado and Yam except that the S-wave separable two-body amplitudes were modified to fit two-nucleon elastic scattering data at higher energies. Comparisons of the results of these multiple scattering calculations to the experimental data show excellent quantitative agreement throughout the energy range and the angular region of this experiment, except for a few cases in which this model is inherently insufficient; namely, regions in which the Coulomb interaction is important, or regions for which a Hulthén wave function is inaccurate and the off-shell effects are not properly taken into account.

Peripheral Orbit Model

Peripheral orbit model, in which an incoming hadron is assumed to revolve in a peripheral orbit around a target hadron, is discussed. The non-diffractive parts of two-body reaction amplitudes of hadrons are expressed in terms of the radius, width an absorptivity of the orbit. The radius of the orbit is about 1 fm and the width of the orbit is determined by the range of the interaction between the hadrons. The model reproduces all available experimental data on differential cross-sections and polarizations of $K^{-}p\to K^{-}p$ and $\bar K^{\circ}n$ reactions for all angles successfully. This contribution is not included in the proceedings since it will appear in Progress of Theoretical Physics Vol. 51 (1974) No 2. Any person interested in the subject may apply for reprints to the author.

Two body reactions and the quark model

A simple quark model for two-body hadronic amplitudes is presented and applied to pp ( p p ) and K ±p elastic scattering. Hadronic processes are described in terms of quark-quark scattering, using Glauber theory to take into account the effects of multiple scattering. Exchange degenerate Regge poles are introduced at the quark level. A predictive model for Regge cuts is obtained. It has some features in common with the dual absorption model in its correlation of dip structure and shrinkage in elastic processes with the exoticity of the s-channel but also significant differences, for example in the interpretation of the p p dip. The qualitatively different structure in the pp differential cross section is also reproduced. It breaks exchange degeneracy in a well-defined way and in doing so offers an explanation of the differences between pp and K +p total cross sections. The difference in their differential cross sections is a natural consequence of the model and structure similar to the pp structure is predicted to appear in the K +p differential cross section in the region t ≈ −2(GeV/ c) 2.

Intermediate energy nucleon-deuteron elastic scattering

A fully symmetrized multiple-scattering series is considered for the formulation of nucleon-deuteron elastic scattering. An off-shell continuation of the experimentally known two-body amplitudes that retains the exchange symmetries required for the calculation is presented. The one-boson exchange terms are evaluated exactly in this off-shell prescription. The first two terms of the multiple-scattering series are calculated explicitly whereas multiple-scattering effects are obtained as minimum variance estimates from the 146 MeV data of Postma and Wilson. The multiple-scattering corrections indeed consist of low-order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Separable-Interaction Model for Deuteron Breakup

This paper is the second in a planned series of papers in which is developed an exactly soluble three-nucleon model for describing Nd scattering processes at energies above 30 MeV. The model described here is a small refinement of the one previously described. It is obtained from the low-energy three-body model of Aaron, Amado, and Yam by a simple modification of the S-wave separable two-body amplitudes to fit two-nucleon elastic scattering data at higher energies. By comparison of the calculated differential cross sections with experiment at proton projectile energies of 46, 65, 85, 100, and 156 MeV, the medel is shown to provide a reasonable description of the /sup 2/H(p, 2p) and /sup 2/H(p, pn) reactions throughout this energy range. Some quantitative justification for the two-nucleon amplitudes employed supplants the hand-waving arguments of the first paper.

New Scheme of Dual Models and Exotic Peaks

A simple $s$-channel resonance model based on a new scheme of duality is proposed and is shown to explain successfully (i) the appearance of distinct exotic peaks with slopes and relative heights similar to those of the ordinary Regge exchanges, and (ii) the rapid falloff of exotic cross sections vs energy, which have been recently observed in ${K}^{\ensuremath{-}}p$ and $\overline{p}p$ backward scattering. We also discuss the predictions of the model for the spherical-harmonic moments and the dip systematics of two-body hadronic amplitudes. In particular, the model predicts the persistence of the Odorico dips as well as the usual wrong-signature-nonsense-zero dips up to high energies if the increase of Im${\mathrm{\ensuremath{\alpha}}}_{\mathrm{s}}$ is not faster than linear in $s$. Experimental data now available support our approach.

Theory of Boson Resonances

We propose a bootstrap theory of boson resonances which consists of new self-consistency conditions for boson resonances. We derive these conditions by saturating in terms of resonances the once-subtracted dispersion relations for their two-body decay amplitudes where subtractions are introduced by choosing appropriately an arbitrary parameter that appears in the usual continuations of these amplitudes. We then study the simplest solution to all these conditions in the sense that the resonances are minimal in their numbers, with the input that pseudoscalar and vector mesons form the observed nonets. The boson spectrum predicted by this solution is not very different from the observed one, some crucial tests of which are also given.

Virtual-Photon Total Cross Sections on Nuclei and the Phases Between Two-Body Amplitudes

Experimental results of virtual-photon total cross sections on nuclei are explained in terms of an eikonal model and the corresponding two-body amplitudes ${f}_{\ensuremath{\gamma}\ensuremath{\rho}}$ and ${f}_{\ensuremath{\gamma}\ensuremath{\gamma}}$. The relative phase between these amplitudes has a strong influence on the resultant total cross section and the amount of nuclear shadow observed in the reaction. Given experimental data with fewer uncertainties, this phase could be determined from two-body cross sections and the total cross section on nuclei.