Spectator Particle Research Articles

Final state interactions in 4He [formula omitted]H at large proton energy

At large proton energy, the final state interactions of the knocked out nucleon in ( e, e ′ p) reactions off nuclear targets can be described within the eikonal approximation, treating the spectator particles as a collection of fixed scattering centers. We use a generalization of this approach, suitable to take into account the possible occurrence of color transparency, to carry out an accurate calculation of the missing momentum distribution of the process 4He( e, e ′ p) 3H. The pattern of final state interactions effects is analyzed for different kinematical setups in the domain corresponding to 2≤ Q 2≤20 (GeV/ c) 2.

Relativistic quasipotential equations withu-channel exchange interactions

Various quasipotential two-body scattering equations are studied at the one-loop level for the case of $t$- and $u$-channel exchange potentials. We find that the quasipotential equations devised to satisfy the one-body limit for the $t$-channel exchange potential can be in large disagreement with the field-theoretical prediction in the case of $u$-channel exchange interactions. Within the spectator model, the description of the $u$-channel case improves if another choice of the spectator particle is made. Since the appropriate choice of the spectator depends strongly on the type of interaction used, one faces a problem when both types of interaction are contained in the potential. Equal-time formulations are presented, which, in the light-heavy particle system corresponding to the mass situation of the $\pi N$ system, approximate in a reasonable way the field-theoretical result for both types of interactions.

Exact and approximate triangle amplitudes for (in-)elastic three-body processes with charged particles

The triangle amplitudes, which within the framework of the multiple-scattering approach represent the leading contribution to the amplitude for three-body elastic and inelastic reactions, contain the off-shell Coulomb T-matrix describing the intermediate-state scattering of the projectile off each of the target particles. We present results of the exact numerical calculation of that amplitude in which the rescattering particles have charges of opposite sign (`attractive case'), for several atomic processes. This is facilitated by a `new' representation of the Coulomb T-matrix which turns out to be very effective for numerical purposes. One interesting result is that the charge sensitivity of the full triangle amplitude apparently disappears at the elastic threshold, for all scattering angles. Furthermore, we propose a new approximation for the triangle amplitudes which can be viewed as a `renormalization' by a simple analytic expression, of the well known approximation which consists in replacing by the potential . While the latter is known to be generally inadequate, this new approximation is shown to yield results in excellent agreement with the numerically calculated exact amplitude, for atomic elastic reactions, over a wide range of (medium to high) projectile energies and scattering angles (including the near-forward-scattering direction). An even simpler approximate amplitude is derived which contains no quadratures at all. It yields similarly good results provided the masses of the two particles experiencing intermediate-state rescattering are of the same order of magnitude but differ from that of the spectator particle. In addition, the explicit forms of the approximate amplitudes are used to derive a variety of interesting theoretical results.

Form factors for semi-leptonic and radiative decays of heavy mesons to light mesons

To know and understand form factors of hadronic currents is of decisive importance for analysing exclusive weak decays. The ratios of different form factors of a given process depend on the relativistic spin structure of initial and final particles. It is shown --- assuming simple properties of the spectator particle --- that these ratios can entirely be expresssed in terms of particle and quark mass parameters. For quark masses large compared to the spectator mass the Isgur-Wise relations follow. The corresponding amplitudes for heavy-to-light transitions show a very similar structure. In particular, the $F_0$ and $A_1$ form factors behave again differently from the $F_1, A_2, V$ and $T_1$ form factors.

Confinement and scaling in deep inelastic scattering.

We show that parton confinement in the final state generates large $1/Q^2$ corrections to Bjorken scaling, thus leaving less room for the logarithmic corrections. In particular, the $x$-scaling violations at large $x$ are entirely described in terms of power corrections. For treatment of these non-perturbative effects, we derive a new expansion in powers of $1/Q^2$ for the structure function that is free of infra-red singularities and which reduces corrections to the leading term. The leading term represents scattering from an off-mass-shell parton, which keeps the same virtual mass in the final state. It is found that this quasi-free term is a function of a new variable $\bar x$, which coincides with the Bjorken variable $x$ for $Q^2\to\infty$. The two variables are very different, however, at finite $Q^2$. In particular, the variable $\bar x$ depends on the invariant mass of the spectator particles. Analysis of the data at large $x$ shows excellent scaling in the variable $\bar x$, and determines the value of the diquark mass to be close to zero. $\bar x$-scaling allows us to extract the structure function near the elastic threshold. It is found to behave as $F_2\sim (1-x)^{3.7}$. Predictions for the structure functions based on $\bar x$-scaling are made.

Form factor relations for heavy-to-light transitions

Assuming simple properties of the spectator particle in weak decays the form factors of hadronic current matrix elements are shown to be related to a single universal function. The Isgur-Wise result for heavy-to-heavy transitions follows as well as similar relations for heavy-to-light decay processes. The approximation should hold for total energies of the final particle large compared to the confinement scale. A comparison with experimentally determined D-decay form factors and QCD sum rule results for B-decays is very encouraging.

Global variables and impact parameter determination in nucleus-nucleus collisions below 100 MeV/u

Several global variables are tested for determining the impact parameter in 4π measurements of charged products. For the system Ar + Al from 25 to 85 MeV/u, simulated reactions are used to study the correlation between the real impact parameter value and the experimentally determined one. Even with a perfect detector, the total multiplicity and the mid-rapidity charge give a poor correlation. Filtering through the acceptance of an actual detector (Mur + Tonneau at GANIL) provides a poor correlation with the total charge, and an acceptable one with the total perpendicular momentum. The average (mass weighted) parallel velocity V av gives the best correlation and is less sensitive to the incident energy and to the mechanisms used in the simulation. Measurements extending to very forward angles are needed to accurately sort events by impact parameter. Real data are used to study the variation of other global variables versus V av : they exhibit the expected average trend, with broad fluctuations. The eccentricity and flow angle allow the evolution of central reactions with the incident energy to be followed. The proportion of relative motion transformed into energy perpendicular to the beam direction decreases when the incident energy increases; its absolute value, however, doubles from 25 to 65 MeV/u. In experimental studies where good separation between participant (pre-equilibrium) and spectator (equilibrium) particles is wanted in addition to good impact parameter sorting, the projectile mass should be in the range 1.2–2.5 times the target mass.

Current conservation and interaction currents in relativistic meson theories.

The relation between the nucleon-nucleon interaction and exchange currents needed for current conservation are derived for the Bethe-Salpeter formalism, and for the approach in which the spectator particle is restricted to its mass shell. For both approaches, it is shown how to achieve current conservation for a completely general isospin dependent, energy dependent interaction with arbitrary phenomenological electromagnetic form factors for the nucleon and mesons, and with strong form factors at the meson-nucleon vertices. Contrary to what has often been stated in the literature, the development shows that current conservation places no restrictions on the use of different electromagnetic form factors for mesons and nucleons, and that phenomenological meson-nucleon form factors can be introduced in a way which is consistent with current conservation. The longitudinal part of the exchange current is uniquely determined by current conservation, and for the common case of an interaction that only depends on the invariant momentum transfer variable an explicit expression for this longitudinal exchange current is given. The transverse part, which contains all electromagnetic form factors, is unconstrained by current conservation.

Influence of the detection geometry in the analysis of experimental observables in projectile breakups

The effect of geometrical considerations in the detection of flying spectator particles in projectile fragmentation processes is discussed. It is shown that different Fermi momenta have different probabilities of being detected in a detector of finite opening. A comparison of experimental inclusive deuteron spectra from the ${(\mathrm{}}^{3}$He,d) reaction on $^{59}\mathrm{Co}$ with the spectator particle mechanism, including the corrections for the probabilities of detection of various Fermi momenta, shows that very good agreement can be found for the centroid position, width, and angular dependence of the peak due to the projectile fragmentation.

Relativistic Faddeev theory of the pi NN system with application to pi d scattering.

We formulate a novel relativistic Faddeev theory of the ..pi..NN system using a variable-mass isobar ansatz for the ..pi..N and NN amplitudes and the requirement that the spectator particles be always on their mass shells. This theory takes into account the two possible time orderings in the propagator of the exchange particle and describes correctly the coupling between the two-body and three-body channels. As a first application of this theory, we study pion-deuteron elastic scattering by calculating all the observables in the region of the 3,3 resonance for which data exist.

Rotation aligned bands and configuration dependent interaction in189Hg

High spin states in189Hg have been studied using the181Ta(14N, 6n) reaction. The various one- and three-quasiparticle rotational bands were interpreted within the cranked shell model. The band-crossing frequencies are found to depend on the number of spectator particles. The effect can be accounted for by a residual two-body interaction of appr. −0.11 MeV.

Massive Transfer in Heavy-Ion Reactions: Possible Applications in Nuclear Structure Studies

Experimental data are summarized for massive transfer, a type of heavy-ion reaction in which a massive portion of the projectile is transferred to the target nucleus and a light fragment is observed as a forward-peaked, energetic spectator particle. The γ-ray spectra obtained in coincidence with the light fragment indicate that low-L partial waves do not participate in the reaction. γ-ray multiplicities are consistent with the massive fragment being absorbed at a distance corresponding to the critical distance for fusion. Channel-selected energy spectra and angular distributions are presented for alpha particles and Z = 1 particles associated with massive transfer. A recent model by Udagawa and Tamura that is based on their multi-step direct reaction theory accounts well for these experimental data. Possible applications of massive transfer in high-spin spectroscopy, in the sysnthesis of cold nuclei near the yrast line, and in the study of neutron-rich nuclei are discussed.

Reaction mechanisms and isospin effects for the π±+D→p+ π±+n processes at Pπ=340 MeV/ c

The first kinematically complete counter measurements of the D( π ±, pπ ±)n reactions in the Δ(1232) region are reported. Calculations based on low order diagrams compare well with the data. The ratio pπ +/pπ − depends strongly on the spectator particle momentum, and its behavior is qualitatively reproduced.

Two-spectator quasifree processes

Two-spectator quasifree processes (graphs with two spectator particles) for the 3He( 3He, dd)pp reaction at the symmetric angle pairs θ = 30.1° at E 3He = 50 MeV and θ = 37° at E 3He = 78 MeV are investigated. The theoretical cross sections are calculated with the PWIA model. The measured cross sections are smaller but have shapes which are in good agreement with the calculation. The ratio N = experiment/theory is approximately 0.05 at 50 MeV and 0.1 at 78 MeV. The reaction 2H(d, pp)nn also was studied at the symmetric angle pair θ = 34.8° and E 2H = 34.7 MeV and the ratio is about 0.14.

Neutron-neutron quasifree scattering in the 2H(n, nn)p reaction at En = 14.1 MeV

Neutron-neutron quasifree scattering has been studied in the deuteron break-up reaction 2H(n, nn)p at E n = 14.1 MeV. Two coplanar and symmetric configurations have been investigated in a kinematically complete experiment where the detection of the spectator particle was not possible. The experimental cross sections are compared with “exact” calculations derived from Faddeev-type equations solved with S- and P-wave nucleon-nucleon separable interactions. These calculations agree both in shape and magnitude with the differential cross section for the θ 1 = − θ 2 = 40° configuration ( E p min = 0). At θ 1 = − θ 2 = 30° ( E p min = 180 keV). however, the absolute value of the measured cross section is too high and an observed structure in the shape of the differential cross section is in sharp conflict with the now available “exact” calculations.

Green's functions of three-particle subresolvents containing separable potentials

Analytic expressions for Green's functions of three-particle subresolvents (including one spectator particle) are given, i.e. the configuration space representation of the operator-valued functionGα(z)=(z−K−Vα)−1 whereK is the total kinetic energy of the three-particle system andVα is the interaction of the pairΒγ. A sum of separable potentials is well suited to exhibit the structure of the corresponding Riemann surface such that from these results also some conclusions may be drawn about the full Green's operator of the three-particle system.

Study of the spectator angle distribution in the dp to ppn reaction at 3.3 GeV/c deuteron momentum

The experimental polar angle distribution of the spectator nucleon in the dp to pnp reaction is studied in different intervals of the spectator momentum and four-momentum transfer. The results are compared with those from the impulse model calculations which take account of the ambiguity in the spectator particle identification. Agreement between the calculations and experiment is observed. The final state interaction of two nucleons is also considered.

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.

On the dynamics of multiple-reggeon exchange cuts

We discuss the circumstances under which multiple-pomeron exchange amplitudes can become iterative and show how the intermediate states involved in these amplitudes can be related to the states produced in diffractive dissociation. In order to obtain a soluble model, we construct a simple integral equation, which in an iterative way leads to a multi-pomeron exchange series, including contributions of cut mechanisms involving spectator particles. From a particular solution of this equation we are able to illustrate how the longitudinal-momentum distributions of the diffractive intermediate states influence the relative strength of the cuts. Further from a qualative analysis, we show why one might expect the helicity-non-flip vacuum amplitudes to have strong cuts, while all other amplitudes have weak cuts. A number of related points are also discussed.

Simple Estimate of the Attenuation of Quasifree Scattering in Nucleon-Deuteron Breakup

A semiclassical model has been developed to estimate the attenuation of quasifree scattering in nucleon-deuteron breakup. According to this model the probability that an initial quasifree scattering event undergoes multiple scattering is just the probability that one or the other of the emerging high-energy particles strikes the spectator particle before leaving the volume of space occupied by the target deuteron. The model yields directly a prediction for the probability of such a rescattering for events in which the nucleons in the deuteron are far apart. An approximate form is assumed for the short-range behavior of this rescattering probability. With this approximation the predictions of the model for the peak value of the $D(p,2p)n$ cross section agree well with experiment in the energy range 20-50 MeV and the predicted energy spectrum at ${E}_{p}=45$ MeV agrees with experiment in both size and shape.