Quasi-elastic pion scattering on 16O: A comparison between the Δ-hole approach and a standard first-order calculation

We present calculations of quasi-elastic pion scattering on ¹⁶O in both the Δ- hole model and a standard first-order theory. The basic approach is a modified “DWIA”, where the same in-medium πN t-operator is used for the transition and the optical potential generating the distorted pion wave functions. In order to allow a meaningful comparison with the recent SIN data, all technical complications such as background interactions, non-static vertex-corrections, 1/A effects, are taken into account, and the DWIA amplitude is evaluated without further numerical simplification like, e.g., factorization. In contrast to the closure approximation, the Δ-hole model predicts correctly the doubly differential cross sections for (π, π') on ¹⁶O over a wide range of angles and energy-losses.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Proton-nucleus elastic scattering at 156 MeV

Cross sections for the elastic scattering of 156 MeV protons on eleven targets ranging from ¹²C to ²⁰⁹Bi were measured and an optical model analysis has been performed. The effect of different optical potentials in DWIA inelastic scattering calculations is shown by some examples.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

Analysis of13C(γ,π+)13Bg.s. and13C(e,é)13C* (15.11 MeV)

The DWIA calculation of the differential cross section for photoproduction of π⁺ from¹³C was carried out with the photon multipole expansion. It is shown that the Cohen-Kurath wave function can reproduce the data quite well. We also calculated the ratio of theM1 transition to theE2 transition to be 1.9. The transverse form factor for¹³C(e, é)¹³C* was evaluated consistently with the same wave function as used for^l3C(γ, π⁺)¹³B.     

Multiple diffractive analysis of elastic and inelastic scattering by 1 GeV protons on 12C, 58Ni,and 208Pb

Recent elastic and inelastic scattering experiments of 1 GeV protons on ¹²C, ⁵⁸Ni, and ²⁰⁸Pb have been analyzed using multiple diffractive scattering theory.Elastic angular distributions have been calculated, including pair correlations in many-particle densities. There is evidence from the Ni and Pb data for the presence of correlations, but some evaluated correlation corrections do not produce detailed agreement.It is shown that the Glauber series for coherent inelastic scattering can be approximately summed to yield an eikonal form of the DWIA. In particular the smaller angle parts of the inelastic distributions are well described in this approximation.The expression for the summed incoherent inelastic cross section is considered as a sum rule. It is found that for ¹²C the excitation of the three lowest excited states exhaust ? 25 % of the sum rule up to ?t ? 1 fm^?2. For larger t quasi-elastic knock-out largely exhausts the sum rule.     

Analysis of elastic and inelastic α-12C data (Eα = 1.37 GeV) with a multiple diffraction model

High-energy inelastic α-¹²C distributions are analyzed with an eikonalized DWIA. Using an elastic phase function parametrized to fit the elastic α-¹²C distribution and further inelastic form factors from electron scattering data, we obtained reasonable agreement for the 2⁺ and 0⁺ distributions. We observe and discuss the anomalous absence of a predicted diffraction minimum in the 3^? distribution as is also the case for the 1 GeV p-¹²C data.     

Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

Off-shell effects in the coherent π0 photoproduction off nuclei

The strong sensitivity of coherent π⁰ photoproduction to the choice of the reaction energy ω in the elementary t_πγ (ω)-matrix is demonstrated. The best agreement of the DWIA results with the experimental data is achieved when ω is chosen as an eigenvalue of the free relativistic hamiltonian of the πN system. This is in agreement with the consequences of the relativistic potential theory.     

High energy elastic and inelastic p-12C scattering and nuclear deformation

Starting from a microscopic deformed picture of the ¹²C nucleus, and using angular momentum projected wave functions, the elastic and inelastic 1 GeV p-scattering differential cross sections have been analysed within the framework of the Glauber theory. From a comparison of the results obtained in a full Glauber calculation and in the optical limit, it has been shown that the elastic scattering and, to a lesser extent, the transition to the 2⁺(4.44 MeV) level are only weakly affected by the long-range correlations. In contrast the scattering to the 4⁺(14.08 MeV) state includes crucial multi-step contributions which affect the differential cross section both in shape and magnitude. Similarly the corrections to the DWIA are essential for the transition to the 3^?(9.64 MeV) state and a satisfactory explanation of the qualitative differences observed between the 2⁺ and 3^? inelastic cross sections in ¹²C is given. The great sensitivity of the cross sections to the nuclear deformation is shown and a generally good agreement with experiment for both the electron form factors and 1 GeV p cross sections has been obtained for the ground-state intraband transitions using a single oblate intrinsic state. The importance of a correct treatment of the rotational motion through the angular momentum projection is underlined and the use of the adiabatic approxmation is critically examined.     

Isobar dynamics and pion-nucleus elastic scattering

A new formalism is developed for studying pion-nucleus scattering in a model which takes into account the dynamics of the (3, 3) pion-nucleon resonance, or Δ isobar. This treatment is used to calculate π⁺ elastic scattering from ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb at energies from 114 to 240 MeV. Some results for π^? elastic scattering are also given. From fits to π⁺ scattering data it is found that the Δ-nucleus interaction is well described by a spherical local complex potential proportional to the nuclear density. The central strength of this potential depends on energy but not on nuclear mass number. Some difficulties in determining the parameters of this potential from elastic scattering are discussed.     

Isovector correlations and pion single charge exchange reactions in light nuclei

The reactions ⁷Li(π⁺, π⁰)⁷Be(g.s.), ⁷Li(π⁺, π⁰)⁷Be1(429keV) and ¹³C(π⁺, π⁰)¹³N(g.s.) are treated in DWIA, including corrections arising from two-step processes in which an intermediate state is reached in the course of the charge exchange. The distortions are introduced by means of a first-order optical potential; no special assumptions of extreme high energy limits are made. The closure sum over intermediate states in the two-step charge exchange mechanism leads to an isovector two-particle correlation function whose properties for p-shell nuclei are discussed in detail. Consequences of the introduction of effective transition operators for the single-step mechanism, with and without spin-flip, and for the two-step contribution are discussed, as are the allowable modifications in nuclear shell radii consistent with present knowledge of Coulomb energies. Comparison is made with experiment — in the case of the separated ⁷Be states, for the first time — and with other theoretical approaches.     

Quasi-free scattering of polarized protons

Cross section and analyzing power, energy-sharing spectra have been measured for the ¹⁶O($\text{p}$, 2p) reaction at an incident energy of 200 MeV for twenty-four different pairs of angles of the detected final-state protons. This general survey is intended to test the validity of the distorted wave impulse approximation (DWIA), particularly with respect to the predicted j-dependent analyzing power caused by the distorting optical potentials and nuclear spin-orbit coupling. Although the data in general confirm this j-dependence, agreement in detail between DWIA calculations and the analyzing power data becomes worse as the momentum of the recoiling nucleus increases. Predictably, the cross-section calculations show more sensitivity to the optical-model parameters than do the analyzing powers. Within the present limits imposed by scanty elastic scattering data, there seems to remain a choice between predicted ($\text{p}$, 2p) cross sections which either are unreasonably large or which have the incorrect energy-sharing shapes. More comprehensive elastic scattering and total reaction cross section data are clearly needed.     

Photoproduction of ϱ′(1.2) and ϱ′(1.6) in the final states π+ π− π+ π− and π+ π− π0 π0

The elastic photoproduction of four pions has been studied at incident photon energies between 2.8 and 4.8 GeV. Production cross-sections are presented and an analysis of the angular decay correlations is also described, indicating a large 1^? contribution in both final states, π⁺ π^? π⁺ π^? and π⁺ π^? π⁰ π⁰. A quantitative understanding of these and other available 4π photoproduction data in terms of the ρ′(～1.2GeV) and the ρ′(～1.6) is presented.     

Study of theK + K − π+ π− system centrally produced in the reactions π+ p→π+(K + K − π+ π−)p andpp→p(K + K − π+ π−)p at 85 GeV/c

The reactions π⁺ p→π⁺(K ⁺ K ^? π⁺ π^? p andpp→p(K ⁺ K ^? π⁺ π^?)p where the (K ⁺ K ^? π⁺ π^?) system is centrally produced have been studied at 85 GeV/c. 48% of the final state proceeds through single or double vector meson resonant production i.e.,K ^*0(890) (37%), ? (4%),ρ ⁰ (7%). Evidence is found for associatedK ^*0 (890) \(\bar K\) ^*o (890) production (6.4±1.1%) with a cross section ten times higher than that found for associated ? ? production in the same experiment.     

High-spin two-quasiparticle bands in76Br

Excited states of the doubly-odd nucleus V6Br have been studied with in-beam γ-ray spectroscopy techniques. In addition to the positive parity band that has been extended up to I=(13) a I^π=4^? isomer (T_1/2=0.5±0.2 ns) and two bands of negative parity have been identified. The bands are discussed in terms of two-quasiparticle configurations. For the band built on the 4_? isomer the configuration πg9/2?νf5/2 or p3/2 is proposed.     

Étude théorique de la diffusion quasi-libre des pions sur les noyaux

The experimental results of the reaction ¹²C(π⁺, π⁺ p)¹¹B at about 130 MeV can be explained satisfactorily by using a modified distorted wave impulse approximation. The strong inelasticity in the elastic channel at these energies makes the knock-out reaction essentially peripheral. We show that under these circumstances the knock-out reaction can be used to obtain information about the off-shell pion-nucleon scattering amplitude. Future experiments in this direction are suggested. We have introduced an invariant half-off-shell pion-nucleon scattering amplitude and have re-examined the DWIA method in a relativistic way.     

Comparison of the π+ and π− elastic scattering from 12C over the πN (3,3) resonance region

Pion-carbon scattering was measured for both π⁺ and π^? at 162 and 226 MeV. The significant differences observed between the π⁺ and π^? elastic cross sections in the diffraction minima are shown to be of opposite sign below and above the πN (3,3) resonance. In addition, differences between the π⁺ and π^? cross sections are also observed at 162 MeV at backward angles.     

High momentum components of the deuteron wave function

The tail of spectator distribution for the reaction K⁺d ?K⁺ π^?pp is studied with the inclusion of inelastic intermediate states in the double scattering. The result seems to indicate the existence of high momentum components for the deuteron wave function.     

Study of the reaction ¯pd→p s π+2π−π0 at 5.5 GeV/c incident momentum

A study of a 150000-picture exposure of ¯pd at 5.5 GeV/c yielded 152 events satisfying the hypothesis ¯pd→p _s π⁺2π^?π⁰. For the events with proton spectator in the momentum range 100–280 MeV/c we obtained the cross section of 0.11±0.02 mb. Assuming the validity of the impulse approximation we estimate a cross section of 0.43±0.06 mb for the reaction ¯pn→ π⁺2π^?π⁰. The rate for single ? meson production and an upper limit for double ? production are given. A modified multiperipheral Regge model was used in order to describe the general features of the data.