Pion production in two-body pd collisions

The reactions d(p, π⁺)t and d(p, π^o)³ He are analyzed in terms of the pp → π⁺d sub-process. The exclusion principle induces an additional exchange contribution involving the πd scattering amplitude. Acceptable deuteron and tritron (³H) wave functions which reproduce the charge form factors yield results consistent with experimental angular distributions at 470, 590, 754 and 1192 proton lab. energies. The forward peak is not sensitive to details of the wave functions. Both the direct and exchange form factors develop a zero which is imposed by the dip in the ³He charge form factor. The associated interference pattern governs the backward cross section.     

π-N scattering in the operator droplet model

π-N scattering is treated within the framework of the operator droplet model. We have incorporated spin dependent effects, and we calculate the differential cross section, polarization and spin rotation parameters, R and A, at infinite energy. Considerable structures in R and A have been found in contrast with the prediction of the present favourite idea of S-channel helicity conservation for high-energy scattering. The original parametrization of the fit of Byers and Yang for π⁻p → π^On is used to calculate energy dependent amplitudes in elastic πN scattering. Without any new parameters, we have obtained a good fit for total cross sections, polarization and a consistent fit for the R- and A-parameters. Further possible developments are indicated.     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.     

Inelasticity corrections in the elastic proton-deuteron back-angle scattering at intermediate energies

The elastic proton-deuteron scattering cross sections at back angles have been calculated in the light of Kerman-Kisslinger model, using a generalised baryon transfer mechanism on the assumption that theN ^*'s exist (with a probability～1 %) in the deuteron and that the backward peak is caused by their exchange. The effect of numerous competing open inelastic channels at intermediate energies on the elastic cross section is computed in a particularly simple model of Sopkovich. The resultant damping of the back scattering amplitude is expressed directly in terms of the forward angle elastic scattering data. The results are compared with the experimental cross sections in the energy range of 1.5–2.5 GeV.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

A new determination of the πN coupling constantf 2

The coupling constantf ² has been determined from forward dispersion relations for theπN helicity flip and no-flip amplitudes, using the recent information on total cross sections, phase shifts and charge exchange forward cross sections. The calculation gives also the values of the amplitudes and the first derivative at the crossing symmetry point.     

Multistep contributions to 13C(π+, π°)13N within a modified eikonal formalism

Analog (π⁺, π⁰) charge exchange on ¹³C in the (3, 3) resonance region is considered within a modified eikonal formalism, which makes use of traditional eikonalization only for pion-nuclear processes, but not for pion-nucleon processes. Corrections to DWIA, based on two-step processes as suggested by Eisenberg and Gal are evaluated. The calculated charge exchange total cross section is found to increase due to these corrections by 15 %, and is still well below the measured one for T_π > 150 MeV.     

Polarisationsmessungen an Elektronenstrahlen nach der Transmission durch magnetisierte Eisenschichten

Magnetized iron foils of a thickness of 500 Å were transmitted by 60 keV electrons. The spin polarization of the electron beam was investigated by Mott scattering after transmission. No polarization effect was found. Since the lowest detectable polarization degree wasP=0·003 the atomic polarization cross section must be assumed to be smaller than 0·8·10^?20cm². This cross section is the sum of the spin exchange cross section and the spin dependent part of the total scattering cross section. If the electron binding energy is neglected, the spin depentend part of the total scattering cross section can be calculated from the theory of Møller scattering. In the case of our conditions-60 keV and an aperture of 10^?3 radian-the calculated cross section is smaller than the experimental upper limit. In further experiments the electron beam was split into the energy spectrum by an electrostatic analyzer placed between the iron foil and the Mott scattering foil. In these measurements only small parts of the energy spectrum were investigated, however, even here no detectable polarization occured.     

Electromagnetic contributions to proton- and neutron-4He scattering

A proper treatment of various electromagnetic contributions toN-⁴He scattering enables one to determinen(p)-⁴He observables fromp(n)-⁴He data. Several calculations ofn-⁴He observables considering different electromagnetic effects are presented. It is shown that the contribution of thep-⁴He Coulomb corrections ton-⁴He polarizations and differential cross sections dominates over other electromagnetic effects forθ _c.m.≧30°. For smaller scattering angles, neutron magnetic scattering is important and produces a divergingn-⁴He differential cross section atθ=0° and a large peak (Mott-Schwinger effect) in the polarization. The influence of thep- andn-⁴He vacuum polarizations on then-⁴He observables is found to be small.     

The importance of spin flip in pion charge exchange reactions

Pion scattering from ³He is investigated in the context of a simple reaction model. It is shown that for energies below around 200 MeV the spin flip mode can dominate the ³He(π^?, π⁰)³H differential cross-section at most angles, and contribute up to 50% of the total charge exchange cross-section.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

Quasi-free scattering of pions on 3, 4He

Differential cross sections for ^{3, 4}He(π, π') are presented for angles of 60° and 120° at 200 MeV and 120° at 295 MeV. The momentum spectra for the scattered pions are dominated by a peak attributed to quasi-free scattering from individual nucleons. There are significant differences between the scattering on ³He and ⁴He as well as between the scattering of π⁺ and π^? on ³He. The data are compared to a simple model incorporating the free π+N scattering amplitudes. Modifications for the structure and dynamics of the target nucleus are discussed.     

A remark on the coupling of the ρ-trajectory to the π-π system

A finite energy sum rule for theπ-π scattering suggests that theρ-trajectory chooses nonsense at the point α_ρ=0, and that the spin of theg(1650) meson isJ ^p =1^?.     

Oscillatory screening and quantum interference effects on electron collisions in quantum plasmas

The oscillatory screening and collision-induced quantum interference effects on electron-electron collisions are investigated in dense quantum plasmas. The modified Debye-Hückel potential with the total spin states of the system is considered to obtain the differential electron-electron scattering cross section in quantum plasmas. It is shown that the electron-electron scattering cross section decreases with an increase of the quantum wave number. In addition, the minimum position of the cross section has been appeared with increasing the collision energy at the scattering angle θL=π/4. It is also found that the oscillatory screening effects strongly suppress the cross section near θL=π/4. In addition, it is found that the quantum interference effects suppress the cross section, especially, for the forward and backward scattering cases.     

Regge pole model for invariant functions. V

The total cross section, the differential cross section and the polarization data ofπN charge exchange as well as elastic scattering is described by the fourρ, ρ′, P, P′ Regge type poles in good agreement with experiment.     

Total cross section measurements for charge exchange of He++ ions with He and Ar atoms

Total charge exchange cross sections were measured for He⁺⁺ in He and Ar gas in the energy range from 50 to 540 eV using a single beam apparatus. For He⁺⁺ in He the measured cross section is in agreement with calculations for symmetric resonant charge exchange. For He⁺⁺ in Ar the cross section for charge exchange decreases with decreasing energy below 300 eV. The measured cross section suggests the formation of Ar⁺ ions to be more important at lower energies and the production of Ar⁺⁺ to be dominant at higher energies.     

The DWIA analysis of the pion photoproduction on carbon

The inclusive pion spectra in the¹²C(γ,π) reaction are calculated in the distorted wave impulse approximation (DWIA). The final state pion-nucleus interaction was constructed within the framework of the multiple scattering theory. The sensitivity of the cross section to the choice of different optical potential variants is investigated.     

A study of the reaction12C(π +,π + +p)11B

We have measured the cross section for the reaction¹² C(π ⁺,π ⁺+p)¹¹B in a coincidence experiment with an incident pion energy of 100 MeV and find that the residual¹¹B nucleus remains predominantly in the ground state. A test of the nucléon charge exchange model by Hewson [3] is discussed.     

Medium corrections to the first order optical potential for low-energy pion-4He scattering

We study the Pauli-principle corrections for low energy π-⁴He elastic scattering. In our approach we take into account explicitly the spin and isospin dependence of the Pauli-principle effect. Furthermore we discuss the combined effect of the Pauli-principle correction and the nuclear binding. Contrary to the Pauli principle we treat the binding corrections in an approximate way, using an effective mass for the residual nucleus. In our calculations we use the first-order optical potential of Celenza, Liu and Shakin. The Pauli-principle correction is found to have a considerable effect on the differential cross section. Our results indicate that the Pauli-principle corrections are largely compensated by the nuclear binding.