Low Partial Waves Research Articles

On the anomalous large-angle scattering of α-particles

Abstract The anomalous large-angle scattering of α-particles at moderate energies from elements throughout the periodic table has been a subject of considerable experimental study and has evoked a wide range of novel theoretical explanations. We show that the conventional nuclear optical potential can explain much, if not all, of the anomalous scattering. The dominant physical parameter determining back-angle scattering is the strength, W 0 , of the imaginary part of the optical potential. Changes in W 0 by a modest factor of two or three lead to changes in back-angle scattering by several orders of magnitude. In turn, we provide two explanations for this astonishing sensitivity of back-angle scattering to W 0 . In the first, it is the rather sudden emergence of the giant resonances of the high-partial-wave strength functions, as W 0 decreases, and the odd-even alternation of these giant resonances familiar for low partial waves. In the second semi-classical explanation it is the effect of the interference between the wave reflected at the internal angular momentum barrier with the wave reflected at the nuclear radius. Both explanations elucidate the sensitivity of the optical model to back-angle α-particle scattering.

Three-body model of deuteron breakup and stripping, II

A previously investigated three-body model of the deuteron-nucleus system, limited to relative angular momentum l = 0 for the two active nucleons, is reevaluated. Full attention is given to self-consistency between elastic and breakup channels. Introduction of the reaction of breakup on the elastic channel now reduces the elastic reflection coefficients in low partial waves by nearly a factor of 2 and causes substantial shifts in phase. Breakup amplitudes in low partial waves are also greatly reduced. As before, the breakup part of the wavefunction contains a broad spectrum of n- p continuum states. The breakup part of the wavefunction at zero n- p separation is localized at small radii, within and just outside the target nucleus, where it is comparable in magnitude with the projected elastic channel wavefunction. As a result, the projected elastic channel wavefunction is a poor approximation to the full wavefunction at n- p coincidence. Deuteron stripping theories that use the projected elastic wavefunction in a truncated waves Born series must correspondingly be quite misleading. To investigate deuteron stripping further, the exact result of the coupled channels calculation is compared with several standard approximate models. Although there is a close qualitative resemblance among the results of all the approaches, the best single approximation to the coupled channels result is found from the familiar phenomenological approach, in which a local optical potential is fitted to the elastic scattering “observed” in the coupled channels calculation. The coupled channels results are also used to analyze the approximations in the Johnson-Soper method. Several formal aspects of the three-body model are discussed.

The effect of the Delta (1236) on the imaginary component of nucleon-nucleon phase-shifts

A study is made, within the Delta -configuration approach, of several processes which could contribute to the imaginary components of nucleon-nucleon phase-shifts. However, as in earlier estimates with this model, the final results for low partial waves are far from the values suggested by phase-shift analyses. The imaginary components in high partial waves are calculated in the Born approximation and could be utilised in removing some of the ambiguities in phase-shift analyses at energies less than than 1 GeV. In addition, a new transition potential for generating Delta configurations is derived in such a way as to be more consistent with the two-pion exchange contribution of recent semi-theoretical nucleon-nucleon potentials.

Partial-wave analysis including π exchange for πN → N ππ in the c.m. energy range 1.65–1.97 GeV

We study the inelastic scattering processes πN → N ππ from c.m. energies 1.65–1.97 GeV using an isobar model. The effect of including a non-zero high partial wave contribution on the determination of low partial wave scattering amplitudes is analysed in detail. The proper formulation of a high partial wave input due to the π-exchange process πN → ϱN is presented. The major improvements due to including the π-exchange high partial wave input in the analysis of low-energy πN → N ππ scattering are found to be the elimination of the overall phase ambiguity in the scattering matrix and improvement in the representation of the angular scattering distribution by the fit parametrization for c.m. energies above 1.8 GeV. We find that our analysis and the previous major isobar analysis of these reactions at these energies share serious deficiencies (such as the failure to properly satisfy partial-wave unitarity and the poor representation of various single-particle distributions), but certain strong features of the data are well determined by both analyses.

MESON STRUCTURE WAVE FUNCTIONS IN THE RELATIVISTIC STRATON MODEL

The Bethe-Salpeter equation for bound states of a spinor straton-antistraton pair is discussed under the assumption that the interaction between the straton-antistraton pair is purely scalar and may be described by a relativistically covariant v-potential. The structure wave function of the meson is expanded according to the O(4) group, and solved numerically first by keeping the lowest partial waves, and then the in-fluence of the higher partial waves are considered. Numerical results of the wave functions are given both in the momentum space and configuration space, and the mean square radius of the meson is evaluated. It is shown that the low partial wave-large component approximation is valid for tightly bound systems. As a comparison, the loosely bound systems are also discussed.

Low partial waves in 12C+ 12C elastic scattering

A correlation between minima at 90° in the angular distributions and deep minima in the 90° excitation functions for the elastic scattering of identical light ions is noted. In the case of 12C+ 12C at E c. m =51 MeV, it is shown that the low partial waves are essential to reproduce this effect.

Isobar formalism and one-pion-exchange partial-wave cross sections inπN→ππN

This work is a prelude to a phase-shift analysis of $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ which we are presently performing. We here review the partial-wave isobar formalism for the above process and introduce the notation being used in our analysis. We compute the partial-wave projections of the one-pion-exchange diagrams because we hope to use the high-partial-wave contributions of these diagrams, which are not modified by the interactions, to remove phase ambiguities in the partial waves being varied. A study of the low partial waves, even though they violate unitarity badly, gives modest insights into the results of previous partial-wave analyses.

A new approach to the phase-shift analysis of nucleon-nucleon scattering in the energy region between 300 MeV and 1000 MeV

A method for the phase-shift analysis ofN-N elastic scattering is proposed in the inelastic region around 1 GeV. In order to find the best fit, the parameters of the one-boson exchange amplitudes are varied as well as the phase-shift parameters (δ, ν) of low partial waves. The p-p and n-p scattering data between 300 and 1000 MeV are analysed and the results are given. Effects of violation of charge independence in π-N coupling constant are examined.

Double-Layer Model Analysis of Elastic Scattering of Complex Nuclei

Heavy ion elastic scattering is analyzed in terms of the double-layer model which gives emphasis on the separation of the interaction region between complex nuclei into two parts: a surface region described by an optical potential and an absorptive interior region which is replaced by a boundary condition at the boundary of the two regions R′. In this model, lower partial waves can be modified by the boundary condition while higher ones are determined mainly by the optical potential in the surface region. A backward rise with a prominent oscillation in the angular distribution is well reproduced due to the effective contribution of the lower partial waves. The inner limit of the surface region R′ can be well determined and the logarithmic derivative of an incoming wave -iKR′ is confirmed to be an appropriate boundary condition.

The 1s-2s and 1s-2p excitation of atomic hydrogen by electron impact

The 1s to 2s and 1s to 2p total and differential cross sections for electron impact excitation of atomic hydrogen are calculated from 13 eV to 300 eV. The 1s-2s-2p close-coupling approximation is used for the low partial waves and the unitarized Born approximation for the high partial waves. At the highest energy up to 500 partial waves are included. The calculated differential cross sections are in quite good agreement with the measurements of Williams and Willis (1975).

Field-theoretic Low equation approach to pion-nucleus scattering

From the pion-nucleus Low equation in the one-meson approximation we obtain an uncoupled, nonlinear, singular integral equation to determine the crossing symmetric elastic pion-nucleus scattering amplitude. The driving term of this equation is evaluated in an impulse single-scattering approximation for (${J}^{\ensuremath{\pi}}={0}^{+}$, $I=0$) ground state nuclei. It is found that unitarity requires that we include the effects of the strong absorption of the low partial waves in the entrance and exit channels. Thus, we introduce distortion of the pion waves by a procedure used in the inelastic peripheral scattering of elementary particles. Numerical results are presented for the interative solution of this equation for $\ensuremath{\pi}$-$^{12}\mathrm{C}$ scattering in the energy region of the (3, 3) resonance.NUCLEAR REACTIONS $\ensuremath{\pi}$-nucleus scattering theory with field-theoretic Low equation. $^{12}\mathrm{C}(\ensuremath{\pi}, \ensuremath{\pi})$, $E$ in (3, 3) resonance region; calculated $\ensuremath{\sigma}$, $\ensuremath{\sigma}(\ensuremath{\theta})$.

ππ partial waves from 0.6 to 1.8 GeV

We use high statistics π −p → π − π +n data at 17.2 GeV/ c to calculate the ππ partial-wave amplitudes in the energy range 0.6< M ππ < 1.8 GeV. We perform both energy-independent and energy-dependent analyses using Barrelet zero techniques. We find four possible solutions for the partial waves, each containing the leading ϱ, f, g resonances but with very different lower partial waves. Two solutions contain a ϱ' resonance in the g region, but it is not possible to establish the existence of other possible broad daughter resonances. We show that accurate measurements of π −p → π 0 π 0n should select the physical solution.

Resonance ambiguities, Barrelet zeros, and duality in K −p→ Λπ0

The method of Barrelet zeros has been used to study the ambiguities of our partial wave solutions for the reactions K −p→ Λπ 0 from 1550 to 2170 MeV. Details of this two-body analysis technique are presented and ambigous sets of partial waves corresponding to the same d σ/d ω and (d σ/d ω) P are analysed. Seven ambigous solutions have been found which maintain the dominant ∑ resonant structure [D3(1660), D5(1765), F5(1920), F7(2040)] but differ in the resonant couplings (t = Γ e Γ r /Γ ) for these states, as well as in the resonant structure in the lower partial waves. Evidence is given for the possible existence of new resonant states in the F5, D5 and F7 partial waves and for additional resonances in lower waves. The resonant structure suggested by the additional solutions is more prolific than the structure previously indicated for this reaction. Several solutions contain resonant “daughter” states at the same mass but with different J P in qualitative agreement with Veneziano models and suggestive of the Harari-Freund conjecture of purely resonant scattering in non-diffractive, inelastic channels. The ambiguities are experimentally distinguishable only by measurement of R and A, which are predicted from the solutions. Each solution has been shown to be consistent with semi-local duality from observed averaging about zero exhibited by Im A′( s, t), the invariant, t-channel helicity non-flip amplitude calculated at t = 0 and at t = m K ∗ 2 . Local averaging was not seen in B ( s, t), the t-channel helicity flip amplitude. The variation of resonant coupling among these solutions for the dominant resonances suggests that SU(3) tests involving the Λπ channel should be reconsidered. The results indicate that partial wave ambiguities should be more carefully studied and that the possible ∑ resonances should be looked for in other KN reactions.

Impedance mismatch for the scattering of heavy ions calculated with deep and strongly absorbing potentials

For deep and strongly absorbing potentials reflection from the surface of the potentials gives the dominant contribution to the scattering of the low partial waves. This effect is not treated in semiclassical theories.

A phenomenological analysis of pion photoproduction

Data on single pion photoproduction in the resonance region have been fitted with a model used previously by one of the authors (RLW). In updating the older fit a considerable amount of new data has been incorporated, the energy range has been extended to a total c.m. energy W = 2.0 GeV, and the procedure followed in making the fit has been changed so as to make greater use of the computer. In the model used for the analysis the pion photoproduction amplitude is composed of three parts: (1) the electric Born approximation, (2) Breit-Wigner resonances, and (3) additional “background” contributions in the lower partial waves. The electromagnetic couplings of many of the πN resonances with masses below 2 GeV have been determined in the analysis, and the results are compared to quark model predictions.

(p, d) Reactions at 52 MeV. II.58Ni(p, d)57Ni(Analysis)

Angular distributions for the 58 Ni(p, d) 57 Ni reaction at E p =51.93 MeV are analyzed using the distorted wave Born approximation theory and the adiabatic theory for the deuteron breakup. dependence of the calculated results is investigated in detail. Modification of low-partial wave contributions is required to obtain reasonable fit with DWBA. well-radius description in the form factor calculation is found to show general superiority to conventional well-depth description.

One‐Pion Exchange Model in the Vector Theory for the Reaction πN → πN. The Present Status. Connection with the Absorption

AbstractIn the present paper it is shown that the Born diagram model with an overall phenomenological form factor suggested in papers [2, 3] on the basis of the ideas of universal interaction of Q‐meson with hadrons describes well the experimental data on the reaction π−p → Q°n in a wide range of energies 2.7 GeV/c ≦ QL ≦ 17 GeV/c at small momentum transfers |t| ≦ 0.2 (GeV/c)2. The connection of the Born diagram model with the other high energy models is considered. On one hand, we show that the absorption account in many respects, though not literally, comes to forming an overall form factor. On the other hand, the normalization of amplitudes of the traditional absorptive one‐pion exchange models to the Born diagrams at t = 0 lays on the absorptive parameters the condition σtotC/8πA = 1 corresponding to the total absorption of the low partial waves. In this case the one‐pion exchange models with absorption coincide at all t with the Born diagram model with absorption and the reaction aplitudes are independent of a choice of the initial vector theory Lagrangian.

Kaon photoproduction

A simple Regge model for high-energy K + photoproduction is constructed from kaon and exchange degenerate K ∗ (892) - K ∗∗ (1420) trajectories, together with absorption of the low partial waves. Use of SU(3) symmetry and vector-meson-dominance results leaves little freedom in choice of parameters. The model requires the Λ recoil polarization asymmetry to be negative in accordance with recent measurement. The main purpose however is to prepare for an attempt, by extrapolation of the photoproduction model to lower energies and spacelike photon four-momenta, to predict cross sections for K + electroproduction. This is dealt with in the following paper.

Rigorous constraints between the low partial waves for pion-pion scattering

A complete set of rigorous constraints between low partial waves for pion-pion scattering is derived.

Nucleon-nucleon interaction from pion-nucleon phase shift analysis: The NN peripheral partial waves

The low energy peripheral nucleon-nucleon partial wave phase parameters are calculated from our present knowledge of pion-pion and pion-nucleon phase shifts. The results are compared with phenomenological energy independent and energy dependent phase shift analyses.