Incident Pion Kinetic Energy Research Articles

Analyses of \pi^{\pm} nucleus elastic scattering data at T_\pi = 40, 30, 20 MeV using a suggested scaling method

The data for elastically scattered charged pions from few nuclei, namely ^{12}C, ^{16}O, ^{28}Si, ^{32}S, ^{40}Ca, ^{56}Fe, ^{58}Ni, and ^{90}Zr have been analyzed by obtained potentials using a suggested scaling procedure. Originally the \pi ^{\pm}-^{12}C elastic scattering data at 50 MeV was nicely fitted by a parameterized simple local optical potential extracted from available phase shifts using inverse scattering theory. The potential parameters of the \pi ^{\pm}-^{12}C systems were scaled to \pi ^{\pm}-^{16}O systems and then successively to other few systems covering the scattering of charged pions from target nuclei, namely \pi ^{\pm}-^{28}Si, \pi ^{\pm}-^{32}S, \pi ^{\pm}-^{40}Ca, \pi ^{\pm}-^{56}Fe, \pi ^{\pm}-^{58}Ni and \pi ^{\pm}-^{90}Zr . The obtained scaled potentials showed a remarkable success in explaining the available measured elastic differential cross sections, and in predicting other ones for the systems under consideration. The reaction cross sections have been calculated for all these systems at the three incident pion's kinetic energies, T\pi = 40, 30, 20 MeV. Unfortunately, experimental reaction cross sections are totally absent or cloudy and unconfident. As such, and at this stage, we consider our calculated values useful and pending for future investigations. For the systems and energies considered herein, simple scaling relations are well established. This will be beneficial in analyzing similar nuclear scattering data, as low-energy pion-nucleus and kaon-nucleus elastic scattering data; and, hopefully, in explaining pionic atom data.

Analyses of Low-Energy <i>π</i><sup>-</sup>-<sup>12</sup>C Elastic Scattering Data

A new updated simple local optical potential is proposed for analyzing low-energy π--12C elastic scattering data at 80 MeV and below. This potential is composed of two real terms and an imaginary term. The nature of the real part of the potential is repulsive at smaller radii and attractive at larger ones. In fact, the height of the repulsive term is found to change linearly with the incident pion kinetic energy. On the other hand, the imaginary part of the potential is attractive, shallow and non-monotonic with a dip at about 1.6 fm. Such a nature of the potential makes it feasible to predict π--12C cross sections at other energies in the energy region considered herein. Coulomb effects are incorporated by following Stricker’s prescription. This study will serve positively in studying both pionic atoms and the role of negative pions in radiotherapy.

Analytical approach to the problem of constructing operators of effective pion-nucleon interaction at low and intermediate energies

The dynamics of pion-nucleon scattering in the S 11 and S 31 states has been investigated on the basis of the analytical approach to construction of operators of effective interactions between compound systems of strongly interacting particles with allowance for inelasticity effects at incident pion kinetic energies T < 1.5–2.5 GeV. Information about the structure of discontinuities of partial πN-scattering amplitudes in the states under consideration is derived using the available phase-shift data and effective local potentials are constructed by solving the inverse scattering problem. The possibility of description of discontinuities of partial amplitudes at dynamical cuts using exchange mechanisms in the t-and u-scattering channels and contact interactions of the Lagrangian of the chiral perturbation theory is analyzed.

LOW ENERGY PION-NUCLEON SCATTERING

The CHAOS Collaboration at TRIUMF has measured differential cross sections for π±p elastic at incident pion kinetic energies of 19.9, 25.8, 32.0, 37.1, 43.3, 57.0, and 67.0 MeV. The data analysis at the five lowest energies has been completed at the University of Tübingen. In order to measure at forward angles, in the Coulomb-Nuclear Interference region, the CHAOS detector was modified from its standard configuration with a specially developed range telescope. μ±p scattering at forward angles was also measured simultaneously, and used for validation of acceptance simulations.

Total and partial pion absorption cross sections on4Hein the Δ resonance region

This paper presents a large solid angle measurement of the positive pion absorption cross section on 4He and its decomposition into partial channels. The total absorption cross sections at incident pion kinetic energies of Tπ+=70, 118, 162, and 239 MeV are 35±5, 52±4, 51±5, and 27±2 mb, respectively. These values are lower than those reported in some previous experiments. At all pion energies a large fraction of the absorption cross section is due to multinucleon channels.Received 2 September 1997DOI:https://doi.org/10.1103/PhysRevC.58.942©1998 American Physical Society

Pion elastic and inelastic 21+ scattering on 58,60,62,64Ni at T pi =180 MeV.

Angular distributions for {pi}{sup +} and {pi}{sup {minus}} elastic and inelastic scattering from the {ital Z}=28 closed-proton-shell nuclei {sup 58,60,62,64}Ni have been measured at an incident pion kinetic energy of 180 MeV. Values for the neutron and proton matrix elements for the transition to the {ital J}{sup {pi}}=2{sup +}{sub 1} state have been extracted using the distorted wave impulse approximation in which the {pi}{sup +} and {pi}{sup {minus}} data were fitted simultaneously and the neutron and proton vibrational transition strengths were treated as free parameters. While all transitions are predominantly collective, extracted values of {ital M}{sub {ital n}}/{ital M}{sub {ital p}} indicate increasing collectivity as a function of neutron number and are consistent with the collective limit of {ital N}/{ital Z} for {sup 64}Ni. {copyright} {ital 1996 The American Physical Society.}

Pion double charge exchange on the even selenium isotopes.

Pion-induced double charge exchange (${\mathrm{\ensuremath{\pi}}}^{+}$,${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$) on $^{76,78,80,82}\mathrm{Se}$, leading to the double isobaric analog states (DIAS) and the ground states of $^{76,78,80,82}\mathrm{Kr}$, has been studied at a laboratory angle of ${5}^{0}$ and incident pion kinetic energy of 293.2 MeV. Cross sections for these transitions have been extracted, and those for the DIAS are compared to two simple models of pion double charge exchange.

Reaction pi +p--> pi + pi 0p near threshold and chiral symmetry breaking.

We have measured total cross sections for the reaction [pi][sup +][ital p][r arrow][pi][sup +][pi][sup [minus]][ital p] at incident pion kinetic energies of 190, 200, 220, 240, and 260 MeV. We use this result to deduce a new value of the chiral symmetry breaking parameter, [xi]=[minus]0.25[plus minus]0.10, in a global constrained fit of the five [pi][pi][ital N] near-threshold amplitudes. Consequently, we report new soft pion model values for the [ital s]-wave [pi][pi] scattering lengths.

π+π− coincidence measurement in the 4He( π+, π+π−) reaction at Tπ+ = 280 MeV

The pion-induced pion-production reaction ( π +, π + π −) on 4He has been studied at an incident pion kinetic energy of 280 MeV. The outgoing pions were detected in coincidence and the measured four-fold differential cross sections are compared with a quasifree πN → ππN microscopic model. Finally, the results are directly compared with recent data from the 16O( π +, π + π −) and 2H( π +, π + π −)pp reaction at the same incident energy.

Multinucleon pion absorption in the 4He( pi +,ppp)n reaction.

Three-proton emission cross sections for the $^{4}\mathrm{He}$(${\mathrm{\ensuremath{\pi}}}^{+}$,ppp)n reaction were measured at an incident pion kinetic energy of ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}^{+}$=165 MeV over a wide angular range in a kinematically complete experiment. Angular correlations, missing momentum distributions, and energy spectra are compared with three- and four-body phase-space Monte Carlo calculations. The results provide strong evidence that most of the three-proton coincidences result from three-nucleon absorption. From phase-space integration the total three-nucleon absorption cross section is estimated to be ${\mathrm{\ensuremath{\sigma}}}^{3\mathit{N}}$=4.8\ifmmode\pm\else\textpm\fi{}1.0 mb. The cross section involving four nucleons is small and is estimated to be ${\mathrm{\ensuremath{\sigma}}}^{4\mathit{N}}$2 mb. On the scale of the total absorption cross section in $^{4}\mathrm{He}$, multinucleon pion absorption seems to represent only a small fraction.

Composite particle emission following negative pion absorption on 12C at T pi -=165 MeV.

Double differential and total cross sections of the ({pi}{sup {minus}},{ital pd}), ({pi}{sup {minus}},{ital dp}), and ({pi}{sup {minus}},{ital dd}) reactions on {sup 12}C were measured over a wide angular range at an incident pion kinetic energy of 165 MeV. The shape of the angular distributions of the differential cross sections of these reactions is in most cases similar to that of the {sup 12}C({pi}{sup {minus}},{ital pp}){ital X} reaction. These similarities seem to indicate a pickup mechanism in certain regions of phase space following three-nucleon absorption. Contributions from both three-nucleon absorption and two-step processes are found to be important for the above type of reactions.

The [formula omitted] reaction at 165 MeV

Angular correlations of the 12 C(π - , pp)X reaction cross sections were measured over a wide angular range at an incident pion kinetic energy of 165 MeV and the results were compared to published data. A broad peak was observed in the angular distribution of the differential cross section that deviates from the angular distribution expected from a three-body phase space calculation for the two detected protons. The observed angular correlation disagrees with correlations previously reported in the literature.

Three-nucleon pion absorption in carbon.

We have performed an experiment in which we have detected three protons in coincidence, following the absorption of positive pions in carbon. Data were collected with twelve plastic scintillator detectors, covering a fairly large region of the available phase space, at three incident pion kinetic energies: ${T}_{\ensuremath{\pi}}$=130, 180, and 228 MeV. Comparisons are made with phase space calculations which simulate quasifree three-nucleon and four-nucleon absorption mechanisms. The first of these provides an excellent description of the bulk of the data. Some of the observed events appear to come from quasideuteron absorption, followed by a final-state interaction of one of the outgoing protons. There is no evidence for absorption mechanisms involving more than three nucleons. Estimates are made for the contributions of the three-nucleon absorption mechanisms to the total pion absorption cross section. These are relatively small.

A SEARCH FOR π-N INTERACTION BY QUARK MODEL

By means of quark potential model and Warke approximation, and introducing as compensation intermediate potential (-1)T+JKre(-r/a2) in the phenomenological one gluon exchange quark interaction potential, the pion-nucleon interaction potential is calculated. The phase shifts of p-N scattering in the six channels S11, S31, P11, P31, P13, P33 are determined for the incident pion kinetic energy in the laboratory coordinate system up to 700 MeV. These results are compared with the experimentally determined phase shifts.

Improved calculations of the π- 12C optical potential

The π- 12C optical potential is evaluated including the Fermi motion of the nucleons, first order binding corrections and nucleon-nucleon correlations. It appears clearly that the static and factorization approximations are not justified when incident pion kinetic energies are in the range 60–300 MeV. The usual Fermi averaging procedure is shown to be only partially adequate. However the calculated cross sections are not in good agreement with the experimental data. The absorptive part of the optical potential evaluated in this manner is still too weak at low energies.

Neutron Polarization inπ−pCharge-Exchange Scattering at 310 MeV

We report the measurement of the polarization in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+n$ at an incident-pion kinetic energy (lab) of 310 MeV and at an angle of 30\ifmmode^\circ\else\textdegree\fi{} in the c.m. system. The polarization was obtained from measurements of the left-right asymmetry in the scattering of the neutrons from liquid helium at lab-scattering angles of 75\ifmmode^\circ\else\textdegree\fi{} and 125\ifmmode^\circ\else\textdegree\fi{}. The measured polarization is 0.24\ifmmode\pm\else\textpm\fi{}0.07.

The reaction π−p → πOπOn AT T π=378 MeV and the S-wave ππ phase shift

A phenomenological study of the reaction π −p → π O π O n at an incident pion kinetic energy of 378 MeV is conducted within the framework of the isobar model. Through a study of both the total and differential cross-section data, we are able to obtain constraints on both the elastic partial-wave absorption parameters and the J = I = 0 ππ phase shift. In particular, we find a 0= 0.2 −0.1 +0.08 μ −1.

New Phase-Shift Parametrization Based on a Phase-Shift Dispersion Relation

The dispersion relation for the phase shift used by Ball and Frazer is generalized to include the effects of zeros and poles in the $S$ matrix. For complex $S$-matrix zeros near the physical cut, one obtains a new parametrization for a resonant state. For $l=0$, the usual Breit-Wigner phase shift is found. The method is easily extended to resonances in higher partial waves (in terms of two parameters for the case of pure elastic unitarity). The results are used to describe three partial waves in $\ensuremath{\pi}N$ scattering: ${P}_{33}$, ${D}_{13}$, and ${P}_{11}$. Excellent agreement with the published ${P}_{33}$ phase shifts is obtained by using our resonant form plus the integral over the inelastic cut. The inelastic contribution to the phase shift is small at low energies but becomes important for ${E}_{L}&gt;300$ MeV (${E}_{L}$ is the incident-pion kinetic energy). Inelastic effects in the ${D}_{13}$ partial wave can account for almost all of the phase shift up to ${E}_{L}=500$ MeV. A narrow resonance plus inelasticity gives a good fit to the phase shifts up to ${E}_{L}=900$ MeV. Our fit to the ${P}_{11}$ phase shift depends on the nucleon pole, the Roper resonance, a zero in the $S$ matrix below the elastic threshold, and inelastic effects. A good fit to the low-energy phase shifts can be obtained only if one assumes large inelasticity above 1 BeV; however, the model does account for the qualitative behavior of the ${P}_{11}$ phase shift.

Pion-Proton Charge-Exchange Scattering from 500 to 1300 MeV

Differential cross sections for the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ were measured at nine incident-pion kinetic energies in the interval from 500 to 1300 MeV. The negative pion beam from the bevatron was focused on a liquidhydrogen target completely surrounded by a cubic array of six steel-plate spark chambers. The spark chambers were triggered on events with neutral final states. Charge-exchange events were identified from the one-shower and two-shower events in the spark-chamber pictures. By the Monte Carlo technique, the ${\ensuremath{\pi}}^{0}$ distributions were calculated from the bisector distributions of the two-shower ${\ensuremath{\pi}}^{0}$ events together with the observed $\ensuremath{\gamma}$-ray distributions of the one-shower ${\ensuremath{\pi}}^{0}$ events. These ${\ensuremath{\pi}}^{0}$ distributions were fitted with both Legendre-polynomial expansions and power-series expansions by the method of least squares. The extrapolated forward differential cross sections are in good agreement with the dispersion calculations. The Legendre coefficients for the differential cross sections in isospin state $T=\frac{1}{2}$ were obtained by combining our results with available data on ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ elastic scattering. In the light of existing phase-shift solutions, the behavior of these coefficients is discussed. The ${D}_{5}{F}_{5}$ interference term that peaks near 900 MeV is verified to be in isospin state $T=\frac{1}{2}$ only. We report here also the total neutral cross sections and the cross sections for the production of neutral multipion final states $2{\ensuremath{\pi}}^{0}n$ and $3{\ensuremath{\pi}}^{0}n$. The $4\ensuremath{\pi}$ solid angle and the calibrated energy response of the spark chambers contribute to the accuracy of the results.

Recoil proton polarization measurements in pion-nucleon elastic scattering

The angular distributions of the recoil proton polarization in π + p elastic scattering have been measured at 410 and 492 MeV incident pion kinetic energy, by using a carbon plate spark chamber (Bareyre et al . 1965 a, b ). The experimental arrangement is shown in figure 1. The water Cherenkov counter selected the scattered pion and the spark chamber was triggered by the coincidence C1 C2 C3 C4 C5 Ch1 (or Ch2). The chamber was placed at two angular positions (30° and 43°). All measurements have been repeated symmetrically with respect to the beam, to check possible left-right instrumental biases. We have measured a total of 180 000 protons scattered in the chamber. They were treated by a program which: (1) reconstructs the geometry of the events; (2) selects the p -C elastic scattering by using the number of carbon plates traversed as a measure of the range; (3) and checks for possible biases.