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.

Nuclear fragmentation and charge-exchange reactions induced by pions in the Δ-resonance region

Dynamics of the nuclear fragmentations and the charge exchange reactions in pion-nucleus collisions near the $\Delta$(1232) resonance energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. An isospin, momentum and density-dependent pion-nucleon potential is implemented in the model, which influences the pion dynamics, in particular the kinetic energy spectra, but weakly impacts the fragmentation mechanism. The absorption process in pion-nucleon collisions to form the $\Delta$(1232) resonance dominates the heating mechanism of target nucleus. The excitation energy transferred to the target nucleus increases with the pion kinetic energy and is similar for both $\pi^{-}$ and $\pi^{+}$ induced reactions. The magnitude of fragmentation of target nucleus weakly depends on the pion energy. The isospin ratio in the pion double charge exchange is influenced by the isospin ingredient of target nucleus.

Pion production in high-energy neutrino reactions with nuclei

[Background] A quantitative understanding of neutrino interactions with nuclei is needed for precision era neutrino long baseline experiments (MINOS, NOvA, DUNE) which all use nuclear targets. Pion production is the dominant reaction channel at the energies of these experiments. [Purpose] Investigate the influence of nuclear effects on neutrino-induced pion production cross sections and compare predictions for pion-production with available data. [Method] The Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model is used for the description of all incohrent channels in neutrino-nucleus reactions. [Results] Differential cross sections for charged and neutral pion production for the MINER$\nu$A neutrino and antineutrino flux are calculated. An estimate for the coherent cross section is obtained from a comparison of data with theoretical results. The invariant mass ($W$) distribution of the $\Delta$ resonances produced is analyzed. [Conclusions] Final state interactions affect the pion kinetic energy spectra significantly. The data for charged pion production at MINER$\nu$A are compatible with the results of calculations using elementary data taken from an old Argonne National Laboratory experiment. Remaining differences can be attributed to coherent production; the data for antineutrino induced neutral pion production, where no coherent contribution is present, are reproduced quite well. In contrast, the MiniBooNE data, taken at a lower energy, are consistently higher than the theoretical description. The analysis of $W$-distributions shows that experimental cuts on this quantity lead to shape distortions for nuclear targets.

Investigation of recent weak single-pion production data

MiniBooNE [1] and MINERvA [2] charge current {\pi} + production data in the Delta region are discussed. It is argued that despite the differences in neutrino flux they measure the same dynamical mechanism of pion production and should be strongly correlated. The correlation is clearly seen in the Monte Carlo simulations done with NuWro generator but is missing in the data. Both normalization and the shape of the ratio of measured differential cross sections in pion kinetic energy are different from the Monte Carlo results, in the case of normalization a discrepancy is by a factor of 1.49.

Reaction mechanisms atMINERνA

The MINER$\nu$A experiment investigates neutrino interactions with nucleons needed for an understanding of electroweak interactions of hadrons. Since nuclear targets are being used many-body effects may affect the extracted cross sections and the energy reconstruction. The latter is essential for the extraction of neutrino oscillation properties. We investigate the influence of nuclear effects on neutrino interaction cross sections and make predictions for charged current quasielastic (QE) scattering, nucleon-knock-out and pion- and kaon-production on a CH target. The Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model is used for the description of neutrino-nucleus reactions. Integrated and differential cross sections for inclusive neutrino scattering, QE processes and particle production for the MINER$\nu$A neutrino flux are calculated. The influence of final state interactions on the identification of these processes is discussed. In particular, energy and $Q^2$ reconstruction for the MINER$\nu$A flux are critically examined. The $Q^2$ dependence of the inclusive cross sections is found to be sensitive to the energy reconstruction. Cut-offs in flux distributions have a large effect. Final state interactions affect the pion kinetic energy spectra significantly and increase the kaon cross sections by cross feeding from other channels.

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.

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π± scattering from 6Li and 12C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of 6Li and 12C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.

Probing the nuclear symmetry energy using single and doubleπ−/π+ratios from mirror reaction systems

Within the framework of an isospin and momentum-dependent hadronic transport model, the single and double ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratios in mirror reaction systems of ${}^{22}\mathrm{O}+{}^{22}\mathrm{Na}$ and ${}^{22}\mathrm{Si}+{}^{22}\mathrm{Na}$ at the incident beam energy of 400 MeV/nucleon are studied. It is found there are opposite symmetry energy effects on the single ratios from the neutron-rich and the proton-rich reactions. Due to the opposite isospin degrees of freedom, the double ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio taken from neutron-rich and proton-rich reactions displays more sensitivity to the density dependence of the nuclear symmetry energy in broader pion kinetic energy region; thus the double charged pion ratio from the mirror systems may be a useful probe for the high-density behavior of the nuclear symmetry energy.

Cluster Model Analysis of Pion Elastic and Inelastic Scattering from 12C

Angular distributions of differential cross sections for the 12C(π±, π±)12C and 12C(π±, π±)12C* reactions at pion kinetic energy ranging from 50 to 260 MeV have been analyzed with the 3α-particle model of 12C. The model provides good fits to a wide range of data. Differential cross sections for inelastic transitions to the (2 + ; 4.44 MeV) and (3 − ; 9.64 MeV) states in 12C are computed and the deformation lengths δ2 and δ3 are extracted. It is found that the extracted deformation lengths are sensitive to the nuclear model used and similar to the corresponding values found with other probes and nuclear models.

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.

Extended partial-wave analysis ofπNscattering data

We present results from a comprehensive partial-wave analysis of pi+-p elastic scattering and charge-exchange data, covering the region from threshold to 2.6 GeV in the lab pion kinetic energy, employing a coupled-channel formalism to simultaneously fit pi-p-->eta n data to 0.8 GeV. Our main result, solution SP06, utilizes a complete set of forward and fixed-t dispersion relation constraints applied to the piN elastic amplitude. The results of these analyses are compared with previous solutions in terms of their resonance spectra and preferred values for couplings and low-energy parameters.

Low-energy pions in nuclear matter and ππ photoproduction within a BUU transport model

A description of the low-energy scattering of pions and nuclei within a BUU transport model is presented. Implementing different scenarios of medium modifications, the mean free path of pions in nuclear matter at low momenta and pion absorption reactions on nuclei have been studied and compared to data and to results obtained via quantum-mechanical scattering theory. We show that even in a regime of a long pionic wavelength the semi-classical transport model is still a reliable framework for pion kinetic energies greater than ≈ 20-30MeV. Results are presented on π-absorption cross-sections in the regime of 10 MeV ⩽ T π kin ⩽ 130MeV and on photon-induced ππ production at incident beam energies of 400-500MeV.

PION PRODUCTION AND COLLECTIVE FLOW EFFECTS IN INTERMEDIATE ENERGY NUCLEUS–NUCLEUS COLLISIONS

Invoking the formation of a fireball we analyze the experimental data on pion multiplicity from La + La collision at [Formula: see text] and its kinetic energy spectrum. We discuss the freeze-out scenario, the possible role of the delta and strange particles and whether the hadronic repulsion (leading to an excluded volume effect) plays any role at the thermochemical and the hydrodynamical freeze-out stage. The importance of collective flow is realized in explaining the pion spectrum at this collision energy. The analysis also provides evidence of the presence of strange particles and the delta resonance in partial chemical equilibrium, at an initial chemical freeze-out stage when the hydrodynamic flow has not developed to have any significant effect. At the final "hydrodynamical freeze-out" we do not find any evidence of the deltas and the strange particles when the thermal temperature has dropped considerably. The importance of the collective flow vis a vis the resonance decay contribution is also discussed in explaining the pion kinetic energy spectra. Further, all the model parameters are determined uniquely, unlike previous analysis, thus avoiding any arbitrariness.

Different Methods for Pion-nucleus Optical Potential

Elastic and inelastic cross-sections for pion scat tering on 12 C at pion kinetic energy ranging from 50 to 260 MeV are computed using three independent methods of π ± -nucleus optical potential, the 3 α-particle model of the nucleus, the equivalent loca l Kisslinger potential and the Laplacian one. Reasonable fits to the measured values are obtained for 12 C without adjusting free parameters. The ability of these methods to account for elastic, in elastic, total and reaction cross-section data are somewhat similar. The Kisslinger-based local potent ial is the more suitable for describing the elastic and inelastic cross-sections of π ± -nucleus scattering . It seems that the 3 α -particle model of 12 C is not useful in the description of pion scattering on 12 C at least in the ∆-resonance region.

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.

Study of the πn → π{-}π{-}p reaction at 430 MeV energy

The total cross-section for the π{-}n → π{-}π{-}p reaction has been measured at a pion kinetic energy of 430MeV in a deuterium bubble chamber. The cross-section value was found to be 0.197±0.016mb that is much smaller than the predictions of the chiral perturbation theory. The differential spectra are compared with calculations made in the framework of the model of Bolokhov et al. 13.60.LeMeson production [:AND:]13.85.LgTotal cross-sections

Low energy analyzing powers in pion–proton elastic scattering

Analyzing powers of pion–proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS and a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for π+p scattering, and at 67.3 and 87.2 MeV for π−p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.

Dispersion relation constrained partial wave analysis ofπNelastic andπN→ηNscattering data: The baryon spectrum

We present results from a comprehensive partial-wave analysis of pi+-p elastic scattering and charge-exchange data, covering the region from threshold to 2.1 GeV in the lab pion kinetic energy, employing a coupled-channel formalism to simultaneously fit pi-p\to\eta n data to 0.8 GeV. Our main result, solution FA02, utilizes a complete set of forward and fixed-t dispersion relation constraints, from threshold to 1 GeV, and from t = 0 to -0.4 (GeV/c)^2, applied to the piN elastic amplitude. A large number of systematic checks have been performed, including fits with no charge-exchange data and other database changes, fits with few or no dispersion relation constraints, and changes to the Coulomb correction scheme. We have also reexamined methods used to extract Breit-Wigner resonance parameters. The quality of fit to both data and dispersion relation constraints is superior to our earlier work. The results of these analyses are compared with previous solutions in terms of their resonance spectra and preferred values for couplings and low-energy parameters, including the piNN coupling constant.

Semiexclusive pionic double charge exchange on4He

The semiexclusive reaction ${}^{4}\mathrm{He}({\ensuremath{\pi}}^{+},{\ensuremath{\pi}}^{\ensuremath{-}}pp)pp$ has been studied at pion kinetic energies of 105 MeV and 115 MeV. Signatures from the production of the hypothetical $\ensuremath{\pi}\mathrm{NN}$ resonance ${d}^{\ensuremath{'}}$ have been searched for in the invariant mass ${M}_{\ensuremath{\pi}\mathrm{pp}}$ spectra. No hint for a dominant ${d}^{\ensuremath{'}}$ production, as anticipated from double charge exchange excitation functions on nuclei, has been found. The data are satisfactorily described by sequential single charge exchange.

Pion-nucleon interaction in a covariant hadron-exchange model

We develop a relativistic covariant and unitary description of the pion-nucleon interaction in a hadron-exchange model. The model is based on the solution of a dimensionally reduced (quasipotential) Bethe-Salpeter equation for the partial-wave off-shell $\pi N$ scattering amplitudes with the potential consisting of the field-theoretical $s$- and $u$-channel nucleon, Roper, Delta, $D_{13}$, $S_{11}$ exchanges, and the $t$-channel $\rho$ and $\sigma$ meson exchanges. The contributions of the spin-3/2 Delta and $D_{13}$ resonances are treated within the Rarita-Schwinger formalism and different forms of the $\pi N\Delta$ vertex are investigated. The free parameters of the model are fitted to the $\pi N$ phase-shift data of the KH80 and SM95 partial-wave analyses in the region up to 600 MeV pion kinetic energy. The resulting on-shell solution provides a good description of the $\pi N$ scattering lengths, as well as the energy behavior of the S, P, and D partial waves. The sensitivity of the phase shifts on various model-dependent effects is examined.