Pion Nucleus Research Articles

Pion–nucleus elastic scatterings incorporating medium effects within the Eikonal–Glauber model

Pion–nucleus elastic scatterings incorporating medium effects within the Eikonal–Glauber model

Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance

Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance

Pion–nucleon sigma term σπNand deeply bound pionic atoms

AbstractWe investigate the possibility of determining the value of the pion–nucleon sigma term σπN precisely by the experimental observables of deeply bound pionic atoms. We discuss the sensitivity of the observables to σπN and take into account the typical errors of up-to-date experiments on deeply bound pionic atoms. We find that the gap in the binding energies and the width of the deeply bound pionic states are good observables for σπN value determination with experimental data. We also discuss the expected difficulties for the accurate determination of the value of σπN due to the correlation between the σ term and the potential parameter in the pion–nucleus optical potential.

Structure of double pionic atoms

Abstract We study theoretically the structure of double pionic atoms, in which two negatively charged pions ($\pi^-$) are bound in the atomic orbits. The double pionic atom is considered to be an interesting system from the point of view of the multi-bosonic systems. In addition, it could be possible to deduce valuable information on the isospin $I = 2$$\pi\pi$ interaction and the pion–nucleus strong interaction. In this paper, we take into account the $\pi\pi$ strong and electromagnetic interactions, and evaluate the effects on the binding energies by perturbation theory for the double pionic atoms in heavy nuclei. We investigate several combinations of two pionic states and find that the order of magnitude of the energy shifts due to the $\pi\pi$ interaction is around 10 keV for the strong interaction and around 100 keV for the electromagnetic interaction for the ground states.

Constraining resonance properties through kaon production in pion–nucleus collisions at low energies

Hadronic interactions are crucial for the dynamical description of heavy-ion reactions at low collision energies and in the late dilute stages at high collision energies. In particular, the properties and decay channels of resonances are an essential ingredient of hadronic transport approaches. The HADES collaboration measured particle production in collisions of pions with carbon and tungsten nuclei at E kin = 1.7 GeV (Adamczewski-Musch et al 2019 Phys. Rev. Lett. 123 022002). Such reactions are of high interest, because they allow to probe the properties of baryonic resonances produced in a much cleaner environment than the usual nucleus–nucleus collisions. We study these reactions with two transport approaches: SMASH (simulating many accelerated strongly-interacting hadrons) and UrQMD (ultra relativistic quantum molecular dynamics) which follow the same underlying concept but with different implementations. The differential spectra in rapidity and transverse momentum are used to show how model parameters, as the decay channels of high mass resonances and angular distributions of kaon elastic scattering, can be constrained. It is found that the data favor the production of more particles with lower momentum over the production of few particles with higher momentum in these decays. In addition, the shape of the rapidity distribution of the kaons strongly depends on the angular distribution of the elastic kaon–nucleon cross section.

Pion nucleus Drell\u2013Yan process and parton transverse momentum in the pion

We present a thorough analysis of unpolarized Drell–Yan (DY) pair production in pion–nucleus scattering. On the nucleus side, we use nuclear parton distributions along with parametrisations of the nucleon partonic transverse distribution available in the literature. Partonic longitudinal and transverse distributions of the pion are those obtained in a recent calculation in a Nambu–Jona Lasinio (NJL) framework, with Pauli–Villars regularization. The scale of the NJL model is determined with a minimisation procedure comparing NLO predictions based on NJL evolved pion distributions to rapidity differential DY cross sections data. The resulting distributions are then used to describe, up to next-to-leading logarithmic accuracy, the transverse momentum spectrum of dilepton pairs up to a transverse momentum of 2 GeV. With no additional parameters, fair agreement is found with available pion–nucleus data, confirming the virtues of the NJL description of pion parton structure. We find sizable evolution effects on the shape of the distributions and on the generated average transverse momentum of the dilepton pair. We furthermore discuss the possibility of gaining information about the behavior of the pion unpolarized transverse momentum dependent parton distribution from pion nucleus DY data.

Elastic Scattering Cross Section of Pion (.π+ ) with N, 16O and 28Si

Abstract The pion–nucleon and nucleus scattering at intermediate energies have been intensively studied in recent years on the basis of meson exchange theory. In this work the optical potentials of the pion-nucleon (π+ N) interactions are obtained on the basis of the single-boson-exchange (SBE). We used sets of boson parameters suggested by the Julich group, to get the radial forms of the interacting pion nucleon optical potential V(r), and we use the effective nuclear density of the target nuclei (oxygen and Silicon) to obtain the pion nucleus optical potential. The differential crosses sections for (π+ 16O) and (π+ 28Si) are calculated by using the first born approximation, the scattering angle in the frame of the center of mass system, within the framework of time independent Schrodinger equation, and in the π+ energy region Plab < 0.5 GeV. All results are found in a good agreement with the available experimental data.

On the Production of J/ψ-Mesons in Pion–Nucleus Collisions

The processes of J/ψ-mesons production in pion–nucleus collisions are considered. For the determination of the inclusive spectra πA → J/ψX, the model was used which takes into account the energy losses of hard gluons in the interactions of hadron states with the nucleus nucleons. The results of calculations are presented together with the experimental data of NA3 Collaboration on π–Pt195 → J/ψX spectra at the incident pions energies of 150 and 280 GeV.

EPPS16: nuclear parton distributions with LHC data

We introduce a global analysis of collinearly factorized nuclear parton distribution functions (PDFs) including, for the first time, data constraints from LHC proton–lead collisions. In comparison to our previous analysis, EPS09, where data only from charged-lepton–nucleus deep inelastic scattering (DIS), Drell–Yan (DY) dilepton production in proton–nucleus collisions and inclusive pion production in deuteron–nucleus collisions were the input, we now increase the variety of data constraints to cover also neutrino–nucleus DIS and low-mass DY production in pion–nucleus collisions. The new LHC data significantly extend the kinematic reach of the data constraints. We now allow much more freedom for the flavor dependence of nuclear effects than in other currently available analyses. As a result, especially the uncertainty estimates are more objective flavor by flavor. The neutrino DIS plays a pivotal role in obtaining a mutually consistent behavior for both up and down valence quarks, and the LHC dijet data clearly constrain gluons at large momentum fraction. Mainly for insufficient statistics, the pion–nucleus DY and heavy-gauge-boson production in proton–lead collisions impose less visible constraints. The outcome – a new set of next-to-leading order nuclear PDFs called EPPS16 – is made available for applications in high-energy nuclear collisions.

Applicability of pion–nucleus Drell–Yan data in global analysis of nuclear parton distribution functions

Despite the success of modern nuclear parton distribution functions (nPDFs) in describing nuclear hard-process data, they still suffer from large uncertainties. One of the poorly constrained features is the possible asymmetry in nuclear modifications of valence u and d quarks. We study the possibility of using pion–nucleus Drell–Yan dilepton data as a new constraint in the global analysis of nPDFs. We find that the nuclear cross-section ratios from the NA3, NA10 and E615 experiments can be used without imposing significant new theoretical uncertainties and, in particular, that these datasets may have some constraining power on the u/d-asymmetry in nuclei.

Modification of {$\mit \Delta $}(1232) in the Neutrino Nucleus Reaction

The remarkable observations in the pion induced and charge exchange reactions on a nucleus are the significant shift and broadening of the $\Delta (1232)$-peak relative to free pion nucleon scattering. For the forward going massless leptons, the weak process $(\nu_l,l)$ on a nucleon, according to Adler's partially conserved axial current theorem, is connected to the pion nucleon scattering. This mechanism is also applicable to the nucleus. Therefore, the modification of the $\Delta$-peak in a nucleus can be seen in the $(\nu_l,l)$ reaction since it is connected to the pion nucleus scattering. To investigate this issue quantitatively, the double differential cross sections of the forward going ejectile $l$ energy distribution in the $(\nu_l,l)$ reaction are calculated in the $\Delta$-excitation region for both proton and nucleus. The measured pion nucleon and pion nucleus scattering cross sections in the quoted energy region are used in these reactions as input. Since the $(\nu_l,l)$ reaction is connected to the pion induced scattering, the features of the previous reaction is shown analogous to those of the later.

Application of a folding-model optical potential to analyzing inelastic pion–nucleus scattering and the in-medium effect on a pion–nucleon amplitude

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π±-mesons on 28Si, 40Ca, 58Ni, and 208Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2+ and 3− collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β2) and octupole (β3) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.

Coherent pion production in neutrino-nucleus scattering

In this article, we study the coherent pion production in neutrino-nucleus interaction in the resonance region using the formalism based on partially conserved axial current (PCAC) theorem which relates the neutrino-nucleus cross section to the pion-nucleus elastic cross section. The pion nucleus elastic cross section is calculated using the Glauber model in terms of pion-nucleon cross sections obtained by parameterizing the experimental data. We calculate the differential and integrated cross sections for charged current coherent pion production in neutrino carbon scattering. The results of integrated cross section calculations are compared with the measured data. Predictions for the differential and integrated cross sections for coherent pion productions in neutrino iron scattering using above formalism are also made.

Partial inelasticity coefficients of negative pions in p, d, α, 12C+12C and p, 12C+181Ta collisions at 4.2 GeV/c per nucleon

The partial inelasticity coefficients of the negative pions were determined in minimum bias p, d, α, 12 C +12 C and p, 12 C +18 Ta collisions at 4.2A GeV/c taking into account the average number of participant nucleons of a projectile nucleus. In nucleus–nucleus collisions, the average values of partial inelasticity coefficients (〈K(π-)〉) of the negative pions did not depend on the mass numbers of projectile and target nuclei. Increase of 〈K(π-)〉 in going from p+12 C to d, α, 12 C +12 C collisions was due to an additional source of production of fast negative pions in nucleus–nucleus collisions — a charge exchange conversion of one or more neutrons of a projectile nucleus into a proton and π-. Linking the experimental results of the present analysis at intermediate energy with those obtained at high and ultra-high energies, it was concluded that the average values of partial inelasticity coefficients of pions in nucleon–nucleus and nucleus–nucleus collisions manifest a transitive behavior. At intermediate energies, the values of 〈K(π-)〉 were smaller by a factor of two and more as compared to those at high energies, and they increased further with increasing incident energy, reaching a plateau at E0 &gt; 100A GeV.

Centrality and system-size dependencies of temperatures of soft and hard components ofptdistributions of negative pions inHe4+C12,C12+C12, andC12+Ta181collisions atsNN=3.14GeV

Collision centrality as well as the system-size dependencies of the temperatures of the soft (${p}_{t}=0.1\ensuremath{-}0.5\phantom{\rule{4.pt}{0ex}}\text{GeV}/c$) and hard (${p}_{t}=0.5\ensuremath{-}1.2\phantom{\rule{4.pt}{0ex}}\text{GeV}/c$) components of the experimental transverse momentum distributions of the negative pions produced in $^{4}\mathrm{He}{+}^{12}\mathrm{C}, ^{12}\mathrm{C}{+}^{12}\mathrm{C}$, and $^{12}\mathrm{C}{+}^{181}\mathrm{Ta}$ collisions at $4.2A\phantom{\rule{4.pt}{0ex}}\text{GeV}/c$ ($\sqrt{{s}_{NN}}=3.14\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$) are analyzed. For the studied collision systems and selected collision centralities, the temperatures are extracted from fitting separately the soft and hard ${p}_{t}$ components of the negative pions by one-temperature Hagedorn and one-temperature Boltzmann functions. The extracted temperatures of both the soft and hard components of the ${p}_{t}$ distributions of ${\ensuremath{\pi}}^{\ensuremath{-}}$ depend on the geometry (size) and degree of overlap of the colliding nuclei in peripheral, semicentral, and central nucleus--nucleus collisions at $\sqrt{{s}_{NN}}=3.14\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. The gap (differences) between the extracted temperatures in the studied collision systems increases with increasing the degree of overlap of the colliding nuclei, i.e., with an increase in the collision centrality and the corresponding increase in the numbers of participant nucleons and binary collisions. The temperature of the soft ${p}_{t}$ component of the negative pions in $^{12}\mathrm{C}{+}^{12}\mathrm{C}$ ($^{12}\mathrm{C}{+}^{181}\mathrm{Ta}$) collisions increases (decreases) with increasing of the collision centrality. The temperature of the hard ${p}_{t}$ component of ${\ensuremath{\pi}}^{\ensuremath{-}}$ in $^{12}\mathrm{C}{+}^{181}\mathrm{Ta}$ ($^{4}\mathrm{He}{+}^{12}\mathrm{C}$) collisions increases (decreases) consistently with an increase in the collision centrality. The temperature of the soft ${p}_{t}$ component of ${\ensuremath{\pi}}^{\ensuremath{-}}$ decreases with an increase in the system size in semicentral and central nucleus--nucleus collisions at $\sqrt{{s}_{NN}}=3.14\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. In central collisions, the temperature of the hard ${p}_{t}$ component increases consistently with an increase in system size. The physical interpretations of the results obtained are given. The quantitative results on temperatures extracted from the ${p}_{t}$ spectra of negative pions in nucleus--nucleus collisions at $4.2A\phantom{\rule{4.pt}{0ex}}\text{GeV}/c$ are compared to those obtained in lower, intermediate, and higher energies in other Joint Institute for Nuclear Research (JINR), Gesellschaft f\"ur Schwerionenforschung (GSI), and SPS experiments.

In-medium modified π–ρ–ω mesonic Lagrangian and properties of nuclear matter

We investigate the bulk properties of symmetric nuclear matter within the framework of an in-medium modified chiral solitonic model with π, ρ and ω mesons. We consider the modification of meson degrees of freedom in nuclear matter, based on phenomenology of pion–nucleus scattering and the empirical nuclear mass formula. We discuss the results of the density dependence of the volume term in the mass formula and the incompressibility of symmetric nuclear matter, comparing them with relativistic mean-field models. The mass dropping of the ρ meson in nuclear matter is also obtained and discussed.

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions VIII: aluminium nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ int thick stationary aluminium target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20∘<θ<125∘. Cross-sections on aluminium nuclei are compared with cross-sections on beryllium, carbon, copper, tin, tantalum and lead nuclei.

Multiplicity scaling of target protons in high-energy nucleus–nucleus and hadron–nucleus interactions

Multiplicity scaling of target protons emitted from nucleus–nucleus (16O–AgBr interactions at 2.1 AGeV and 32S–AgBr interactions at 200 AGeV), pion–nucleus (π−–AgBr interactions at 350 GeV/c) and proton–nucleus interactions (p–AgBr interactions at 200 GeV/c) has been investigated. The experimental points are found to lie approximately on the curve described by ψ(z) = Azexp ( − Bz) with A = 3.36 ± 0.19 and B = 1.74 ± 0.06 for all the four interactions. A comparison of the fit with the function ψ(z) = (Az + Bz3 + Cz5 + Dz7)exp ( − Ez) has also been performed.

Meson Production in Antinucleon Annihilation on Nuclei

Pion production in coherent antiproton annihilation reactions on nuclei is studied in a fully quantum mechanical description. The elementary elastic NN and the NN! n annihilation vertices are obtained from a t-matrix accounting for coupled chan- nels e ects. The theoretical amplitudes are used to derive a microscopic NA optical model potential and the meson production vertices. Pion nucleus final state interaction are taken into account by adding higher pion-nucleon resonances beyond the -resonance. Nuclear structure aspects are described by HFB-theory. Results for pA, A and meson production cross sections are presented.

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions VII: tin nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary tin target, of proton and pion beams with momentum from \pm3 GeV/c to \pm15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. Cross-sections on tin nuclei are compared with cross-sections on beryllium, carbon, copper, tantalum and lead nuclei.