Pion-nucleus Interaction Research Articles

Coherent meson production in antinucleon annihilation on nuclei

A phenomenological optical potential for antinucleon-nucleon (NN) interaction in an energy range of 1 to 15 GeV is presented in an eikonal model. In addition to the discussion of the strength and energy dependence, the potential is used to describe initial state interactions for coherent meson production on nuclei. To describe nuclear matter effects, Hartree-Fock Bogoliobuv (HFB) densities are used. As a first step we calculate the production of two mesons, namely pions. To cover the large energy range, the final state pion-nucleus ( πA) interaction is improved by adding resonances beyond the Δ resonance to a Kisslinger-type ansatz. Results for NN and πA cross sections are presented.

Effects of final-state interactions in neutrino-nucleus interactions

Final-state interaction (FSI) effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of formation time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current ${\ensuremath{\pi}}^{0}$ production data in $\ensuremath{\sim}1$ GeV neutrino flux experiments is demonstrated.

In-medium pion and partial restoration of chiral symmetry

The partial restoration of chiral symmetry in nuclear medium is investigated in a model-independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation 〈 q ¯ q 〉 ∗ / 〈 q ¯ q 〉 = ( F π t / F π ) Z π ∗ 1 / 2 with the in-medium quark condensate 〈 q ¯ q 〉 ∗ , in-medium pion decay constant F π t and in-medium pion wave-function renormalization Z π ∗ . Calculating Z π ∗ at low density from the isoscalar pion–nucleon scattering data and relating F π t to the isovector pion–nucleus scattering length b 1 ∗ , it is concluded that the enhanced repulsion of the s-wave isovector pion–nucleus interaction observed in the deeply bound pionic atoms directly implies the reduction of the in-medium quark condensate. The knowledge of the in-medium pion mass m π ∗ is not necessary to reach this conclusion.

Pion emission in 2H, 12C, 27Al( [formula omitted]) reactions at threshold

The very first data from MAX-lab in Lund, Sweden on pion photoproduction at threshold energies are presented. The decrease of the total π + yield in γ+ 12C, 27Al reactions below 200 MeV as well as the d σ / d Ω cross-section data essentially follow the predictions of an intranuclear-cascade model with an attractive potential for the pion–nucleus interaction. However, d 2 σ / d Ω d T , cross-section data at 176 MeV show deviations which call for refinements of the model and possibly also for the inclusion of coherent pion-production mechanisms.

Inclusive pion production by pions on nuclei and determination of root-mean-square radii of proton and neutron distributions

A brief nonanalytic survey of data available in the literature for parameters that characterize nuclear sizes is given, and the potentials of some methods for determining these sizes are compared. Attention is given primarily to determining nuclear sizes in experiments that study pion-nucleus interaction. For pointlike protons and neutrons, values of parameters that describe the radial dependences of their densities according to the Fermi distribution are presented in a tabular form. The method proposed previously at the Institute of Theoretical and Experimental Physics (ITEP, Moscow) for determining nuclear sizes on the basis of measuring differential cross sections for π∓ + A → πforw± + X processes in the kinematical region where the recorded interaction event occurs on a single proton (neutron) of nucleus A, the presence of the remaining nucleons manifesting itself in shadowing effects, is described, and examples of the application of this method are given.

OVERVIEW OF PION-NUCLEUS INTERACTION AT LOW ENERGIES

Predictions of the existence of well-defined deeply bound pionic atom states for heavy nuclei and the eventual observation of such states by the (d,3He) reaction have revived interest in the pion-nucleus interaction at threshold and in its relation to the corresponding pion-nucleon interaction. Explanation of the 'anomalous' s-wave repulsion in terms of partial restoration of chiral symmetry and/or in terms of energy-dependence effects have been tested in global fits to pionic atom data and in a recent dedicated elastic scattering experiment. The role of neutron density distributions in this context is discussed in detail for the first time.

Photoproduction of πmesons from nuclei

Photoproduction of neutral pions from nuclei (carbon, calcium, niobium, lead) has been studied for incident-photon energies from 200 MeV to 800 MeV with the TAPS detector using the Glasgow photon tagging spectrometer at the Mainz MAMI accelerator. Data were obtained for the inclusive photoproduction of neutral pions and the partial channels of quasifree single-π0, double-π0, and π0π± photoproduction. They have been analyzed in terms of the in-medium behavior of nucleon resonances and the pion-nucleus interaction. They are compared to earlier measurements from the deuteron and to the predictions of a Boltzmann-Uehling-Uhlenbeck (BUU) transport model for photon-induced pion production from nuclei.

Deeply bound pionic 1s states in Sn isotopes

We successfully observed deeply bound pionic 1s states in Sn isotopes ( 115Sn, 119Sn, 123Sn) using the Sn( d, 3He) pion-transfer reaction under the recoil-free condition. The 1s binding energies and widths were determined to high precision. The present results indicate that the isovector part of the s-wave pion-nucleus interaction is significantly enhanced, giving a clear evidence for partial restoration of chiral symmetry in the nuclear medium.

Experimental indication of a reduced chiral order parameter from the 1s π− state in 205Pb

The isovector potential parameter (b1) of the s-wave pion–nucleus interaction was deduced to be b1=−0.116+0.015−0.017mπ−1 by using the binding energy and width of the recently observed deeply bound 1s π− state in 205Pb combined with the known 1s states of light pionic atoms. An enhancement of b1 over the free-πN value (|−0.090|) is indicated, which may infer that the chiral order parameter (squared pion decay constant, fπ2) is reduced by a factor of 0.78+0.13−0.09 in the nuclear medium of 205Pb where the bound π− is located. The isoscalar part is accounted for as arising mainly from a double-scattering effect, without invoking a large density-quadratic term.

Pion, pion-pion, and pion-nucleus interactions

This survey is devoted to describing the early studies of I.I. Gurevich on pion physics that were performed by the photoemulsion method and the studies of the pion-pion interaction that were made by his colleagues on the basis of the hydrogen-bubble-chamber and the magnetic-spectrometer method (as well as on the basis of the photoemulsion method). Two approaches—an extrapolation of experimental data from the physical region to the pion pole and a theoretical calculation based on the Roy integral equations—are used to deduce information about the pion-pion interaction. The first results obtained for pion-pion and pion-nucleus interactions in the experiments that are being currently performed in Brookhaven and at CERN (ππ interaction) and at TRIUMF (Canada) and in Brookhaven (pion-nucleus interaction) are presented, along with the existing theoretical concepts in these realms of physics.

Deeply bound 1s and 2p pionic states in 205Pb and determination of the s-wave part of the pion-nucleus interaction.

We observed well-separated 1s and 2p pi(-) states in 205Pb in the 206Pb(d,3He) reaction at T(d) = 604.3 MeV. The binding energies and the widths determined are B(1s) = 6.762+/-0.061 MeV, Gamma(1s) = 0.764(+0.154)(-0.171) MeV, B(2p) = 5.110+/-0.045 MeV, and Gamma(2p) = 0.321(-0.062)(+0.060) MeV. They are used to deduce the real and imaginary strengths of the s-wave part of the pion-nucleus interaction, which translates into a positive mass shift of pi(-) in 205Pb.

Empirical deduction of a medium-modified chiral order parameter from 1s π− states in heavy nuclei

We propose a model-independent procedure to deduce empirically the isovector strength b 1 of the pion–nucleus interaction, which is related to possible modification of the pion-decay constant f π , and thus of the chiral order parameter, in the nuclear medium. The first procedure is to compare the 1s binding energies of π − in two nuclei which have different ( N − Z )/ A values, such as 205 Pb and 115 Sn. The second, more direct way is to deduce b 1 from an observed isotope shift of the 1s binding energy, such as in 115 Sn and 123 Sn.

Zero-energy π−–D scattering: precise determination of the πN scattering lengths and of the charged coupling constant

The recent progress in the study of the pion–nucleus s-wave interaction by the discovery of discrete excited states below the pion threshold in heavy nuclei is reviewed. These states are populated by ( d, 3He ) reactions at bombarding energies of 500–600 MeV, with the 3He observed at forward direction under kinematic conditions, where a large energy (in the order of a pion mass), but only a small momentum is transferred (recoil-free). The resulting distinct pattern of states can be uniquely assigned to deeply bound π− states coupled to well known neutron–hole states with the configurations (nl)π(n′l′j)n−1. With sufficient energy resolution in the ( d, 3He ) spectroscopy it was for the first time possible to determine the excitation energy of each configuration with respect to the ground state of the residual nucleus with A−1 and from this also the binding energy, Bnl, and even the natural width, Γnl, of the pionic state.A summary of the results on binding energies and widths of pionic 1s and 2p states in nuclei with large neutron excesses, such as 207Pb, 205Pb, 123Sn, 119Sn and 115Sn is given. The structure of these states is determined by a superposition of a large repulsive s-wave π−–nucleus interaction and an attractive Coulomb interaction, such that the pions are bound in a potential pocket at the surface of the nuclei, which leads to a halo-like pion distribution around the nucleus. The repulsive s-wave interaction reduces the binding energies of the 1s states in the Pb nuclei by roughly a factor of two and the widths to about 760 keV, which makes them discrete with no overlap to other states. The pion–nucleus interaction has its maximum contribution from an effective density ρe≈0.6ρ0. So it is a sensitive tool to test in-medium effects by comparison with the known s-wave pion–nucleon interaction. An empirical procedure is developed to derive the s-wave pion nucleus potential parameters unambiguously by using only 1s-state binding energies and widths of pionic atoms of light N=Z nuclei as well as of deeply bound pionic 1s states of heavy nuclei with large neutron excesses. The isovector s-wave parameter was deduced as b1=−0.115±0.007mπ−1, which is found to be enhanced over the free πN scattering length (−0.090mπ−1). This result indicates that the order parameter of chiral symmetry breaking, fπ∗(ρ0)2, is reduced by a factor of ∼0.64 in a nucleus with density ρ0=0.17 fm. We also obtained the scaling parameter for the density dependence of the isovector pion–nucleus interaction strength to αρ0∼0.36 in good agreement with theoretical expectations. Thus we find clear evidence for partial chiral symmetry restoration in a nuclear medium.

Investigation of low energy pion-nucleus interaction using electrofission data for heavy nuclei at the pion threshold

A theoretical approach to describe electro- and photofission processes at intermediate energies was worked out. Photopion reabsorption mechanisms by two and three nucleons (2NA and 3NA) were incorporated in the calculations. The comparison with electrofission data for preactinides showed that a substantial 3NA component should be added in the pion absorption to fit the data near photopion threshold, in accordance with a recent theoretical estimate. It was also shown that the shape of the fission response curve is sensitive to detailed aspects of the pion mean free path.

Si, GaAs and diamond damage in pion fields with application to LHC

The concentration of primary radiation defects induced by charged pions, in the energy range 20MeV–50GeV, in the bulk of silicon, GaAs and diamond has been calculated in order to characterise the radiation resistance of these materials. The mechanisms by which pions impart energy to the lattice have been analysed and their contribution has been evaluated starting from the data on pion–nucleus interaction. The energy partition of the primary recoil nuclei between ionisation and displacements has been considered in the frame of the Lindhard theory. The energy dependence of the concentration of primary radiation defects presents two maxima: one in the region of the delta resonance, and another one around 1GeV. The main conclusion is that diamond is hardner to pion irradiation than both silicon and GaAs in the whole energy range investigated. The pion-induced degradation in the inner detector system at LHC has been evaluated, starting from the simulated spectra, and considering different detector materials: diamond, silicon and GaAs.

Theoretical study of pion damage in A 3B 5 compounds

A theoretical study of the radiation effects, from the point of view of the non-ionising energy loss and of the concentration of primary defects, in some A 3B 5 semiconductors, has been performed. These effects have been analysed for charged pions, in the energy range 50 MeV–50 GeV. The investigated materials have been GaAs, InP, GaP, InAs and InSb, and the results have been compared with silicon, as a reference material, keeping into account the peculiarities of the pion–nucleus interaction, and the recoil energy redistribution in the lattice. The results of the calculations have put in evidence the higher radiation resistance of Si, GaP and GaAs in the whole energy range investigated, with respect to the other analysed materials: InP, InAs and InSb, that proved to be of interest from this point of view only in the intermediate energy region.

Nuclear sigma term in the Skyrme model: Pion-nucleus interaction

The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the $\mathrm{NN}$ interaction with respect to the quark mass, ${m}_{q}\ensuremath{\partial}{V}_{\mathrm{NN}}/\ensuremath{\partial}{m}_{q}.$ The $\mathrm{NN}$ potential is evaluated in the Skyrmion-Skyrmion picture within the quantized product ansatz. The contribution of the $\mathrm{NN}$ potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the $s$-wave pion-nucleus optical potential is estimated including such a contribution. The results are consistent with the analysis of the experimental data.

Composition of the nuclear periphery from antiproton absorption

Thirteen targets with mass numbers from 58 to 238 were irradiated with the antiproton beam from the Low Energy Antiproton Ring facility at CERN leading to the formation of antiprotonic atoms of these heavy elements. The antiproton capture at the end of an atomic cascade results in the production of more or less excited residual nuclei. The targets were selected with the criterion that both reaction products with one nucleon less than the proton and number of the target be radioactive. The yield of these radioactive products after stopped-antiproton annihilation was determined using gamma-ray spectroscopy techniques. This yield is related to the proton and density in the target nucleus at a radial distance corresponding to the antiproton annihilation site. The experimental data clearly indicate the existence of a neutron-rich nuclear periphery, a neutron halo, strongly correlated with the target separation energy Bn and observed for targets with Bn < 10 MeV. For two-target nuclei 106Cd and 144Sm, with larger binding energies, a proton-rich nuclear periphery was observed. Most of the experimental data are in reasonable agreement with calculations based on current antiproton-nucleus and pion-nucleus interaction potentials and on nuclear densities deduced with the help of the Hartree-Fock-Bogoliubov approach. This approach was, however, unable to account for the 106Cd and 144Sm results.

π++12Celastic scattering between 18 and 44 MeV

Differential cross sections for {pi}{sup +}+{sup 12}C elastic scattering in the energy range of 18{endash}44 MeV for six scattering angles have been measured with an increment in the incident energy of 2 MeV. The measured cross sections are compared to calculations within the framework of a unitary scattering theory of the pion-nucleus interaction. It is shown that the excitation function at angles around 90{degree} is dominated by the D wave of the pion-nucleus interaction. {copyright} {ital 1998} {ital The American Physical Society}

Non-ionising energy deposition of pions in GaAs and Si for radiation damage studies

The dependence of the displacement damage induced by pions in GaAs has been evaluated, in the energy range 50 –1000 MeV, using the Lindhard theory and parametrised values of the pion-nucleus interaction. The curves corresponding to the NIEL produced by protons, neutrons, and pions in Si and in GaAs intersect, in the limit of calculation errors, in the region 50 – 80 MeV, at a NIEL of 2 – 5.5 MeV cm 2 /g. The energy dependence of the NIEL of pions in Si and GaAs is discussed in correlation with the simulated pion spectra at new hadron colliders.