We describe a model for pion production off nucleons and coherent pions from nuclei induced by neutrinos in the 1 GeV energy regime. Besides the dominant Delta pole contribution, it takes into account the effect of background terms required by chiral symmetry. Moreover, the model uses a reduced nucleon-to-Delta resonance axial coupling, which leads to coherent pion production cross sections around a factor two smaller than most of the previous theoretical estimates. Nuclear effects like medium corrections on the Delta propagator and final pion distortion are included.
At low energies the particle-hole (ph) part of the pionic susceptibility in isospin-symmetric nuclear matter is known to behave very differently from the susceptibility in finite nuclei due to the presence of an energy gap in the ph excitation spectrum. In this note we show that for charged pions in N > Z nuclei the changes due to the gap are very similar to those in the symmetric case, except at very low momenta, where a qualitatively different behavior is found.
We study the possible occurrence of surface pion condensation in finite nuclei in the relativistic mean field (RMF) theory. We are led to this conjecture due to the essential role of pions in few-body systems and the recent (p,n) experiments performed at RCNP for spin-isospin excitations of medium and heavy nuclei. We calculate explicitly various N=Z closed shell nuclei with finite pion mean field in the RMF framework and demonstrate the actual occurrence of surface pion condensation.
The nonlinear model of pionic condensate in nuclei by G. Preparata can be efficiently verified by investigation of the quasielastic knockout process of pions out of nuclei by high energy electrons. First, a momentum distribution (MD) of the collective pions has a bright maximum at q=0.3 Gev.Second the excitation spectrum of a recoil nucleus is concentrated at low energies E lesser than 1MeV. The results for the pion knockout from mesonic clouds of individual nucleons are absolutely different. The latter results are presented both for pion and rho-meson clouds localized on nucleons.
We have calculated the effect of the inclusion of final state interactions on pion production from nuclei with incident pion beams. We find that the effect of absorption, along with geometric considerations, explains much of the enhancement at low invariant mass seen in recent data for invariant mass spectra with increasing atomic number. While the variation among nuclei is well reproduced for all charge states, the enhancement for the ratio for heavy nuclei to deuterium for the pi^+ pi^- final state is only partially understood.
We calculate the cross sections for inclusive one-pion, two-pion and eta photoproduction in nuclei in the photon energy range from 300 MeV to 900 MeV within the framework of a semi-classical BUU transport model. Our results are compared with existing experimental data and discussed with respect to a calculation of the total photoabsorption cross section.
All available theoretical estimates of neutrino-induced coherent pion production rely on the 'local approximation' for the Delta propagator. The validity of this approximation is scrutinized. It is found that the local approximation overestimates the neutrino-induced coherent pion production on nuclei significantly, by up to 100%.
We introduce the chiral symmetry in the description of finite nuclei with the hope to unify the hadron and nuclear physics. This trial becomes possible by introducing finite pion mean field, which contributes largely to enhance the spin-orbit splitting so as to provide the j-j magic number. We discuss the qualitative consequence of the finite pion mean field for various observables.
The binding energies of the deeply bound 1s and 2p states in pionic atoms of $^{207}$Pb, recently established experimentally in the $^{208}$Pb(d,$^3$He) reaction, have been used by several groups to derive the pion effective mass in nuclear matter. We show that these binding energies are fully consistent with `normal' pionic atoms and that the real part of the pion-nucleus potential at the center of $^{207}$Pb is 28$\pm$3 MeV and not 20 MeV as suggested previously.
The charged current pion production induced by neutrinos in $^{12}{C}$, $^{16}{O}$ and $^{56}{Fe}$ nuclei has been studied. The calculations have been done for the coherent as well as the incoherent processes assuming $Δ$ dominance and take into account the effect of Pauli blocking, Fermi motion and the renormalization of $Δ$ in the nuclear medium. The pion absorption effects have also been taken into account.
We have studied the pion^{-} capture in nuclei leading to two photons, using improved many body methods which have been tested with success in one photon pion^{-} radiative capture, muon^{-} capture and neutrino scattering. The qualitative features of the experimental data are reproduced but there are still some disagreement at small relative photon angles. The reaction is a potential source of information on details of the gamma-gamma-pion-pion vertex where chiral corrections can be relevant. New and more precise experiments are planned which make calculations like the present one relevant an…
We present a relativistic model for electroweak pion production from nuclei, focusing on the $Δ$ and the second resonance region. Bound states are derived in the Hartree approximation to the $σ-ω$ Walecka model. Final-state interactions of the outgoing pion and nucleon are described in a factorized way by means of a relativistic extension of the Glauber model. Our formalism allows a detailed study of neutrino pion production through $Q^2$, $W$, energy, angle and out-of-plane distributions.
We give a brief review on the important role of the pion-exchange interaction characterized by the strong tensor force. In order to illustrate the role of the pion, we have proposed a new mean field theory with the charge and parity mixing, by which the pion is treated explicitly in the mean field framework. We introduce the essence of the new mean field theory and illustrate the calculated results of the pion (tensor force) correlation by taking the alpha particle as an example.
The reaction A(pi,pi pi)X has been studied at low energies, paying particular attention to the interaction of the two final pions in the scalar isoscalar (I=J=0) channel. We have developed a microscopic model for the pion production, and then implemented the two pion final state interaction by using the results of a non-perturbative unitary coupled-channels method based in the standard chiral Lagrangians. The resulting model, describes well the reaction on the nucleon for all different isospin channels. Finally, we have considered the reaction in nuclei. Our calculation takes into account Ferm…
We show theoretical results for $(γ, π^0 π^0)$ production on nucleons and nuclei in the kinematical region where the scalar isoscalar $ππ$ amplitude is influenced by the $σ$ pole. The final state interaction of the pions modified by the nuclear medium produces a spectacular shift of strength of the two pion invariant mass distribution induced by the moving of the $σ$ pole to lower masses and widths as the nuclear density increases.
The degree to which a nucleus can act as a source for coherent pion pairs is investigated for intermediate-energy heavy-ion collisions. Creation through both isovector and isoscalar channels is considered. Two experimental signals are proposed for evidence of two-pion coherent production, two-pion enhancement and the focusing of outgoing pions along the beam axis.
The inclusive pion double charge exchange process on nuclei is considered in the framework of the Gribov-Glauber approach. It is shown that inelastic rescatterings related to production of two (and more) pions in the intermediate state give an important contribution to the process of double charge exchange at kinetic energies above ~ 0.5 GeV. This mechanism dominates at energies greater or about 1 GeV and allows to explain the weak energy dependence of the double charge exchange cross section observed experimentally.
The radiative pion capture process in nuclei is approached by using a continuum shell-model description of the nucleus, together with a phenomenological treatment of the two particle-two hole effects. It is found that these effects play an important role to reproduce the observed experimental photon energy distribution. This distribution as well as the integrated one depends significantly on the details of the mean field potential. This makes this process interesting to investigate the nuclear structure dynamics.
We have studied charged current one pion production induced by $ν_μ(\barν_μ)$ from some nuclei. The calculations have been done for the incoherent pion production processes from these nuclear targets in the $Δ$ dominance model and take into account the effect of Pauli blocking, Fermi motion and renormalization of $Δ$ properties in the nuclear medium. The effect of final state interactions of pions has also been taken into account. The numerical results have been compared with the recent results from the MiniBooNE experiment for the charged current 1$π$ production, and also with some of the old…
The 1S0 pairing gap in isospin-symmetric nuclear matter and finite nuclei is investigated using the chiral nucleon-nucleon potential at the N3LO order in the two-body sector, and the N2LO order in the three-body sector. To include realistic nuclear forces in RHB (Relativistic Hartree Bolgoliubov) calculations we rely on a separable form of the pairing interaction adjusted to the bare nuclear force. The separable pairing force is applied to the analysis of pairing properties for several isotopic and isotonic chains of spherical nuclei.
The inclusive A(gamma,pi+ pi-)X reaction is studied theoretically. A sizeable enhancement of the cross section is found, in comparison with the scaling of the deuteron cross section (sigma_deuteron * A/2). This enhancement is due to the modifications in the nuclear medium of the gamma N ----> pi pi N amplitude and the pion dispersion relation. The enhancement is found to be bigger than the one already observed in the (pi,pi pi) reaction in nuclei.
Nuclear PCAC relation is studied in the framework of the effective theory of nuclear interaction, in which the interaction of real pion production-absorption is expressed by many-body operators, and does not include the one-nucleon operator as was assumed in the conventional works, while the effective axial-vector current includes the one-nucleon current in contrast to the former interaction. This problem is investigated under the simple linear $σ$-model. Results are as folows: 1) The theory describes consistently the PCAC relation and the pion production-absorption process. 2) The conventiona…
We study the $(γ,p)$ reaction on $^{208}Pb$ leading to $^{207}Pb$ with a bound pion attached to it in the lowest 1s or 2p pionic levels. The reaction can be made recoilless to optimize the production cross section but we must choose a bit higher photon energy to overcome the Coulomb barrier in the proton emission. The cross sections obtained are easily measurable and can be larger than 50 per cent of the background from inclusive ($γ$,p). This makes it a clear case for the detection of the pionic atom signals, converting this reaction into a practical tool to produce deeply bound pionic atoms.
A simple but useful guide for understanding the structure of light nuclei is presented. It is based on counting the number of interacting pairs in different spin-isospin (S,T) states for a given spatial symmetry, and estimating the overall binding according to the sum of sigma_i.sigma_j tau_i.tau_j expectation values, as suggested by one-pion-exchange. Applied to s- and p-shell nuclei, this simple picture accounts for the relative stability of nuclei as A increases and as T changes across isobars, the saturation of nuclear binding in the p-shell, and the tendency to form d, t, or alpha subclus…
A relativistic and non-local model for the coherent photoproduction of pions on spin-zero nuclei is presented. The production operator is derived from an effective Lagrangian model that contains all the degrees of freedom known to contribute to the elementary process. Using the framework of DWIA, the matrix elements of this operator are evaluated using relativistic bound state wave functions. Final state interactions are accounted for via a pion-nucleus optical potential. The effects of in-medium modifications of the production operator are discussed. We give results for $^{12}C$ and $^{40}Ca$…
We have introduced coherent state neutral pion into Antisymmetrized Molecular Dynamics. With the aid of coherent state technique, it becomes possible to calculate transition matrix elements of the pion field operator and to study excited states containing pions. For large pion-nucleon coupling fpiN > 1.6, pions have a finite expectation value and bring large energy gain in 12C. We discuss two aspects of pionic effects in spectroscopy; the LS interaction like effect and the mixing of different nucleon parity states, which would modify low energy nuclear levels.
We present a few simple observations on the occurrence of $π$-condensation in Nuclei, aimed at clarifying the nature of the $π$-condensation implied by the coherent nuclear $π$-N-$Δ$ interaction, proposed in 1990 to explain the puzzling emergence of the Shell-Model. We show that such condensation is totally unrelated to the one proposed by A. B. Migdal at the beginning of '70, which can easily be shown not to occur at the normal nucleon density $ρ_{N}\simeq$ 0.17 fm${}^{-3}$.
A unified picture of nucleon antinucleon annihilation into pions emerges from a classical description of the pion wave produced in annihilation and the subsequent quantization of that wave as a coherent state. When the constraints of energy-momentum and iso-spin conservation are imposed on the coherent state, the pion number distribution and charge ratios are found to be in excellent agreement with experiment.
The ALICE Collaboration measure the three- and four-pion Bose-Einstein correlations (BECs) in Pb-Pb collisions at the Large Hadron Collider (LHC). It is speculated that the significant suppressions of multi-pion BECs are due to a considerable degree of coherent pion emission in the collisions. In this paper, we study the multi-pion BEC functions in a granular source model with coherent pion-emission droplets. We find that the intercepts of multi-pion correlation functions at the relative momenta near zero are sensitive to droplet number in the granular source. They decrease with decreasing dro…
The nuclear density functional framework, based on chiral dynamics and the symmetry breaking pattern of low-energy QCD, is extended to the description of collective nuclear excitations. Starting from the relativistic point-coupling Lagrangian previously introduced [Nucl. Phys. A770 (2006) 1], the proton-neutron (quasiparticle) random phase approximation is formulated and applied to investigate the role of chiral pion-nucleon dynamics in excitation modes involving spin and isospin degrees of freedom, e.g. isobaric analog states and Gamow-Teller resonances.
We present our results for the exclusive electroproduction of pions off nucleons and nuclei at high values of $Q^2$. In electroproduction of nuclei $A(e,e'π)$ we consider the Color Transparency (CT) effect recently observed at JLAB. It is shown that the description of $π$ production off nucleons is mandatory for the proof of the CT signal at JLAB. We further develop the models for exclusive production of $π$ off nucleons at JLAB and HERMES. At first we describe a model based on exclusive-inclusive connection. In the second approach we combine a Regge pole approach with the residual effect of n…
We investigate the early onset of pionic color transparency ($π$CT) observed at Jefferson Laboratory (JLAB) in semi--exclusive pion electroproduction reaction $A(e,e'π^+)$ off nuclei. In the present description the primary $γ^*p \to π^+ n$ interaction is described very well both for the longitudinal and the transverse polarizations. For the final state interactions a coupled--channel treatment of the interactions of transmitted hadrons allows to go beyond the Glauber approximation. We show that a proper distinction between the soft hadronic and hard partonic components of the electroproduction…
We calculate the contribution to the nuclear energy density functional which arises from iterated pion-photon exchange between nucleons. In heavy nuclei, this novel charge symmetry breaking interaction leads to an additional binding of each proton by about 0.2 MeV. Compared to that the analogous effect from irreducible pion-photon exchange is negligibly small. As a possible mechanism to resolve the Nolen-Schiffer anomaly we propose the iteration of one-photon exchange with an attractive short-range NN-interaction. The corresponding energy per proton reads: $\bar E[ρ_p]=(2α/15π^2)(π^2 -3+6 \ln2…
We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimantal data for nuclei with mass numbers $A=2$ and $3$, or alternatively to results from lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mas…
We calculate cross sections for coherent pion production in nuclei induced by neutrinos and antineutrinos of the electron and muon type. The analogies and differences between this process and the related ones of coherent pion production induced by photons, or the (p,n) and $(^3 He, t)$ reactions are discussed. The process is one of the several ones occurring for intermediate energy neutrinos, to be considered when detecting atmospheric neutrinos. For this purpose the results shown here can be easily extrapolated to other energies and other nuclei.
The properties of infinite matter and finite nuclei are studied by using the chiral sigma model in the framework of the relativistic mean field theory. We reconstruct an extended chiral sigma model in which the omega meson mass is generated dynamically by the sigma condensation in the vacuum in the same way as the nucleon mass. All the parameters of chiral sigma model are essentially fixed from the hadron properties in the free space. In nuclear matter, the saturation property comes out right, but the incompressibility is too large and the scalar and vector potentials are about a half of the p…
We compare calculations for the production of charged pions by pion or proton beams off nuclei calculated within our coupled channel transport model (GiBUU) with recent data of the HARP collaboration for beam energies from 3 up to 13 GeV. Predictions for the 30 GeV data for pions and kaons from the NA61/SHINE experiment are included.
Coherent pion electroproduction on the deuteron is studied in the $Δ(1232)$ resonance region in the impulse approximation, i.e., neglecting pion rescattering and two-body effects. The elementary reaction on the nucleon is described in the framework of an effective Lagrangian approach including the dominant $P_{33}(1232)$ resonance and the usual background terms of the Born contributions for $π^0$ production. We have studied the influence of these different contributions on the various structure functions which determine the unpolarized exclusive differential cross section in a variety of kinem…
It is pointed out that so far all theoretical estimates of coherent pion production off nuclei induced by neutrinos rely on the 'local approximation' well known in photonuclear physics. The effects of dropping this approximation are discussed. It is found that in a plane wave approximation for the pion the local approximation overestimates the coherent neutrino-induced pion production on nuclei.
We analize two reactions: the electroproduction at small x and the Drell-Yan production by protons on nuclei. We show that nuclear shadowing in electroproduction is larger if the virtuality of inter- mediate hadrons is properly taken into account. In the Drell-Yan production, initial state interactions of fast partons are included. With this input, the excess pion contribution improves the description of data for both reactions.
We develop the formalism for coherent two pion photoproduction in nuclei and perform actual calculations of cross sections for $π^-π^+$ and $π^0π^0$ photoproduction on $^{12}C$. We find that due to the isospin symmetry the cross section for $π^0π^0$ production is very small and has a maximum when the pions propagate together. However, the kinematical region where the energies and polar angles of the two $π^0$ mesons are equal and their relative azimuthal angle $ϕ=180^0$ is forbidden. Conversely in the $π^-π^+$ production the pions prefer to have a relative azimuthal angle 180$^0$ and the produ…
A relativistic and quantum mechanical framework to compute nuclear transparencies for pion photo- and electroproduction reactions is presented. Final-state interactions for the ejected pions and nucleons are implemented in a relativistic eikonal approach. At sufficiently large ejectile energies, a relativistic Glauber model can be adopted. At lower energies, the framework possesses the flexibility to use relativistic optical potentials. The proposed model can account for the color-transparency (CT) phenomenon and short-range correlations (SRC) in the nucleus. Results are presented for kinemati…
Within a dynamical model, rescattering effects are studied in coherent pion photoproduction on the deuteron in the $Δ$(1232) resonance region. The model consists of a system of coupled equations for the N$Δ$, NN$π$ and NN channels. Pion rescattering leads in general to a significant reduction of total and differential cross sections resulting in a better description of experimental data. Only a few polarization observables are sensitive to rescattering effects. In particular $T_{20}$ allows an analysis of the reaction mechanism for specific kinematics. The question how rescattering affects the…
The contribution of the two-step process gamma + d -> p + n -> pi0 + d to the imaginary part of the amplitude for coherent pion production on the deuteron is calculated exploiting unitarity constraints. The result shows that this absorptive process is not negligible and has to be considered in an extraction of the elementary neutron production amplitude from the gamma + d -> pi0 + d cross section at threshold. In addition, it is argued that a consistent calculation of gamma + d -> pi0 + d in baryon chiral perturbation theory beyond next-to-leading order requires the inclusion of this absorptiv…
Threshold neutral pion photoproduction on light nuclei is studied in the framework of baryon chiral perturbation theory. We obtain a general formula for the electric dipole amplitude in the special case of neutral pion photoproduction on a nucleus. To third order in small momenta, the amplitude is a sum of 2- and 3-body interactions with no undetermined parameters. With reasonable input from the single nucleon sector, our result for neutral pion photoproduction on the deuteron is in agreement with experiment.
We calculate the quasifree photoproduction of pions and eta mesons on nuclei from 12C to 208Pb. Assuming that for the quasifree process the cross sections for pi/eta - photoproduction on a nucleon in medium are -- besides a lowering due to Pauli blocking -- identical to those on a free nucleon, we use these as an input. The produced mesons or resonances then propagate through the nucleus where they can undergo several scattering and absorption processes. This final state interaction, which leads to a lowering of the initial meson yield up to 70%, we simulate in a coupled channel Boltzmann-Uehl…
We present calculations of the reaction $A(e,e^\prime πN)B$ in the distorted wave impulse approximation. The reaction allows for the study of the production process in the nuclear medium without being obscured by the details of nuclear transition densities. First, a pion electroproduction operator suitable for nuclear calculations is obtained by extending the Blomqvist-Laget photoproduction operator to the virtual photon case. The operator is gauge invariant, unitary, reference frame independent, and describes the existing data reasonably well. Then it is applied in nuclei to predict nuclear c…
We investigate a domain-structured source in the pion interferometry of relativistic nuclear collisions. The source emits coherent pions intermittently with the background of chaotic pions. The coherent pions examined are either of a general nature or of disoriented chiral condensate. Two- and three-pion correlations for the source are shown to agree well with the recent NA44 experimental data.
We study the mass of a nucleon in a nucleus using a model recently introduced for a nucleon current with a pion cloud component. The method of QCD sum rules is used to determine the mass shifts for nucleons to first order in nuclear density in oxygen-16 and calcium-40, with the pion propagator determined by an optical potential for pion-nucleus scattering. Mass shifts due to the pionic contributions range from negligible in oxygen to -100 MeV in calcium at central nuclear density, with larger shifts in the nuclear surface. The consistency of this model with chiral perturbation theory is demons…
In this talk we report on two physical processes, the photoproduction of $ρ$ mesons in nuclei and the $π^0 π^0$ photoproduction in nuclei at low energies. In the first case the aim is to observe experimentally the theoretically predicted changes on the $ρ$ properties in the nuclear medium. In the second case one wishes to investigate the modifications of the $ππ$ interaction in the nuclear medium in the region of the $σ$ meson. In the first case we observe that it is quite difficult to see large effects due to the $ρ$ modification in the medium because the detection of the $ρ$ is done through …
We propose simple Monte Carlo method for calculating parton distribution in nuclei. The EMC effect is automatically included by means of two parameters, which characterize the change of nuclear pion field. Good agreement with experimental data in the broad range of variable x is obtained.
Coherent pi0 photo- and electroproduction on 4He and 12C nuclei is investigated in the framework of a distorted wave impulse approximation in momentum space. The elementary process is described by the recently developed unitary isobar model. Medium effects are considered by introducing a phenomenological Delta self-energy. The recent experimental data for 4He and 12C can be well described over a wide range of energies and emission angles by the assumption that the Delta-nuclear interaction saturates.
Using a pair of the lightest mirror nuclei, $^3$He and $^3$H, we study the effect of the medium modification of pion fields on the flavor non-singlet structure function. The change of the pion fields leads to an enhancement of the flavor asymmetry of the antiquark distributions in a nucleus.
A perturbative QCD treatment of the pion wave function is applied to computing the scattering amplitude for coherent high relative momentum di-jet production from a nucleon.
In these lectures I first explain, in a rather basic fashion, the construction of effective field theories. I then discuss some recent developments in the application of such theories to two- and three-nucleon systems.
The structure functions calculated in the Chiral bag model reproduce quite well, after appropriate perturbative evolution to large energy scales, the experimental data. We use these results to interpret the structure of the $EMC$ data as a quenching of the pion decay constant due to the in medium behavior of the nucleon. This explanation supports recent proposals of this phenomenon whose origin is the scale invariance of the $QCD$ lagrangian.
We describe the double charge exchange (DCX) reaction of pions with different nuclear targets at incident kinetic energies of 120-180 MeV within the GiBUU transport framework. The DCX process is highly sensitive to details of the interactions of pions with the nuclear medium and, therefore, represents a major benchmark for any model of pion scattering off nuclei at low and intermediate energies. We achieve a good quantitative agreement with the extensive data set obtained at LAMPF. Furthermore, we present first results on electron scattering off nuclei for beam energies of 700-1500 MeV and vir…
We study the pion-induced inclusive $Λ(1520)$ hyperon production from nuclei near threshold within a nuclear spectral function approach accounting for incoherent primary $π^-$ meson--proton ${π^-}p \to K^0Λ(1520)$ production processes. We calculate the absolute differential and total cross sections for the production of $Λ(1520)$ hyperons off carbon and tungsten nuclei at laboratory angles of 0$^{\circ}$--10$^{\circ}$, 10$^{\circ}$--45$^{\circ}$ and 45$^{\circ}$--85$^{\circ}$ by $π^-$ mesons with momentum of 1.7 GeV/c as well as their relative (transparency ratio) differential and integral yie…
Coherent photoproduction of two neutral pions on the deuteron and ^3He is calculated. The isoscalar and isovector parts of the elementary photoproduction amplitude was determined by fitting the measured total cross section on protons and neutrons. The dependence of the cross section on the isospin of the target nucleus is discussed.
The coherent $ω$-meson photoproduction from nuclei is proposed as a phenomenological method to evaluate the momentum dependence of $ω$-meson mass shift and width in nuclear matter. We analyze available data on un-separated coherent and incoherent $ω$-meson photoproduction from nuclei and extract the imaginary part of the the complex forward $ω{N}$ scattering amplitude, which is proportional to the in-medium $ω$-meson width. The accuracy of the currently available data is not sufficient to evaluate the real part of forward $ω{N}$ scattering amplitude and reconstruct the momentum dependence of t…
