The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with $A=15,17,39$ and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current doesn't improve the description of nuclear isovector magnetic moments for the concerned nuclei.
The experimental discovery that the nucleus is approximately transparent to low energy pions is reviewed. The consequences of this for nuclear deep inelastic scattering and Drell-Yan interactions are discussed. I argue that low energy nucleus data imply that there is little nuclear enhancement of the pion cloud of a nucleon, and try to interpret this in terms of nucleon-nucleon correlations.
Off-shell aspects of the one-pion-exchange potential and their relationship to different forms of the nonstatic (subleading-order) chiral two-pion-exchange nucleon-nucleon potential are discussed. Various types of off-shell behavior are categorized and numerous examples are given. Recently derived potentials based on chiral approaches are supplemented by a rather general form of the two-pion-exchange potential derived using old-fashioned methods. The latter is closely related to a general form of one-pion-exchange relativistic corrections and nonstatic two-pion-exchange three-nucleon forces de…
This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/ nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the $πNN$ coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium within certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.
Proton-antiproton annihilation into two pions and three pions is studied in a baryon-exchange model. Annihilation diagrams involving nucleon as well as Delta-resonance exchanges are included consistently in the two- and three-pion channels. Effects from the initial-state interaction are fully taken into account. A comparison of the influence of the Delta exchange on the considered annihilation channels is made and reveals that its importance for three-pion annihilation is strongly reduced as compared to two-pion annihilation. It is found that annihilation into three uncorrelated pions can yiel…
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.
A microscopic model for the $N\bar N\toππ$ process is presented in the meson exchange framework, which in the pseudophysical region agrees with available quasiempirical information. The scalar ($σ$) and vector ($ρ$) piece of correlated two--pion exchange in the pion--nucleon interaction is then derived via dispersion integrals over the unitarity cut. Inherent ambiguities in the method and implications for the description of pion--nucleon scattering data are discussed.
The saturation properties of the nuclear matter taking pion correlations into account is studied. We construct a Bogoliubov transformations for the pion pair operators and calculate the energy associated with the pion pairs. The pion dispersion relation is investigated. We next study the correlation energy due to one pion exchange in nuclear matter and neutron matter at random phase approximation using the generator coordinate method. The techniques of the charged pion correlations are discussed in the neutron matter calculations. We observe that there is no sign of the pion condensation in th…
We investigate the possibility of measuring the pion dispersion relation in nuclear matter through the anomalous coupling in the reaction γ- γ' π_0. It is shown that this reaction permits the study of pionic modes for space-like momenta. If the pion is softened in nuclear matter due to mixing with the delta-hole state, significant strength for this reaction is expected to move into the space-like region. Competing background processes are evaluated, and it is concluded that useful insight can be obtained experimentally, but only through a difficult exclusive measurement.
A meson exchange model of the $ππ$ interaction which fits free $ππ$ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave $ππ$ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the $NN$ central potential due to the exchange of two correlated pions, resulting in an $NN$ interaction which fails to saturate. A possible mechanism for restoring the theoretical stabil…
In this letter we study the high energy behavior of the forward differential cross section for the $^{18}O(π^+,π^-)^{18}Ne$ double charge exchange reaction. We have evaluated the sequential and the meson exchange current mechanisms. The meson exchange current contribution shows a very weak energy dependence and becomes relevant at incident pion kinetic energies above 600 MeV.
The structure and electroweak properties of the pion in symmetric nuclear matter are presented in the framework of the Nambu--Jona-Lasinio model. The pion is described as a bound state of a dressed quark-antiquark pair governed by the Bethe-Salpeter equation. For the in-medium current-light-quark properties we use the quark-meson coupling model, which describes successfully the properties of hadron in a nuclear medium. We found that the light-quark condensates, the pion decay constant and pion-quark coupling constant decrease with increasing nuclear matter density. We then predict the modifica…
Parity nonconserving two-pion exchange in elastic pp scattering is investigated in the presence of phenomenological strong distortions in various models. Parity violation is included in the nucleon-pion vertex considering NN and N Delta(1232) intermediate states in box and crossed box diagrams. Using the derived parity nonconserving two-pion exchange potential we calculate the longitudinal analyzing power A_L in elastic $pp$ scattering. The predicted effect is of the same order as vector meson exchanges.
We study the pp \to ppπ^0 reaction near threshold based on heavy-baryon chiral perturbation theory. We show that the two-pion-exchange diagrams give much larger contribution than the one-pion-exchange diagram which is of lower chiral order in Weinberg's counting scheme. We also discuss the relation of our results to the momentum counting scheme.
We discuss various aspects of pion physics in the nuclear medium. We first study s-wave pion-nucleus interaction in connection with chiral symmetry restoration and quark condensate in the nuclear medium. We then adress the question of p-wave pion-nucleus interaction and collective pionic modes in nuclei and draw the consequences for in medium $ππ$ correlations especially in the scalar-isoscalar channel. We finally discuss the modification of the rho meson mass spectrum at finite density and/or temperature in connection with relativistic heavy ion collisions.
Photocouplings for the nucleon resonances most relevant to total photoabsorption are calculated in a constituent quark model including gluon and pion exchange. The sensitivity of the results to the different ingredients of the model is discussed.
Three instances are discussed in which results produced by chiral perturbation theory can be reliably pushed to high space-like values of transferred momenta: 1. nuclear interactions, 2. nucleon sigma-term and 3. space-like structure of the pion
In this paper a short review of the theoretical problems of the pionic radioactivity is presented. The essential experimental results obtained in the 18 years of existence of the nuclear pionic radioactivity are reviewed. Moreover, using the recent results on the spontaneous fission half lives of the heavy nuclei with Z >= 100 new predictions on the pionic yields in the region of superheavy elements are established.
We show how to renormalize chiral two pion exchange perturbatively if one pion exchange has already been fully iterated at leading order. This particular choice corresponds to the implementation of the counting proposal of Nogga, Timmermans and van Kolck at subleading orders. We illustrate why the perturbative treatment of the two pion exchange contributions is mandatory in order to avoid certain inconsistencies in Weinberg's counting. In addition, renormalizability implies modifications of the power counting which we explore for the particular case of the singlet channel.
We present 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 chiral two-pion exchange component of the long-range pp interaction is studied in an energy-dependent partial-wave analysis. We demonstrate its presence and importance, and determine the chiral parameters c_i (i=1,3,4). The values agree well with those obtained from pion-nucleon amplitudes.
Correlations of two like charged pions emitted from a hot and charged spherically expanding nuclear system are investigated. The motion of the pions is described quantum mechanically using the Klein-Gordon equation which includes Coulomb field and pion absorption. Flow modifies the radial distribution of the source function and rescales the pion wave functions. The radii extracted from the correlation functions are calculated in sideward and outward direction as a function of the pair momentum. Comparison with recent measurements at SIS and AGS energies is made.
We discuss a self-consistent method to calculate the properties of cold asymmetric nuclear matter which is dressed with isoscalar scalar pion condensates. The nucleon-nucleon interaction is mediated by these pion pairs, omega- and rho- mesons. The parameters of these interactions are evaluated self-consistently using the saturation properties of nuclear matter like binding energy, pressure, compressibility and symmetry energy. The computed equation of state of pure neutron matter (PNM) is used to calculate mass and radius of a pure neutron star.
We consider two methods to find the effective parameters of the pion traversing a nuclear medium. One is the first order chiral perturbation theoretic evaluation of the pion pole contribution to the two-point function of the axial-vector current. The other is the exact, first order virial expansion of the pion self-energy. We find that, although the results of chiral perturbation theory are not valid at normal nuclear density, those from the virial expansion may be reliable at such density. The latter predicts both the mass-shift and the in-medium decay width of the pion to be small, of about …
The universal curve $σ/A$ of nuclear photoabsorption is investigated within a Fermi gas model of nuclear matter. An energy range from pion threshold up to 400 MeV is considered. The interactions between nucleon, pion, $Δ$-isobar and photon are considered in the non-relativistic approximation with corrections of the order $1/M$ taken into account with respect to proton mass. Analytical expressions are obtained, in which the influence of nuclear correlations, two-nucleon contributions and relativistic corrections is studied explicitely. An extension of the model calculation to nucleon knock-out …
Two-particle two-hole contributions to electromagnetic response functions are computed in a fully relativistic Fermi gas model. All one-pion exchange diagrams that contribute to the scattering amplitude in perturbation theory are considered, including terms for pionic correlations and meson-exchange currents (MEC). The pionic correlation terms diverge in an infinite system and thus are regularized by modification of the nucleon propagator in the medium to take into account the finite size of the nucleus. The pionic correlation contributions are found to be of the same order of magnitude as the…
We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.
A cascade model has been developed to study pion induced multichannel reactions (quasielastic, SCX, DCX, absorption and pion production) at pion energies above 0.5 GeV. Special attention has been paid to pion double charge exchange. Pion production is a determinant feature in the high energy pion nucleus reactions, and the DCX signal not related to pion production is sizeable only at forward angles and for high energy outgoing pions. The contribution to DCX of the conventional mechanism, with two quasielastic SCX steps decreases very fast as a function of the energy and reaches very low values…
Dynamics of the nuclear fragmentations and the charge exchange reactions in pion-nucleus collisions near the $Δ$(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 $Δ$(1232) resonance dominates the heating mechanism of target nucleus. The excitation e…
The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Contributions of the one-nucleon and one-pion exchange mechanisms to the cross section and polarization observables are investigated in explicit form. Results of numerical calculations for the cross section, tensor analyzing power and spin transfers are presented. The one-pion exchange contribution is essential for describing the spin averaged cross section, while in polarization observables it is found to be less important.
We evaluate the pion and isobar propagators in cold nuclear matter self consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the pi N Delta vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the Delta resonance at nuclear saturation density. …
We derive the leading two-pion exchange contributions to the two-nucleon electromagnetic current operator in the framework of chiral effective field theory using the method of unitary transformation. Explicit results for the current and charge densities are given in momentum and coordinate space.
The leading contribution to the three-pion exchange nucleon-nucleon potential is calculated in the framework of chiral symmetry. It has pseudoscalar and axial components and is dominated by the former, which has a range of about 1.5 fm and tends to enhance the OPEP. The strength of this force does not depend on the pion mass and hence it survives in the chiral limit.
The s-wave isoscalar amplitude for pion-pion scattering in a nuclear medium is evaluated using a nonperturbative unitary coupled channels method and the standard chiral Lagrangians. The method has proved successful to describe the pion-pion properties in the scalar isoscalar channel up to 1.2 GeV giving rise to poles in the t matrix for the f0(980) and the sigma. The extension of the method to the nuclear medium implies not only the renormalization of the pions in the medium, but also the introduction of interaction terms related to contact terms in the pion-nucleon to pion-pion-nucleon intera…
Three recent experiments, which looked at pionic effects in nuclei have concluded that there are no excess pions. This puts into serious question the conventional meson-exchange picture of the nucleon-nucleon interaction. Based on arguments of partial restoration of chiral symmetry with density we propose a resolution to this problem.
We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon--hole and delta-isobar--nucleon hole contributions to the pion self-energy incorporates the s-wave scattering, which requires a more accurate evaluation. Therefore relativistic approach containing only these diagrams does not describe appropriately the pion self-energy in isospin symmetric nuclear matter. We conclude that, a correct relativistic approach to the pion self-energy should involve a more sophisticated calculation in order to satisfy the known experimental results on the near-thresh…
We examine the effect of adding pion exchange between quarks and pion self-energy corrections to the Los Alamos Relativistic Quark model with a short distance cutoff of the Bethe form. The contributions to the nucleon and the Delta-baryon are small. We conclude that the model is stable under this change in the sense that significant changes to the model parameters are not required.
Two- and three-pion correlation functions are investigated for a source that is not fully chaotic. Various models are examined to describe the source. The chaoticity and weight factor are evaluated in each model as measures of the strength of correlations and compared to experimental results. A new measure of three-pion correlation is also suggested.
We carefully calculate the nucleon-nucleon interaction due to two pion exchange processes by properly evaluating the corresponding Feynman diagrams. In the estimation, we have made no approximation, and instead, we carry out the numerical integrations of three Feynman parameters. It is found that the two pion exchange potential gives rise to the attractive force which corresponds to the effective scalar meson with its mass of $m_s\simeq 4.7 m_π$ and its strength of ${g_s^2\over 4π}\simeq 1.45 $. There is a strong isospin dependence of $(\bmτ_1\cdot \bmτ_2)^2 $ which cannot be simulated by the …
The doubly differential cross sections for the $^4$He$(π^+,π^-) 4p$ reaction were calculated using both a two-nucleon sequential single charge exchange model and an intranuclear cascade code. Final state interactions between the two final protons which were the initial neutrons were included in both methods. At incident pion energies of 240 and 270 MeV the low-energy peak observed experimentally in the energy spectrum of the final pions can be understood only if the contribution of pion production is included. The calculated cross sections are compared with data.
The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the 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 contribution. The results are consistent with the analysis of the experimental data.
Conventional theories of nuclear interactions predict a net increase in the distribution of virtual pions in nuclei relative to free nucleons. Analysis of data from several nuclear experiments has led to claims of evidence against such a pion excess. These conclusions are usually based on a collective theory (RPA) of the pions, which may be inadequate. The issue is the energy dependence of the nuclear response, which differs for theories with strong NN correlations from the RPA predictions. In the present paper, information about the energy dependence is extracted from sum rules, which are cal…
The structure of the weak axial pion exchange current is discussed in various models. It is shown how the interplay of the chiral invariance and the double counting problem restricts uniquely the form of the pion potential term, in the case when the nuclear dynamics is described by the Schroedinger equation with the static nucleon-nucleon potential.
We derive the leading one-loop contribution to the one-pion exchange and short-range two-nucleon electromagnetic current operator in the framework of chiral effective field theory. The derivation is carried out using the method of unitary transformation. Explicit results for the current and charge densities are given in momentum and coordinate space.
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.
A consistent analysis of relativistic pionic correlations and meson-exchange currents for electroweak quasielastic electron scattering from nuclei is carried out. Fully-relativistic one-pion-exchange electromagnetic operators are developed for use in one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Then the exchange and pionic correlation currents are set up fully respecting the gauge invariance of the theory. Emphasis is placed on the self-energy current which, being infinite, needs to be renormalized. This is achieved starting in the Hart…
Two- and three-pion correlations are investigated in cases when disoriented chiral condensate (DCC) occurs. A chaoticity and weight factor are used as measures of two- and three-pion correlations, and the various models for DCC are investigated. Some models are found to yield the chaoticity and weight factor in a reasonable agreement with recent experimental data.
We study the perturbative renormalizability of chiral two pion exchange for the singlet and triplet channels within effective field theory, provided that the one pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed in order to obtain finite results when the cut-off is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that chiral two pion exchange can be treated perturbatively up to a center-of-mass momentum of k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in …
We utilize precise weak interaction experiments on atomic muon capture and beta decay in the A = 3 nuclei, and take into account the effects of nuclear "anomalous thresholds" to extract the pseudoscalar pi-^3He-^3H coupling parameter, G^{eff}(m_π^2) = 45.8+- 2.4. This is an order of magnitude improvement in precision over that from the use of pion-nuclear scattering data and dispersion relations.
Our previous study of the near-threshold pp\to ppπ^0 reaction based on a hybrid nuclear effective field theory is further elaborated by examining the momentum dependence of the relevant transition operators. We show that the two-pion exchange diagrams give much larger contributions than the one-pion exchange diagram, even though the former is of higher order in the Weinberg counting scheme. The relation between our results and an alternative counting scheme, the momentum counting scheme, is also discussed.
We outline the progress made in the past five years by the São Paulo group in the development of a two-pion exchange nucleon-nucleon potential within a Lorentz-invariant framework of (baryon) chiral perturbation theory.
The chiral two-pion exchange nucleon-nucleon interaction has nowadays a rather firm conceptual basis, but depends on low-energy constants, which may be extracted from fits to data. In order to facilitate this kind of application, we present here a parametrized version of our relativistic expansion of this component of the force to $O(q^4)$, performed recently.
We put forward a formalism to calculate the relativistic particle - hole and delta - hole excitation polarization insertion for pion propagator by using the particle - hole - antiparticle representation of nucleon and delta propagators in nuclear matter. The real and the imaginary part of the polarization insertion and the dispersion relation for pion propagator are calculated numerically. We find that the short range correlation enhances the delta - hole excitation but suppresses the particle - hole excitation, it also suppresses the pion condensation. We find that the effect of the short ran…
We consider the relationship between P-wave pi-N scattering and the strength of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain why effective theories that do not contain the delta resonance as an explicit degree of freedom tend to overestimate the strength of the TPE3NI. The overestimation can be remedied by higher-order terms in these ``delta-less'' theories, but such terms are not yet included in state-of-the-art chiral EFT calculations of the nuclear force. This suggests that these calculations can only predict the strength of the TPE3NI to an accuracy of +/-25%…
We show that a hydrodynamical model with continuous particle emission instead of sudden freeze out can explain both the strange particle abundances and pion abundance from NA35 without extra assumption (e.g., sequential freeze out, modified equation of state, sudden plasma hadronization,...). In this scenario, the observation of a larger pion abundance is natural and does not imply a higher initial entropy and early plasma phase.
We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $πN$ scattering amplitude which includes $Δ$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $πN$ amplitude satisfies chiral symmetry constraints and fits $πN$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the…
Short range meson-exchange mechanisms such as $ρ\toωπ^0$ contribute significantly to the amplitude for $pp\rightarrow ppπ^0$ near threshold in addition to pion rescattering. The uncertainty of the latter contribution, which depends on poorly determined parameters, is estimated. Allowing for this uncertainty and taking the short range meson-exchange contributions into account makes it possible to reproduce the measured cross section.
Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.
We investigate quantum corrections to a classical intranuclear cascade simulation of pion single charge exchange on the deuteron. In order to separate various effects the orders of scattering need to be distinguished and, to that end, we develop signals for each order of scattering corresponding to quasi-free conditions. Quantum corrections are evaluated for double scattering and are found to be large. Global agreement with the data is good.
The s-wave correlated $π$-$π$ strength distribution in cold nuclear matter is investigated. The in-medium single pions are renormalized by means of the usual p-wave couplings to nucleons and $Δ$'s. Two groups of models for the $π$-$π$ interaction are studied. The first one uses phenomenological models which reproduce the phase shifts but do not respect the soft-pion theorems. With increasing density a strong accumulation of strength in the subhreshold region is observed. Slightly above saturation density there even occurs an instability with respect to s-wave $π$-$π$ pair condensation. These e…
