Pions In Nuclear Matter Research Articles

Electroweak properties of pions in a nuclear medium

The charge form factor and weak decay constant of the pion as well as the pion-quark coupling constant in symmetric nuclear matter are explored in the framework of the Nambu--Jona-Lasinio model, where the pion is described as a bound state of dressed quark-antiquark pair obtained by the Bethe-Salpeter equation. For the in-medium current quark properties, we adopt the quark-meson coupling model, which describes successfully many hadron properties in a nuclear medium. The pion decay constant and the pion-quark coupling constant are found to decrease with increasing density as well as the magnitude of the light quark condensate. But the pion mass is found to be insensitive to density up to $1.25$ times the normal nuclear density. The pion charge form factor in the space-like region is also explored and is found to have a similar $Q^2$ dependence as the form factor in vacuum showing $1/Q^2$-behavior in large $Q^2$ region, where $Q^2$ is the negative of the four-momentum transfer squared. The modifications of the charge radius of the charged pion in nuclear matter are then estimated and the root-mean-square radius at the normal nuclear density is predicted to be larger than that in vacuum by about 20\%.

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

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

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

In the present paper we investigate a method to describe low-energy scattering events of pions and nuclei within a Boltzmann-Uehling-Uhlenbeck (BUU) transport model. Implementing different scenarios of medium modifications, we studied the mean free path of pions in nuclear matter at low momenta and compared pion absorption simulations to data. Pursuing these studies we have shown, that also in a regime of a long pionic wave length the semi-classical BUU model still generates reasonable results. We present results on pi-induced events in the regime of 10 MeV < Tkin < 130 MeV and photo-induced pi pi production at incident beam energies of 400-460 MeV.

Density Dependence of the Mass and Decay Constant of Pion inNuclear Matter in the Dyson–Schwinger Equation Approach of QCD

With the Dyson–Schwinger equation formalism at finite chemicalpotential, we study the density dependence of the mass and decayconstant of pion in nuclear matter. The calculated resultsindicate that both the mass and the decay constant remain almost constant at small chemical potential. As the chemical potentialgets quite large, the decay constant increases and the massdecreases with the increasing of the chemical potential, and bothof them vanish suddenly as a critical value is reached.

Transparency of nuclei and mean free path of protons and pions in nuclear matter at intermediate energies

In the second resonance region of photon energies, the differential yields of neutral and charged pions are measured in the (γ, πp) reactions on Li, C, and Al nuclei versus the proton energy and the azimuthal angle of pion emission. These experimental data are analyzed on the basis of a model that takes into account both single and double quasifree pion photoproduction. This results in deriving the mean free paths of protons and neutral and charged pions and in estimating the transparency of the participant nuclei.

The [formula omitted] interaction in nuclear matter from a study of the [formula omitted] reactions

The pion-production reactions π+A→π+π±A′ were studied on 2H, 12C, 40Ca, and 208Pb nuclei at an incident pion energy of Tπ+=283 MeV. Pions were detected in coincidence using the CHAOS spectrometer. The experimental results are reduced to differential cross sections and compared to both theoretical predictions and the reaction phase space. The composite ratio CππA between the π+π± invariant masses on nuclei and on the nucleon is also presented. Near the 2mπ threshold pion pairs couple to (ππ)I=J=0 when produced in the π+→π+π− reaction channel. There is a marked near-threshold enhancement of Cπ+π−A which is consistent with theoretical predictions addressing the partial restoration of chiral symmetry in nuclear matter. Furthermore, the behaviour of Cπ+π−A is well described when the restoration of chiral symmetry is combined with standard P-wave renormalization of pions in nuclear matter. On the other hand, nuclear matter only weakly influences Cπ+π+A, which displays a flat behaviour throughout the energy range regardless of A.

The dispersion relation of the pion in nuclear matter

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 range correlation on the pion dispersion relation depends very much on the form of the short range correlation and the parameters involved.

The two-pion exchange NN potential in nuclear matter and nuclear stability

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 stability of nuclear matter is explored and found to be effective.

Perturbative calculation of subthreshold pion production

A novel method to solve the Boltzmann-Nordheim-Vlasov equation, based on the concept of mean free path, is applied to subthreshold pion production. The main ingredient of the calculation is the elementary differential production probability which is suitably parametrized to fit existing experimental data. The calculations give a slope in reasonable agreement with the data. A mean free path of ∼5 fm for pions in nuclear matter is deduced.

Quasiparticle properties of the pion and heavy-ion collisions

The quasiparticle spectrum of the pion in nuclear matter is discussed. It contains the three branches: spin-isospin sound, quasifree pion, and the $\ensuremath{\Delta}$-hole branch. It is demonstrated how the spin-isospin branch is related to the phenomena of pion condensation and precritical scattering. Experimental consequences are derived. An event-by-event analysis of the $n$-particle momentum distribution allows one to measure the order parameter ${\stackrel{\ensuremath{\rightarrow}}{k}}_{\ensuremath{\pi}}$ of the condensate and the amount of pre-equilibrium to equilibrium cross section. The importance of the quasifree pion branch for subthreshold pion production is shown. The inclusive ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$-production cross section at 0 degrees and a kinetic energy of 34 MeV is calculated for Ne + NaF at 100, 200, and 300 MeV/N.NUCLEAR REACTIONS Heavy-ion collisions, pion in nuclear matter, pion condensation, precritical scattering, $n$-particle momentum distribution, collective parameters, subthreshold pion production $\mathrm{Ne}+\mathrm{NaF}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+X$ at 100, 200, and 300 MeV/N.

Correlations and self-consistency in pion scattering (II)

In an attempt to overcome certain difficulties of summing higher order processes in pion multiple scattering theories, we derive a new, systematic expansion for the interaction of a pion in nuclear matter within the context of the Foldy-Walecka theory, incorporating nucleon-nucleon correlations and an idea of self-consistency. We evaluate the first two orders in the expansion as a function of the nonlocality range; the expansion appears to be rapidly converging, in contrast to expansion schemes previously examined.

Pion-nucleus scattering and the Pauli principle

A density expansion of the pion self-energy for pions in nuclear matter is reexamined. It is shown that a single hole-line expansion of the self-energy (i) is equivalent to using a strongly quenched $\ensuremath{\pi}N$ scattering amplitude in the medium, and (ii) results in an inconsistent treatment of the virtual pions necessarily present in a field-theoretic description of the problem. Exchange of intermediate pions gives rise to nucleon-nucleon, as well as pion-nucleon scattering diagrams that both contribute to the pion self-energy in an essential way. The nucleon-nucleon scattering proceeds, for instance, via a one-pion-exchange potential that is, however, highly nonstatic for energy transfers between nucleons close to the incident energy. Such interactions are singled out automatically for special treatment in a field-theory approach to the problem, and should not be introduced in an ad hoc manner as part of an empirical $\mathrm{NN}$ interaction in nuclear matter. We evaluate the coherent and charge exchange contributions to the pion-nucleus optical potential, proportional to the total density and the neutron-proton density difference, respectively. The Pauli principle is found to provide a small correction to the coherent part, both in the hole-line and density expansion formalisms. However, the charge exchange part of the potential is almost completely damped at low energies in the hole-line expansion, while the inclusion of backward-going graphs (random-phase-approximation correlations) restores it to its value based on free space $\ensuremath{\pi}N$ charge exchange amplitudes (i.e., no net Pauli effect).NUCLEAR REACTIONS Compared density and hole line expansions for pion-nucleus optical potential; influence of Pauli principle on effective amplitude.

Pions in nuclear matter—an approach to the pion-nucleus optical potential

The optical potential for pions propagating in nuclear matter is investigated from a many-body point of view. An exact expression for the optical potential is obtained in terms of the nuclear matter density-density correlation function. Explicit calculations of the pion self-energy, which is simply related to the optical potential, are performed via an expansion in the nuclear density n 0 . The familiar result of multiple scattering theory, 4π n 0f 0 where f 0 is the pion-nucleon scattering length, is recovered in lowest order. The terms quadratic in n 0 account for the long range Pauli correlation corrections to the pion-nucleon scattering process (quenching), as well as dispersion and absorption contributions coming from nucleon-nucleon collisions in the medium. The latter terms are proportional to off-shell nucleon-nucleon scattering amplitudes. Our treatment is compared and contrasted with that of Ericson and Ericson. In particular, we are able to establish what approxmations in the nuclear many-body problem lead to their form of s-wave potential that includes long-range correlation effects, as well as their p-wave potential that has a nonlinear density dependence (the Lorentz-Lorenz effect). Estimates of the dispersion and absorption terms are made using two simple models to describe interacting nuclear matter.

Poin Dynamics in Nuclear Matter

Behavior of pions in nuclear matter is different from that of free pions due to strong interactions with nuclear-particles. The modified pion propagator and pion-nucleon coupling are calculated in this paper with the static approximation for nucleons. It is expected that the pion mass is decreased in the nucleus by about 15 Mev and the coupling constant is increased by 15 percent. Implication of these results is discussed.

Radiochemical Studies of the Interaction of Lead with Protons in the Energy Range 0.6 to 3.0 Bev

Lead targets have been bombarded with protons of several energies between 0.6 and 3.0 Bev and formation cross sections have been determined for about 30 nuclides of $Al140$ produced in these bombardments. The excitation functions, both for the lightest products studied ($Al35$) and for neutron-deficient barium isotopes, rise steeply with increasing energy. For intermediatemass products ($50lAl120$), the changes in formation cross sections with increasing energy are much smaller and may largely be interpreted as a shift towards more neutron-deficient products and as a broadening of the yield-mass distribution. At 3 Bev the spallation and fission product regions have merged, and the cross sections for forming all mass numbers below the target mass are equal within an order of magnitude. The changes in yield pattern above about 0.4 Bev are shown to be associated with increasing probabilities of very large transfers (of the order of 1 Bev) from the incident proton to the struck nucleus, and this trend is explained in terms of an energy transfer mechanism involving the production, scattering, and reabsorption of pions. Besides the well-known modes of de-excitation---particle evaporation (spallation) and fission---a new mode termed fragmentation is postulated to account for some of the observed products, especially the light fragments. Fragmentation is thought to be associated with the short mean free paths of pions in nuclear matter which cause local heating and can thus lead to dissociation of the nucleus into fragments in a time short compared to that required for equipartition of energy.