Bengt Friman

Scattering of vector mesons off nucleons

Abstract We construct a relativistic and unitary approach to ‘high’ energy pion– and photon–nucleon reactions taking the πN , πΔ , ρN , ωN , ηN , KΛ , KΣ final states into account. Our scheme dynamically generates the s - and d -wave nucleon resonances N (1535), N (1650) and N (1520) and isobar resonances Δ (1620) and Δ (1700) in terms of quasi-local interaction vertices. The description of photon-induced processes is based on a generalized vector-meson dominance assumption which directly relates the electromagnetic quasi-local four-point interaction vertices to the corresponding vertices involving the ρ and ω fields. We obtain a satisfactory description of the elastic and inelastic pion– and photon–nucleon scattering data in the channels considered. The resulting s -wave ρ – and ω –nucleon scattering amplitudes are presented. Using these amplitudes we compute the leading density modification of the ρ and ω energy distributions in nuclear matter. We find a repulsive energy shift for the ω meson at small nuclear density but predict considerable strength in resonance–hole like ω -meson modes. Compared to previous calculations our result for the ρ -meson spectral function shows a significantly smaller in-medium effect. This reflects a fairly small coupling strength of the N (1520) resonance to the ρN channel.

P-wave polarization of the ϱ-meson and the dilepton spectrum in dense matter

We study the p-wave polarization operator of the ϱ-meson due to ϱN interactions via the N∗(1720) and Δ(1905) resonances and compute the corresponding production rate for e+e− pairs at finite temperature and baryon density. At high baryon density we find a significant shift of the spectrum to lower invariant masses.

Renormalization group approach to neutron matter: quasiparticle interactions, superfluid gaps and the equation of state

Renormalization group methods can be applied to the nuclear many-body problem using the approach proposed by Shankar. We start with the two-body low momentum interaction Vlowk and use the RG flow from the particle–hole channels to calculate the full scattering amplitude in the vicinity of the Fermi surface. This is a new straightforward approach to the many-body problem which is applicable also to condensed matter systems without long-range interactions, such as liquid 3He. We derive the one-loop renormalization group equations for the quasiparticle interaction and the scattering amplitude at zero temperature. The RG presents an elegant method to maintain all momentum scales and preserve the antisymmetry of the scattering amplitude. As a first application we solve the RG equations for neutron matter. The resulting quasiparticle interaction includes effects due to the polarization of the medium, the so-called induced interaction of Babu and Brown. We present results for the Fermi liquid parameters, the equation of state of neutron matter and the 1S0 superfluid pairing gap.

Photoproduction of vector mesons off nucleons near threshold

We propose a simple meson-exchange model of the photoproduction of ϱ- and ω-mesons off protons near threshold (Eγ ≲ 2 GeV). This model provides a good description of the available data and implies a large ϱ-nucleon interaction in the scalar channel (σ-exchange). We use this phenomenological interaction to estimate the leading contribution to the self-energy of ϱ-mesons in matter. The implications of our calculation for experimental studies of the ϱ-meson mass in nuclei are discussed.

Polarization Contributions to the Spin Dependence of the Effective Interaction in Neutron Matter

We calculate the modification of the effective interaction of particles on the Fermi surface due to polarization contributions, with particular attention to spin-dependent forces. In addition to the standard spin-spin, tensor, and spin-orbit forces, spin nonconserving effective interactions are induced by screening in the particle-hole channels. Furthermore, a novel long-wavelength tensor force is generated. We compute the polarization contributions to second order in the low-momentum interaction V(low k) and find that the medium-induced spin-orbit interaction leads to a reduction of the 3P2 pairing gap for neutrons in the interior of neutron stars.

Low-momentum nucleon–nucleon interaction and Fermi liquid theory

Abstract We use the induced interaction of Babu and Brown to derive two novel relations between the quasiparticle interaction in nuclear matter and the unique low-momentum nucleon–nucleon interaction V low k in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. We derive the full renormalization group equations in the particle–hole channels from the induced interaction. The new constraints, together with the Pauli principle sum rules, define four combinations of Fermi liquid parameters that are invariant under the renormalization group flow. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints and the Pauli principle sum rules. The effects of tensor forces are discussed.

Saturation from nuclear pion dynamics

Abstract We construct an equation-of-state for nuclear matter based on the chiral Lagrangian. The relevant scales are discussed and an effective chiral power expansion scheme, which is constructed to work around the nuclear saturation density, is presented. A realistic equation-of-state is obtained by adjusting one free parameter, when the leading and subleading terms in the expansion are included. The saturation mechanism is due to correlations induced by the one-pion-exchange interaction. Furthermore, we find a substantial deviation from the Fermi-gas estimate of the quark condensate in nuclear matter already at the saturation density.

From chiral Lagrangians to Landau-Fermi liquid theory of nuclear matter

A simple relation between the effective parameters of chiral Lagrangians in medium as predicted by BR scaling and Landau-Fermi liquid parameters is derived. This provides a link between an effective theory of QCD at mean-field level and many-body theory of nuclear matter. It connects in particular the scaling vector-meson mass probed by dileptons produced in heavy-ion collisions (e.g., CERES of CERN-SPS) to the scaling nucleon-mass relevant for low-energy spectroscopic properties, e.g., the nuclear gyromagnetic ratios δg1 and the effective axial-vector constant gA∗.

Thermodynamics of Delta resonances

Abstract The thermodynamic potential of a system of pions and nucleons is computed including the π N interactions in the P 33 channel. A consistent treatment of the width of the resonance in this channel, the Δ (1232) resonance, is explored in detail. In the low-density limit we recover the leading term of the virial expansion for the thermodynamic potential. An instructive diagrammatic interpretation of the contributions to the total baryon number is presented. Furthermore, we examine within a fireball model the consequences for the pion spectra in heavy-ion collisions at intermediate energies, including the effect of collective flow. A consistent treatment of the Δ width leads to a substantial enhancement of the pion yield at low momenta.

CONVERTING MIXED PHASE INTO HADRONS

Abstract We study the transition of expanding QCD matter from the mixed to the hadronic phase and its effects on the transverse flow of hadrons. In the transverse expansion a rarefaction shock develops. Physically allowed values of the energy densities and flow velocities at the shock front are determined. The transverse rapidity of the flow is determined as a function of pion multiplicity. We show that the lifetime of the mixed phase is by and large determined by the longitudinal expansion and is not appreciably affected by the transverse rarefaction, thus making long lifetimes for the entire system possible.