arXiv subjects
Publications and source records attributed to B. Friman.
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application to S-wave pairing. Furthermore, we point out that the inclusion of tensor and spin-orbit forces leads to spin non-conserving effective interactions in nuclear matter.
We show that the renormalization group decimation of modern nucleon potential models to low momenta results in a unique nucleon interaction V_{low k}. This interaction is free of short-ranged singularities and can be used directly in many-body calculations. The RG scaling properties follow directly from the invariance of the scattering phase shifts. We discuss the RG treatment of Fermi liquids. The RG equation for the scattering amplitude in the two particle-hole channels is given at zero temperature. The flow equations are simplified by retaining only the leading term in an expansion in small momentum transfers. The RG flow is illustrated by first studying a system of spin-polarized fermions in a simple model. Finally, results for neutron matter are presented by employing the unique low momentum interaction V_{low k} as initial condition of the flow. The RG approach yields the amplitude for non-forward scattering, which is of great interest for calculations of transport properties and superfluid gaps in neutron star interiors. The methods used can also be applied to condensed matter systems in the absence of long-ranged interactions.
We construct a relativistic and unitary approach to 'high' energy pion- and photon-nucleon reactions taking the $πN, πΔ$, $ρN$, $ωN$, $ηN, K Λ, K Σ$ 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 4-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.
We present a relativistic and unitary approach to pion- and photon-nucleon scattering taking into account the $πN$, $ρN$, $ωN$, $ηN$, $πΔ$, $K Λ$ and $K Σ$ channels. Our scheme dynamically generates the s- and d-wave nucleon resonances N(1535), N(1650), N(1520) and N(1700) and isobar resonances $Δ(1620)$ and $Δ(1700)$ in terms of quasi-local two-body interaction terms. We obtain a fair description of the experimental data relevant for slow vector-meson propagation in nuclear matter. The s-wave $ρ$- and $ω$-meson nucleon scattering amplitudes, which define the leading density modification of the $ρ$- and $ω$-meson spectral functions in nuclear matter, are predicted.
The study of the $πN\to ρ^0 N$ and $πN \to ωN$ amplitudes below and close to the vector meson production threshold ($1.4<\sqrt s <1.8$ GeV)reveals a rich structure arising from the presence of baryon resonances in this energy range. These resonances are reflected in the interference pattern of the $e^+e^-$ decays of the $ρ^0$- and $ω$-mesons produced in $π^- p$ and $π^+ n$ reactions. We discuss the shape and magnitude of the $ρ^0$-$ω$ interference in the $π^-p \to e^+e^- n$ and $π^+n \to e^+e^- p$ reaction cross sections as functions of the total center of mass energy $\sqrt s$. We find contrasted results: the interference is largely destructive for the $π^-p \to e^+e^- n$ cross section but constructive for the $π^+n \to e^+e^- p$ cross section. An experimental study of these reactions would provide significant constraints on the coupling of vector meson-nucleon channels to low-lying baryon resonances.
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.
We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. 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 as well as the Pauli principle sum rules.
We employ meson-nucleon scattering data to deduce the properties of the low-mass vector mesons in nuclear matter, and present results for the $ρ$ and $ω$ in-medium spectral functions. The corresponding thermal emission rate for lepton pairs is also discussed.
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.
We emphasize the central role played by the spectral function in the description of hadrons in matter and discuss the applicability of the quasiparticle concept to the propagation of hadrons in dense nuclear matter. Theoretical and experimental results relevant for the in medium properties of vector mesons and kaons are briefly reviewed. We also present novel results for the $ρ$ and $ω$ spectral functions in nuclear matter, deduced from a coupled channel analysis of pion-nucleon scattering data.
The properties of vector mesons in nuclear matter are discussed. I examine the constraints imposed by elementary processes on the widths of $ρ$ and $ω$ mesons in nuclear matter. Furthermore, results for the $ρ$- and $ω$-nucleon scattering amplitudes obtained by fitting meson-nucleon scattering data in a coupled-channel approach are presented.
We compute the modification of the quark condensate $<\bar{q} q>$ in relativistic nucleus-nucleus collisions and estimate the 4-volume, where the quark condensate is small ($<\bar{q}q>/<\bar{q} q>_0\leq$ 0.1--0.3) using hadron phase-space distributions obtained with the quark-gluon string model. As a function of the beam energy the 4-volume rises sharply at a beam energy $E_{lab}/A \simeq$ (2--5) GeV, remains roughly constant up to beam energies $\simeq 20$ GeV and rises at higher energies. At low energies the reduction of the condensate is mainly due to baryons, while at higher energies the rise of the 4-volume is due to the abundant mesons produced. Based on our results we expect that moderate beam energies on the order of 10 GeV per nucleon are favourable for studying the restoration of chiral symmetry in a baryon-rich environment in nucleus-nucleus collisions.
The thermodynamic potential of a system of pions and nucleons is computed including the piN interactions in the P33 channel. A consistent treatment of the width of the resonance in this channel, the Delta(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 Delta width leads to a substantial enhancement of the pion yield at low momenta.
We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.
The properties of vector mesons in nuclear matter are discussed. Results for the momentum dependence of the $ρ$-meson self energy in matter due to $ρN$ interactions are presented, and consequences for the production rate of $e^+e^-$ pairs in hot and dense matter are discussed. I also examine the constraints imposed by elementary processes on the widths of $ρ$ and $ω$ mesons in nuclear matter, and conclude that in recent models the in-medium widths of these mesons are overestimated.
We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory with hadrons and photons is constructed, which includes non-resonant Born terms as well as the S$_{11}$(1535) and S$_{11}$(1650) baryon resonances. Due to the coupling between the channels, the production of eta-mesons is strongly affected by the S$_{11}$(1650) although its direct coupling to the $η$N channel is negligible. The rho- and omega-meson exchange terms are important for achieving a consistent description of both pion- and photon-induced reactions.
The spatial dependence of static meson correlation functions at finite baryon density is studied in the Nambu -- Jona - Lasinio model. In contrast to the finite temperature case, we find that the correlation functions at finite density are not screened but exhibit long-range oscillations. The observed phenomenon is analogous to the Friedel oscillations in a degenerate electron gas.