Properties of finite nuclei in a relativistic quantum field theory

A renormalizable relativistic quantum field theory is used to study finite nuclei in the mean-field Thomas-Fermi approximation. Mass formula parameters are calculated and proton densities illustrated for ⁴⁰Ca and ²⁰⁸Pb. The Dirac equation is solved to determine single-particle spectra.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Time-dependent Schrödinger approach to sub-barrier fission

The time-dependent Schrödinger equation for the fission of²¹³At through a one-dimensional potential barrier was solved numerically within a finite spatial grid. Several initial quasi-stationary vibrational states at and below the top of the barrier were considered. The time dependence of the decay rate γ(t) was calculated. The non-exponential evolution of the process in the very early stages (≦10^?20 s) differs considerably from the asymptotic (stationary) one. Fission is therefore delayed by the sum of this preexponential time, of the tunneling time and of the time necessary for the descent from the outer turning point to the scission point. These non-dissipative quantum times play the same role as the classical transient times usually included in the analyses of experimental data on pre-scission emission of light particles andγ rays.     

Neutron-induced fission cross sections of short-lived actinides with the surrogate reaction method

Neutron-induced fission cross sections for ^242,243Cm and ²⁴¹Am have been obtained with the surrogate reaction method. Recent results for the neutron-induced cross section of ²⁴³Cm are questioned by the present data. For the first time, the ²⁴²Cm cross section has been determined up to the onset of second-chance fission. The good agreement at the lowest excitation energies between the present results and the existing neutron-induced data indicates that the distributions in spin and parity of states populated with both techniques are similar.     

A relativistic nuclear field theory with π and ρ mesons

The relativistic quantum field theory of Walecka is extended to include the interactions of π and ρ mesons. The proposed model is a non-abelian gauge theory and is renormalizable. The corresponding mean-field theory is derived and applied to calculations of cold nuclear matter.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Relativistic hartree-fock description of high-density nuclear matter

Relativistic Hartree-Fock equations are solved for an infinite system of nucleons and mesons. At high densities there exists a phase transition from a Fermi “sphere” to a Fermi “shell”, characterized by a discontinuity in the heat capacity. The precise value of the critical density is sensitive to the approximations.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.