Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.     

The transparency of nuclei to nucleons and pions in a relativistic Glauber approximation

We present a selection of results obtained within the context of a relativistic eikonal model. First, results of relativistic Glauber calculations for the nuclear transparency extracted from photon-induced pion production are presented. Second, computed differential cross-sections for the ¹² C(p, 2p) are compared to data.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.     

Volume emission of pions in relativistic heavy-ion collisions

We consider the possibility of volume emission of pions by the Δ(1232) decay in a hot compressed projectile-target residue. We calculate the momentum distribution of the pions created by the two-body Δ(1232) decay. Reabsorption is taken into account assuming a quasi-deuteron model. We argue that low-energy pions created deep inside the hot zone are likely to escape and contribute to the pion inclusive spectrum.     

Nucleon-nucleon effective field theory without pions

Nuclear processes involving momenta much below the mass of the pion may be described by an effective field theory in which the pions do not appear as explicit degrees of freedom. The effects of the pion and all other virtual hadrons are reproduced by the coefficients of gauge-invariant local operators involving the nucleon field. Nucleon-nucleon scattering phase shift data constrains many of the coefficients that appear in the effective Lagrangean but at some order in the expansion coefficients enter that must be constrained by other observables. We compute several observables in the two-nucleon sector up to next-to-next-to leading order in the effective field theory without pions, or to the order at which a counterterm involving four-nucleon field operators is encountered. Effective range theory is recovered from the effective field theory up to the order where relativistic corrections enter or where four-nucleon-external current local operators arise. For the deuteron magnetic moment, quadrupole moment and the np → dγ radiative capture cross section a four-nucleon-one-photon counterterm exists at next-to-leading order. The electric polarizability and electric charge form factor of the deuteron are determined up to next-to-next-to-leading order, which includes the first appearance of relativistic corrections.     

The scalar relativistic approximation

A new method has recently been proposed for the approximate calculation of relativistic effects in atoms and solids. In this method, which is called the scalar relativistic approximation (SRA), the spin-orbit coupling term appearing in Dirac's equation is dropped; occasionally the minority component of the wave function is also neglected in defining the charge density. We propose here another derivation of the SRA that clarifies the approximations. A simple analytical treatment of the SRA for the hydrogen atom is given, and, as an example of the application of the SRA to the calculation of atomic states, results of self-consistent, local-density calculations for the ytterbium atom are given. The results show that, except for the spin-orbit splitting, relativistic effects (due to the Darwin and mass-velocity terms) are taken into account by the SRA very well.     

Nuclear electroproduction of negative pions below threshold

We calculate the electroproduction of negative pions into bound atomic states. The effect of the strong π-nucleus interaction is included in the calculation.     

Photoproduction of pions from deuterons in impulse approximation

The differential cross section for photoproduction of pions from deuterons is calculated in the relativistic impulse approximation. In the discussion of the resulting formula special emphasis is given to the following three problems: test of the impulse approximation, test of the photoproduction amplitudes, and measurement of the deuteron wave-function.     

Semiclassical approximation for relativistic potentials

We consider the application of semiclassical approximation to relativistic potentials for massless particles where the kinetic energy is a nontrivial, nonlocal operator. Quantization rules are derived for an arbitrary confining potential and compared to some exact results forS-waves. These results admit of a partial generalization to smalll values.     

RPA calculation of the effective charge in a hartree-fock basis

Using a Hartree-Fock basis the diagrams of the Tamm-Dancoff and random-phase approximations have been summed to calculate the effective charge in the (1s0d) shell. The enhancement of the effective charge found by this summation is much less than in an oscillator basis, in fact in most cases the HF RPA result is smaller than the value obtained from the lowest order core polarization diagram in an oscillator basis. The HF neutron effective charges are thus too small. For protons the enhancement of the bare effective charge in a HF basis must also be taken into account, but for cases involving the 0d_5/2 orbital the final result appears rather small.     

Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998     

Nuclear pions and the Gottfried and Bjorken sum rules

The thermodynamic potential (TDP) of the boson sector of the Weinberg-Salam model in an external uniform magnetic field at finite temperature and nonzero chemical potential is calculated in one-loop approximation. In the high temperature limit with the use of Mellin summation technique explicit expressions for the thermodynamic potential are obtained to analyze its new minimum, different from the ordinary Higgs one. This new minimum is due to the root singularity in the oneloop expression for the TDP, originating as a consequence of the tachyonic mode in the spectrum of gauge boson in the magnetic field. It is demonstrated that in the high temperature limit the Higgs minimum possesses properties common with the ordinary superconductors and Abelian Higgs model. The influence of the magnetic field on the Higgs minimum is indirect and has a sufficiently complicated character. The presence of the non-zero chemical potential lowers the critical temperature leading to the disappearance of the Higgs minimum.     

A study of transverse charge density of pions in relativistic quantum mechanics

The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.     

The effective W approximation

We generalize the effective photon approximation to include the massive W^± and Z gauge bosons of the Weinberg-Salam model. The W^± and Z bosons are treated as partons in the proton and we present predictions for the structure functions of both transversely and longitudinally polarized W's and Z's. Our results are valid only at high energies, (√s ? 20 TeV), and greatly simplify calculations involving vector bosons in the intermediate state of a scattering process. As examples, we use our treatment of the W and Z as partons to calculate hadronic production of heavy Higgs bosons from WW scattering and also to compute the associated production of a heavy charge $\text{2}\text{3}$ and charge $\text{?}\text{1}\text{3}$ quark from W-gluon scattering.