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.     

Relativistic analysis of nuclear ground state densities at 135 to 200 MeV

A relativistic analysis of p +⁴⁰Ca elastic scattering with different nuclear ground state target densities at 135 to 200 MeV is presented in this paper. It is found that the IGO densities are more consistent in reproducing the data over the energy range considered here. The reproduction of spin-rotation-function data with the simultaneous fitting of differential cross-section and analyzing power, and the appearance of wine-bottle-bottom shaped Re U_eff(r) in the transition energy region, sensitively depends on the input nuclear ground state densities and are not solely the relativistic characteristic signatures. We also found that the wine-bottle-bottom shaped Re U_eff (r) is preferred by the spin observables in the transition energy region (i.e. 181 MeV to 200 MeV)     

J/Ψ suppression in relativistic heavy ion collisions through final state interactions with excited nucleons

TheJ/Ψ suppression in relativistic heavy ion collisions through final state interactions with excited state nucleons is estimated in a manner analogous to that of Gerschel and Hüfner for ground state nucleons. If excited state nucleons are larger in size than nucleons in their ground state, theJ/Ψ absorption cross section is increased. Because of relativistic time dilation this effect does not significantly alter theJ/Ψ suppression previously found.     

Nuclear transparency in a relativistic quark model

We examine the nuclear transparency for the quasi-elastic (e,e′p) process at large momentum transfers in a relativistic quantum-mechanical model for the internal structure of the proton, using a relativistic harmonic oscillator model. A proton in a nuclear target is struck by the incident electron and then propagates through the residual nucleus suffering from soft interactions with other nucleons. We call the proton “dynamical” when we take into account of internal excitations, and “inert” when we freeze it to the ground state. When the dynamical proton is struck with a hard (large-momentum transfer) interaction, it shrinks, i.e. small-sized configuration dominates the process. It the travels through nuclear medium as a time-dependent mixture of nitrinsic excited states and thus changing its size. Its absorption due to the soft interactions with nuclear medium depends on its transverse-size. Since the nuclear transparency is a measure of the absorption strength, we calculate it in our model for the dynamical case, and compare the results with those for the inert case. The effect of the internal dynamics is observed, which is in accord with the idea of the “color transparency”. We also compare our results with the experimental data in regard of q²-dependence as well as A-dependence, and find that the A-dependence may reveal the color-transparency effect more clearly. Similar effects of the internal dynamics in the other semi-exclusive hard processes are briefly discussed.     

PARTIAL RESTORATION OF THE CHIRAL SYMMETRY AND THE π CONDENSATION IN NUCLEAR MATTER

From the relativistic semiclassieal theory of π condensation[1], we deduced that, in the σ model, because of the variation of the radius of the magic circle with nuclear density, the π condensation in nuclear matter is possible. The calculated critical density is slightly higher than that of the normal ground state nuclear matter.     

Ionization energies and optical spectra of 5d-metal hexafluorides as calculated in the Dirac-Slater model

A relativistic self-consistent Dirac-Slater model has been used in a study of the electronic structure of 5d-metal hexafluorides. Experimental absorption spectra have been compared with calculated energies obtained as one-electron energy differences. The calculated “crystal field” splitting between the relativistic analog oft _2g ande _g levels, as well as spinorbit splitting of thet _2g level, has been found to be in good agreement with experimental data. Ionization energies which agree well with available spectra have been calculated using a transition state procedure. From a Mulliken population analysis of the molecular levels and ground state charge densities the validity of the classical crystal-field model is discussed.     

Relativistic mean-field study on proton skins and proton halos in exotic nuclei

We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei ^26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of ²⁵Al and ²⁶P and found that the isovector potential from the p meson has an important effect on the differences.     

Fermi-liquid properties of nuclear matter in a relativistic mean-field theory

The Fermi-liquid properties of the model nuclear system described by a relativistic quantum field theory are examined in terms of a relativistic extension of Landau's Fermi-liquid theory. The relativistic Landau parameters are derived microscopically from the ground state energy in the mean-field approximation, and are used to describe the thermodynamic properties of the system, such as the compressibility, the symmetry energy and the hydrodynamic sound velocities. We reproduce the previous results at nuclear saturation density (n₀ = 0.19 fm⁻³) and extrapolate to all density regions. It is shown that the system exhibits instability against the long wavelength density fluctuations in the low density region (n_B <0.70 n₀) and becomes stable at and above the nuclear saturation density due to the relativistic reduction of the attractive scalar meson component in the quasiparticle interaction. In the extreme high-density region, we reproduce the correct causal results for sound velocities. The existence of collisionless zero-sound oscillation is also examined.     

Gamma spectroscopy with RIBs from RISING to AGATA

Nuclear spectroscopy using radioactive isotope beams requires dedicated set-ups. State-of-the-art Ge arrays recently started to provide valuable γ spectroscopic data. At the SIS/FRS facility at GSI exotic beams at relativistic energies were employed for Coulomb excitation and secondary fragmentation experiments with the fast beam RISING set-up. Shell evolution far off stability, pn-pairing, symmetries and nuclear shapes were studied in nuclei ranging from ³⁶Ca to ¹³⁶Nd. The observation of a I = 27 ħ state demonstrated that high spin states can be reached in massive fragmentation reactions. This and the large sensitivity of relativistic in-beam experiments opens a rich ground for advanced nuclear structure studies. Combining RISING with AGATA γ-tracking detectors and improved particle detection is planned for future experimental investigations.     

Nuclear ground-state properties in a relativistic Meson-Field theory

We investigate the ability of a relativistic Mean-Field theory to reproduce nuclear ground state properties by an exhaustive fit to experimental data. We find that the bulk properties of nuclei from¹⁶O to²⁰⁸Pb can be adjusted very well. There remain problems with level density and fluctuations in the charge density similar as in fits using the conventional Skyrme Hartree-Fock model.     

Doppler-free spectroscopy of the 8s state of Cs

Doppler-free two-photon spectroscopy and ion detection in a thermionic diode were used to measure the hyperfine splitting and absolute term energy of the 8S state of Cs. The results, a=219.3(2) MHz for the magnetic dipole coupling constant, and E(8S)=24317.1499(4) cm^-1 for the term value of the c.g. of the 8S state relative to the c.g. of the ground state, agree well with earlier, less precise measurements. The hyperfine coupling also agrees well with a recent relativistic Hartree-Fock calculation.     

Hyperfine and Zeeman studies of low-lying atomic levels of181Ta and the nuclear electric quadrupole moment

The hyperfine structure of the atomic levels 5d ³ 6s ^{2 4} F _{7/2, 9/2} and⁴ P _1/2 in¹⁸¹Ta has been studied by atomic-beam magnetic-resonance. Using intermediate coupling wave functions derived for the configurations (5d+6s)⁵ the hyperfine structure data of six low-lying metastable states have been analyzed with respect to the effective operator formalism. The effective radial parameters for the magnetic dipole and electric quadrupole interactions are determined from these measurements and compared with relativistic calculations. The value obtained for the spectroscopic quadrupole moment of the¹⁸¹Ta nuclear ground state is Q_hfs=3.44(17) barn (uncorrected for configuration interaction effects).     

Phase transition of the baryon-antibaryon plasma in hot and dense nuclear matter

We investigate the presence of thermodynamic instabilities in a hot and dense nuclear medium where a phase transition from a gas of massive hadrons to a nearly massless baryon, antibaryon plasma can take place. The analysis is performed by requiring the global conservation of baryon number and zero net strangeness in the framework of an effective relativistic mean field theory with the inclusion of the Δ(1232)-isobars, hyperons and the lightest pseudoscalar and vector meson degrees of freedom. Similarly to the low density nuclear liquid-gas phase transition, we show that such a phase transition is characterized by both mechanical instability (fluctuations on the baryon density) that by chemical- diffusive instability (fluctuations on the strangeness concentration). It turns out that, in this situation, phases with different values of antibaryon-baryon ratios and strangeness content may coexist.     

Ab initio theory of complex electronic ground state of superconductors: I. Nonadiabatic modification of the Born-Oppenheimer approximation

The ARPES of high-T_c cuprates and theoretical results of low-Fermi energy band structure fluctuation for different groups of superconductors indicate that electron coupling to pertinent phonon modes drive system from adiabatic into anti-adiabatic state (ω>E_F). At these circumstances, not only Migdal-Eliashberg approximation is not valid, but basic adiabatic Born-Oppenheimer approximation (BOA) does not hold. At these circumstances, electronic structure has to be studied as explicitly dependent on instantaneous nuclear coordinates Q as well as on instantaneous nuclear momenta P.In the present paper—part I, it has been shown that Q, P-dependent modification of the BOA for ground electronic state can be derived by sequence of canonical transformations of the basis functions. The effect of nuclear coordinates and momenta on electronic structure is presented in the form of corrections to zero-, one- and two-particle terms of clamped nuclear Hamiltonian. In the anti-adiabatic state, correction to electronic ground state energy (zero-particle term correction) is negative and system can be stabilized in the anti-adiabatic state at distorted geometry with respect to adiabatic equilibrium structure and gap in one-particle spectrum of quasi-continuum states at Fermi level can be opened. Stabilization effect is solely the consequence of nuclear dynamics (P) that is crucial in anti-adiabatic state. It has been shown that nuclear dynamics also increases electron correlation until system at nuclear motion remains in a bound state. Corresponding corrections to electronic wave function are also specified.On the other hand, when system remains at vibration motion of nuclei in adiabatic state, the influence of nuclear dynamics (P-dependence) is negligible. In this case, all basic effects are covered through nuclear coordinates (Q-dependence) within the adiabatic BOA and standard results of solid-state (or molecular) physics are recovered.     

Fractional exclusion statistics applied to relativistic nuclear matter

The effect of statistics of the quasiparticles in the nuclear matter at extreme conditions of density and temperature is evaluated in the relativistic mean-field model generalized to the framework of the fractional exclusion statistics (FES). In the model, the nucleons are described as quasiparticles obeying FES and the model parameters were chosen to reproduce the ground state properties of the isospin-symmetric nuclear matter. In this case, the statistics of the quasiparticles is related to the strengths of the nucleon-nucleon interaction mediated by the neutral scalar and vector meson fields. The relevant thermodynamic quantities were calculated as functions of the nucleons density, temperature and fractional exclusion statistics parameter α. It has been shown that at high temperatures and densities the thermodynamics of the system has a strong dependence on the statistics of the particles. The scenario in which the nucleon-nucleon interaction strength is independent of the statistics of particles was also calculated, but it leads in general to unstable thermodynamics.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Magnetic moments of <Superscript>33</Superscript>Mg in the time-odd relativistic mean field approach

The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN se...