Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.     

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories, the energy region in which special relativity holds can be sandwiched from both the high-and low-energy sides by domains where special relativity is violated. An example is provided by ³He-A, where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of special relativity in the ultralow-energy corner is accompanied by the redistribution of the momentum-space topological charges among the fermionic flavors. At this ultralow energy, an exotic massless fermion with topological charge N ₃=2 arises whose energy spectrum mixes classical and relativistic behaviors. This effect can lead to neutrino oscillations, if neutrino flavors are still massless on this energy scale.     

Differential L-shell radiative recombination rate coefficients for bare uranium ions interacting with low-energy electrons

Results of the calculations of differential L?shell radiative recombination (RR) rate coefficients for bare uranium ions colliding with free electrons using the nonrelativistic dipole approximation and fully relativistic calculations are reported. The rate coefficients were obtained for very low, in the range of meV, relative electron-ion energies. We demonstrate that even for such low relative ion-electron energies the relativistic effects significantly modify the differential RR rate coefficients for the L?subshells and, as a result, the measurements of the relative electron energy dependence of the L-RR rates could be used for studying of the relativistic effects. These effects are strongest for the L ₃-subshell, which is discussed here in more details.     

Effect of temperature on $$\mathbf{In}_{{\varvec{x}}} \mathbf{Ga}_{1-{{\varvec{x}}}} \mathbf{As}/\mathbf{GaAs}$$ quantum dots

Analytical solution of the Dirac equation for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential for spin symmetry is studied using asymptotic iteration method. One-dimensional Dirac equation consisting of the radial and angular parts can be obtained by the separation of variables. By using asymptotic iteration method, the relativistic energy equation and orbital quantum number (l) equation can be obtained, where both are interrelated. Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number n _r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system can be determined by reducing the relativistic energy equation to the non-relativistic energy equation. Thermodynamical properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.     

Equilibration in intermediate-energy heavy-ion collisions within a relativistic mean-field two-fluid model

A two-fluid model with meanσ- andω-fields is formulated for the treatment of heavy-ion collisions at incident energies around 1 GeV/u. In this energy range Fermi and Bose statistics for baryons and pions, respectively, cannot be replaced by Boltzmann statistics. The collisional coupling between the two fluids is formulated in terms of the effective nucleon-nucleon cross-sections in nuclear medium taking Pauli blocking into account. For two counterstreaming nuclear fluids the comparison of results obtained from our relativistic mean-field two-fluid model (RMF-TFM) and the relativistic Landau-Vlasov equation shows good agreement in the gross properties of the equilibration process.     

Lifetimes and transition probabilities in Kr V

Weighted oscillator strengths (gf), weighted transition probabilities (gA) and lifetimes are presented for all experimentally known dipole transitions and levels of Kr V. Values were determined by four methods. Three of them are based on the Hartree–Fock method, including relativistic corrections and core-polarization effects, with electrostatic parameters optimized by a least-squares procedure in order to obtain energy levels adjusted to the corresponding experimental values. The fourth method is based on a relativistic multiconfigurational Dirac–Fock approach. In addition, 47 new classified lines belonging to the Kr V spectrum are presented.     

The effect of relativistic curvature calibration corrections for a non-retarding hemispherical sector analyzer: revision of the absolute S1s binding energy of H2S and the KLL auger energy of PH3

Application of required curvature corrections to the linear (relativistic) calibration procedure previously employed reduce (by 0.48 eV) the reported Sis binding energy of H₂S to 2478.43 eV and the S KLL Auger energy (by 0.01 eV) to 2098.55 eV. Only the former value is significantly altered. For phosphorus compounds, the P1s binding energy of PH₃ is essentially unchanged at 2150.87 eV but the P KLL energy is reduced by 0.27 eV to 1841.29 eV.None of the shifts previously reported are affected by this readjustment but the absolute extra-atomic relaxation values derived previously via the Auger parameter are affected. Revision of R^ea_s values for phosphorus downward by 0.3 eV and sulfur values upward by 0.48 eV improves the agreement between the two series. New values are tabulated. The magnitude of relativistic curvature corrections required for various excitation and calibration situations for the non-retarding hemispherical sector analyzer is given.     

Coarse-graining scale and effectiveness of hydrodynamic modeling

We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics from the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic hydrodynamic equation is defined must be the energy frame, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order hydrodynamic equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory gives the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.     

The mass effects on two-dimensional relativistic fermions

We investigate chemical potential, internal energy and specific heat of ideal relativistic fermions in two spatial dimensions taking into account the finite mass effect and the finite carrier concentration. The results show that the heavy mass and low carrier concentration fermions trend to be non-relativistic. The light mass and high carrier concentration lead more relativistic behavior. For massless fermions, the total kinetic energy equals to a constant for a given density (n), which is a function of n^3/2. Meanwhile, the specific heat for massless fermions keeps the linear increasing behavior with temperature with constant slope rather than the slope of zero, which is deduced from the non-relativistic case.     

Anisotropic fluid in a spherical spacetime: I. Radiation from a compact star

Generalizing work of Misner and Sharp, we develop the general relativistic theory of any spherically symmetric spacetime, allowing for shearing stresses (hence unequal principal pressures) in the matter. Assumptions specific to the system considered are required to determine the time-evolution of the principal pressures. For a gas of noninteracting massless particles, the necessary equations follow from relativistic kinetic theory. The equations for null radiation are solved in the steady-state case, neglecting both: (a) the mass loss of the central body, and (b) the effect of the radiation on the background (Schwarzschild) geometry. Once the velocity-field of the radiation is specified, its energy-momentum tensor follows by integration. The form of the velocity-field cannot be uniquely fixed by the theory because it varies from case to case. Asymptotically, at large distances R, the energy density and principal pressures of null radiation usually fall off as R^?4 while its proper speed increases as R. A one-parameter family of model stars emitting null radiation in flat spacetime is constructed. These differ in how narrow a cone the radiation is beamed into. Radiation emitted isotropically differs markedly from that which is emitted with sharp directionality.     

Is there a tachyon in the Nambu-Goto string with massive ends?

The dependence of Casimir energy on quark mass is investigated in the model of relativistic strings with massive quarks attached to the ends. The quark dynamics are treated in the nonrelativistic approximation, and the equations of motion and boundary conditions are linearized. The Casimir energyE as a function of quark massm is found by two methods (numerically and analytically). Different subtraction procedures for both approaches result in different functional dependences ofE onm. But both cases have values ofm for which the Casimir energy is definitely positive. The sign of this energy is known to coincide with the sign of the squared mass of the ground state in the string spectrum. Hence, the obtained result indicates that it is possible at least in principle to solve the tachyon problem in the model of relativistic strings with massive ends.     

Relativistic corrections in coupled channel mixing

We examine relativistic effects in a coupled channel mixing calculation of corrections to charmonium energy levels. We find that the relativistic effect on the coupled channel mixing is large. Thus a relativistic treatment is necessary and may possibly lead to a larger admixture ofD andS states.     

Testing the mechanism of QGP-Induced energy loss

We present an analytic model of jet quenching, based on the (D)GLV energy loss formalism, to describe the system size dependence of QGP-induced parton absorption in relativistic heavy ion collisions. Numerical simulations of the transverse momentum dependence of jet quenching are given for central Au+Au and Cu+Cu reactions. Low p _Tdijet correlations are shown to be sensitive to the reappearance of the lost energy as soft hadrons. At high p _Twe find that the attenuation of dihadrons is similar to that of single inclusive particles. Comparison to recent data from PHENIX and STAR is given as a test of the jet quenching theory.     

Determination of the S and P° Rydberg energy levels of rubidium-like ions by the method of interpolation of relativistic quantum defects

The method of interpolation of relativistic quantum defects is used for determining the energies of Rydberg levels of rubidium-like ions. For this purpose, the values of relativistic quantum defects calculated by the Dirac-Fock method at three points, two of which correspond to discrete levels and the third, to the ionization threshold, are approximated by a second-degree polynomial. By using the continuous function μ(E) thus obtained, one can readily determine the energy value for any discrete level. A formula for calculating the threshold value of the quantum defect μ(0) (the phase shift δ(0)) is given. The approximation coefficients corresponding to the nS _1/2, nP°_1/2, and nP°_3/2 levels are presented. For better agreement with the experimental results, an empirical correction to the quantum defect is introduced, which weakly depends on energy. The calculations were performed for 17 members of the rubidium isoelectronic sequence (from Rb to Fr⁵⁰⁺).     

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.     

Estimating the adsorption energy of element 113 on a gold surface

We report first-principle based studies of element 113 (E113) interactions with gold aimed primarily at estimating the adsorption energy in thermochromatographic experiments. The electronic structure of E113-Au _n systems was treated within the accurate shape-consistent small core relativistic pseudopotential framework at the level of non-collinear relativistic density functional theory (RDFT) with specially optimised Gaussian basis sets. We used gold clusters with up to 58 atoms to simulate the adsorption site on the stable Au(111) surface. Stabilization of the E113-Au _n binding energy and the net Bader charge of E113 and the neighboring Au atoms with respect to n indicated the cluster size used was appropriate. The resulting adsorption energy estimates lie within the 1.0–1.2 eV range, substantially lower than previously reported values.     

Collapse of systems of relativistic particles

We prove in a very simple way that if a system of N non-relativistic particles interacting by Coulomb or gravitational forces has a (negative) binding energy increasing faster than N, the corresponding system necessarily collapses for N big enough if particles are given relativistic kinetic energy. At the same time our method allows to improve considerably a recently obtained sufficient condition on coupling constants for the collapse of ordinary matter.     

On-shell faddeev equations: A democritean approach to the three-body problem

Coupling the mass-energy relationδE≧mc² to the uncertainty relationδE δt ≧ ? produces fluctuations in the number of particles at short distances and scatterings of particle pairs independent of any specific “interaction” mechanism. This observation allows the construction of a scattering theory in which there are only particles and the void, but particle number can change. We consider a system of three massive particles (hadrons) in the energy region below the first production threshold for a fourth hadron and above the first anomalous threshold for the presence of a fourth “virtual” hadron. The on-shell Faddeev equations, containing only two-particle scattering phases for positive two particle energies, provide a convergent, unitary, and readily soluble dynamics for this system. If any of the pairs can coalesce into a different particle with a rest energy less than the sum of the rest energies of the pair, the equations can be readily extended to describe 3-2 and 2–3 transitions involving this particle (coalescence, breakup) elastic scattering from it, and if there is more than one such particle 2-2 rearrangements. The three-body “bound state” requires a well defined analytic continuation. Features of more conventional calculations of three-nucleon problems which provide examples of this structure are discussed. Since only free particles occur in the theory, and the only failure of energy conservation is that required by the uncertainty principle for (free-particle) intermediate states, these one-variable equations might be extended to particles with the relativistic connection between mass, energy and momentum, and transitions in which the full rest energy of the particle which appears or disappears must be provided. The non-linear “crossed” theory for such particles has not been written down, but if the relativistic boundary condition model of Brayshaw is viewed as representing these crossed processes by a phenomenological core, then a crossed theory requiring the π to be a bound state of three π's might predict the π-π S-wave scattering length in theI=0 state in terms of the pion Compton wavelength (and hence the position and the width of the?) and will then show that the? in turn generates asingle ω resonance at about the right place. Implications are discussed.     

Off-shell effects in the coherent π0 photoproduction off nuclei

The strong sensitivity of coherent π⁰ photoproduction to the choice of the reaction energy ω in the elementary t_πγ (ω)-matrix is demonstrated. The best agreement of the DWIA results with the experimental data is achieved when ω is chosen as an eigenvalue of the free relativistic hamiltonian of the πN system. This is in agreement with the consequences of the relativistic potential theory.