Relativistic Continuum Research Articles

Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance (ISGMR) in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. The negative energy states in the Dirac sea are also included in the single particle Green's function in the no-sea approximation. The single particle Green's function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energy-weighted sum rule m−1 and the centroid energy of the ISGMR in 120Sn and 208Pb are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.

Extreme Exotic Calcium Lambda Hypernuclei in the Relativistic Continuum Hartree—Bogoliubov Theory

Exotic calcium lambda hypernuclei properties with the neutron number of 20-400 by a step of 20 are discussed by employing the relativistic continuum Hartree-Bogoliubov theory with a zero range pairing interaction. The Bethe-Weizsäcker mass formula of a multi-strange system and the Woods-Saxon-type potential of lambda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca lambda hypernuclei are also investigated.

Plane waves in a relativistic, homogeneous and isotropic elastic continuum

The propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic characteristics, namely energy per particle, pressure and Lamé coefficients, and considered in the comoving proper-time gauge. For all modes with the given wave covector, differential equations governing the time dependence of the amplitudes are derived. In particular, longitudinal acoustic waves are described, in analogy with the nonrelativistic theory, by two coupled first-order equations. As an example, plane waves in a stiff ultrarigid continuum are considered.

D-Dimensional Dirac Fermions BEC-BCSCrossover Thermodynamics

An effective relativistic continuum massive Proca Lagrangianaction is used to account for the Lorentz vector condensation effectson the equation of state of the strongly interacting fermions system.The interior quantum fluctuation effects are incorporated as anexternal field approximation indirectly through a fictive generalized ThomsonProblem counterterm background. The general analytical formulas for thed-dimensional thermodynamics are given near the unitary limit region.In the non-relativistic limit for d = 3, the universal dimensionlesscoefficient ξ = 4/9 and energy gap Δ/εf = 5/18 are reasonably consistent with the existing theoretical andexperimental results. In the unitary limit for d = 2 and T = 0, the universalcoefficient can even approach the extreme occasion ξ = 0 correspondingto the infinite effective fermion mass m* = ∞, which can be mapped to thestrongly coupled two-dimensional electrons and is quite similar tothe three-dimensional Bose–Einstein condensation of ideal boson gas.Instead, for d = 1, the universal coefficient ξ is negative,implying the non-existence of phase transition from superfluidity to normalstate. The solutions manifest the quantum Ising universal classcharacteristic of the strongly coupled unitary fermions gas.

Ground State Energy of Unitary Fermion Gas with the ThomsonProblem Approach

The dimensionless universal coefficient ξ defines the ratio ofthe unitary fermions energy density to that for the idealnon-interacting ones in the non-relativistic limit with T = 0. Theclassical Thomson problem is taken as a nonperturbative quantummany-body arm to address the ground state energy including the lowenergy nonlinear quantum fluctuation/correlation effects.With the relativistic Dirac continuum field theory formalism, theconcise expression for the energy density functional of the stronglyinteracting limit fermions at both finite temperature and density isobtained. Analytically, the universal factor is calculated to be ξ = 4/9. The energy gap is Δ = (5/18)kf2/(2m).

Giant halos in relativistic and nonrelativistic approaches

The phenomena of giant halo and halo of neutron-rich even-Ca isotopes are investigated and compared in the frameworks of the relativistic continuum Hartree-Bogoliubov (RCHB) and non-relativistic Skyrme Hartree-Fock-Bogoliubov (HFB) calculations. With two parameter sets for each of the RCHB and the Skyrme HFB calculations, it is found that although halo phenomena exist for Ca isotopes near neutron drip line in both calculations, the halo of the Skyrme HFB calculations starts at a more neutron-rich nucleus than that of the RCHB calculations, and the RCHB calculations have larger neutron root-mean-square (rms) radii systematically in N{>=}40 than those of the Skyrme HFB calculations. The former difference comes from the difference in shell structure. The reasons for the latter can be partly explained by the neutron 3s{sub 1/2} orbit, causes more than 50% of the difference among the four calculations for neutron rms radii at {sup 66}Ca.

COMPARISON OF RELATIVISTIC AND NON-RELATIVISTIC APPROACHES IN HALO

The phenomena of giant halo and halo of neutron-rich even- Ca isotopes are investigated and compared in the framework of the relativistic continuum Hartree-Bogoliubov (RCHB) and non-relativistic Skyrme Hartree-Fock-Bogoliubov (HFB) calculations. With two parameter sets for each of the RCHB and the Skyrme HFB calculations, it is found that although halo phenomena exist for Ca isotopes near neutron drip line in both calculations, the halo of the Skyrme HFB calculations starts at a more neutron-rich nucleus than that of the RCHB calculations, and the RCHB calculations have larger neutron root-mean-square (rms) radii systematically in N ≥ 40 than those of the Skyrme HFB calculations. The former difference comes from difference in shell structure. The reasons for the latter can be partly explained by the neutron 3s1/2orbit, which causes more than 50 % of the difference among the four calculations for neutron rms radii at66Ca .

TheXMM‐NewtonView of the Relativistic Spectral Features in AX J0447−0627

The XMM-Newton observation of the optically type 1 active galactic nucleus (AGN) AX J0447-0627 (z = 0.214) unambiguously reveals a complex, bright, and prominent set of lines in the 4-8 keV rest-frame energy range. Although from a phenomenological point of view, the observed properties can be described by a simple power-law model plus five narrow Gaussian lines (at rest-frame energies of ~4.49, ~5.55, ~6.39, ~7.02, and ~7.85 keV), we find that a model comprising a power law (Γ ~ 2.2), a reflected relativistic continuum, a narrow Fe I Kα line from neutral material, as well as a broad Fe Kα relativistic line from a ionized accretion disk, represents a good physical description of the data. The "double-horned" profile of the relativistic line implies an inclination of the accretion disk of ~45° and an origin in a narrow region of the disk, from Rin ~ 19GM/c2 to Rout ~ 30GM/c2. The narrow Fe I Kα line from neutral material is probably produced far from the central black hole, most likely in the putative molecular torus. Although some of these properties have already been found in other type 1 AGNs and discussed in the literature, at odds with the objects reported so far we measure high equivalent widths of the observed lines: ~1.4 keV for the double-horned relativistic line and ~0.4 keV for the narrow line.

Magic numbers for superheavy nuclei in relativistic continuum Hartree–Bogoliubov theory

The magic proton and neutron numbers are searched in the superheavy region with proton number Z = 100 – 140 and neutron number N = ( Z + 30 ) – ( 2 Z + 32 ) in the relativistic continuum Hartree–Bogoliubov (RCHB) theory with effective interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies S 2 p and S 2 n , the two-nucleon gaps δ 2 p and δ 2 n , the shell correction energies E shell p and E shell n , the pairing energies E pair p and E pair n , and the pairing gaps Δ p and Δ n , Z = 120 , 132, and 138 and N = 172 , 184, 198, 228, 238, and 258 are suggested to be the magic numbers within the present approach. The α-decay half-lives are also discussed. In addition, the potential energy surfaces of possible doubly magic nuclei are obtained by using the deformation-constrained relativistic mean field (RMF) theory, and the shell effects stabilizing nuclei are investigated.

A Classical Model for the Extended Electron I

In order to avoid divergence of its self-energy the free electron at rest is described as a relativistic continuum of finite extent. It has the form of an axisymmetric torus of finite aspect ratio, which rigidly rotates around its axis of symmetry with superluminal speed (v > c). It is shown that there is a class of stationary solutions of the free-boundary value problem. The parameter dependence of these solutions is related to experimental data.

Larmor radiation from the ultra-intense field ionization of atoms

The angle- and energy-resolved Larmor radiation from atomic ionization in the focus of ultra-intense laser field is calculated using a semi-classical, trajectory ensemble model of ionization. We find that including the quantum nature of the atomic ionization decreases the radiation yield by an order of magnitude compared to a classical electron calculation due to interference effects in the extended probability of the electron wavefunction and the quantum nature of tunnelling ionization. The evolution of the radiation from non-relativistic to relativistic continuum dynamics is presented as a function of the laser intensity with Larmor radiation not becoming prominent until 1019 W cm−2. For the ionization of Na10+ at a density of 1015 atoms cm−3 and a peak-focused laser intensity of 1020 W cm−2, the radiation is highly directional at an angle of 45° from the laser electric field with photon energies out to 500 eV.

Electron momentum states and bremsstrahlung radiation from the ultraintense field ionization of atoms

Relativistic continuum dynamics for electrons from the ionization of atoms in an ultraintense (10 to the 17th W/cm square to 10 to the 20th W/cm square) laser focus are analyzed using a semi-classical wavelet model. The results quantify the energy and angle resolved photoionization yields due to the developing relativistic dynamics in ultraintense fields. Using the final state momentum, the bremsstrahlung radiation yield is calculated and shows a linear relationship between the radiation cutoff and the laser intensity. At 10 to the 20th W/cm square photons with energies out to 10MeV should be observed. The results are quantitatively comparable to the observed angle resolved photoelectron spectra of current ultraintense laser-atom experiments. The results show the azimuthal angular distributions becoming more isotropic with increasing intensity.

Spin Axioms in Different Geometries of Relativistic Continuum Physics

The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9+9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from 6 to 3 basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.

Giant, hyperon, and deformed halos near the particle drip line

Recent work on the existence of giant halo and hyperon halo in relativistic continuum Hartree-Bogoliubov (RCHB) theory is reviewed. Experimental support of giant halos in Na and Ca isotopes near the neutron drip line is discussed and the progress on deformed halo is presented.

Neutron halos in hypernuclei

Properties of single-Lambda and double-Lambda hypernuclei for even-N Ca isotopes ranging from the proton dripline to the neutron dripline are studied using the relativistic continuum Hartree-Bogoliubov theory with a zero-range pairing interaction. Compared with ordinary nuclei, the addition of one or two Lambda-hyperons lowers the Fermi level. The predicted neutron dripline nuclei are, respectively, Ca-75(Lambda) and Ca-76(2Lambda) as the additional attractive force provided by the Lambda-N interaction shifts nuclei from outside to inside the dripline. Therefore, the last bound hypernuclei have two more neutrons than the corresponding ordinary nuclei. Based on the analysis of two-neutron separation energies, neutron single-particle energy levels,the contribution of continuum and nucleon density distribution, giant halo phenomena due to the pairing correlation, and the contribution from the continuum are suggested to exist in Ca hypernuclei similar to those that appear in ordinary Ca isotopes.

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energies $E_b$ and two neutron separation energies $S_{2n}$ very well. The predicted neutron drip line nuclei are $^{28}$O, $^{72}$Ca, $^{98}$Ni, $^{136}$Zr, $^{176}$Sn, and $^{266}$Pb, respectively. Halo and giant halo properties predicted in Ca isotopes with $A>60$ are investigated in detail from the analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes are studied also. Furthermore, we study the neighboring lighter isotopes in the drip line Ca region and find some possibility of giant halo nuclei in the Ne-Na-Mg drip line nuclei.

ASPECTS OF DUALITY IN NODAL LIQUIDS

Starting from a microscopic t–J like model and a SU(2) spin-charge separation ansatz, a relativistic continuum gauge Lagrangian is obtained in the vicinity of a nodal point of the Fermi surface. The excitations in the pseudogap phase are described by topological excitations in the dual model which has a Z2 global symmetry due to the effect of instantons. Confinement of spinon and holons emerge from this picture. The adjoint and fundamental strings are associated with stripes. As the spin gap decreases a local Z2 symmetry emerges.

CHIANTI—An Atomic Database for Emission Lines. VI. Proton Rates and Other Improvements

The CHIANTI atomic database contains atomic energy levels, wavelengths, radiative transition probabilities, and electron excitation data for a large number of ions of astrophysical interest. Version 4 has been released, and proton excitation data are now included, principally for ground configuration levels that are close in energy. The fitting procedure for excitation data, both electrons and protons, has been extended to allow nine-point spline fits in addition to the previous five-point spline fits. This allows higher quality fits to data from close-coupling calculations where resonances can lead to significant structure in the Maxwellian-averaged collision strengths. The effects of photoexcitation and stimulated emission by a blackbody radiation field in a spherical geometry on the level balance equations of the CHIANTI ions can now be studied following modifications to the CHIANTI software. With the addition of H I, He I, and N I, the first neutral species have been added to CHIANTI. Many updates to existing ion data sets are described, while several new ions have been added to the database, including Ar IV, Fe VI, and Ni XXI. The two-photon continuum is now included in the spectral synthesis routines, and a new code for calculating the relativistic free-free continuum has been added. The treatment of the free-bound continuum has also been updated.

Variational formulation and symmetries of the relativistic nondissipative continuum

Variational formulation and symmetries of the relativistic nondissipative continuum

The relativistic continuum Hartree–Bogoliubov description of charge-changing cross section for C, N, O and F isotopes

The ground state properties including radii, density distribution and one neutron separation energy for C, N, O and F isotopes up to the neutron drip line are systematically studied by the fully self-consistent microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) theory. With the proton density distribution thus obtained, the charge-changing cross sections for C, N, O and F isotopes are calculated using the Glauber model. Good agreement with the data has been achieved. The charge changing cross sections change only slightly with the neutron number except for proton-rich nuclei. Similar trends of variations of proton radii and of charge changing cross sections for each isotope chain is observed which implies that the proton density plays important role in determining the charge-changing cross sections.