Relativistic Many Body Research Articles

Multiconfiguration Dirac–Hartree–Fock and Relativistic Many Body Perturbation Theory calculations of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors of Zr XXXIX

An extensive and accurate data set of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors have been calculated for the lowest 71 odd and even parity states arising from the 1s2 and 1snl(n=1−6,0≤l≤n−1) configurations of helium-like Zr. Calculations were performed using the Multiconfigurational Dirac–Hartree–Fock​ (MCDHF) followed by the Relativistic Configuration Interaction (RCI) method. Although no measurements or other theoretical results are available for comparison, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Relativistic Many-Body Perturbation Theory (RMBPT) method. Transition rates for electric-multipole (dipole (E1), quadrupole (E2)) and magnetic-multipole (dipole (M1), quadrupole (M2)) have been also calculated. Breit interactions and quantum electrodynamics effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising from the two sets of calculations MCDHF/RCI and RMBPT are quite close. Almost all atomic data of helium-like Zr ion presented in this paper are calculated for the first time. We expect that our results can be used as a reference point for any further calculations of plasma processes (electron impact excitation, dielectronic recombination). Furthermore, our values can contribute to the NIST database by essentially providing the data for the lowest singly excited states of Zr XXXIX.

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

Relativistic Many-Body Perturbation Theory approach to electron-ion recombination of He- and Be-like systems

We report on efforts to perform fully correlated calculations of effective three-body systems with a Rel-ativistic Many-Body Perturbation Theory approach. A preliminary version of the program is used on resonances in Ge27+, formed in collisions of electrons with Be-like Ge28+. We will show a comparison between experimental and calculated spectra, including both dielectronic and trielectronic recombination resonances. Results for some pure three electron systems will also be shown.

Exploring Relativistic Many-Body Recoil Effects in Highly Charged Ions

The relativistic recoil effect has been the object of experimental investigations using highly charged ions at the Heidelberg electron beam ion trap. Its scaling with the nuclear charge Z boosts its contribution to a measurable level in the magnetic-dipole (M1) transitions of B- and Be-like Ar ions. The isotope shifts of 36Ar versus 40Ar have been detected with sub-ppm accuracy, and the recoil effect contribution was extracted from the 1s(2)2s(2)2p 2P(1/2) - 2P(3/2) transition in Ar13+ and the 1s(2)2s2p 3P1-3P2 transition in Ar14+. The experimental isotope shifts of 0.00123(6) nm (Ar13+) and 0.00120(10) nm (Ar14+) are in agreement with our present predictions of 0.00123(5) nm (Ar13+) and 0.00122(5) nm (Ar14+) based on the total relativistic recoil operator, confirming that a thorough understanding of correlated relativistic electron dynamics is necessary even in a region of intermediate nuclear charges.

QED effects in lithiumlike krypton

The ${(2s}_{1/2}{\ensuremath{-}2p}_{1/2})$ Lamb shift in lithiumlike krypton was obtained through a recombination measurement. The Lamb shift was extracted from the recombination spectrum by comparison with a calculation of the dielectronic-recombination resonance positions. The energy calibration used in this work is based on an accurate energy determination of one arbitrary point in the spectrum. Our value for the ${2s}_{1/2}{\ensuremath{-}2p}_{1/2}$ energy difference is 71.243(8) eV. The relativistic many-body contributions to the Lamb shift can be calculated very precisely, which enabled an extraction of an ``experimental'' quantum-electrodynamical contribution of 1.539(8) eV. This precision is beyond what can be achieved with conventional estimates of the screened quantum-electrodynamical effects. The main error originates from the uncertainty in the length of the ion-beam orbit. Improved knowledge of this value can improve our result significantly.

Comments on “Relativistic Many-Body Calculations of Transition Probabilities for the 2l12l2[LSJ]-2l32l4[L'S'J'] Lines in the Be-like Ions”

Safronova et al (1999 Physica Scripta 59 286) used the relativistic many-body perturbation theory (MBPT) formulas to calculate the transition rates for Be-like ions. Substantial discrepancies existed between theory and experiment. In this comment, we discuss the origin of the discrepancies.

Relativistic and Many-Body Effects on Total Binding Energies of Cesium and Other Highly-Charged Ions

The determination of atomic masses from highly ionized atoms using Penning Traps requires precise values for electronic binding energies. In the present work, binding energies of several ions (from several elements) are calculated in the framework of two relativistic many-body methods: Relativistic Many-Body Perturbation Theory (RMBPT) and Multi-Configuration Dirac– Fock (MCDF). The ions studied in this work are: Cl (He and Li-like), Se (F and Ne-like), Cs (He, Be, Ne, Al, Cl, Ar, K, Kr, Xe-like and neutral Cs), Hg, Pb and U (Br and Kr-like). Some of them are presented in this paper. Cesium has been treated in more details, allowing for a systematic comparison between MCDF and RMBPT methods. The Cs ions binding energies allow for the determination of atomic Cs mass, which can be used in a QED-independent fine structure constant determination.

Relativistic many-body calculations of excitation energies and oscillator strengths in Ni-like ions

Excitation energies for $3l\ensuremath{-}{4l}^{\ensuremath{'}}$ particle-hole states of Ni-like ions are determined to second order in relativistic many body perturbation theory. The calculations start from a closed-shell Dirac-Fock potential, and include second-order Coulomb and Breit-Coulomb interactions. Retarded electric-dipole matrix elements (in length and velocity forms) are calculated in second order for transitions from excited $3l\ensuremath{-}{4l}^{\ensuremath{'}}$ states to the closed-shell ground state. Wavelengths for 3-4 and 4-4 transitions are compared with experimental data, and with other high-precision calculations. Trends of oscillator strengths as functions of nuclear charge Z are shown graphically for selected transitions.

Meson structure in a relativistic many-body approach

Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, Tamm-Dancoff (TDA), and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion, and the meson spin, orbital, and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.

Relativistic many-body and QED effects on the hyperfine structure of lithium-like ions

The hyperfine splitting of the ground state of three-electron ions is studied in detail with the help of the multi-configuration Dirac-Fock method. We study the role of the magnetic electron-electron interaction and of the negative energy continuum. An all-order evaluation of some vacuum polarization corrections is performed. The Bohr-Weisskopf effect is evaluated in a simple model.

Glueball spectroscopy in a relativistic many-body approach to hadronic structure.

A comprehensive, relativistic many-body approach to hadron structure is advanced based on the Coulomb gauge QCD Hamiltonian. Our method incorporates standard many-body techniques which render the approximations amenable to systematic improvement. Using BCS variational methods, dynamic chiral symmetry breaking naturally emerges and both quarks and gluons acquire constituent masses. Gluonia are studied both in the valence and in the collective, random phase approximations. Using representative values for the strong coupling constant and string tension, calculated quenched glueball masses are found to be in remarkable agreement with lattice gauge theory.

Relativistic many-body and QED calculations on atomic systems

Relativistic many-body and QED calculations on atomic systems

The Relativistic Many-Body Perturbation Treatment of the Long Range Part of the Nuclear Force

Based on the many-body perturbation theory and cloudy bag model, the long range part of the nuclear force is discussed. The results show that it agrees with one-pion exchange-potential in respect of both the radial dependence and the strength.