Relativistic and QED corrections for the ground state lithiumlike ionization energies

The ground state ionization energies of Z ≤ 10 lithiumlike ions are calculated using fully correlated Gaussian wavefunctions. Leading-order relativistic corrections are evaluated, while QED corrections are established with small uncertainties by directly calculating the Araki-Sucher energy and expanding the three-electron Bethe logarithm in 1/Z. The non-relativistic α6 level shifts have also been calculated, and we have used these energies to recommend ionization energies, which include estimates of the influence of the relativistic portion of the α6 energy. The results emphasize the importance of the direct computation of the complete α6 correction, but also the need for new, higher accuracy experimental ionization limits.

Light-cone distribution amplitudes of the nucleon and ∆ baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Beyond Schrödinger-Poisson: nonrelativistic effective field theory for scalar dark matter

Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schrödinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out ‘fast modes’ and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one.

Relativistic Corrections to Phase Shift Calculation in the GNXAS Package

Modern XAFS (X-ray Absorption Fine Structure) data-analysis is based on accurate multiple-scattering (MS) calculations of the x-ray absorption cross-section. In this paper, we present the inclusion and test of relativistic corrections for the multiple-scattering calculations within the GnXAS suite of programs, which is relevant to the treatment of the XAFS signals when atoms with high atomic number are contained into the system. We present a suitable strategy for introducing relativistic corrections without altering the basic structure of the programs. In particular, this is realized by modifying only the Phagen program calculating the atomic absorption cross sections and scattering t-matrices for the selected cluster. The modification incorporates a pseudo-Schrödinger Equation (SE) replacing the Dirac relativistic form. The phase-shift calculations have been put to a test in two known molecular and crystalline cases: molecular bromine Br2 and crystalline Pb. Calculations in an extended energy range have been shown to be very close to the non-relativistic case for Br2 (Br K-edge) while corrections have been found to exceed 25% for amplitude and phases of the XAFS multiple-scattering signals (Pb L3-edge). Benefits in the structural refinement using relativistic corrections are discussed for crystalline Pb at room temperature.