Relativistic many-body calculations of energies ofn= 3 states of Be-like ions

Abstract

Be-like ions with nuclear charges Z in the range 4-30 and for Z = 54 are determined to second order in relativistic many-body perturbation theory starting from a frozen-core Dirac-Fock basis. Secondorder Coulomb and second-order Breit-Coulomb correlation energies are evaluated. Corrections for the frequency dependence of the Breit interaction are taken into account in lowest order. Lamb-shift corrections to the energies are also included in lowest order. Comparisons are made with other theoretical calculations and with experimental data. We obtain an excellent agreement with experiment for term splitting, even for low-Z ions. Results for the 2p-3d excitation energies for Xe 50+ are also in very good agreement with experiment.

SYSTEMATIC CALCULATIONS OF ENERGY LEVELS AND TRANSITION RATES OF BE-LIKE IONS WITH Z = 10–30 USING A COMBINED CONFIGURATION INTERACTION AND MANY-BODY PERTURBATION THEORY APPROACH

“…The present MBPT calculated energies agree well with the recommended values from the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST; Kramida et al 2014), i.e., less than 0.05% for most levels. The present calculations are generally more accurate than early systematic calculations, and represent a significant extension of the MBPT calculations performed by Gu (2005aGu ( , 2005b and Safronova et al (1996Safronova et al ( , 1997Safronova et al ( , 1999aSafronova et al ( , 1999bSafronova et al ( , 1999c. We hope that these results will be useful in analyzing older experiments and planning new ones.…”

“…For 70 levels our MBPT energies differ from the NIST data by over 0.1%. Safronova et al (1997). Table 4 lists these 10 levels including possible misidentifications or interchanged labels in the NIST ASD for clarity and calling for further investigations.…”

“…The present MBPT energies agree with the NIST values better than 0.05% for 171 of the 198 levels, and 12 levels are also listed in Table 3 for which the relative deviations are larger than 0.1% (up to about 0.6% for P 2s4p 1 1 in V XX). Table 3 also lists the theoretical results of Safronova et al (1996Safronova et al ( , 1997; hereafter referred to as MBPT2), Froese Fischer & Tachiev (2004;MCDHF1), and Froese Fischer & Tachiev (2009;MCDHF2) for the total of 83 levels mentioned above. Generally good agreement among the four calculations implies that the uncertainties of the NIST recommended values might be large.…”

“…Most of the systematic calculations involved only the 10 lowest fine-structure levels belonging to the (1s )2s 2 2 , 2s2p, and 2p 2 configurations (the n = 2 complex), such as those calculations performed by Mühlethaler & Nussbaumer (1976), Cheng et al (1979), Zhang & Sampson (1992), Ynnerman & Fischer (1995), Jönsson et al (1998), Safronova et al (1996), Safronova et al (1999b), Safronova et al (1999c), Kingston & Hibbert (2000), Kingston & Hibbert (2001), Gu (2005a), Bogdanovich & Chou (2007), Cheng & Chen (2008), and Andersson et al (2009). Beyond the n = 2 complex, there are a few systematic studies involving the n = 3 states (the ′ l l 2 3 configurations with = l s, p and ′ = l s, p, d) in highly charged Be-like ions, which include calculations (Froese Fischer & Tachiev 2004, 2009) using the multiconfiguration Dirac-Hartree-Fock method and calculations (Safronova et al 1997(Safronova et al , 1999a) using the relativistic many-body perturbation theory (MBPT) approach. In all of these calculations, the transitions among the n = 3 states are seldom involved and the n = 3-2 electric-dipole forbidden transitions have not been included.…”

MCDHF Calculations and Beam-Foil EUV Spectra of Boron-Like Sodium Ions (Na VII)

“…Considering the increased availability of inexpensive computing power, this can be seen as the beginning of large-scale ab initio calculations of the atomic structure of B-like ions. In 1996, Safronova et al turned the relativistic MBPT apparatus to calculations of n = 2 and n = 3 levels and transition rates in B-like ions [32][33][34]. In 1998, Galavís et al [35] applied the SUPERSTRUCTURE code to B-like ions with the principal aim being the transition rates within the n = 2 level complex.…”