Coulomb correlation in presence of spin-orbit coupling: application to plutonium

Attempts to go beyond the local density approximation (LDA) of Density Functional Theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods like LDA+$U$, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used a simple model interaction $U$. In this article we generalize the solution of the full Coulomb matrix involving $F^{(0)}$ to $F^{(6)}$ parameters, which is usually presented in terms of an $\ell m_\ell$ basis, into a $jm_{j}$ basis of the total angular momentum, where we also include spin-orbit coupling; this type of theory is needed for a reliable description of $f$-state elements like plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in multiplet theory but that have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $jm_j$ basis results provide a very good approximation to the full Coulomb matrix result, in contrast to the much less accurate results for the more conventional $\ell m_\ell$ basis

On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.Comment: 10 pages, 5 figure

Physical parameters of a relativistic jet at very high redshift: the case of the blazar J1430+4204

Context. The high-redshift (z = 4.72) blazar J1430+4204 produced a major radio outburst in 2005. Such outbursts are usually associated with the emergence of a new component in the inner radio jet. Aims. We searched for possible changes in the radio structure on milli-arcsecond angular scales, to determine physical parameters that characterise the relativistic jet ejected from the centre of this source. Methods. We analysed 15-GHz radio interferometric images obtained with the Very Long Baseline Array (VLBA) before and after the peak of the outburst. Results. We did not identify any significant new jet component over a period of 569 days. We estimated the Doppler factor, the Lorentz factor, and the apparent transverse speed of a putative jet component using three different methods. The likely small jet angle to the line of sight and our values of the apparent transverse speed are consistent with not detecting a new jet feature.Comment: (6 pages, 4 figures) accepted for publication in Astronomy and Astrophysic

On the reliability of polarization estimation using Rotation Measure Synthesis

We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. (2009). The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower S/N if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrainted solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically-derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.Comment: accepted for publication in the Astrophysical Journa

Spin-other-orbit operator in the tensorial form of second quantization

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. One of the basic features of this approach is the use of tables of standard quantities, without which the process of obtaining matrix elements of spin-other-orbit interaction operator between any electron configurations is much more complicated. Some special cases are shown for which the tensorial structure of the spin-other-orbit interaction operator reduces to an unusually simple form

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to find graphically the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second quantization operators. As a result, it allows us to use standard quantities uniformly for both diagona and off-diagonal matrix elements

The ATESP 5 GHz radio survey. III. 4.8, 8.6 and 19 GHz follow-up observations of radio galaxies

[Abridged] Physical and evolutionary properties of the sub-mJy radio population are not entirely known. The radio/optical analysis of the ATESP 5 GHz sample has revealed a significant class of compact flat/inverted radio-spectrum sources associated to early-type galaxies up to redshift 2. Such sources are most plausibly triggered by an AGN, but their observational properties are not entirely consistent with those of standard radio galaxy populations. In the present work we aim at a better understanding of the radio spectra of such sources and ultimately of the nature of AGNs at sub-mJy flux levels. We used the ATCA to get multi-frequency (4.8, 8.6 and 19 GHz) quasi-simultaneous observations for a representative sub-sample of ATESP radio sources associated with early-type galaxies (26 objects with S>0.6 mJy). This can give us insight into the accretion/radiative mechanism that is at work, since different regimes display different spectral signatures in the radio domain. From the analysis of the radio spectra, we find that our sources are most probably jet-dominated systems. ADAF models are ruled out by the high frequency data, while ADAF+jet scenarios are still consistent with flat/moderately inverted-spectrum sources, but are not required to explain the data. We compared our sample with high (>20 GHz) frequency selected surveys, finding spectral properties very similar to the ones of much brighter (S>500 mJy) radio galaxies extracted from the Massardi et al. (2008) sample. Linear sizes of ATESP 5 GHz sources associated with early type galaxies are also often consistent with the ones of brighter B2 and 3C radio galaxies, with possibly a very compact component that could be associated at least in part to (obscured) radio-quiet quasar-like objects and/or low power BL Lacs.Comment: Accepted for publication in Astronomy & Astrophysic

Survey of Planetary Nebulae at 30 GHz with OCRA-p

We report the results of a survey of 442 planetary nebulae at 30 GHz. The purpose of the survey is to develop a list of planetary nebulae as calibration sources which could be used for high frequency calibration in future. For 41 PNe with sufficient data, we test the emission mechanisms in order to evaluate whether or not spinning dust plays an important role in their spectra at 30 GHz. The 30-GHz data were obtained with a twin-beam differencing radiometer, OCRA-p, which is in operation on the Torun 32-m telescope. Sources were scanned both in right ascension and declination. We estimated flux densities at 30 GHz using a free-free emission model and compared it with our data. The primary result is a catalogue containing the flux densities of 93 planetary nebulae at 30 GHz. Sources with sufficient data were compared with a spectral model of free-free emission. The model shows that free-free emission can generally explain the observed flux densities at 30 GHz thus no other emission mechanism is needed to account for the high frequency spectra.Comment: 10 pages, 7 Postscript figures, to be published in A&

The Curious Case of the “Heartworm” Nebula

© 2022. The Author(s). Published by the American Astronomical Society. This work is licensed under the terms of the Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/The curious Galactic features near G357.2−0.2 were observed with the MeerKAT radio interferometer array in the UHF and L bands (0.56–1.68 GHz). There are two possibly related features: a newly identified faint heart-shaped partial shell (the “heart”), and a series of previously known but now much better imaged narrow, curved features (the “worm”) interior to the heart. Polarized emission suggests that much of the emission is nonthermal and is embedded in a dense plasma. The filaments of the worm appear to be magnetic structures powered by embedded knots that are sites of particle acceleration. The morphology of the worm broadly resembles some known pulsar wind nebulae (PWNe) but there is no known pulsar or PWN which could be powering this structure. We also present eROSITA observations of the field; no part of the nebula is detected in X-rays, but the current limits do not preclude the existence of a pulsar/PWN of intermediate spin-down luminosity.Peer reviewe

Three-body treatment of the penetration through the Coulomb field of a two-fragment nucleus

On the basis of the Faddeev integral equations method and the Watson- Feshbach concept of the effective (optical) interaction potential, the first fully consistent three-body approach to the description of the penetration of a charged particle through the Coulomb field of a two-particle bound complex (composed of one charged and one neutral particles) has been developed. A general formalism has been elaborated and on its basis, to a first approximation in the Sommerfeld parameter, the influence of the nuclear structure on the probability of the penetration of a charged particle (the muon, the pion, the kaon and the proton) through the Gamow barrier of a two-fragment nucleus (the deuteron and the two lightest lambda hypernuclei, lambda hypertriton and lambda hyperhelium-5, has been calculated and studied.Comment: LaTeX, 30 pages, 4 eps figure