Hydrogen atom in a magnetic field: The quadrupole moment

The quadrupole moment of a hydrogen atom in a magnetic field for field strengths from 0 to 4.414e13 G is calculated by two different methods. The first method is variational, and based on a single trial function. The second method deals with a solution of the Schroedinger equation in the form of a linear combination of Landau orbitals.Comment: 4 pages, 1 figure, 1 table; RevTeX. Final (proofs-stage) version of the text; corrected numbers in Table 1 and in Eq.(15

Testing cosmological variability of fundamental constants

One of the topical problems of contemporary physics is a possible variability of the fundamental constants. Here we consider possible variability of two dimensionless constants which are most important for calculation of atomic and molecular spectra (in particular, the X-ray ones): the fine-structure constant \alpha=e^2/\hbar c and the proton-to-electron mass ratio \mu=m_p/m_e. Values of the physical constants in the early epochs are estimated directly from observations of quasars - the most powerful sources of radiation, whose spectra were formed when the Universe was several times younger than now. A critical analysis of the available results leads to the conclusion that present-day data do not reveal any statistically significant evidence for variations of the fundamental constants under study. The most reliable upper limits to possible variation rates at the 95% confidence level, obtained in our work, read: |\dot\alpha/\alpha| < (1.4e-14)/yr, |\dot\mu/\mu| < (1.5e-14)/yr on the average over the last ten billion years.Comment: 9 pages, 2 figures, 2 tables, LaTeX using aipproc.sty (included). In: X-ray and Inner-Shell Processes, R.W. Dunford, D.S. Gemmel, E.P. Kanter, B. Kraessig, S.H. Southworth, L. Young (eds.), AIP Conf. Proc. (AIP, Melville, 2000) vol. 506, p. 50

A hydrogenic molecular atmosphere of a neutron star

A model of a hydrogenic content of atmosphere of the isolated neutron star 1E1207.4-5209 is proposed. It is based on the assumption that the main component in the atmosphere is the exotic molecular ion $H_3^{2+}$ and that there exists a magnetic field in the range of $(4 \pm 2) \times 10^{14}$ G. Photoionization H_3^{2+} \rar e + 3p and photodissociation H_3^{2+} \rar H + 2p correspond to two absorption features at 0.7 KeV and 1.4 KeV, respectively, discovered by {\it Chandra} observatory (Sanwal et al, 2002). The model predicts one more absorption feature at 80-150 eV corresponding to photodissociation H_3^{2+} \rar H_2^+ + p.Comment: 8 pages, 1 figur

Radiative properties of highly magnetized isolated neutron star surfaces and approximate treatment of absorption features in their spectra

In the X-ray spectra of most X-ray dim isolated neutron stars (XDINSs) absorption features with equivalent widths (EWs) of 50 -- 200 eV are observed. We theoretically investigate different models to explain absorption features and compare their properties with the observations. We consider various theoretical models for the magnetized neutron star surface: naked condensed iron surfaces and partially ionized hydrogen model atmospheres, including semi-infinite and thin atmospheres above a condensed surface. The properties of the absorption features (especially equivalent widths) and the angular distributions of the emergent radiation are described for all models. A code for computing light curves and integral emergent spectra of magnetized neutron stars is developed. We assume a dipole surface magnetic field distribution with a possible toroidal component and corresponding temperature distribution. A model with two uniform hot spots at the magnetic poles can also be employed. Light curves and spectra of highly magnetized neutron stars with parameters typical for XDINSs are computed using different surface temperature distributions and various local surface models. Spectra of magnetized model atmospheres are approximated by diluted blackbody spectra with one or two Gaussian lines having parameters, which allow us to describe the model absorption features. To explain the prominent absorption features in the soft X-ray spectra of XDINSs a thin atmosphere above the condensed surface can be invoked, whereas a strong toroidal magnetic field component on the XDINS surfaces can be excluded.Comment: 54 pages, 17 figures, accepted for publication in A&

Neutrino-pair bremsstrahlung by electrons in neutron star crusts

Neutrino-pair bremsstrahlung by relativistic degenerate electrons in a neutron-star crust at densities (10^9 - 1.5x10^{14}) g/cm^3 is analyzed. The processes taken into account are neutrino emission due to Coulomb scattering of electrons by atomic nuclei in a Coulomb liquid, and electron-phonon scattering and Bragg diffraction (the static-lattice contribution) in a Coulomb crystal. The static-lattice contribution is calculated including the electron band-structure effects for cubic Coulomb crystals of different types and also for the liquid crystal phases composed of rod- and plate-like nuclei in the neutron-star mantle (at 10^{14} - 1.5x10^{14} g/cm^3). The phonon contribution is evaluated with proper treatment of the multi-phonon processes which removes a jump in the neutrino bremsstrahlung emissivity at the melting point obtained in previous works. Below 10^{13} g/cm^3, the results are rather insensitive to the nuclear form factor, but results for the solid state near the melting point are affected significantly by the Debye-Waller factor and multi-phonon processes. At higher densities, the nuclear form factor becomes more significant. A comparison of the various neutrino generation mechanisms in neutron star crusts shows that electron bremsstrahlung is among the most important ones.Comment: 17 pages, 13 figures, LaTeX using aa.cls and epsf.sty. A&A, in pres

Absorption Features in Spectra of Magnetized Neutron Stars

The X-ray spectra of some magnetized isolated neutron stars (NSs) show absorption features with equivalent widths (EWs) of 50 - 200 eV, whose nature is not yet well known. To explain the prominent absorption features in the soft X-ray spectra of the highly magnetized (B ~ 10^{14} G) X-ray dim isolated NSs (XDINSs), we theoretically investigate different NS local surface models, including naked condensed iron surfaces and partially ionized hydrogen model atmospheres, with semi-infinite and thin atmospheres above the condensed surface. We also developed a code for computing light curves and integral emergent spectra of magnetized neutron stars with various temperature and magnetic field distributions over the NS surface. We compare the general properties of the computed and observed light curves and integral spectra for XDINS RBS\,1223 and conclude that the observations can be explained by a thin hydrogen atmosphere above the condensed iron surface, while the presence of a strong toroidal magnetic field component on the XDINS surface is unlikely. We suggest that the harmonically spaced absorption features in the soft X-ray spectrum of the central compact object (CCO) 1E 1207.4-5209 (hereafter 1E 1207) correspond to peaks in the energy dependence of the free-free opacity in a quantizing magnetic field, known as quantum oscillations. To explore observable properties of these quantum oscillations, we calculate models of hydrogen NS atmospheres with B ~ 10^{10} - 10^{11} G (i.e., electron cyclotron energy E_{c,e} ~ 0.1 - 1 keV) and T_eff = 1 - 3 MK. Such conditions are thought to be typical for 1E 1207. We show that observable features at the electron cyclotron harmonics with EWs \approx 100 - 200 eV can arise due to these quantum oscillations.Comment: 4 pages, 3 figures, conference "Astrophysics of Neutron Stars - 2010" in honor of M. Ali Alpar, Izmir, Turke

Cyber-Physical Systems Technologies: Applications in Industry and Education

Industry 4.0 concept development forms new trends as cloud computing,&nbsp; big data analysis, the industrial internet of things, machine-to-machine technologies. Cyber-physical systems (CPS) paradigm is based on these trends and integrates of computation, networking and physical processes. Synergy Center at Peter the Great St. Petersburg Polytechnic University works in the areas of intelligent systems for data processing and control, motion control systems for robotics, complex automation and mechatronics as components of CPS. Keywords: Industry 4.0, Cyber-physical systems, Digital twin; intelligent control system, automation, Global digitalisation, Practical-oriented online courses, Skills training, Joint international educational programmes