The magnetic dipole transitions in the homonuclear molecular ion ${\mathrm{H}}_2{}^{+}$ are obtained for a range of $v$ and $L$, vibrational and total orbital momentum quantum numbers, respectively. Calculations are performed in the nonrelativistic approximation. Spin consideration is also included.

As the methods, instrumentation, and resolution of three-dimensional spatial analysis have improved over the past twenty years, it is now possible to image the internal microstructure of multiphase materials in detail in three dimensions. Three-dimensional X-ray microtomography offers a unique opportunity for high spatial resolution imaging that can be achieved in compact desktop systems using X-ray microfocus sources. Recently, a modern desktop cone-beam X-ray microtomography system for quantitative analysis of materials in three dimensions was installed at the Institute of Nuclear Physics of the Ministry of Energy of the Republic of Kazakhstan. This paper presents the design, description of the main components, and technical parameters of this X-ray microtomography system, called IMAX. This system is designed to acquire, process, store X-ray images, and reconstruct three-dimensional data from angular projections for the study of internal structures and non-destructive testing of materials. The system consists of a microfocus X-ray source providing an X-ray energy range from 35 to 80 keV, a flat panel scintillation detector system allowing high-resolution digital imaging, optomechanical platforms for sample positioning, and radiation shielding. The first results of test measurements using this X-ray system are presented.

The nonrelativistic ionization energy levels of a helium atom are calculated for S, P, D, and F states. The calculations are based on the variational method of “exponential” expansion. The convergence of the calculated energy levels is studied as a function of the number of basis functions N. This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate up to 28–35 significant digits.

This paper presents the application of combined non-destructive diagnostic methods—neutron and X-ray tomography, conducted using the TITAN neutron radiography and tomography facility at the WWR-K reactor, as well as the IMAX X-ray tomography facility, to visualize the internal structure of 2032 and 18650 battery cells provided by the Research, Design, and Technology Center for Electrochemical Engineering at Dubna State University. The obtained X-ray and neutron tomography data revealed inhomogeneities in the distribution of the base materials, as well as areas of low and high radiation attenuation, gaps, and voids at the boundaries between the electrodes and the battery case. The analysis results demonstrate the high efficiency of X-ray and neutron tomography for quality assessment during the manufacture of such batteries. The conducted test demonstration experiments allow for the development of methods for the combined application of these methods and provide a basis for their further use in the research and development of new battery systems.