Projector operators for the no-core shell model

Projection operators for the use within ab initio no-core shell model, are suggested.Comment: 3 page

New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.Comment: 25 pages, LaTex fil

Development of the method of quaternion typification of Clifford algebra elements

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and prove a number of new properties of Clifford algebra. We use k-fold commutators and anticommutators. In this paper we consider Clifford and exterior degrees and elementary functions of Clifford algebra elements.Comment: 15 page

Deuteron-equivalent and phase-equivalent interactions within light nuclei

Background: Phase-equivalent transformations (PETs) are well-known in quantum scattering and inverse scattering theory. PETs do not affect scattering phase shifts and bound state energies of two-body system but are conventionally supposed to modify two-body bound state observables such as the rms radius and electromagnetic moments. Purpose: In order to preserve all bound state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound state (deuteron) binding energy but also the bound state wave function. Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of $^3$H and $^4$He binding energies in the No-core Full Configuration (NCFC) approach based on extrapolations of the No-core Shell Model (NCSM) basis space results to the infinite basis space. Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of $^3$H and $^4$He nuclei and their correlation (Tjon line). Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of $^3$H (in the range of approximately 1.5 MeV) and $^4$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei

Moving system with speeded-up evolution

In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using the relativistic quantum theory. The example of a moving system is given whose evolution turns out to be speeded-up instead of being dilated. A discussion of this paradoxical result is presented.Comment: 10 pages, LaTe

Analysis of the Problems of Training Bachelors in the Direction of “Technosphere Security” Taking Into Account the Cognitive Characteristics of New Generations of Students

The research aims to analyze possible ways to improve undergraduate student performance in current conditions. The use of new directions in the methods of training and conducting training in undergraduate agricultural higher education institutions in the “Technosphere safety” training program. When developing teaching methods and technologies, teachers should consider changes in the cognitive abilities of the Generation Z students, which differ significantly from previous generations in terms of attention, information perception, and communication abilities. The author argues a need for the digital transformation of education in the wake of the trend towards the digital transformation of the economy and agriculture. This is primarily an opportunity to activate the combination of the group educational process in the classroom using the capabilities of current computer technologies with the individualization (personification) of education when each student gets the opportunity for independent creative work with remote control and correction by the teacher

Numerical simulation of shock-wave structure for argon and helium

3 pags. ; 4 figs.We compare the thickness of shock-wave fronts at different Mach numbers, modeled via Navier–Stokes sNSd equations, with experimental results from the literature. Monoatomic argon and helium are considered. In this modeling a finite-difference scheme with second-order spatial accuracy is employed. For argon the calculated density thickness is in good agreement with the experimental results. For helium the NS results agree well with those from the bimodal model and with the few available experimental data. © 2005 American Institute of Physics.Peer reviewe