In this paper, we propose a method that makes it possible to use an ultrathin calorimeter for direct measurements of cosmic rays with energies of TeV and higher. The problems of determining the primary energy with a thin calorimeter, due to large fluctuations in shower development, the low statistics of analyzed events and the large size required for the calorimeter, are considered in detail. A solution to these problems is proposed on the basis of a lessening fluctuation method. This method is based on the assumption of the universality of the development of cascades initiated by particles of the same energy and mass. For energy reconstruction, so-called correlation curves are used. The main analyzed quantities are the size of the cascade and the rate of its development. The method was tested using the calorimeter of the PAMELA collaboration. Based on simulations, it is shown that the primary energy can be determined on the ascending branch of the cascade curve. This fact solves the problems associated with the need to increase the calorimeter thickness with an increase in primary energy and with the limitation of the analyzed events. The proposed technique is universal for different energies and different nuclei.

The problem of scattering by spherically asymmetric potentials is considered where angular momentum not only ceases to be a conserved quantity but is also not a convenient basis for the expansion of wave functions and scattering amplitudes. Numerical solutions of the two-dimensional differential equation for the scattering amplitude of a particle and a coupled pair on a semitransparent disc of finite thickness are obtained. The effect of resonant diffraction is shown. A numerical scheme can be used to describe the scattering of a particle by deformed atomic nuclei.

Many problems of numerically solving the Schrödinger equation require that we choose asymptotic distances many times greater than the characteristic size of the region of interaction. If the solution...

An algorithm based on direct discretization of a two-dimensional equation is proposed for numerically solving the problem of two-dimensional scattering. The asymptotic distance is reduced by...

The probabilities of resonance tunneling through a potential barrier for a rigid molecule and a molecule with excitation are compared. It is shown that the resonance spectrum is mostly determined by the transmission resonance spectrum for a rigid molecule. Analytical expressions for the probability of barrier tunneling by a rigid molecule yield estimates for measured values, including quantum diffusion, averaged over the resonance spectrum.