Calculation of the Critical Distances in a System of Two Colliding Nuclei Beyond the Monopole Approximation
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EMATICAL MODELING IN NUCLEAR TECHNOLOGIES
Calculation of the Critical Distances in a System of Two Colliding Nuclei Beyond the Monopole Approximation A. A. Roenkoa,* and K. A. Sveshnikovb aBogoliubov
Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia bFaculty of Physics, Moscow State University, Moscow, 119234 Russia *e-mail: [email protected] Received July 5, 2019; revised July 12, 2019; accepted July 18, 2019
Abstract—A method for calculating electronic levels in compact superheavy nuclear quasimolecules based on solving the Dirac equation in spherical coordinates using a multipole expansion of a two-center potential is developed. It is shown that, for internuclear distances up to ~100 fm, such a technique enables fast convergence, which allows one to calculate the electronic energy levels with an accuracy better than 10–6. Moreover, all the multipole moments can be calculated analytically. The critical distances between the similar colliding nuclei have been calculated in the range Z ~ 87–100 for bottom electronic levels: even 1σ g and odd 1σu , respectively. Keywords: critical distance, Dirac equation, heavy ion collisions, superheavy quasimolecules DOI: 10.1134/S1063778819120251
INTRODUCTION The study of compact nuclear quasimolecules formed in the processes of heavy ion collisions is of great interest in view of the planned experiments on the heavy ion colliders which will be introduced in the near future: FAIR (Germany), NICA (Russia), HIAF (China), etc. In particular, the supercritical region is of special attention when the total charge of colliding nuclei exceeds the critical charge Z cr 170 , since in this case the discrete electronic levels are immersed in the negative continuum domain. This should lead to a nonperturbative rearrangement of the QED vacuum, accompanied by the creation of vacuum positrons [1–3]. In this case, an important characteristic of two colliding nuclei is the critical distance Rcr between the nuclei, for which the binding energy of the electronic level is exactly two electron rest masses. To date, a large number of different methods have been developed to solve the two-center Dirac еquation (see [4–11] and references therein), which allow, among other things, to determine the value of Rcr . According to recent estimates [6–11], the critical distance between colliding nuclei with the total charge Z Σ 170 −190 is 10–50 fm, which coincides with the diameter of the colliding nuclei in order of magnitude and turns out to be several orders of magnitude less than the distances in the molecules. For this reason, most of the methods based on representation of the wave function of an electron as a linear combination of atomic orbitals (LCAO), widely used in quantum chemistry, turn out
to be poorly applicable in this case, since it is necessary to significantly increase the number of basis elements with decreasing internuclear distance. At the same time, the Coulomb field created by two closely spaced nuclei differs from a
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