Quantum corrections to the Relativistic mean-field theory

Abstract

In this paper, we have compared the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We have obtained an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. Conclusions are the following.(1) On the basis of the relations above, we found the potential VRMF of the RMF theory for nucleons which has the wave functions f and g for nucleons with joint part h coincident exactly analytically with the nucleon wave function of DOS model with potential V shell . This fact confirms that it is possible to describe quantum properties of nucleus in framework of the RMF theory exactly the same as in DOS model. However, a difference between VRMF and V shell is essential for any nucleus.(2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indicates that g and f have no sense of the wave functions of quantum physics. But, h provides proper description of quantum properties of nucleons inside the nucleus. (3) We calculate meson function w 0 (and corresponding potential Vw in framework of RMF theory) based on the found nucleon density above. (4) f and g are not solutions of Dirac equation with Vw. If the meson theory describes quantum properties of nucleus well, then a difference between Vw and VRMF should be as small as possible. We introduce new quantum corrections characterizing difference between these potentials. We find that (a) The function w 0 should be reinforced strongly, (b) The corrections are necessary to describe the quantum properties of the nuclei.