Transition from mesoscopy of low levels of the liquid-drop model of nucleus to macroscopy of critical mass of uranium and plutonium with regard to partition theory

2^nd International Conference on Atomic and Nuclear Physics

November 08-09, 2017 | Las Vegas, USA

V P Maslov

National Research University, Russia

Scientific Tracks Abstracts: J Astrophys Aerospace Technol

Abstract :

The author changed and supplemented the standard scheme of partitions of integers in number theory to make it completely concur with the Bohrâ�?�?Kalckar correspondence principle. We revise the partition theory of integers in accordance with the Bohrâ�?�? Kalkar correspondence principle (1938) relating the physical notion of nucleus to number theory. This principle has given rise to a series of papers. We use results due to Auluckâ�?�?Kothari (1946), Agarwalaâ�?�?Auluck (1951), and Srivatsanâ�?�?Murthyâ�?�?Bhaduri (2006). We understand entropy as the natural logarithm of the number p (M) of partitions of with repeated summands and q(M) of partitions without repeated summands. The transition of ln p (M) to ln q (M) through mesoscopic values of is studied. In order to make the analogy between the the atomic nucleus and the theory of partitions of natural numbers more complete, to the notion of defect of mass author assigns the â�?�?defectâ�? of any real number (i.e., the fractional value that must be added to a in order to obtain the next integer). This allows to carry over the Einstein relation between mass and energy to a relation between the natural numbers M and N, where N is the number of summands in the partition of the given number M into natural summands, as well as to define a forbidding factor for the number M, and apply this to the Bohrâ�?�?Kalckar model of heavy atomic nuclei and to the calculation of the maximal number of nucleons in the nucleus.

Biography :

V P Maslov is a Professor of National Research University Higher School of Economics (School of Applied Mathematics). In 1984, he was elected to full membership of the Mathematical section of Russian Academy of Sciences directly, without passing through the corresponding member stage. He has published over 600 papers and over 20 monographs. He introduced a series of important notions of which Maslov-type index theory, Maslov classes, Maslov form, Maslov correction, Maslov WKB method, Maslov cycle, Maslov dequantization are best known.