V P Maslov
National Research University, Russia
Title: 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
Biography
Biography: V P Maslov
Abstract
The author changed and supplemented the standard scheme of partitions of integers in number theory to make it completely concur with the Bohr–Kalckar correspondence principle. We revise the partition theory of integers in accordance with the Bohr–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 Auluck–Kothari (1946), Agarwala–Auluck (1951), and Srivatsan–Murthy–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 “defect” 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 Bohr–Kalckar model of heavy atomic nuclei and to the calculation of the maximal number of nucleons in the nucleus.