The Bohr–Kalckar Correspondence Principle and a New Construction of Partitions in Number Theory*

Mathematical notes. 2017. Vol. 102. No. 4. P. 533–540.

Maslov V. P.

The author attempts to change and supplement the standard scheme of partitions of
integers in number theory to make it completely concur with the Bohr–Kalckar correspondence
principle. 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”
{a} = [a + 1] − a of any real number a (i.e., the fractional value that must be added to a in order
to obtain the nearest larger integer). This allows to carry over the Einstein relation between mass
and energy to a relation between the whole numbersM and N, whereN is the number of summands
in the partition ofM into positive summands, as well as to define the 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.

Keywords: bosons, topological phase transition, fermions, critical mass, partitions in number theory, droplet model of the nucleus