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

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” $\overline{\{a\}} =[a+1]-a$ 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 numbers $M$ and $N$, where $N$ is the number of summands in the partition of $M$ 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.