  This paper deals with the formation of a bound dineutron in the outgoing
channel of the $^{159}$Tb(n,$^2$n)$^{158g}$Tb nuclear reaction followed by
assumed transformations of this reaction products $^{159g}$Tb and $^2$n. Such
nuclear processes were studied in detail from the point of view of $^{160}$Tb /
$^{160}$Dy / $^{160}$Ho amount of nuclei versus time dependence. Some signs of
fusion process between heavier nuclei ($^{158}$Tb and/or $^{158}$Gd) and the
deuteron, that is a bound dineutron decay product, were detected as unexpected
increasing of 879.38 keV gamma-ray peak count rate due to $^{160}$Dy
gamma-transitions. The mathematical model, including three systems of
differential equations, was developed to describe the experimental data. This
development requires a reasonable estimate of the half-life of a bound
dineutron, which was found to be equal 5,877 s as an upper limit. We
mathematically modeled the experimentally observed delayed in time buildup of
the $^{160}$Tb radioactivity with a maximum at about 495 d since the neutron
irradiation completion of the Tb sample, based on the similarity with the
parent-daughter nuclei radioactivity decay and nuclear accumulation processes.
