Possible mechanisms of creation of both hyperheavy nuclei by electron-nuclear collapse and neutron matter by condensation of ultracold neutrons are discussed. The fundamental possibility of the existence of such objects was previously substantiated by A.B.Migdal, who suggested that the known set of proton-neutron nuclei with mass numbers from 0 to 300 and a maximum specific binding energy of about 8 MeV / nucleon at A≈60 corresponds to the first region, beyond which (starting from about the charge Z≈ ( hc/e2 )3/2 ≈1600 ) there is an additional region describing a possible state of nuclear matter, stabilized by a pion condensate. In this region, the maximum specific energy corresponds to ≈15 MeV / nucleon at A ≈ 100000. It is shown that neutron matter can be obtained under certain conditions, and its systematization can be realized as an addition to the Periodic Table. When solving such problems, it becomes quite real to study not only physical, but also chemical, and possibly engineering and technical properties. Analysis shows that the stability of neutron matter at the microlevel is ensured by the Tamm interaction and the Hund beta equilibrium. Such matter can be quite stable not only on the mega-level (neutron stars) due to gravitational interaction, as was a priori assumed earlier, but also on the scale of "ordinary" matter. The process of neutronization is possible not only with critical gravitational interaction, but also by other mechanisms (supercritical increase in the atomic number of elements due to electron-nuclear collapse and condensation of ultracold neutrons), which opens the way to the fundamental possibility of obtaining both neutron matter in laboratory conditions and superheavy nuclei. Based on the works of Migdal, Tamm and Hund, the possibility of the existence of stable neutron matter (with Z >> 175, N >> Z, A> 10 3 -10 5 and a size of 200-300 femtometers and more) is argued at the microlevel, and not only at the mega-level, as is now considered in astrophysics. A critical analysis of the well-established concept of the minimum possible mass of neutron stars is carried out. The following quantum technological approaches to the realization of UCN condensation are proposed: 1. Slow isothermal compression; 2. Refrigerator for dissolving helium-3 and helium-4; 3. Use of a conical concentrator for UCN focusing (Vysotskii cone); 4. Magnetic trap; 5. Additional UCN laser cooling. Neutron matter is considered as a potential cosmological candidate for dark matter. One should take into account the possibility of the formation of fragments of neutron matter as dark matter (neutral, femto-, pico- and nanoscale, the cooling of relics makes it difficult to detect them by now) already at the initial origin of the Universe, which is the dominant process. The observable part of the Universe is formed by the residual part of protons, and then by decayed single neutrons and unstable fragments of neutron matter (with Z> 175, N >> Z, but A <10 3 -10 5 ).
OBTAINING NEUTRON MATTER AND HYPERHEAVY NUCLEI: POSSIBLE QUANTUM-TECHNOLOGICAL INSTRUMENTAL APPROACHES