Direct method for detecting intranuclear clusters of nuclear matter-clusters and determining their effective numbers was developed. The idea of the method is based on the functional coincidence of kinematics for light nuclei in the free state and clusters of the same mass within the nuclear volume. The reliability of the method is additionally confirmed by two experimental methods. The experiments were carried out at the Kazakhstan U-150M accelerator on a beam of [Formula: see text]-particles with energy of 29[Formula: see text]MeV. The first method consists in measuring the half-width of the elastic scattering peak from the angle and a comparison between the differential cross-sections of elastically scattered [Formula: see text] particles on free light nuclei and the differential cross-sections obtained by the authors on intranuclear multicluster. Using the second method, the correlation method, an experiment was performed to record the scattered [Formula: see text] particle on the 9 Be nucleus-matrix and the recoil nucleus identical to it ([Formula: see text] particle). Thus, the kinematics of the [Formula: see text] 4 He reaction, where 4 He is an intranuclear [Formula: see text] cluster, indicates the presence of an intranuclear alpha cluster, which is further confirmed by the authors, an experimental measurement of intranuclear multicluster.

A theoretical study of even–even nuclei (2 ≤ Z ≤ 8) with extreme neutron excess stable with respect to one-neutron emission, including nuclei beyond the neutron drip line (NDL), is performed. The calculations are based on the Hartree–Fock (HF) method with Skyrme forces (SkI2) and allowance for axial deformation and the Bardeen–Cooper–Schrieffer (BCS) pairing approximation. It is shown that beyond the NDL, 18He and 40C isotopes form peninsulas of nuclei stable with respect to one-neutron emissions. The restoration of stability beyond the NDL for 18He and 40C can be explained by the complete filling of neutron subshells with high angular momentum and the introduction of corresponding neutron levels in the region of discrete bound states.

Using HF + BCS method with Skyrme forces we analyze the neutron drip line. It is shown that around magic and new magic numbers the drip line may form stability peninsulas. It is shown that the location of these peninsulas does not depend on the choice of Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.

The resonance capture of multineutrons by the 88Sr and 27Al nuclei has been calculated by the Hartree–Fock method with the Skyrme forces (Ska) taking into account pairing in the Bardeen–Cooper–Schrieffer approximation. The calculated binding energies of multineutrons, rms radii, pairing energies, and quadrupole deformation parameters point in favor of the resonance capture mechanism.

Using HF + BCS method we study light nuclei with nuclear charge in the range 2 ≤ Z ≤ 8 and lying near the neutron drip line. The HF method uses effective Skyrme forces and allows for axial deformations. We find that the neutron drip line forms stability peninsulas at 18 He and 40 C . These isotopes are found to be stable against one neutron emission and possess the highest known neutron to proton ratio in stable nuclei.

Properties of even-even nuclei with extreme neutron excess in the vicinity of neutron magic numbers up to and beyond the neutron drip line (NDL) are calculated by the Hartree-Fock (HF) method using Skyrme forces (Ska, SkM*, Sly4, SkI2, SkP) with allowance for axial deformation and BCS-approximation pairing. It is shown that chains of isotones with the neutron numbers N = 32, 58, 82, 126, 184, and 258 beyond the NDL form peninsulas of nuclei stable with respect to emission of one neutron, and occasionally peninsulas of nuclei stable with respect to the emission of two neutrons. The length of these peninsulas in ( N , Z ) space depends on the choice of the Skyrme forces, while their locations are at the same N = 32, 58, 82, 126, 184, and 258 and do not depend on the choice of forces. The investigated isotones restore stability beyond the NDL due to the complete filling of subshells with high angular momentum and to the intrusion of corresponding neutron levels in the region of discrete bound states. The stability of the numerical solution to the HF equations for nuclei belonging to the peninsulas of stability is analyzed.

Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that around magic and new magic numbers the drip line may form stability peninsulas. It is shown that the location of these peninsulas does not depend on the choice of Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.

Recently it was proved that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of N neutrons E(N), which interact through these forces one has E(N) = -cN(3) + O(N-8/3), where c > 0 is a constant. This means that: (i) the energy per particle and neutron density diverge rapidly for large neutron numbers; (ii) bound states of N neutrons exist for N large enough. The neutron matter collapse is possible due to the form of the repulsive core in three-body forces, which vanishes when three nucleons occupy the same site in space. The obtained results partly change the paradigm, in which the stability of neutron stars is attained through the Pauli principle; the strong repulsive core in the nucleon interactions is by no means less important.

Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that the drip line may form stability peninsulas. These peninsulas locate along fixed neutron numbers on the nuclear chart, which correspond to magic and new magic numbers, and are the same for all Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.

It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of $N$ neutrons $E(N)$, which interact through these forces, we prove mathematically that $E(N) = -cN^3 + \mathcal{O}(N^{8/3})$, where $c>0$ is a constant. This means that: (i) the energy per particle and neutron density diverge rapidly for large neutron numbers; (ii) bound states of $N$ neutrons exist for $N$ large enough. The neutron matter collapse is possible due to the form of the repulsive core in three-body forces, which vanishes when three nucleons occupy the same site in space. The old variant of the forces Urbana VI, where the phenomenological repulsive core does not vanish at the origin, resolves this problem. We prove that to prevent the collapse one should add a repulsive term to the Urbana IX potential, which should be larger than 50 MeV when 3 nucleons occupy the same spatial position.

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.

Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that the drip line may form stability peninsulas. These peninsulas locate along fixed neutron numbers on the nuclear chart, which correspond to magic and new magic numbers and are the same for all Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.

Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that around magic and new magic numbers the drip line may form stability peninsulas. It is shown the location of these peninsulas does not depend on the choice of Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.

On the basis of the Hartree-Fock method as implemented with Skyrme forces (Ska, SkM*, Sly4, and SkI2) and with allowance for an axial deformation and nucleon pairing in the Bardeen-Cooper-Schrieffer approximation, the properties of extremely neutron-rich even-even nuclei were calculated beyond the neutron drip line known earlier from theoretical calculations. It was shown that the chains of isotopes beyond the neutron drip line that contain N = 32, 58, 82, 126, and 184 neutrons form peninsulas of nuclei stable against the emission of one neutron and, in some cases, peninsulas of nuclei stable against the emission of two neutrons. The neutron- and proton-density distributions in nuclei forming stability peninsulas were found to be spherically symmetric. A mechanism via which the stability of nuclei might be restored beyond the neutron drip line was discussed. A comparison with the results of calculations by the Hartree-Fock-Bogolyubov method was performed for long chains of sulfur and gadolinium isotopes up to the neutron drip line.

The properties of extremely neutron-excessive nuclei with Z ≥ 70, including the region of transuranium elements, are calculated beyond the previously theoretically known neutron drip line (NDL). The calculations are based on the Hartree-Fock approach using Skyrme forces (SkM*, SkI2, SLy4, Ska) with allowance for axial deformation and pairings in the BCS approximation. It is shown that the series of isotones with neutron number N = 258 outside of 2n NDL forms a peninsula of stable nuclei (PSN) with respect to the emission of one neutron. For SkM* forces, a PSN is formed by 344 Rn, 346 Ra, 348 Th, and 350 U nuclides.

Manifestations of the neutron halo in extremely neutron-rich nuclei are investigated by the Hartree-Fock method using the Skyrme forces (SkM*, Ska, Sly4, SkI2) with allowance for axial deformation. The investigated nuclei, which lie beyond the theoretical neutron drip line (NDL), form peninsulas of nuclei stable with respect to one-neutron emission and belong to chains of isotones with the neutron number N = 32, 58, 82, 126, 184, and 258.