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Nucleon pair correlations in atomic nuclei are analyzed within a nuclear microscopic model with residual isovector pairing forces. These are formulated in the boson representation of fermion operators whereby the collective mode of pair excitations can be isolated without restricting the size of the one-particle basis. This method allows one to analyze the fluctuations in the nonsuperfluid phase of nuclear matter, its phase transition to the superfluid phase, and strong pair correlations. The performance of the method is exemplified by numerical results for the nuclei in the vicinity of the doubly magic 56Ni nucleus.

A short review of the results on the structure of superheavy nuclei is presented.

The lowest quadrupole $\ensuremath{\gamma}$-vibrational ${K}^{\ensuremath{\pi}}={2}^{+}$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies ${E}_{\ensuremath{\gamma}}$ and reduced transition probabilities $B(E2)$ of ${2}_{\ensuremath{\gamma}}^{+}$ states are calculated with the Skyrme forces SV-bas and ${\mathrm{SkM}}^{*}$. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of ${E}_{\ensuremath{\gamma}}$ by 0.3--0.5 MeV and thus in a better agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of ${E}_{\ensuremath{\gamma}}$ and too weak collectivity of ${2}_{\ensuremath{\gamma}}^{+}$ states still persist. It is shown that domains of nuclei with low and high ${2}_{\ensuremath{\gamma}}^{+}$ collectivity are related to the structure of the lowest two-quasiparticle states and conservation of the Nilsson selection rules. The description of ${2}_{\ensuremath{\gamma}}^{+}$ states with SV-bas and ${\mathrm{SkM}}^{*}$ is similar in light rare-earth nuclei but deviates in heavier nuclei. However SV-bas much better reproduces the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The accuracy of SRPA is justified by comparison with exact RPA. The calculations suggest that a further development of the self-consistent calculation schemes is needed for a systematic satisfactory description of the ${2}_{\ensuremath{\gamma}}^{+}$ states.

The position of the neutron and proton drip-lines as well as properties of the isotopes Fe , Ni and Zn with neutron excess and neutron deficit are studied within the Hartree–Fock approach with the Skyrme interaction (Ska, SkM*, Sly4). The pairing is taken into account on the basis of the BCS approach with the pairing constant G = (19.5/A)[1 ± 0.51(N-Z)/A]. Our calculations predict that for Ni isotopes around N = 62 there appears a sudden increase of the deformation parameter up to β = 0.4. The zone with such big deformation, where Ni isotopes are stable against one neutron emission stretches up to N = 78. The magic numbers effects for the isotopes 48 Ni , 56 Ni , 78 Ni , 110 Ni are discussed. The universality of the reasons standing behind the enhancement of stability of the isotopes 40 O and 110 Ni which are beyond the drip-line is demonstrated. Calculated values of the two-neutron separation energy, and proton and neutron root mean square radii for the chain of Ni isotopes show a good agreement with existing Hartree–Fock–Bogoliubov calculations of these values.

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ∼ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes 266–288Pb, which are stable to the emission of one neutron, is predicted.

The properties of neutron-rich Zr isotopes up to the neutron drip line and beyond it have been investigated on the basis of the Hartree-Fock method with the Skyrme forces (Ska, Sly4), taking into account the deformation. By the example of chains of Zr isotopes, good agreement is shown for the two-neutron separation energies and mean-square radii with the known results of Hartree-Fock-Bogolyubov calculations with the Sly4 forces. For the extremely neutron-rich Zr isotopes, states with very large deformation parameters (β ≈ 0.4−0.45) of neutron and proton density distributions can be realized. Beyond the neutron drip line with respect to emission of two neutrons, the existence of 150,152Zr isotopes, which are stable with respect to one-neutron emission, is predicted.

Positions of the proton and neutron drip lines and characteristics of the neutron-deficient and neutron-rich Fe and Ni isotopes have been studied by the Hartree-Fock method with the Skyrme forces (Ska, SkM*, Sly4) with allowance for deformation. Pairing was taken into account on the basis of the BCS approximation with the pairing constant G = (19.5/2)[1 ± 0.51(N − Z)/A]. Manifestation of magic numbers for the nickel isotopes 48Ni, 56Ni, and 78Ni and for the nucleon-stable isotope 110Ni which is beyond the drip line is discussed.

Background: Recent experiments on $\ensuremath{\alpha}$-decay of odd-odd superheavy nuclei give important information on the structure of the low-lying states of these nuclei. For this reason, it is interesting to calculate the excitation spectra of superheavy nuclei in the framework of different approaches and compare the results with the experimental data.Purpose: To calculate the excitation energies of the two-quasiparticle states of nuclei belonging to the $\ensuremath{\alpha}$-decay chain of $^{288}115$ nucleus.Method: Two different single-particle potentials, modified two-center and Skyrme-based potentials, are used to calculate the energies of two-quasiparticle states.Results: The spectra of the low-lying states are calculated. An evolution of the splitting of the pseudospin doublets and an evolution of the energies of the unique parity single-particle states with the nuclear mass number are investigated. The $\ensuremath{\alpha}$-decay spectra of nuclei belonging to the $\ensuremath{\alpha}$-decay chain of $^{288}115$ are obtained and compared with the experimental data. A possibility of the $E1$ transitions in $^{276}\mathrm{Mt}$ following $\ensuremath{\alpha}$ decay of $^{288}115$ is considered.Conclusion: The $E1$ transitions in $^{276}\mathrm{Mt}$ might be related to the transitions $n9/2[604]\ensuremath{\rightarrow}n11/2[725],\phantom{\rule{0.16em}{0ex}}n11/2[725]\ensuremath{\rightarrow}n9/2[615]$, and $p9/2[505]\ensuremath{\rightarrow}p11/2[615]$. Besides the $E1$ transitions, the strong $M1$ and $M2$ transitions are expected in $^{276}\mathrm{Mt}$.

The problem of the drip line in the region of the even isotopes 4–12He, 14–44O, and 38–80Ca with respect to the emission of one or two neutrons is studied in the Hartree-Fock approximation by using the SLy4 and Ska effective Skyrme forces. The “stability peninsula” in the vicinity of 40O is found.

A model of nuclear matter built from alpha-particles is proposed. In this model, nuclei possess the molecular-like structure. Analyzing the numbers of bonds, one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard–Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z=120.

The aim of this report is to formulate the approach to describe evolution of a localized density fluctuation in the region of a nuclear surface.

We consider a uniformly charged incompressible nuclear liquid bounded by a closed surface. It is shown that the evolution of an axisymmetric surface Г(r, t) ≡ σ − ∑(z, t) = 0, r = (σ, φ, z) can be approximately reduced to the motion of a curve in the (σ, z) plane. A nonlinear integro-diffrerential equation for the contour Σ (z, t) is derived. The contour Σ (z, t) and the local curvature are found to be a direct correspondence, which makes it possible to use methods of differential geometry to analyze the evolution of an axisymmetric nuclear surface.

Schwinger's approach gives a fresh look on Tamm's problem (charge, being initially at rest, exhibits an instant acceleration, moves with a finite velocity, and, after an instant deceleration, goes to the state of rest). Schwinger's angular and frequency distributions are compared with Tamm's ones which in turn are compared with exact distributions. Criteria for the validity of Tamm's formulae are checked by numerical calculations.

We study the synchrotron radiation properties in a nondispersive medium for the case when the charge velocity is smaller or greater than the light velocity in the medium. We show that the space distribution of synchrotron radiation has a spiral-like structure at a fixed moment of laboratory time. As time progresses, this spiral-like structure rotates without changing its form. The space-time domains, where particular polarization components disappear and where they are infinite, are determined. Their dependence on the radius of the observation sphere is also studied.

We analyse how the frequency dependence of the dielectric permittivity affects the electromagnetic field radiated by a point charge uniformly moving in a medium. It turns out that a moving charge radiates at every velocity. We study the space distribution of the electromagnetic field and show that its oscillations are due to the time-dependent polarization of the medium induced by the moving charge. Spectral distributions of the radiated energy and the photon number are given. Consequences arising from a choice of polarization different from the usual one are discussed. An analysis of the Kramers-Kronig dispersion relations for the treated problem is given. This consideration may be useful for the experiments recently discussed in the literature.

Some nonlinear aspects of a cluster phenomenon in nuclei are considered using of cubic Nonlinear Schroedinger Equation and Korteveg de Vries Equation. We discuss the following possible nonlinear effects: i) the decribing clusters as solitons; ii) an anomalous large angle scattering of $\alpha$-particles by light and intermediate nuclei; iii) stable vortical objects; iv) and dynamical clusterization in the presence of instability., Comment: 13 pages

In the framework of nonlinear nuclear hydrodynamics with realistic effective Skyrme contact δ-interactions, a Schrödinger equation with a fifth order nonlinearity is deduced. By using quasi soliton-like solutions, which describe well the general properties of nuclei, we studied the behavior of alpha and cluster decays in the reaction channel. Previously, we studied the formation of clusters as solitons on nuclear surface with the help of the third order (cubic) Schrödinger equation.

In heavy-ion collisions a localized stable or long lived excitation might develop. The existence of a fairly well defined nuclear surface makes it possible to discuss localized excitations in the nuclear surface region. In the framework of semiclassical nonlinear nuclear hydrodynamics we have presented a type of vortical excitation that are new in nuclear physics. We have found a class of uniformly rotating solutions to nonlinear Euler-type equations on a sphere. The equations of motion describing a localized vortex on a spherical nuclear surface - a bounded region of constant vorticity, surrounded by irrotational flux - are derived. The qualitative analysis of the main properties of this vortex is presented. These excitations may be linked with hot spots created in peripheral heavy-ion collisions.

The problems of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. Both instabilities may compensate each other and lead to stable solutions (solitons).

The basic equations to describe a plain nuclear vortex of nuclear matter are derived in the framework of nuclear hydrodynamics. The evolution of the shape of the vortex is analogous to the propagation in a plane of the nonlinear dispersion wave. Qualitative analysis of the main features of the vortex is done.

The location of proton and neutron drip-lines and the characteristics of the neutron-deflcient and the neutron-rich isotopes Fe, Ni and Zn on the basis of Hartree-Fock method with Skyrme forces (Ska, SkM*, Sly4) taking into account deformation was investigated. The calculations predict a big jump of deformation parameter up to fl » 0:4 for Ni isotopes in the neighborhood of N » 62. The manifestation of magic numbers for isotopes 48 Ni, 56 Ni , 78 Ni and also for the stable isotope in the respect to neutron emission 110 Ni which is situated beyond the neutron drip-line is

Nuclei properties for neutron rich exotic nuclei near the neutron number N=20, 28 (the chains of Oxygen and Magnesium isotopes), and the border of stability have been investigated in the frame of mean‐field (relativistic mean‐field and deformed Hartree‐Fock with Skyrme forces) approach. It is shown, the stability border may have a more complicated irregular structure as it is used lo think. The neutron rich systems are predicted to be very soft (isomeric stales may exist), The deformation effects are very important near the drip‐line, where the neutron‐matter distribution becomes very diffuse and of large size giving rise to “neutron skin”.

The model of binding alpha-particles in nuclei is suggested. It is shown good (with the accuracy of 1-2%) description of the experimental binding energies in light and medium nuclear systems. Our preliminary calculations show enhancement of the binding energy for super heavy nuclei with Z~120., 4 pages, 2 figures, Will be puplished in World Scientific as Procs. Int. Symposium on Exotic Nuclei, "EXON - 2004", July 5 - 12, 2004, Peterhof, Russia

We considered folded formfactors for the clusterized light nuclei. Having assumed a gaussian form for the alpha-particle formfactor, charge and nuclear formfactors were factorized in two parts: one for alpha-particle and another one for the alpha-particle distribution in the nucleus. Applications to electron and heavy ion scattering are considered.

The aim of this paper is to study the fine structure of the Cherenkov rings. We analyze the experiments performed by one of authors (Zrelov) in which no special focusing devices were used. The broad Cherenkov ring was observed in the plane perpendicular to the motion axis. Using the exact and approximate formulas we investigate how a charge moving uniformly in a medium radiates in a finite space interval (the Tamm problem). The formulas obtained describe the radiation intensity in the whole space, inside and outside the Cherenkov ring. In the plane perpendicular to the motion axis, the radiation fills mainly the finite ring. Its width (proportional to the motion interval) and the energy released in this ring do not depend on the position of the observation plane. Outside the Cherenkov ring, the radiation intensity suddenly drops. Inside it, the radiation intensity exhibits small oscillations which are due to the interference of the Vavilov-Cherenkov radiation and bremsstrahlung. The bursts of the radiation intensity at the ends of the Cherenkov ring are associated with the shock waves arising at the instants when the charge velocity coincides with the light velocity in a medium. For the chosen motion interval, the well-known Tamm formula does not describe the radiation intensity inside the Cherenkov ring for any position of the observation plane. Outside the Cherenkov ring, the Tamm formula is valid only at very large distances. Theoretical calculations are in satisfactory agreement with experimental data. Thus, the combined experimental and theoretical study of the unfocused Cherenkov rings allows one to obtain information on the physical processes accompanying the Cherenkov radiation in the finite spatial interval (bremsstrahlung, transition of the light velocity barrier, etc.).

Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh‐Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use the inverse mean field method to solve single‐particle Schrodinger equation, instead of constrained selfconsistent Hartree‐Fock equations. It is shown, that it is possible to simulate one‐dimensional three‐center system in the approximation of reflectless single‐particle potentials. The soliton‐like solutions of the Korteweg‐de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha‐particle and proton scattering. The analogy between fragmentation into parts of nuclei and buckyballs has led us to the idea of light nuclei as quasi‐crystals. We establish that the quasi‐crystalline structure can be formed when the distance between the alpha‐particles is comparable with the length of the De Broglia wave of the alpha‐particle. Applying this model to the scattering of alpha‐particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.

A static scission configuration in cold ternary fission has been considered in the framework of two mean field approaches. The virial theorems has been suggested to investigate correlations in the phase space, starting from a kinetic equation. The inverse mean field method is applied to solve single-particle Schredinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximation of reflectless single-particle potentials, 11 pages, 1 figure, Fusion Dynamics at the Extremes, Int. Workshop, Dubna, Russia, May 2000. To be published in World Scientific

A static scission configuration in cold ternary fission has been considered in the framework of mean field approach. The inverse scattering method is applied to solve single-particle Schroedinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximation of reflectless single-particle potentials., 8 pages, 1 figure, iopart.cls, to be published in Int.J.Mod.Phys.E

We analyse the well-known Tamm problem treating the charge motion on a finite space interval with the velocity exceeding light velocity in medium. By comparing Tamm's formulae with the exact ones we prove that former do not properly describe Cherenkov radiation terms. We also investigate Tamm's formula cos(theta)=1/(beta n) defining the position of maximum of the field strengths Fourier components for the infinite uniform motion of a charge. Numerical analysis of the Fourier components of field strengths shows that they have a pronounced maximum at cos(theta)=1/(beta n) only for the charge motion on the infinitely small interval. As the latter grows, many maxima appear. For the charge motion on an infinite interval there is infinite number of maxima of the same amplitude. The quantum analysis of Tamm's formula leads to the same results., 28 pages, 8 figures, to be published in J.Phys.D:Appl.Phys

Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of fifth order and classified using a simple mechanical picture. It is shown that a rich spectrum of nonlinear oscillations in one-dimensional nuclear medium exist., Comment: 18 pages, 5 figures

Stability with respect to neutron emission is studied for nuclear isotopes 4-12He, 14-44O, 38-80Ca in the framework of Hartree-Fock approach with Skyrme forces SLy4 and Ska. The data shows possible existence of stability island around 40O.

Analyzing recent experimental data on 1 6 O+ 1 6 O elastic scattering at different energies, we provided the set of calculations using the simplest parametrization of the repulsive core potential. Within the framework of sudden approximation for Hamiltonian with the effective Skyrme interaction new ansatz for the repulsive core potential has been derived. The preliminary estimation indicates the strong exponential dependence of the core potential on the separation of the surfaces.

Closed expressions are obtained for angular and frequency radiation intensities produced by a charge moving inside the dielectric sphere S, with observations made outside S (in fact, this is a typical experimental situation when a charge moves in one medium while measurements are made in the other one). It is shown that the difference in media properties inside and outside S drastically affects angular and frequency distributions. Also, a charge motion is considered which begins and terminates in medium 2 and which passes either through the dielectric sphere filled with medium 1 or through the metallic one. The energy flux in medium 2 involves the Vavilov–Cherenkov, transition radiation and the one arising from the charge instantaneous beginning and termination of motion. The evaluated angular and frequency distributions for various charge velocities and medium properties inside and outside S show that the standard identification of the charge velocity by its radiation on the part of the charge trajectory where βn>1 is not always valid. We analyze also the frequently used interpretation of the transition radiation in terms of instantaneous charge deceleration in one medium and its sudden acceleration in another one, and find them as to be insufficient. On the other hand, attempts to interpret the transition radiation in terms of semi-infinite motions terminating in one medium and beginning in the other one turn out to be correct if one takes into account the terms corresponding to the Vavilov–Cherenkov radiation.