Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

     

Analysis of elastic proton-nucleus scattering on the basis of the Glauber-Sitenko approach with allowance for intermediate excitations of nuclei

On the basis of the Glauber-Sitenko approach, the cross sections and spin observables for proton-nucleus scattering at intermediate energies are calculated with allowance for intermediate excitations of target nuclei. The calculations are performed by using the Hartree-Fock and model-independent nuclear densities and nucleon-nucleon amplitudes determined from partial-wave analyses. It is shown that the inclusion of intermediate excitations of nuclei strongly affects the behavior of observables in the region of moderately small scattering angles.     

Pairing correlations and soft dipole excitations in nuclei on the neutron-drip line

Paring correlations and soft dipole excitations in weakly bound nuclei on the edge of neutrondrip line are studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei ⁶He and ¹¹Li, as well as a skin nucleus ²⁴O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron-type correlation plays a dominant role in the halo nuclei ⁶He and ¹¹Li having the coupled spin of the two neutrons S = 0, while the correlation similar to the BCS type is important in ²⁴O. Contributions of the spin S = 1 and S = 0 configurations are separately discussed in the low-energy dipole excitations. The calculated results are compared with recent experimental data of ⁶He and ¹¹Li. The text was submitted by the authors in English.     

Zero-motion correlations in high-energy proton elastic scattering on40Ca with noneikonal nucleon-nucleon amplitude

Using a noneikonal expression for the two-body scattering amplitude, consistent with the proton-nucleon scattering data, the cross-section of the 1.04 GeV-proton elastic scattering on⁴⁰Ca is calculated by the Glauber-Sitenko theoretical scheme in the framework of the coherent density fluctuation model (CDFM) as well as of the independent-particle model (IPM). It is shown that the use of the noneikonal amplitude in the CDFM calculation improves the agreement with the experimental data especially at larger scattering angles in contrast to the case of the independent-particle model. To that end a decisive role play the zero-motion flucton correlations taken into account in the CDFM.     

Elastic deuteron scattering on 12C and 16O nuclei in the alpha-cluster model

On the basis of the dispersive alpha-cluster model for target nuclei and the theory of multiple diffractive scattering, differential cross sections and analyzing powers for the elastic scattering of 400 and 700-MeV deuterons on ¹²C and ¹⁶O target nuclei were calculated in the pointlike-deuteron approximation. In these calculations, the amplitude for incident-deuteron scattering on nuclei was constructed with the aid of amplitudes for dα scattering that were obtained from a fit to data on d ¹⁶O scattering. The same features were calculated on the basis of the diffraction approximation with allowance for the internal deuteron structure by using the amplitudes obtained earlier for nucleon scattering on ¹²C and ¹⁶O nuclei within the same dispersive alpha-clustermodel. The latter made it possible to perform calculations without employing adjustable parameters. The observables calculated on the basis of either approach agree with available experimental data.     

Nucleon Isovector Pairing in Nuclei: Microscopic Approach,Boson Representation,and Collective Model

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.     

Diffractive scattering of loosely bound nuclei involving two charged clusters on nuclei

The theory of diffractive interaction between loosely bound nuclei featuring two charged clusters and nuclei is developed with allowance for Coulomb interaction. The differential cross sections for the scattering of ⁶Li, ⁷Be, and ⁸B nuclei on ¹²C nuclei are calculated, and the results of these calculations are compared with data from recent experiments.     

The antiproton-nucleus elastic scattering and the alpha-cluster model with dispersion

The elastic scattering differential cross sections of intermediate energy antiprotons on¹²C and¹⁶O nuclei and the elastic scattering polarization observables of antiprotons on these nuclei have been calculated on the basis of theα-cluster model with dispersion and multiple diffraction theory. The results of these calculations are compared with the experimental data.     

Two-step mechanisms of two-proton decays of nuclei

A formalism for describing two-step two-proton decays of nuclei is developed on the basis of the multiparticle theory of deep-subbarrier one-proton decays of nuclei that employs integral expression for the decay widths in question. This formalism relies on the idea that the interaction between the emitted protons has but a slight effect on the widths with respect to the two-proton decays being considered. It is shown that such a decay is naturally broken down into the sequential one-proton decays of an (A, Z) parent nucleus and an (A ? 1, Z ? 1) intermediate nucleus, these decays being related by the Green’s function G(A ? 1, Z ? 1) that describes the intermediate nucleus with allowance for its real and virtual states, which give rise to, respectively, the sequential and the virtual two-step two-proton decay of the parent nucleus. It is also shown that the widths with respect to sequential two-step two-proton decays coincide with the analogous widths constructed within the R-matrix theory of nuclear reactions leading to the production of unstable particles and with their counterparts obtained with the aid of solving the set of kinetic equations for the chain of nuclei undergoing radioactive decays. It is found that the widths with respect to virtual two-step two-proton decays are close in structure to the widths constructed for the simultaneous two-proton decays of nuclei by using integrated formulas within a simplified model of the method of three-particle hyperspherical polynomials.     

Time features of delayed neutrons and partial emissive-fission cross sections for the neutron-induced fission of 232Th nuclei in the energy range 3.2–17.9 MeV

The energy dependence of the relative abundances of delayed neutrons and the energy dependence of the half-lives of their precursors in the neutron-induced fission of ²³²Th nuclei in the energy range 3.2–17.9 MeV were measured for the first time. A systematics of the time features of delayed neutrons is developed. This systematics makes it possible to estimate the half-life of delayed-neutron precursors as a function of the nucleonic composition of fissile nuclei by using a single parameter set for all nuclides. The energy dependence of the partial cross sections for emissive fission in the reaction ²³²Th(n, f) was analyzed on the basis of data obtained for the relative abundances of delayed neutrons and the aforementioned half-lives and on the basis of the created systematics of the time features of delayed neutrons. It was shown experimentally for the first time that the decrease in the cross section after the reaction threshold in the fission of ²³²Th nuclei (it has a pronounced first-chance plateau) is not an exclusion among the already studied uranium, plutonium, and curium isotopes and complies with theoretical predictions obtained for the respective nuclei with allowance for shell, superfluid, and collective effects in the nuclear-level density and with allowance for preequilibrium neutron emission     

Two particle — two hole mixing in Hartree-Fock calculations

The constrained Hartree-Fock theory is used for studying the stability of the solutions against two particle — two hole excitations. Quadropole and hexadecapole deformation are imposed on the Hartree-Fock equations to get the true energy minimum and the equilibrium shape. Energy corrections are calculated using second-order perturbations and complete diagonalization. Applications are made to the ²⁰Ne and ²⁸Si nuclei.     

Elastic hadron scattering on Li isotopes at intermediate energies

The elastic scattering of hadrons (protons, charged pions, and positively charged kaons) on ^6,7,8Li nuclei is analyzed on the basis of Glauber-Sitenko diffraction theory. A few nuclear-wave-function versions found within two-and three-particle potential cluster models are used in the calculations. It is shown that the application of these wave functions in diffraction theory makes it possible to describe adequately the experimental differential cross sections and analyzing powers in hadron scattering at intermediate energies. In this study, particular attention is given to a comparison of the scattering of different particles on the same target nucleus, as well as to a comparison of scattering of particles of the same sort on different target nuclei.     

Alpha-like four nucleon correlations in superfluid phases of atomic nuclei

α-like four-nucleon correlations are included in the structure of superfluid ground and low-lying excited states of atomic nuclei within a BCS-like approach. New metastable superfluid and normal states are predicted. These states could be associated with some of the recently discovered I^π = 0⁺ states in different regions of atomic nuclei. A new type of elementary excitations may be constructed on these metastable states in the same way as those constructed on the BCS superfluid ground states. The region of superfluid cold nuclei is enlarged due to the fact that the neutron and proton superfluidity can mutually be induced via the α-like four-nucleon ineractions. This type of correlations lead to a further enhancement of the probabilities of the favoured α-clusterization processes (such as α-decay or α-transfer reactions), two-nucleon transfer reactions and other clusterization processes such as e.g. the heavy cluster decay.     

The collective correlation model of the giant resonance with the surface-delta-interaction

The intermediate structure of the giant resonance of light nuclei (¹²C,¹⁶O,²⁸Si,³²S,⁴⁰Ca) has been investigated in the model of collective correlations by means of the surface-delta-interaction (SDI). The SDI introduces also a coupling of 1p-1h excitations to the surface vibrations. Despite the simplicity of this model the gross features of the absorption cross sections are quite well resembled. Furthermore, this model predicts a considerable inelastic photon scattering into the first excited 2⁺ level.     

Rescattering effects in proton scattering on nuclei 6,8He and 8,9Li in the Glauber theory

The differential cross sections of elastic p^6,8He and p^8,9Li scattering are calculated within the Glauber diffraction theory at intermediate energies of 70 to 700 MeV/nucleon. The calculations are based on realistic three-body wave functions α-n-n (for ⁶He), α-2n-2n (for ⁸He), α-t-n (for ⁸Li), α-t-2n (for ⁹Li), obtained using current nuclear models, and the Glauber operator is expanded into a series of multiple scattering corresponding to the three-body nuclei configuration. The approach allows us to calculate the operator matrix elements with allowance for rescattering on all structural components of the investigated nuclei.     

Allowance for the shell structure of the 42100 Mo and 46110 Pd nuclei in the synthesis of 84200 Po, 88210 Ra, and 92220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: ₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄¹⁰⁰Po, ₄₂¹⁰⁰Mo + ₄₆¹⁰⁰Pd → ₈₈²¹⁰Ra, and ₄₆¹¹⁰Pd + ₄₆¹¹⁰Pd → ₉₂²²⁰U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.     

Reaction cross sections for collisions involving exotic light nuclei within the glauber approach

The reaction cross sections for the interaction of exotic nuclei ⁶He and ¹¹Li with ¹²C nuclei are calculated for energies of about 0.8 GeV per nucleon. The cross sections calculated by the exact Glauber formula are compared with their counterparts found by using the formulas of the optical limit, the rigidtarget approximation, and the few-body approximation. The effect of the structure of the nuclei being considered on the calculated cross sections is examined. The root-mean-square radii of the ⁶He and ¹¹Li nuclei are estimated on the basis of experimental data on the cross sections for the interaction of these exotic nuclei with ¹²C nuclei.     

Interactions between 4He nuclei and protons at intermediate energies

Since the early 1970s, experiments have been performed to investigate the fragmentation of the lightest nuclei (d, ³H, ³He, and ⁴He) on protons at intermediate energies (～0.2–2 GeV per nucleon). These experiments were set up in ITEP and LHE JINR and realized in an exclusive approach with the help of liquid hydrogen bubble chambers. This investigation is of great interest from two points of view: first, the possibility of detailed theoretical analysis of the data obtained in 4π geometry on the basis of a good understanding of the structure of the wavefunctions of these nuclei and, second, the search for exotic interaction mechanisms. This overview presents the latest, most interesting results of the ITEP experiment on the study of ⁴Hep interactions at ⁴He momenta of 2.7 and 5 GeV/c, on cross sections, elastic scattering, pair correlations of secondary nucleons, cumulative production of nucleons and the lightest nuclei (d, ³H, and ³He), the main features of exclusive reactions, and the search for possible multiquark bag production (dibaryons and tribaryons). The essential results of the independent JINR experiment at 8.6 and 13.6 GeV/c also come under discussion.