Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

Classification of <Emphasis Type="Italic">T</Emphasis>-odd asymmetries for prescission and evaporated light particles in ternary and quaternary nuclear fission induced by cold polarized neutrons

A unified mechanism of the emergence of T-odd ROT- and TRI-asymmetries is proposed for describing experimental T-odd asymmetry coefficients D(θ) in the angular distributions of prescission alphaparticles that are emitted in true ternary and quaternary nuclear fission reactions induced by cold polarized neutrons. The mechanism is related to the different ways in which the Coriolis interaction of the total spin of a polarized compound fissile nucleus with the orbital moment of alpha-particles affects even (for ROT-asymmetries) and odd (for TRI-asymmetries) components of the amplitude of an undisturbed angular distribution of emitted alpha-particles. Coefficients D_ROT(θ) and D_TRI(θ) derived with this mechanism for T-odd ROT- and TRI-asymmetries successfully describe the dependences of corresponding experimental coefficients for ²³⁵U and ²³⁹Pu nuclei over the range of angles θ, and for the ²³³U nucleus in the angular range of 60° < θ < 110°. It is explained why only ROT-type T-odd asymmetries emerge for evaporated neutrons and γ-quanta emitted by fission fragments in similar reactions if we allows for the Coriolis interaction of the total spin of the compound fissile nucleus with the orbital moments of the fission fragments and the wriggling vibrations of the above nucleus near its scission point.     

Corona effect in <Emphasis Type="Italic">AA</Emphasis> collisions at the LHC

Following our earlier finding based on RHIC data on the dominant jet production from nucleus corona region, we reconsider this effect in nucleus–nucleus collisions at the LHC energies. Our hypothesis was based on experimental data, which raised the idea of a finite formation time for the produced medium. At the RHIC energy and in low-density corona region, this time reaches about 2 fm/c. Following this hypothesis, the nuclear modification factor R _AA at high p _t should be independent on particle momentum, and the azimuthal anisotropy of high p _t particles, v ₂, should be finite. A separate prediction held that, at the LHC energy, the formation time in the corona region should be about 1 fm/c. New LHC data show that R _AA is not flat and is rising with p _t . We add to our original hypothesis an assumption that a fast parton traversing the produced medium loses the fixed portion of its energy. A shift of about 7 GeV from the original power law p ^?6 production cross section in pp explains well all the observed R _AA dependencies. The shift of about 7 GeV is also valid at the RHIC energy. We also show that the observed at the LHC dependence of v ₂ at high p _t and our previous predictions agree.     

Fission dynamics of excited nuclei within the liquid-drop model

We evaluate the temperature T_scis at the scission point and the saddle-to-scission time τ_scis for the fission of heated nuclei. We use classical Lagrange-like equations of motion within the liquid-drop model. The nuclear surface is parameterized by a two-parameter family of the Lawrence shapes. Conservative forces are defined through the free energy of the nucleus at finite temperatures. We use the friction tensor that is derived from the Navier-Stokes momentum-flux tensor and which takes into account the boundary conditions at the nuclear surface. The scission line is determined from the instability condition of the nuclear shape with respect to variations of the neck radius. A numerical solution to the dynamical equations is obtained for the ²³⁶U nucleus. The viscosity coefficient μ is deduced from a comparison of experimental data on the kinetic energy of fission fragments with the computed one. It is found that μ obtained by using our approach deviates significantly from μ of the standard hydrodynamic model.     

Role of the nuclear and electromagnetic interactions in the coherent dissociation of the relativistic <Superscript>7</Superscript>Li nucleus into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

The differential cross section in the transverse momentum Q and a total cross section of (31 ± 4) mb for the coherent dissociation of a 3-A-Ge V/c ⁷Li nucleus through the ³H + ⁴He channel have been measured on emulsion nuclei. The observed Q dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction (Q ≤ 400 Me V/c) and Coulomb (Q ≤ 50 Me V/c) dissociations are calculated to be 40.7 and 4 mb, respectively.     

Proton production in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The momentum features of protons originating as fragments from ¹⁶Op interactions at 3.25 GeV/c per nucleon are analyzed for the first time under conditions of 4π geometry. It is found that the mechanisms of the production of all protons traveling in the forward direction in the rest frame of the fragmenting nucleus (with the exception of evaporated protons) do not depend on either the primary energy or the target-nucleus type, this regularity being quite universal for the formation of such protons. It is shown that there is a strong correlation between the shape of the momentum spectrum of protons appearing as fragments from such interactions, especially slow protons, and the degree of the excitation of the fragmenting nucleus.     

Experimental investigation of charge-exchange processes involving a target proton in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

For the first time, charge-exchange processes involving a target proton in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon are studied under conditions of 4π geometry. New data on the mean multiplicities fragments and pions, as well as on inelastic cross sections for topological channels of the fragmentation of an oxygen nucleus in charge-exchange reactions involving a target proton that either are accompanied or are not accompanied by charge transfer to a projectile nucleus, are presented. It is shown that, in ¹⁶Op interactions at high energies, charge transfer from a target proton to a projectile nucleus proceeds predominantly via inelastic proton scattering on a neutron of the oxygen nucleus.     

Unified Mechanism behind the Appearance of <Emphasis Type="Italic">T</Emphasis>-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJ_s neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

Special features of the <Emphasis Type="Italic">K</Emphasis> = 0 channel in nuclear fission

The opinion that the K = 0 fission channel is completely closed if the spin J and the parity π of the nucleus undergoing fission do not satisfy the condition (?1) ^J = π is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and π values such that they satisfy the condition (?1) ^J = π. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.     

<Emphasis Type="Italic">T</Emphasis>-odd angular asymmetry in nuclear reactions involving sequential particle emission

A triple T-odd angular correlation is considered in the kinematically similar reactions ¹⁰B(n, αγ) and ²³³U(n, αf) induced by cold polarized neutrons. It is shown that, in the former reaction, this correlation is suppressed by the double parity-conservation selection rule due to the two-step character of the process; however, T invariance does not impose any specific constraints on this correlation. The mechanism through which the T-odd correlation found in ternary-fission reactions is formed seems to be closely related to a nearly simultaneous disintegration of the nucleus involved into two fission fragments and an alpha particle.     

Inclusive deuteron production in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

Experimental data on inclusive deuteron production in ¹⁶Op collisions at high energies were obtained for the first time under conditions of 4π geometry. An irregularity in the momentum spectrum of deuterons in the rest frame of oxygen nuclei is found in the range 0.40 ≤ p ≤ 0.55 GeV/c, and the reasons for its appearance are discussed. The mean multiplicities of secondary fragments are correlated with the presence of deuterons in an event, these correlations being positive for fragments of charge in the range z _f ≤ 4 and negative for fragments of charge in the range 5 ≤ z _f ≤ 7. This is likely to be due to baryon-charge conservation.     

Cumulative production of three-nucleon nuclei in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The production of cumulative three-nucleon nuclei (³H and ³He) in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon were studied for the first time under conditions of 4π geometry. The slope parameter of the cross section for the production of cumulative three-nucleon nuclei was determined, and new data on correlations of the yields of A = 3 cumulative nuclei, charged particles, and fragments in ¹⁶Op interactions are reported. The properties of cumulative and noncumulative events were found to be substantially different, and evidence for the presence of a common universal feature in the mechanisms for the cumulative production of hadrons and light nuclear fragments was obtained.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.     

Dynamical screening of AMM and QED effects for large-<Emphasis Type="Italic">Z</Emphasis> hydrogen-like atoms

The effective interaction ΔU_AMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q² dependence of the electron formfactor F₂(q²)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ? 1/m. The ΔU_AMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔU_AMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ?Z_cr,1s. The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Near-threshold <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis>-meson photoproduction on nuclei

On the basis of the first-collision model that relies on the nuclear spectral function and which includes incoherent processes involving charmonium production in proton–nucleon collisions, the photoproduction of J/ψ mesons on nuclei is considered at energies close to the threshold for their production on a nucleon. The absorption of final J/ψ mesons, their formation length, and the binding and Fermi motion of target nucleons are taken into account in this model along with the effect of the nuclear potential on these processes. The A dependences of the absolute and relative charmonium yields are calculated together with absolute and relative excitation functions under various assumptions on the magnitude of the cross section for J/ψN absorption, the J/ψ-meson formation length, and their inmedium modification. It is shown that, at energies above the threshold, these features are virtually independent of the formation length and the change in the J/ψ-meson mass in nuclear matter but are rather highly sensitive to the cross section for J/ψN interaction. The calculations performed in the present study can be used to determine the unknown cross section for J/ψ-meson absorption in nuclei from a comparison of their results with data expected from experiments in the Hall C of the CEBAF (USA) facility upgraded to the energy of 12 GeV. It is also shown that the absolute and relative excitation functions for J/ψ mesons in photon–nucleus reactions at subthreshold energies are sensitive to the change in the meson mass and, hence, carry information about the properties of charmonium in nuclear matter.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Relationship between <Emphasis Type="Italic">T</Emphasis>-invariance and formation mechanisms for <Emphasis Type="Italic">T</Emphasis>-odd and <Emphasis Type="Italic">T</Emphasis>-even asymmetries in the angular distributions of fission fragments of oriented nuclei

The T-invariance condition was analyzed for the amplitude T _b,a of multiparticle multistep elastic or inelastic a → b nuclear reactions. This condition leads to the equality of the amplitude T _b,a to the amplitude \({\tilde T_{\bar a,\bar b}}\) of \(\bar b \to \bar a\) time-reversed reaction, for which the reaction operator \(\tilde T\) coincides with the inverse-reaction (b → a) operator. It is shown that, in the case where the original, inverse, and time-reversed reactions are governed by a common T-invariant mechanism, the coefficients D of asymmetries appearing in the differential cross sections for these reactions can be represented in the form of a unified scalar (pseudoscalar) function of arguments equal to the momentum and spin vectors of particles of the initial and final channels of the reactions under analysis. It is also shown that the use of the T-invariance condition for the coefficients D of asymmetries in the differential cross section for the original nuclear reaction that are different in P- and T-parity makes it possible to separate mechanisms leading to nonzero coefficients D for a number of the asymmetries under analysis from the remaining mechanisms leading to zero coefficients D of these asymmetries. It is proven that there exist such asymmetries in the differential cross section for the original reaction whose coefficients vanish for all possible T-invariant mechanisms of their appearance, so that, upon proving experimentally the appearance of nonzero coefficients of these asymmetries in the differential cross section for the original reaction, this fact can be used to assess features of T-noninvariant interactions in nuclear systems.