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.     

Determination of nuclear excitation energies from the number of evaporated particles

The mean number ?N_b〉 of particles evaporated in the interaction of ²²Ne, ³²S, and ⁵⁶Fe nuclei with photoemulsion nuclei was measured as a function of the number of alpha particles emitted within the fragmentation cone. It is found that ?N_b〉 decreases with increasing number of the alpha particles and increases with increasing number of projectile nucleons involved in the interaction with a target nucleus and that ? N_b〉 is a linear function of the excitation energy E_ex of the target-nucleus residue. The maximum experimental value of the mean number of evaporated particles is ?N_bmax〉 ? 12–13, which corresponds to E_exc ? 540 ± 60 MeV.     

Special features of the structure of the beta-stability line for nuclei

The mass-number (A) dependence Z _β(A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Z _expt ? Z _β are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously.     

Measurement of the azimuthal anisotropy coefficient <Emphasis Type="Italic">v</Emphasis><Subscript>2</Subscript> for the emission of α particles in nucleus-nucleus collisions at energies 1.88–10.6 GeV/nucleon

The azimuthal anisotropy of the emission of α particles in collisions of the ²²Ne, ²⁴Mg, ⁵⁶Fe, and ¹⁹⁷Au nuclei with photoemulsion nuclei has been measured at projectile energies E_pr = 1.88–10.6 GeV/nucleon. The results are compared with similar measurements for protons. It has been found that the ratio of the azimuthal anisotropy coefficients v₂ for α particles and protons is equal to 6 ± 2 at low energies E_pr ≈ 2 GeV/nucleon, whereas these coefficients coincide with each other for energies E_pr ≥ 4 GeV/nucleon. This difference may indicate that, at low projectile energies, α particles are formed predominantly at the early stage of a collective flow. Formation of α particles for E_pr ≥ 4 GeV/nucleon likely occurs at the stage of nuclear matter scattering.     

Production of cumulative deuterons in collisions of oxygen nuclei with protons at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The production of cumulative nuclei of ²H in ¹⁶O _p collisions at a momentum of 3.25 GeV/c per nucleon was studied for the first time under conditions of a 4π acceptance. The parameter T ₀ characterizing the slope of the spectrum of invariant cross sections for cumulative-deuteron production in ¹⁶Op interactions was determined. The contribution to cumulative-deuteron production from the decay of the alpha-particle clusters in nuclei upon slow-pion absorption by these clusters was found on the basis of an analysis of the momentum distribution of these cumulative nuclei. The estimates obtained for the contribution of these processes from a comparison of the mean multiplicities of particles and fragments in cumulative and noncumulative events agree well with the respective result extracted from the momentum distribution of cumulative deuterons.     

Formation of cumulative nuclei of <Superscript>4</Superscript>He 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 formation of cumulative nuclei of ⁴He in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon was investigated for the first time under conditions of 4π acceptance. The slope parameter of the invariant cross sections for the formation of cumulative nuclei of ⁴He was determined, and new data on the correlations between the yield of these cumulative nuclei and the yield of charged particles and fragments in ¹⁶Op interactions were obtained.     

Measurement of the elliptic flux of Z ⩾ 2 charged particles in collisions of relativistic nuclei with photoemulsion nuclei

The azimuthal asymmetry is measured for the emission of Z ≥ 2 particles from the interaction of ²²Ne, ²⁴Mg, ³²S, ⁵⁶Fe, ¹⁹⁷Au, and ²⁰⁷Pb nuclei with photoemulsion nuclei that is induced by semicentral collisions characterized by projectile energies in the range E _pr = 1.88–200 GeV per nucleon and by impact-parameter (b) values in the range 0.12 ≤ b/b _max ≤ 0.70. The results of these measurements are compared with the results of similar measurements for protons. It is found that, at a low energy of E _pr ≈ 2 GeV per nucleon, the ratio of the azimuthal-anisotropy coefficients v ₂ for Z ≥ 2 particles and protons is 6 ± 2, but that, for energies in the region E _pr ≥ 4 GeV per nucleon, the coefficients in question agree with each other. This may suggest that, at low energies, Z ≥ 2 particles are predominantly formed at an early stage of the development of a collective flow. For E _pr ≥ 4 GeV per nucleon, these particles are presumably formed at the stage of nuclear-matter expansion. Other possible explanations for the results of the observation of an elliptic flux of Z ≥ 2 particles are discussed.     

Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X^±Y^±Z^? consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X^±Y^±Z^? with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X^±X^±Z^?. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X^±X^±Z^?, which are stable at any particle masses, asymmetric trions X^±X^±Z^? possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t⁺d⁺p^? and t⁺d⁺d^? combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.     

PHENIX experiment: Recent results

An overview of the latest physics results obtained in the PHENIX experiment by studying pp, dAu, and AuAu interactions at √sNN = 200 GeV is given. Results of measurements of nuclear-modification factors, direct-photon production, and properties of light vector mesons and particles containing heavy c and b quarks are presented. These results are used to deduce information about the properties of dense parton matter produced in collisions of relativistic heavy nuclei at the Relativistic Heavy Ion Collider (RHIC).     

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.     

<Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript>-boson decays in a strong electromagnetic field

The probability of Z ⁰-boson decay to a pair of charged fermions in a strong electromagnetic field, Z ⁰ → \(\bar f\) f, is calculated. On the basis of a method that employs exact solutions to relativistic wave equations for charged particles, an analytic expression for the partial decay width Γ(?) = Γ(Z ⁰ → \(\bar f\) f) is obtained at an arbitrary value of the parameter ? = \(eM_Z^{ - 3} \sqrt { - (F_{\mu \nu } q^\nu )^2 } \), which characterizes the external-field strength. The total Z ⁰-boson decay width in an intense electromagnetic field, Γ _Z (?), is calculated by summing these results over all known generations of charged leptons and quarks. It is found that, in the region of relatively weak fields (? < 0.06), the field-induced corrections to the standard Z ⁰-boson decay width in a vacuum do not exceed 2%. As ? increases, the total decay width Γ _Z (?) develops oscillations against the background of its gradual decrease to the absolute-minimum point. At ?_min = 0.445, the total Z ⁰-boson decay width reaches the minimum value of Γ _Z (?_min) = 2.164 GeV, which is smaller than the Z ⁰-boson decay width in a vacuum by more than 10%. In the region of superstrong fields (? > 1), Γ _Z (?) grows monotonically with increasing external-field strength. In the region ? > 5, the t-quark-production process Z ⁰ → \(\bar t\) t, which is forbidden in the absence of an external field, begins contributing significantly to the total decay width of the Z ⁰ boson.     

Intergroup azimuthal correlations of secondary particles in the interaction between <Superscript>56</Superscript>Fe nuclei of momentum 2.5 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon and photoemulsion nuclei

Angular correlations between secondary particles emitted in the interaction between ⁵⁶Fe nuclei of momentum 2.5 GeV/c per nucleon and photoemulsion nuclei were measured. These secondaries are partitioned into four groups: s, g, b, and f. For particles from each pair of the above groups, the average values of the collinearity factor and of the asymmetry parameter, as well as the parameter η of the function α(1+η cos ε) approximating the distribution of azimuthal-angle differences ε, were calculated.     

New magic nuclei and conditions of their formation

The systematic studies of the arrangement features of single-particle nucleon subshells in even-even ^90,92,94,96Zr isotopes and behavior of some known “magicity parameters” in isotopes and isotones neighboring the ⁹⁶Zr nucleus have led to the interpretation of ⁹⁶Zr as a new doubly magic nucleus. Analysis of the structure of nucleon shells in the ⁹⁶Zr nucleus revealed a feature, which consisted in that near the Fermi energy it had filled proton (π1f _5/2) and neutron (v2d _5/2) subshells with an identical and large total momentum j = 5/2, which was called the j-j coupling. Above the π1f _5/2 shell, there is another filled shell (π2p _1/2) with two j = 1/2 protons. Applied to other filled shells, this empirical rule allowed revealing several new nontraditional magic nuclei: ⁹⁶Sr (Z = 38, N = 58), π1f _5/2, v2d _5/2, and v3s _1/2 subshells; ⁵⁴Ca (Z = 20, N = 34), π2p _3/2, v1d _3/2, and v2p _1/2 subshells; a pair of ³⁰Si (Z = 14, N = 16) and ³⁰S (Z = 16, N = 14) nuclei, π1d _5/2, v1d _5/2, and (π/v)2s _1/2 subshells; and a pair of ¹⁴C (Z = 6, N = 8) and ¹⁴O (Z = 8, N = 6) nuclei, 1p _3/2, v1p _3/2, and v2p _1/2 subshells. The existence of the magic nuclei ^52,54Ca is widely discussed in the literature, the possibility of the existence of the other nuclei found is confirmed by the systematics of the behavior of the “magicity” parameters. The fact that shells with some nucleon numbers different from the classical magic numbers are closed may be due to the manifestation of a new type of interaction between nuclear protons and neutrons occupying certain subshells.     

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even–even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number 160 ≤ N ≤ 204 are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter η and the relative neutron–proton asymmetry of the surface to the center (R _η ) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter η and the relative neutron–proton asymmetry R _η of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface, facets a superheavy nucleus for β^? decays.     

New neutron magic number <Emphasis Type="Italic">N</Emphasis> = 16 for neutron-rich nuclei

A survey of experimental results obtained at GANIL (Caen, France) on the study of the properties of very neutron-rich nuclei (Z=6–20, A=20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N=16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behavior of the two-neutron separation energies S_2n derived from mass measurements gives very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between the 2s_1/2 and 1d_3/2 orbitals. This fact, strongly supported by the instability of C, N, and O isotopes with N>16, confirms the magic character of N=16 for the region from carbon up to neon, while the shell closure at N=20 tends to disappear for Z≤13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using in-beam γ-ray spectroscopy are also reported.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Multicomponent <Emphasis Type="Italic">n</Emphasis>-(Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions with different atomic substitutions in the Bi and Te sublattices

The thermoelectric properties of n-Bi_{2 ? x} Sb _x Te_{3 ? y ? z} Se _y S _z solid solutions are studied in the temperature range 300–550 K. It is shown that an increase in the parameter β determining the figure-of-merit Z of the material is observed in compositions with the optimally related effective mass of the density of states m/m ₀, the carrier mobility μ₀, and the lattice thermal conductivity κ _L . Within the temperature range 300–350 K, the parameter β and the figure-of-merit Z are found to increase in solid solutions with substitutions in both bismuth telluride sublattices Bi → Sb and Te → Se, S (x = 0.16, y = z = 0.12) for optimum electron concentrations. An increase in the electron concentration and substitutions of atoms only in the tellurium sublattice bring about an increase in the β parameter and the value of Z at higher temperatures. Within the range 350–450 K, the parameters β and Z are observed to increase in a solid solution with a low content of substituted atoms in the tellurium sublattice Te → Se, S for y = z = 0.09 and, at higher temperatures up to 550 K, in compositions with tellurium substituted by selenium only, with increasing content of substituted atoms.     

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.     

Observables for possible QGP signatures in central <Emphasis Type="Italic">pp</Emphasis> collisions

Proton–proton (pp) data show collective effects, such as long-range azimuthal correlations and strangeness enhancement, which are similar to phenomenology observed in heavy ion collisions. Using simulations with and without explicit existing models of collective effects, we explore new ways to probe pp collisions at high multiplicity, in order to suggest measurements that could help identify the similarities and differences between large- and small-scale collective effects. In particular, we focus on the properties of jets produced in ultra-central pp collisions in association with a Z boson. We consider observables such as jet energy loss and jet shapes, which could point to the possible existence of an underlying quark-gluon plasma, or other new dynamical effects related to the presence of large hadronic densities.