Vol 80, No 4 (2017)

A unitary version of the single-particle dispersive optical model was proposed with the aim of applying it to describing high-energy single-hole excitations in medium-heavy mass nuclei. By considering the example of experimentally studied single-hole excitations in the ⁹⁰Zr and ²⁰⁸Pb parent nuclei, the contribution of the fragmentation effect to the real part of the optical-model potential was estimated quantitatively in the framework of this version. The results obtained in this way were used to predict the properties of such excitations in the ¹³²Sn parent nucleus.

Fission barriers in nuclei belonging to the uranium region and their other characteristics are calculated on the basis of the FaNDF⁰ energy density functional. In particular, the neutron-separation energies S_n and S_2n, the proton-separation energies S_p, and the beta-transition energiesQ_β are calculated for uranium, neptunium, and plutonium isotopes. In addition, the deformation energies and parameters of these nuclei are presented along with their radii. A comparison with the predictions of the Skyrme–Hartree–Fock method implemented with several versions of the Skyrme energy density functionals is performed. The role of the octupole deformation β₃ is studied for the ²³⁸U nucleus. It is shown that this deformation does not have any significant effect on the first-barrier height B⁽¹⁾_f or ground-state properties. At the same time, the second-barrier height B(2) f decreases by a factor of about two upon taking into account β₃. A phase transition at A ~ 260 is found for the three isotopic chains being considered: this point is a bifurcation point at which B⁽¹⁾_f (A) forks into two curves. Of these, the curve B⁽²⁾_f (A) splits from it, prolonging the former curve for B⁽¹⁾_f (A) almost continuously, whereas the curve for B⁽¹⁾_f (A) itself goes down sharply.

A two-particle channel in which an unbound nucleus of ⁸Be in the ground state (⁸Be_g.s.) was one of the fragments was selected among events where ¹²C nuclei of momentum 4.5 GeV/c per nucleon undergo coherent dissociation into three alpha particles. The events in question were detected in a track nuclear photoemulsion containing lead nuclei, which was irradiated at the synchrophasotron of the Laboratory of High Energies at the Joint Institute for Nuclear Research (JINR, Dubna). The average transverse momentum of alpha particles produced upon the decay of ⁸Be_g.s. nuclei was 87±6 MeV/c, while that for “single” alpha (α_s) particles was 123±15 MeV/c. The average value of the transverse-momentum transfer in the reaction being considered, Pt(12C), was 223 ± 20 MeV/c. The average value of the cross section for this channel involving Ag and Br target nuclei was 13 ± 4 mb, while the cross section for the reaction on the Pb nucleus was 40 ± 15 mb. The Coulomb dissociation contribution evaluated on the basis of the number of events where the momentum P_t(¹²C) did not exceed 0.1 GeV/c saturated about 20%. In nine events, the measured total transverse energy of the fragments in the reference frame comoving with the decaying carbon nucleus did not exceed 0.45 MeV, which did not contradict the excitation of the participant ¹²C nucleus to the level at 7.65 MeV. The average value of the transverse momentum in those events was 234 ± 25 MeV/c.

The brief history of the development of investigations at the Skobeltsyn Institute of Nuclear Physics, Moscow State University (SINP MSU) in the field of space materials science is outlined. A generalized scheme of a numerical simulation of the radiation impact on spacecraft materials and elements of spacecraft equipment is examined. The results obtained by solving some of the most important problems that modern space materials science should address in studying nuclear processes, the interaction of charged particles with matter, particle detection, the protection from ionizing radiation, and the impact of particles on nanostructures and nanomaterials are presented.

An exponential form of the Pontecorvo–Maki–Nakagawa–Sakatamixingmatrix for neutrinos is discussed. This form makes it possible to separate the contributions of purely rotational components of the mixing matrix and elements that are responsible for CP violation. The logarithm of the mixing matrix and exact values for each parameter of the exponential neutrino mixing matrix are found on the basis of the most recent experimental data on neutrino mixing. The parameters of the real rotational part in the exponential representation of the mixing matrix and the parameters of its imaginary part, which is responsible for CP violation, are evaluated. The hypothesis of complementarity of quark and neutrino mixing is confirmed. Factorization in the form of the product of rotations about the real and imaginary axes is demonstrated.

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.

It is shown that the formation of primordialmassive black holes may be accompanied by a local heating of matter. The proposed heating mechanism is based on the interaction of the Higgs field with a scalar field that is responsible for the formation of black holes.

Sensitivity to anomalous ZZγγ and Zγγγ couplings in Zγγ production was probed for the ATLAS experiment at Large Hadron Collider. Zγγ process with anomalous couplings simulation in ppcollisions with √ s = 13 TeV was performed using VBFNLO MC generator. The expected limits on the Effective Field Theory parameters f_T0/Λ4, f_T5/Λ4, f_T9/Λ4, f_M2/Λ4, f_M3/Λ4 were extracted for 5 fb⁻¹ integral luminosity using the distribution on the invariant mass of Zγγ from the combination of charged leptonic decay channels of Z boson (Zγγ → μ⁺μ⁻γγ and Zγγ → e⁺e⁻γγ).

The classical Kepler–Coulomb problem on the single-sheeted hyperboloid H³₁ is solved in the framework of the Hamilton–Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.

We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, evenwhen the potential does not rise to infinity in every direction. It is shown that the logarithm of the energy displays levels contained in families that are analogous toWannier–Stark ladders. The position of each ladder is proved to be determined by the specific details of the potential and not by its transformation properties. This is done by direct computation of matrix elements. The results are compared with numerical solutions of the Schrödinger equation.

In this paper, the behavior of the few-body electron gas localized in a strongly prolate ellipsoidal quantum dot with the presence of the uniform external magnetic field has been investigated. Due to the specific geometry of the quantum dot it has been shown that the motion of the particles in the considered system can be separated into fast and slow, in the XOY plane and along the OZ direction respectively. Based on the adiabatic approach it has been shown that in the direction of the slow motion the electron gas is localized in the one-dimensional parabolic quantum well. If a long-wavelength radiation falls on the system, then due to the parabolic form of the confining potential, conditions occur to implement the generalized Kohn theorem for this system.

We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. We apply this method to investigate the Borel representation of the light Adler function constructed from the τ data and to determine the residual condensates. It is shown that within the method suggested the optimal values of these lower dimension condensates are close to zero.

A simple discrete model of the two-dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier polynomials. This adds to the other discrete superintegrable models of the oscillator based on Krawtchouk and Meixner orthogonal polynomials in several variables.

We review our recent work on gravitationally bound condensates formed by Hermitian bosons interacting with a potential energy Λ⁴[1 − cos(A/f)]. We have used an expansion method to simplify the equations of motion. The expansion parameters are the binding energy of the condensed bosons, and the ratio between the scale of the Bose field f and the Planck mass. Applying our analysis to QCD axions, we find that the condensates have a limiting mass of O(10¹⁹) kg and a size of O(100) km.

Defining the energy and work for particles interacting with electromagnetic field (EMF) is an open problem, because—due to the gauge-freedom—there exist various non-equivalent possibilities. It is argued that a consistent definition can be provided via the Lorenz gauge. To this end, I work out a system of two electromagnetically coupled classical particles. One of them is much heavier and models the source of work. The definition of energy in the Lorenz gauge is causal and consistent, because it leads to an approximate conservation law due to which the work done by the heavy particle (source of work) can be defined either via the kinetic energy of the heavy particle, or via the full time-dependent energy (kinetic + potential in the Lorenz gauge) of the light particle.