Rotational energy and limits to fusion reactions between two nuclei

The energy balance of the fusion process between two nuclei is discussed with respect to the rotational energy. Two energy regimes are obtained. In the first regime the increase of rotational energy of the compound system as function of incident energy is governed by the moment of inertia of the two-fragment system at the barrier configuration. The faster increase of rotational energy of the compound system is furnished by theQ-value. In a sliding collision only part of theQ-value can be converted into rotational energy. Therefore, the Yrast limit in the population of the compound nucleus cannot be reached. When this source of energy is exhausted at a certain angular momentum, a second regime is obtained; then the increase of angular momentum and rotational energy as function of incident energy must be determined by the moment of inertia of the compound system.     

Ornstein-Uhlenbeck Limit for the Velocity Process of an N-Particle System Interacting Stochastically

An N-particle system with stochastic interactions is considered. Interactions are driven by a Brownian noise term and total energy conservation is imposed. The evolution of the system, in velocity space, is a diffusion on a (3N?1)-dimensional sphere with radius fixed by the total energy. In the N→∞ limit, a finite number of velocity components are shown to evolve independently and according to an Ornstein-Uhlenbeck process.     

On the variation of energy gaps in semiconducting alloy systems

The departure from linearity of energy gaps in a semiconducting alloy system is studied within the framework of virtual crystal approximation. Exact expressions for the slope of energy variation as function of composition x at the two ends x=0 andx=1 are derived. These can be evaluated theoretically with energy band calculation of the two pure materilas for a system. We discuss here several features of the slope.     

Ordering behaviors of the F.C.C. and B.C.C. phase alloys in the InMg,LiMg and AlZn systems

Expressions of the band-structure energy and the electrostatic energy characterized by the usual long-range and short-range order parameters are given to a binary alloy of simple metals with the f.c.c.-type or b.c.c.-type structure.The ordering energy and the local ordering energy are calculated for the InMg, LiMg and AlZn systems. The numerical results explain successfully the facts that the InMg system has the Ll₀-type and Ll₂-type ordered phases, each of which exists over a wide range of concentration and that the LiMg system has a local order with a negative short-range order parameter, while the AlZn system has that with the positive one. A lattice distortion in the Ll₀-type ordered structure of InMg is also discussed.     

Probe-type time-of-flight momentum and energy mapping system

A new time-of-flight (TOF) momentum and energy mapping system is proposed. The system consists of two sub-regions with different axial uniform decelerating field. Two position-sensitive detectors (PSDs) on opposite side of the tube are used for the detection of electrons with different axial motion length due to their initial energy ? and emission angle θ. A non-monotonic dependence of energy-resolving performance on electron initial energy can be achieved by choosing appropriate electric field deceleration for these two sub-regions, which forms an “energy resolution probe” possessing a higher level of energy resolution than that of lower energy part. And the local resolution in the probe region could be specifically enhanced while the other parts of all the detection range do not change so much. It is verified by the illustrating example with relative energy resolution Δ?/? smaller than 0.5% for electron energy in probe range from 36 eV to 45 eV.     

Study of the energy level structure for the isoelectronic series of scandium-like ions

The structure of the energy level system for 39 ions of the scandium isoelectronic sequence is studied on the basis of the relativistic self-consistent field method taking into account the configuration interaction. The Dirac-Fock equations are solved with subsequent diagonalization of the energy matrix. The ground-state ionization potentials are determined for each ion. The energy levels corresponding to the 3d4s ², 3d ²4s, and 3d ₃ configurations are also calculated. The obtained energy values are compared with the experimental data as well as with the results of calculations carried out by other authors.     

Onset of nuclear matter expansion in Au+Au collisions

Using the FOPI detector at GSI Darmstadt, excitation functions of collective flow components were measured for the Au+Au system, in the reaction plane and out of this plane, at seven incident energies ranging from 100A MeV to 800A MeV. The threshold energies, corresponding to the onset of sideward-flow (balance energy) and squeeze-out effect (transition energy), are extracted from extrapolations of these excitation functions toward lower beam energies for charged products with Z ⩾ 2. The transition energy is found to be larger than the balance energy. The impact parameter dependence of both balance and transition energies, when extrapolated to central collisions, suggests comparable although slightly higher values than the threshold energy for the radial flow. The relevant parameter seems to be the energy deposited into the system in order to overcome the attractive nuclear forces.     

On distance variation effects on graphene bilayers

The opening of the energy gap and the total energy of the graphene-like bilayers are investigated using ab initio calculations. The studied model consists of a static single layer of graphene interacting with an extra dynamic one placed at a varying vertical distance d in the (AB) stacking arrangement. The effects of the vertical distance variation on the energy gap and the total energy of the system are discussed first. Starting from a distance around the van der Waals length, the energy gap does not depend on the vertical distance variation and the system exhibits graphene-like properties with minor deformations in the lattice size parameter and the energy dispersion behaviour around K points. However, it has been shown that the diagonal distance variation of the graphene-like bilayer modifies the electronic structure properties. This modification depends on an intermediate stacking arrangement between the (AA) and the (AB) configurations. It has been shown that the diagonal distance variation has an influence on the states of p_z electrons in the (AB) arrangement and it can be explored to open the energy gap.     

On the theory of elastic scattering of slow particles at a 2D potential

A theory is proposed for scattering of particles with a low energy E at an arbitrary 2D potential. This problem is solved using the expansion in the system of zero-energy eigenfunctions. Explicit expressions are obtained for the s-scattering amplitude and for the energy levels of weakly coupled s states. The general formulas derived here are illustrated with an exactly solvable example.     

Inelastic effect in low energy ion-surface collisions: He+Au,Ag

Energy distributions of He⁺ ions scattered by Au and Ag surfaces are measured by an ISS system with high energy resolution, at a scattering angle of 90° and at incident ion energies ranging from 277 to 977 eV. It is found that the observed peak energies deviate toward the low energy side by several electron-volts with respect to the calculated elastic single collision energies. Both the deviation Q' and the inelastic loss energy Q are plotted as a function of incident ion energy for the Au surface.     

Chaotic motion at the emergence of the time averaged energy decay

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the N environment oscillators and becomes chaotic in the interval 13≤N≤15, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of N the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidence shows the connection between the variations of the amplitude of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.     

Superconductivity in the system of p electrons

The problem of superconductivity in an electron system with partly filled sp shell is studied. The scattering amplitudes are determined and the equations of superconductivity are derived from the assumption that the Hubbard energy is the largest energy parameter.     

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.     

Conservation laws of generalized billiards that are polynomial in momenta

This paper deals with dynamics particles moving on a Euclidean n-dimensional torus or in an n-dimensional parallelepiped box in a force field whose potential is proportional to the characteristic function of the region D with a regular boundary. After reaching this region, the trajectory of the particle is refracted according to the law which resembles the Snell -Descartes law from geometrical optics. When the energies are small, the particle does not reach the region D and elastically bounces off its boundary. In this case, we obtain a dynamical system of billiard type (which was intensely studied with respect to strictly convex regions). In addition, the paper discusses the problem of the existence of nontrivial first integrals that are polynomials in momenta with summable coefficients and are functionally independent with the energy integral. Conditions for the geometry of the boundary of the region D under which the problem does not admit nontrivial polynomial first integrals are found. Examples of nonconvex regions are given; for these regions the corresponding dynamical system is obviously nonergodic for fixed energy values (including small ones), however, it does not admit polynomial conservation laws independent of the energy integral.     

The many-body problem with an energy-dependent confining potential

We consider systems of N bosons bound by two-body harmonic interactions, whose frequency depends on the total energy of the system. Such energy dependent confining interactions between the bosons yield remarkable properties of the many-body system. As the quantum numbers increase, the total energy cannot exceed a saturation energy, which is independent of the number of particles N. Moreover, the ground state energy increases with N. As a result, the density of states tends rapidly to infinity as N and/or the quantum numbers increase.     

Ground state of an impurity in a homogeneous system in the hypernetted chain approximation

The hypernetted chain theory of the ground state of a homogeneous N-particle medium NM with an impurity particle is presented. The N identical particles are fermions with spin-isospin degeneracy ν, or bosons (in the limit of ν → ∞). The ground-state wave-function of the system is assumed in the Jastrow form with central, state-independent correlation functions. Central, spin-isospin-dependent two-body interactions both in NM and between the impurity particle and the particles of NM are considered. Expressions for the ground-state energy of the system and for the separation energy of the impurity particle are derived. The simplified case of the chain approximation is also considered.     

Quantitative energy level correlations for linear,bent and internally rotating triatomic molecules

This paper is concerned with the study of the quantitative correlation of the rotation-bending energy levels of a linear or bent triatomic molecule with the energy levels of the molecule when there is free internal rotation of a diatomic fragment [as in, for example, Ar(HCl)]. The LiNC and KCN molecules are used as model systems. A correlation parameter γ_r is introduced to quantify the position a molecule occupies in these correlation diagrams; this parameter has the value +1 for an ideal bent molecule, ?1 for an ideal linear molecule, and ?3 for an ideal free internal rotor triatomic molecule. The rotation-bending energy levels of the HCN-HNC isomerization system, and of the double minimum HO₂ system, are also studied.     

Energy scale calibration of the KEDR tagging system

The KEDR detector tagging system is a symmetric focusing magnetic spectrometer of small-angle electrons born in the interaction region of the VEPP-4M collider. Using this system, which is designed for studying the two-photon processes, the scattered electrons and positrons energy is measured with a resolution of ΔE/E₀= 0.03–0.6% where E₀ is the beam energy. Two different methods are employed for calibrating the tagging system energy scale: the first one involves the electron/positron tagging by the energy of the singlebremsstrahlung photon measured in the BGO calorimeter, and the second one is based on the determination of the recoil electrons spectrum edge in the Compton backscattering of monochromatic laser radiation. The technical implementation and the present status of the calibration system are discussed in this paper.     

Time reversal violation in the nuclear interaction and p-3He scattering

Using T-violating boson-exchange interactions T-violating effects in low energy p-³ He scattering are calculated. The results are below 10^?3 even for full strong (not millistrong) T-violation in the nucleon-nucleon system. It is argued, that the smallness of the effects is not a particularity of the p-³He system but a general property of low energy processes.     

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

We use an infinite-range Maier–Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic–isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling J. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature T. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.