Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

The 3–3–1 Model with RH Neutrinos and Associated ZH Production at High-Energy ${\bf \textit{e}}^{+}{\bf \textit{e}}^{-}$ Collider

In the context of SU(3) _C ?? SU(3) _L ?? U(1) _X (3–3–1) model with right-handed neutrinos, we study the Higgsstrahlung process e ^?+? e ^???→ZH and calculate the cross section of this process at leading order. Our numerical results showed that the production cross sections for this process can be significantly large as \(M_{Z'}\approx \sqrt{s}\). With reasonable values of the Z′ mass M _Z′, Z′ exchange can generate large corrections to the cross sections of this process, which might be detected in the future high-energy linear e ^?+? e ^??? collider experiments.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Quantum correlations from classical Gaussian correlations

Already Schrödinger tried to proceed towards a purely wave theory of quantum phenomena. However, he should give up and accept Born’s probabilistic interpretation of the wave function. A simple mathematical fact was behind this crucial decision. The wave function of a composite system S = (S ₁, S ₂) belongs to the tensor product of two L2 spaces and not to their Cartesian product. It was impossible to consider it as a vector function ψ(x) = (ψ ₁(x), ψ ₂(x)), x ∈ R ³. Here we solved this problem. It is shown that there exists a mathematical formalism that provides a possibility to describe composite quantum systems without appealing to the tensor product of the Hilbert state space, and one can proceed with their Cartesian product. It may have important consequences for the understanding of entanglement and applications to quantum information theory. It seems that “quantum algorithms” can be realized on the basis of classical wave mechanics. However, the interpretation of the proposed mathematical formalism is a difficult problem and needs additional studies.     

Optical-Information Transfer Through Perturbing Media and Determination of the Transfer Function

A version of the solution of the problem of simultaneous determination of the structure and characteristics of a two-dimensional signal and of two-dimensional complex transfer or instrumental functions is considered. The solution is based on measurements of four independent intensity distributions for spectral representation of a signal: I_sr(W_x, W_y) for a signal subjected to the transfer function, I_smrn(W_x, W_y) for a signal affected by additional specially produced modulation and the transfer function, I_srn(W_x, w_y) for a signal of the form I_sr(W_x, W_y) with a certain additional modulation at the output, and /₅mm(w_x,u/_y) for a signal of the form I_smr(W_x, W_y) with a certain additional modulation at the output. The intensity distributions obtained in the work make it possible to calculate the amplitude and phase components of the signal being analyzed and the transfer function. Additional modulations should provide visualization of phase information in one form or another.Linear amplitude modulation, which represents a particular form of spatial modulation, is analyzed. For this case, concrete expressions making it possible to calculate the amplitude and phase characteristics of the spectra of the signal being analyzed and the transfer function and, therefore, the characteristics of both the signal itself and the transfer function are obtained.     

Generic Representation of Y(so(3)) Based on the Lie Algebraic Basis of so(3)

We focus on constructing a generic representation of Y(so(3)) based on the Lie algebraic basis of so(3) basis, and further developing transition of Yangian operator \(\hat {\mathbf {Y}}\). As an application of Y(so(3)), we calculate all the matrix elements of unit vector operators \(\hat {\mathbf {n}}\) in angular momentum basis. It is also discovered that the Yangian operator \(\hat {\mathbf {Y}}\) may work in quantum vector space. In addition, some shift operators \(\hat {O}^{(\pm )}_{\mu }\) are naturally built on the basis of the representation of Y(so(3)). As an another application of Y(so(3)), we can derive the CG cofficients of two coupled angular momenta from the down-shift operator \(\hat {O}^{(-)}_{-1}\) acting on a so(3)-coupled tensor basis. This not only explores that Yangian algebras can work in quantum tensor space, but also provides a novel approach to solve CG coefficients for two coupled angular momenta.     

Two-loop self-energy correction in a strong Coulomb nuclear field

The two-loop self-energy correction to the ground-state energy levels of hydrogen-like ions with nuclear charges Z≥10 is calculated without the Zα expansion, where α is the fine-structure constant. The data obtained are compared with the results of analytical calculations within the Zα expansion; significant disagreement with the analytical results of order α²(Zα)⁶ has been found. Extrapolation is used to obtain the most accurate value for the two-loop self-energy correction for the 1s state in hydrogen.     

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.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

On a modified separation method for nuclear potentials

In order to obtain a regular but energy-dependent nuclear potential, the following modification of the separation method ofMoszkowski andScott is used: we replace the nuclear potentialv _c (r) by a long-range potentialv _l (r)=v _c (r) Θ(r? d ₀) together with a short-range energy dependent repulsionv _s =h(k) Θ(r _c ?r), whered ₀ is the separation distance for vanishing energy andr _c is the hard-core radius. The potentialv=v _s +v _l (r) is fitted to theS-wave scattering data and the binding energy of the deuteron.h(k) turns out to be almost proportional to the scattering energyE _rel for energiesE _rel<150 MeV.     

Analyse von Hyperfeinstrukturen des Eu151, Am241 und einiger 3 d-Elemente mittels „Exchange Polarization“

It is shown how several discrepancies in the optical hfs of the Eu can be understood as consequences of the exchange polarization of the inner and outers-electrons by the spin of the half filled (4f ⁷)-subshell, an effect which should produce additional magnetic fields at the nucleus. Thus from the two different values of the electronic splitting constanta _6s in the two Eu-II ground states the polarization field from the 6s-shell (Δ H _6s ) is determined to be ca. +260 KG, and the formal splitting constantσ (??3 mK) of the (4f ⁷)-subshell yields ca. ?350 KG for the fieldΔ H _(1?5) from the five innern s-shells (n=1?5) in good agreement with the strength of the inner field obtained from recent Mössbauer effect studies.Δ H _(1?5) is deduced to be approximately equal in all sufficiently analysed ground and excited configurations of the neutral and ionised Eu atom ((4f ⁷) 6s, 6p, 5d, 6s ² and 6s 6p). Other elements with half filled subshells (Am, Mn) show similar features in their optical hfs. For Am⁺ ((5f ⁷) 7s) ca. ?2200 KG are found for the inner field (Δ H _(1?6)). For several 3d-elements it was found that the agreement between the calculated polarization fields and those following from experimental results is better than assumed so far.     

Optical properties of lithium niobate and lithium tantalate crystals with impurities and defects

The photoinduced and Raman scattering in lithium niobate and lithium tantalate crystals with impurities and defects have been studied. An exciting laser beam propagated either along the ferroelectric Z axis or perpendicular to it. The conditions for exciting transverse and longitudinal polar optical modes in Raman spectra are established. The regularities of the excitation of Raman spectra in several polarization geometries (X(ZZ)Y, Z(XX, Y Y)Z, Z(XX, Y Y)Z, X(ZX)Y, X(ZX)X and X(ZX)X) have been investigated. Additional (extra) spectral lines are interpreted as a manifestation of a biphonon enhanced by the Fermi resonance and the result of violation of selection rules for pseudoscalar modes of the A ₂ type due to the reduction of the point symmetry group caused by the presence of impurities and defects in real crystals. The conditions for exciting coherent longitudinal and transverse modes in lithium niobate and lithium tantalate single crystals upon stimulated Raman scattering are analyzed. The temperature evolution of the spectra recorded in the X(ZZ)Y geometry near the ferroelectric phase transition point is explained based on the concept of effective soft mode and analysis of the isofrequency opalescence effect. Strong photoluminescence is found in copper-doped lithium niobate crystals.     

Thermooptical and Dielectric Studies of a Calcium-Induced Ferroelectric Phase in a SrTiO<Subscript>3</Subscript> Incipient Ferroelectric

We have examined temperature changes of the light refraction, birefringence, dielectric permittivity, and dielectric hysteresis loops in Sr_{1 – x}Ca_xTiO₃ single crystals with x = 0.014 (SCT-1.4). The dielectric properties of Sr_{1 – x}Ca_xTiO₃ with x = 0.007 (SCT-0.7) have been studied. We have performed ab initio calculations of equilibrium structures and total energies for three low-temperature phases of SrTiO₃ and CaTiO₃, based on which we have determined an expected symmetry of the ground state of their solid solution and spontaneous polarization directions in a calcium-induced ferroelectric phase in Sr_{1 – x}Ca_xTiO₃. In SCT-1.4, we have separated a spontaneous contribution to the light refraction, which arises due to the spontaneous electrooptical effect caused by the spontaneous polarization and its fluctuations. From the spontaneous contribution to the light refraction, based on a previously developed our phenological approach, we have quantitatively determined for the first time the values and temperature dependences of root-mean-square fluctuations of the order parameter—the polarization P_sh = 〈P _fl ² 〉^1/2(short-range, local polar order) in the ferroelectric phase. From optical and dielectric measurements in SCT-1.4, the average value of spontaneous polarization P_s (the contribution from the long-range order) has been determined. We have estimated the values of P_sh and P_s, which characterize the short- and long-range orders in the ferroelectric phase of SCT-0.7. Separate determination of the values and temperature dependences of P_s and P_sh (which considerably exceeds the value of P_s in the ordered phase) has allowed us to reveal on a quantitative level new particular features of the formation of the induced polar phase in Sr_{1 – x}Ca_xTiO₃.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Phenomenology of light- and strange-quark simultaneous production at high energies

This letter presents an extension of EPL116(2017)62001 to light- and strange-quark nonequilibrium chemical phase-space occupancy factors (γ_q,s). The resulting damped trigonometric functionalities relating γ_q,s to the nucleon-nucleon center-of-mass energies (\(\sqrt {{s_{NN}}} \)) looks very similar except different coefficients. The phenomenology of the resulting γ_q,s(\(\sqrt {{s_{NN}}} \)) describes a rapid decrease at \(\sqrt {{s_{NN}}} \) ? 7GeV followed by a faster increase up to ~20 GeV. Then, both γ_q,s become nonsensitive to \(\sqrt {{s_{NN}}} \). Although these differ from γ _s (\(\sqrt {{s_{NN}}} \))obtained at γ _q (\(\sqrt {{s_{NN}}} \))=1, various particle ratios including K⁺/π⁺, K^?/π^?, Λ/π^?, Λ?/π^?, Ξ⁺/π⁺, and Ω/π^?, can well be reproduced, as well. We conclude that γ_q,s(\(\sqrt {{s_{NN}}} \)) should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio K⁺/π⁺.     

Collision between two ortho-positronium (Ps) atoms: A four-body Coulomb problem

The elastic collision between two ortho-positronium (e.g. S = 1) atoms is studied using an ab-initio static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment S = 0, i.e., singlet (+) and S = 2, i.e., triplet (?) states are studied. An augmented Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section (σ), the quenching cross-section (σ_q) and ortho-to-para conversion ratio (σ/σ_q). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.