Dynamic hyperpolarizabilities of excited states of hydrogen

On the basis of the generalized Sturm expansion of the radial part of the Coulomb Green function, a computational method is proposed and numerical results are presented for the dynamic hyperpolarizability γ and the corrections E ⁽⁴⁾ (quadratic in the light intensity) to the quasi-energy of the ground and excited states of hydrogen with principal quantum numbers n≤5 in a monochromatic light field. In this approach, the problem is reduced to the summation of well-convergent double series of the hypergeometric kind, which ensures reliable numerical results both for states with a large n, and in a wide range of field frequencies ω, including the above-threshold frequency range of ?ω?|E _n | (|E _n | is the ionization potential of the state |nlm〉 under investigation). We consider the frequency dependence of γ and E ⁽⁴⁾, their differences for the cases of linear and circular polarizations of the field, and the relation between their real and imaginary parts, which determine the laser field-induced corrections to the position and width of energy levels. For n=5, the significant role of mixing the |nlm〉 states with different values of l by a laser field in the region of resonances on intermediate bound states is demonstrated. The linear (in intensity) corrections to the photoionization cross section for excited states are analyzed and the threshold intensity corresponding to the onset of atomic level stabilization is estimated for a number of states with n=3 and n=5.

     

On semiclassical four‐point correlators in AdS5 × S5

Following the recent advances in the holographic calculation of n‐point correlation functions with two “heavy” (with large quantum numbers) states at strong coupling, we extend these findings by computing specific contributions to four‐point correlators of four heavy BMN operators in �� = 4 supersymmetric Yang–Mills theory.     

Retardation effects: Localized excitations of a soliton in a model of a one-dimensional electron-phonon (Peierls) system

A set of localized mixed electron-phonon excitations has been found in the “quantum” regime M < K²/2C(g²+2KB) = M_c. We suggest that the spectrum is related to possible bound states of ions in the Coulomb field of the charge soliton for sufficiently light ions.     

Bound states of heavy quarks on the light plane

We investigate in detail the light plane formulation of bound state equations and of the interactions of bound states. This formalism is particularly well suited to discuss bound states of heavy quarks since these states can be well approximated as two particle states but yet there are significant relativistic corrections to the conventional nonrelativistic approach. Applications are made to electromagnetic decays of charmonium (ψ→e ⁺ e ^?, η _c →γγ, ψ′→η _c γ, etc.).     

Fragmentation of heavy quarks in polarized quarkonium in the effective heavy quark theory

Fragmentation of abantiquark into polarized B_c ^* mesons has been studied within the framework of the effective theory of heavy quarks. The functions ofb fragmentation into longitudinally polarized and transversely polarizedb S-wave states have been calculated with precise account for corrections of the first order in 1/m_b. The results are shown to agree with the corresponding calculations in quantum chromodynamics. Samara State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, p. 97–104, July, 1996.     

Spectroscopy and Regge trajectories of heavy quarkonia and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> mesons

The mass spectra of charmonia, bottomonia and B _c mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. The dynamics of heavy quarks and antiquarks is treated fully relativistically without application of the nonrelativistic v ²/c ² expansion. The known one-loop radiative corrections to the heavy quark potential are taken into account perturbatively. The heavy quarkonium masses are calculated up to rather high orbital and radial excitations (L=5, n _r =5). On this basis the Regge trajectories are constructed both in the total angular momentum J and radial quantum number n _r . It is found that the daughter trajectories are almost linear and parallel, while parent trajectories exhibit some nonlinearity in the low mass region. Such nonlinearity is most pronounced for bottomonia and is only marginal for charmonia. The obtained results are compared with the available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.     

Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

Kondo scattering and properties of TmSe in the infrared region

The conductivity and permittivity spectra of the intermediate-valence semiconductor TmSe have been measured by terahertz and infrared spectroscopy in a frequency range of 10–10⁴ cm^?1 and a temperature range of 5–300 K. At low temperatures (5 K < T < 100 K), the spectra contain a gap Δ ≈ 2.5 meV, whose appearance is considered to be related to conduction-electron localization at local magnetic moments. At high temperatures (100 K < T < 300 K), the dielectric response is specified by two electronic components: “ light” conduction electrons and “heavy” hybridized f-d states. The microscopic parameters of both components, such as the concentration, mobility, effective mass, relaxation frequency, and the plasma frequency, are determined.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

Influence of external factors on the self-organization of lead and tin telluride nanostructures on the BaF2(111) surface under conditions close to the thermodynamic equilibrium

The morphology of PbTe and SnTe nanostructures grown on BaF₂(111) substrates from the vapor phase in a vacuum under conditions close to the thermodynamic equilibrium has been investigated using atomic force microscopy. The equilibrium shape of PbTe and SnTe quantum dots and the statistical parameters of arrays of these quantum dots have been studied as a function of the thermodynamic conditions of growth, the crystal lattice mismatch between the materials of the quantum dots and substrate, and elastic properties of these materials. It has been established that, when the BaF₂(111) substrate is deformed under external mechanical loading, the self-organization of dislocations on the BaF₂(111) surface can result in the formation of a nanoscale ordered strain relief, which can be used for the fabrication of nanostructures. The morphology of this relief depends on the external load and on the temperature at which the substrate is deformed. It has been shown that the deformation effect on the surface of the substrate and light irradiation of the growth zone of nanostructures affect the nucleation of islands and kinetic processes occurring on the surface of the substrate during their growth. Using the influence of external factors on the BaF₂(111) surface under certain thermodynamic conditions, it is possible to grow SnTe and PbTe nanostructures with different morphologies: continuous epitaxial layers with a thickness of less than 10 nm, homogeneous arrays of quantum dots with a high lateral density (more than 10¹¹ cm²), quasi-periodic lateral nanostructures (nanowires), “single” and “coupled” quantum dots, and “molecules” of quantum dots.

     

Large-scale collective motion in heavy-ion collisions

Heavy-ion fusion and deep inelastic reactions have been studied for symmetric systems in a classical dynamical model with deformation and necking as the collective shape coordinates. The calculated fusion excitation functions (for compound nucleus formation) are in good agreement with the experimental results from the evaporation residue measurements. It is observed that “nuclear molecules” are formed for not too heavy systems. The calculated reaction time for collisions of very heavy ions like ²³⁸U + ²³⁸U is found to be ~10⁻²¹ sec only and thus the width of the positron spectra observed in these reactions can not be explained in the light of quantum electrodynamics. The extra-extra push energies for fusion of heavy nuclei have also been studied.     

Mixing of excitonic states containing light and heavy holes in an isolated GaAs/AlGaAs quantum well in a magnetic field

The Zeeman splitting of the ground states 1s(hh) and 1s(lh) of excitons with heavy and light holes, respectively, in a 15-nm isolated Al_0.3Ga_0.7As/GaAs quantum well in magnetic fields of up to 20 T is investigated according to the photoluminescence excitation spectra in the Faraday geometry (σ⁺− σ⁻ components). The observed anomalous pattern of nonlinear Zeeman splitting and the nonmonotonic behavior of the effective hole g factor are interpreted in terms of the strong mixing of the magnetoexcitonic states containing light and heavy holes. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 52–56 (10 July 1996)     

A Migdal-Kadanoff renormalization-group approach for the XY spin glass

Superconducting rings with mesoscopic Josephson junctions are considered in the presence of a do voltage bias V _o and of non-classical electromagnetic fields (coherent states, squeezed states, number eigenstates etc.). Due to the quantum nature of these devices the current I is a quantum mechanical operator and therefore «I²» is in general different from «I»². Using «I ²» we define the rms current I _rms, and using the various harmonics of «I» as if they belong to a classical current we define the “classical rms current” I _{rms, class}. In the case of classical currents these two quantities are identical, but for quantum currents they are different. We study their difference for various non-classical fields, and find that in some cases this difference is large. These predictions could be observed experimentally through the electromagnetic power that these currents radiate. An experiment that confirms the I _rms and refutes the Irms, class would prove the quantum nature of these currents.     

Electronic structures of the zinc-blende GaN/Ga1−xAlxN compressively strained superlattices and quantum wells

The electronic structures of the zinc-blende GaN/Ga_0.85Al_0.15N compressively strained superlattices and quantum wells are investigated using a 6×6 Hamiltonian model (including the heavy hole, light hole and spin-orbit splitting band). The energy bands, wavefunctions and optical transition matrix elements are calculated. It is found that the light hole couples with the spin-orbit splitting state even at thek=0 point, resulting in the hybrid states. The heavy hole remains a pure heavy hole state atk=0. The optical transitions from the hybrid valence states to the conduction states are determined by the transitions of the light hole and spin-orbit splitting states to the conduction states. The transitions from the heavy hole, light hole and spin-orbit splitting states to the conduction states obey the selection rule Δn=0. The band structures obtained in this work will be valuable in designing GaN/GaAlN based optoelectronic devices.     

Topological pomeron andA-universality

The nuclear mass number dependence of inclusive spectra of secondaries with different quantum numbers in the projectile fragmentation region is analysed. We note that in models with topological pomeron, all the particle spectra fall into two main categories. The first one comprises particles which have a common “valence” quark with the projectile, the second one comprises all the other particles built of “sea” quarks. Thus, in the parameterization \(x\frac{{d\sigma }}{{dx}} \propto A^{\alpha (x)} \) the spectra of all “valence” hadrons (p, n, Λ, π^+,0,?,K ⁺, ... in thepA-interaction) atx→1 can be characterized by the single exponent α_υ =α(x?1) which differs slightly from α _s characterizing the spectra of “sea” hadrons ( \(\bar p, \bar \Lambda \) ,K ^?, ... forpA-interactions). This observation is essentially modelindependent and follows only from the topological structure of the pomeron and Gribov's space-time picture of soft hadronic interactions. Deviations from universality due to preasymptotic corrections and coherent particle production processes are estimated.     

Mass and lifetime limits on new long-lived particles in 300 GeV/c π− interactions

A sensitive search has been done for the production of new long-lived and penetrating particles by 300 GeV/c negative pions. No new state —decaying into at least two charged known particles —has been detected with mass above 1 GeV/c² and lifetime in the range 5·10^?11 s to 5·10^?7s. We give upper limits on production cross sections, and consequences on the existence of heavy “axion-like” particles, heavy neutrinos and supersymmetric particles. In particular, this experiment excludes the existence of light gluinos with lifetime in the range 5·10^?11 to 10^?8s: this closes the last “window of opportunity” for gluinos withM<2 GeV/c² and lifetime measurable in particle physics experiments.     

Optical spectra of (CdF2)0.9(InF3)0.1 semiconductor solid solutions

The differences in the optical spectra of CdF₂:In semiconductors with bistable DX centers (concentrated (CdF₂)_0.9(InF₃)_0.1 solid solutions) and “standard” samples with a lower impurity concentration used to record holograms are discussed. In contrast to the standard samples, in which complete decay of two-electron DX states and transfer of electrons to shallow donor levels may occur at low temperatures, long-term irradiation of a (CdF₂)_0.9(InF₃)_0.1 solid solution by UV or visible light leads to decay of no more than 20% deep centers. The experimental data and estimates of the statistical distribution of electrons over energy levels in this crystal give the total electron concentration, neutral donor concentration, and concentration of deep two-electron centers to be ～5 × 10¹⁸ cm^?3, ～9 × 10¹⁷ cm^?3, and more than 1 × 10²⁰ cm^?3, respectively. These estimates show that the majority of impurity ions are located in clusters and can form only deep two-electron states in CdF₂ crystals with a high indium content. In this case, In³⁺ ions in a limited concentration (In³⁺ (～9 × 10¹⁷ cm^?3) are statistically distributed in the “unperturbed” CdF₂ lattice and, as in low-concentrated samples, form DX centers, which possess both shallow hydrogen-like and deep two-electron states.     

Spectroscopic study of an rf discharge in nitrogen

The absolute populations of the vibrational levels of the B³Πg and C³Π_u states in an rf nitrogen discharge are calculated from the quantum yields of the 1⁺ and 2⁺ systems in the discharge, and the “excitation temperature” of these states is measured. Emission spectroscopic methods are used to determine the vibrational and rotational temperatures of the C³Π_u state, as well as the vibrational temperature of the B³Π_g state. These data are used to estimate the vibrational temperature of the X′∑ _g ⁺ state and the stored energy in the activated nitrogen, and to examine the mechanism by which translational-vibrational degrees of freedom are excited in nitrogen molecules in the discharge.     

Some non-perturbative semi-classical methods in quantum field theory (a pedagogical review)

A pedagogical introduction is given to non-perturbative semi-classical methods for finding solutions to quantum field theories. Both the weak coupling method based on a time-independent classical solution, and the WKB method based on all periodic orbits are developed in detail, proceeding ffrom elementary quantum mechanics to field theory in stages. Both methods are then illustrated in model field theories. The [λø⁴]₂ theory to which the weak coupling method is applied yields a new family of “kink” states whose properties are discussed.The WKB method is illustrated by quantizing “soliton” and “doublet” solutions of the two-dimensional sine-Gordon theory. The results are compared to consequences of Coleman's equivalence proof relating this system to the massive Thirring model. The speculation that solitons may be fermions is discussed, along with indications that the WKB method may ne yielding exact mass ratios for this theory.A final section is devoted to solutions of more realistic four-dimensional models containing fermions, internal symmetry etc. Some quark-confinement models and vortex type solutions come under this category. General remarks are made on this family of solutions, and illustrated using 't Hooft's monopole solution.     

Higher order corrections to the processe^ + e^ - \to v\bar vy

A calculation of the neutrino counting reaction \(e^ + e^ - \to v\bar vy\) is presented and implemented in a Monte Carlo generator of unweighted events. The non-photonic corrections are included following the star-scheme. The photonic corrections have been exponentiated following the “inductive” and the “structure functions” approach. For a realistic experimental set-up, the total corrections around theZ ⁰ pole amount to ～5% with respect to the one-loop result. The final precision achieved is better than 1%.