Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. First, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Lévy-Leblond equations, and define the Galilean generating functional and Green’s functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential , and we derive expressions for the 2- and 4-point Green’s functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in (3 + 1) space-time. This is particularly apparent when we represent the results with diagrams in the extended (4 + 1) manifold, since they usually encompass more diagrams in Galilean (3 + 1) space-time.     

Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Two-boson truncation of Pauli-Villars-regulated Yukawa theory

We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3 + 1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson-one-fermion equations for eigenstates with J_z = 1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.     

Phase diagram of the Gross-Neveu model: exact results and condensed matter precursors

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1 + 1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schrödinger equation with the (single gap) Lamé potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Fröhlich model and ferromagnetic superconductors.     

Investigation of low-energy scattering in the nnpp system on the basis of differential equations for Yakubovsky components in configuration space

The s-wave differential equations for the Yakubovsky components characterizing the nnpp system have been solved by the method of cluster reduction. Two-cluster scattering at energies below the three-particle threshold in the singlet and triplet spin states has been considered. The MT I–III potential model has been used to simulate nucleon-nucleon interaction, and the Coulomb interaction between the protons has been taken into account. The singlet and triplet scattering lengths have been calculated for proton interaction with the triton (³H) and for neutron interaction with the ³He nucleus, and the deuteron-deuteron scattering length has also been determined. The low-energy behavior of the phase shifts and inelasticity factors in the corresponding scattering channels has been investigated. The features of the 0⁺ resonance in the ⁴He nucleus have been determined.     

Quantum tachyons

The interaction of superluminal radiation with matter in atomic bound-bound and bound-free transitions is investigated. We study transitions in the relativistic hydrogen atom effected by superluminal quanta. The superluminal radiation field is coupled by minimal substitution to the Dirac equation in a Coulomb potential. We quantize the interaction to obtain the transition matrix for induced and spontaneous superluminal radiation in hydrogen-like ions. The tachyonic photoelectric effect is scrutinized, the cross-sections for ground state ionization by transversal and longitudinal tachyons are derived. We examine the relativistic regime, high electronic ejection energies, as well as the first order correction to the non-relativistic cross-sections. In the ultra-relativistic limit, both the longitudinal and transversal cross-sections are peaked at small but noticeably different scattering angles. In the non-relativistic limit, the longitudinal cross-section has two maxima, and its minimum is located at the transversal maximum. Ionization cross-sections can thus be used to discriminate longitudinal radiation from transversal tachyons and photons.     

Compactification and signature transition in Kaluza-Klein spinor cosmology

We study the classical and quantum cosmology of a 4 + 1-dimensional space-time with a non-zero cosmological constant coupled to a self-interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor R (t) and an internal scale factor a (t) associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self-interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that a ∼ R⁻¹ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.     

System dependence of the correlation function of IMFs in Ar + Sn at 35 MeV/u

The inclusive reduced velocity correlation functions of the intermediate mass fragments were measured in the reactions of ³⁶Ar + ^112,124Sn at 35 MeV/u. The anti-correlation is observed to be stronger in ³⁶Ar + ¹²⁴Sn system than that in ³⁶Ar + ¹¹²Sn. The difference of the correlation functions between the two reactions is mainly contributed by the particle pairs with high momenta. A three body Coulomb repulsive trajectory model is employed to calculate the emission time scale of the IMFs for the two systems. The time scale is 150 fm/c in ³⁶Ar + ¹¹²Sn and 120 fm/c in the ³⁶Ar + ¹²⁴Sn, respectively.     

Positive secondary Ion emission from Si1−xGex bombarded by O2

The positive secondary ion yields of B⁺ (dopant), Si⁺ and Ge⁺ were measured for Si_1−xGe_x (0 ≤ x ≤ 1) sputtered by 5.5 keV ¹⁶O₂⁺ and ¹⁸O₂⁺. It is found that the useful yields of Ge⁺ and B⁺ suddenly drop by one order of magnitude by varying the elemental composition x from 0.9 to 1 (pure Ge). In order to clarify the role of oxygen located near surface regions, we determined the depth profiles of ¹⁸O by nuclear resonant reaction analysis (NRA: ¹⁸O(p,α)¹⁵N) and medium energy ion scattering (MEIS) spectrometry. Based on the useful yields of B⁺, Si⁺ and Ge⁺ dependent on x together with the elemental depth profiles determined by NRA and MEIS, we propose a probable surface structure formed by 5.5 keV O₂⁺ irradiation.     

The peculiarities of the low-energy ion scattering by polycrystal targets

In the present work, experimental and computer simulation studies of low-energy (E₀ = 80-500 eV) Cs⁺ ions scattering on Ta, W, Re target surfaces and K⁺ ions scattering on Ti, V, Cr target surfaces have been performed for more accurate definition of mechanism of scattering, with a purpose of evaluation of an opportunity of use of slow ions scattering as a tool of surface layers analysis. The choice of the targets was based on the fact that the ratios of atomic masses of target atoms and ions μ = m₂/m₁ were almost the same for all cases considered and greater than 1 (direct mass ratio) however, the difference of binding energies of target atoms in the cases of Cs⁺ and K⁺ scattering was almost twice as much. It has been noticed that the dependencies of the relative energy retained by scattering ions at the maximum of energy distribution versus the initial energy E_m/E₀ (E₀) have a similar shape in all cases. The relative energy retained by scattering ions increases while the initial energy of incidence ions decreases. The curves are placed above each other relative to the binding energies of target atoms, to show what this says about the influence of binding energy on a process of scattering of low-energy ions. The correlation between value of energy change maintained by an ion for different values of E₀ in the case of scattering by targets with different masses of atoms and its binding energies is experimentally established. The contrary behavior of the E_m/E₀ (E₀) dependencies concerning the target atom binding energy quantity E_b for cases with direct (μ > 1) and inverse (μ < 1) mass ratio of colliding particles is established. The comparison of experimental energy distributions with calculated histograms shows that the binary collision approximation cannot elucidate the abnormally great shift in the maxima of relative energy distributions towards greater energy retained by scattering ions.     

Study of S ion-assisted sulfurization of n-GaAs (1 0 0) surface

The chemical structure and site location of sulfur atoms on n-GaAs (1 0 0) surface treated by bombardment of S⁺ ions over their energy range from 10 to 100 eV have been studied by X-ray photoelectron spectroscopy and low energy electron diffraction. The formation of Ga-S and As-S species on the S⁺ ion bombarded n-GaAs surface is observed. An apparent donor doping effect is observed for the n-GaAs by the 100 eV S⁺ ion bombardment. It is found that the S⁺ ions with higher energy are more effective in the formation of Ga-S species, which assists the n-GaAs (1 0 0) surface in reconstruction into an ordered (1 × 1) structure upon subsequent annealing. The treatment is further extended to repair Ar⁺ ion damaged n-GaAs (1 0 0) surface. It is found that after a n-GaAs (1 0 0) sample is damaged by 150 eV Ar⁺ ion bombardment, and followed by 50 eV S⁺ ion treatment and subsequent annealing process, finally an (1 × 1) ordering GaAs (1 0 0) surface with low surface states is obtained.     

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.     

Submillimeter-wave spectroscopy of HCO in the excited vibrational states

The pure rotational transitions of HCO⁺ in excited vibrational states located below 5000 cm⁻¹ over the ground state have been investigated with a high-sensitivity frequency/magnetic field double modulation submillimeter-wave spectrometer in the frequency range of 280-810 GHz. The ions were generated in an extended negative glow discharge through a gas mixture of a few millitorrs of H₂ and CO and 12 mTorr of Ar buffer gas. Throughout the experiments, the cell was maintained at liquid nitrogen temperature. In the present study, we have determined accurate molecular constants for the excited vibrational states. Our analysis suggests that there may be a higher order Coriolis interaction between the (0 3 1) and (1 2 0) states. In previous investigations, the Stark effect caused by the electric field present in the discharge plasma was cited as a reason for non-observations of low-J lines in the (02²0) and for the systematic shifts observed for low-J lines in the (01¹0), (02²0), (03¹0), and (04²0) states of HCO⁺ as well as DCO⁺. In the present investigation, some low-J lines in the (02²0) and (04²0) states have been observed in emission. Furthermore, J = 8-7, J = 9-8 lines in (03^1e1) were detected in emission. This finding indicates that missing low-J lines for the Δ sublevel obtained in the past is not due to the Stark effect but due to small population differences in those levels.     

Experimental signature of entrance channel effect in heavy mass region via evaporation residue cross section and spin distribution measurements

Evaporation residue (ER) cross sections and gamma multiplicity distributions have been measured for ¹⁶O + ¹⁸⁴W and ¹⁹F + ¹⁸¹Ta systems in the excitation energy range of 50–90 MeV, leading to the same compound nucleus ²⁰⁰Pb^∗. Comparison of experimental results of both the systems shows that ER cross sections and moments of gamma multiplicity distribution of ¹⁶O + ¹⁸⁴W system are significantly higher than those of ¹⁹F + ¹⁸¹Ta system at higher excitation energies. Present measurements directly shows the experimental signature of entrance channel effect even with the systems which are not very different with respect to their entrance channel mass asymmetry. It is further demonstrated that the reduction in the ER cross section and moments of spin distribution for ¹⁹F + ¹⁸¹Ta system is mainly due to the suppression of fusion of higher l values.     

Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

In this paper, we develop two new upwind difference schemes for solving a coupled system of convection–diffusion equations arising from the steady incompressible MHD duct flow problem with a transverse magnetic field at high Hartmann numbers. Such an MHD duct flow is convection-dominated and its solution may exhibit localized phenomena such as boundary layers, namely, narrow boundary regions where the solution changes rapidly. Most conventional numerical schemes cannot efficiently solve the layer problems because they are lacking in either stability or accuracy. In contrast, the newly proposed upwind difference schemes can achieve a reasonable accuracy with a high stability, and they are capable of resolving high gradients near the layer regions without refining the grid. The accuracy of the first new upwind scheme is O(h + k) and the second one improves the accuracy to O(ε²(h + k) + ε(h² + k²) + (h³ + k³)), where 0 < ε ? 1/M ? 1 and M is the high Hartmann number. Numerical examples are provided to illustrate the performance of the newly proposed upwind difference schemes.     

Fabrication of multilayered Ge nanocrystals embedded in SiOxGeNy films

Multilayered Ge nanocrystals embedded in SiO_xGeN_y films have been fabricated on Si substrate by a (Ge + SiO₂)/SiO_xGeN_y superlattice approach, using a rf magnetron sputtering technique with a Ge + SiO₂ composite target and subsequent thermal annealing in N₂ ambient at 750 °C for 30 min. X-ray diffraction (XRD) measurement indicated the formation of Ge nanocrystals with an average size estimated to be 5.4 nm. Raman scattering spectra showed a peak of the Ge-Ge vibrational mode downward shifted to 299.4 cm⁻¹, which was caused by quantum confinement of phonons in the Ge nanocrystals. Transmission electron microscopy (TEM) revealed that Ge nanocrystals were confined in (Ge + SiO₂) layers. This superlattice approach significantly improved both the size uniformity of Ge nanocrystals and their uniformity of spacing on the ‘Z’ growth direction.