Preservation of logarithmic concavity by the Mellin transform and applications to the Schrödinger equation for certain classes of potentials

We prove that the Mellin transform of a function log-concave (convex) is, after division by (+1), where is the argument of the transform, itself log-concave (convex) in . This theorem is first applied to the moments of the ground state wave function of the Schrödinger equation where the Laplacian of the central potential has a given sign, and generalized to other situations. This is used to derive inequalities linking thel ^th derivative of the ground state wave function at the origin for angular momentuml and the expectation value of the kinetic energy, and applied to quarkonium physics. A generalization to higher radial excitations is shown to be plausible by using the WKB approximation. Finally, new bounds on ground-state energies in power potentials are obtained.     

Comparative analysis of (p,d), (d,t) and (3He, α) reactions on13C nucleus

The angular distributions of the (p, d), (d, t) and(³He, ) reactions on¹³C have been analysed within the framework of DWBA in which additional information on nuclear vertex constants was introduced. Although all these reactions seem to be similar single nucleon transfer, their mechanism is shown to be quite different and so is the information extracted thereof. While from the (p, d) reactions spectroscopic factors may be extracted unambiguously, from the (d, t) reactions it is possible to obtain directly the values of vertex constants only, which in turn are consistent with those determined by extrapolation of the experimental cross sections of the (p, d) reactions to the pole.In the case of (³He, ) reactions, however, the analysis indicates inadequacy of the DWBA concerning the calculations of central partial amplitudes. For a more reliable extraction of structural information, besides the correct normalization of peripheral amplitudes, a contribution of more complex mechanisms must be taken into account.     

Nd3+ near UV and visible fluorescence in YAP:Nd

The present paper summarizes detailed investigations of Nd³⁺ fluorescence spectra in YAP:Nd laser crystal in the broad spectral range of 370–1100 nm at liquid nitrogen temperature. Especially, Nd³⁺ near UV and visible fluorescence spectra were studied for the first time in this crystal. The Nd³⁺ near UV and visible fluorescence spectra of this crystal consist of many narrow lines (up to 50). The Nd³⁺ near UV and visible fluorescence lines arise mainly from⁴D_3/2 and²P_3/2 Nd³⁺ terms (transitions from⁴D_3/2,²P_3/2 to lower lying Nd³⁺ levels are responsible for their appearance). At room temperature the fluorescence spectra consist of broad bands with narrow lines (mainly⁴D_3/2⁴F_3/2,⁴F_5/2 and²H_9/2 transitions).     

Dependence of the S-matrix on the choice of field variables in the effective Lagrangian

The dependence of the on-shellS-matrix on the change of the Lagrangian induced by a nonlinear substitutionF() is investigated by means of a graphical analysis. A cancellation mechanism is found and used to show that the tree approximation of theS-matrix is independent of such a substitution and that the Jacobian of the substitution has to be introduced in order to cancel a new class of singular one-loop graphs and to recover the primaryS-matrix at the one-loop level.     

Nonclassical states generated via four-wave mixing

The nonclassical properties of quantum fields generated by four- or three-wave mixing are investigated on the basis of assumptions of two-photon coherent (squeezed) input states and the approximation of strong pumping. The influence of losses is shown supposing the model of mutually independent phonon reservoirs. The possibility of producing squeezed and sub-Poisson light outputs is demonstrated in single or superposed modes using computer solutions.The author wishes to acknowledge helpful discussions with Dr. J. Peina and Dr. M. Kárská.     

Effect of multijunction grill length on its lower hybrid current drive efficiency

The distance between the junction of subsidiary waveguides in the main waveguide and the grill mouth has an important influence upon the spectrum of radiated waves, the total reflection coefficient, the power distribution among the separate waveguides and the actual phases of incident waves. This effect is nearly as important as that of the phase shift between the adjacent waveguides and it is necessary to carry out optimization with respect to this parameter in the grill design.     

Optical constants of titanium and silicon dioxide films

In this paper a study of optical constants of titanium and silicon dioxide films prepared in Balzers BAK 600 and BA 510 conventional high-vacuum apparatus is described. Both the dispersion and the geometrical thickness were determined from normal reflectance spectrum by adapted general algorithm of the statistical interpretation of measured data. The dependence of optical constants on oxygen pressure for both materials and the evaporation rate dependence for titanium dioxide were obtained. The time changes of these constants were also measured.     

Radiative kinks and fermionic zero modes in a (λφ6)1+1 model

We consider bidimensional scalar models including kink solutions _k (x). Using the hidden supersymmetric properties of the Dirac equation, we describe a general method to find normalizable fermionic zero modes. In particular, we apply the technique to a ( ⁶)₁₊₁ model. Going to the one-loop order of the effective potential, the emergence of a radiative kink provides an interesting scalar background in order to discuss the Dirac equation.     

XPS investigation of LPE garnet films

XPS spectra of YIG, YIG:Bi, YIG:Ca and YIG:Co(Ge, Ca) epitaxial garnet films were measured at room temperature. The positions of the main iron, yttrium, oxygen, bismuth, cobalt and lead spectral lines were determined and their changes with the surface treatments were investigated. It was found that divalent and trivalent states of iron and cobalt ions can be resolved, the chemical shifts being in oposite directions.The authors would like to thank Dr. J. imová for careful EPMA analysis of the samples.