Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr-Sommerfeld quantization rule yields the exact expression for the energy spectrum.Comment: 14 pages, 2 figures, Uses RevTeX4 styl

The Wigner function of a q-deformed harmonic oscillator model

The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the $q$-oscillator model under consideration. The Wigner function is expressed as a basic hypergeometric series, related to the Al-Salam-Chihara polynomials. It is shown that, in the limit case $h \to 0$ ($q \to 1$), both the Wigner and Husimi distribution functions reduce correctly to their well-known non-relativistic analogues. Surprisingly, examination of both distribution functions in the q-deformed model shows that, when $q \ll 1$, their behaviour in the phase space is similar to the ground state of the ordinary quantum oscillator, but with a displacement towards negative values of the momentum. We have also computed the mean values of the position and momentum using the Wigner function. Unlike the ordinary case, the mean value of the momentum is not zero and it depends on $q$ and $n$. The ground-state like behaviour of the distribution functions for excited states in the q-deformed model opens quite new perspectives for further experimental measurements of quantum systems in the phase space.Comment: 16 pages, 24 EPS figures, uses IOP style LaTeX, some misprints are correctd and journal-reference is adde

Exact solution of the position-dependent effective mass and angular frequency Schr\"odinger equation: harmonic oscillator model with quantized confinement parameter

We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position. The free Hamiltonian of the proposed model has the form of the BenDaniel--Duke kinetic energy operator. The position-dependency of the mass and the angular frequency is such that the homogeneous nature of the harmonic oscillator force constant $k$ and hence the regular harmonic oscillator potential is preserved. As a consequence thereof, a quantization of the confinement parameter is observed. It is shown that the discrete energy spectrum of the confined harmonic oscillator with position-dependent mass and angular frequency is finite, has a non-equidistant form and depends on the confinement parameter. The wave functions of the stationary states of the confined oscillator with position-dependent mass and angular frequency are expressed in terms of the associated Legendre or Gegenbauer polynomials. In the limit where the confinement parameter tends to $\infty$, both the energy spectrum and the wave functions converge to the well-known equidistant energy spectrum and the wave functions of the stationary non-relativistic harmonic oscillator expressed in terms of Hermite polynomials. The position-dependent effective mass and angular frequency also become constant under this limit

A relativistic model of the NN-dimensional singular oscillator

Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the $N$-dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic three-dimensional singular oscillator. We have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra.Comment: 8 pages, accepted for publication in J. Phys.

The Relativistic Linear Singular Oscillator

Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised taking into account referees suggestions

Infrared renormalons and single meson production in proton-proton collisions

In this article, we investigate the contribution of the higher twist Feynman diagrams to the large-$p_T$ inclusive pion production cross section in proton-proton collisions and present the general formulae for the higher twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher twist cross sections with the ones obtained in the framework of the frozen coupling approximation and leading twist cross section. We obtain, that ratio $R$ for all values of the transverse momentum $p_{T}$ of the pion identical equivalent to ratio $r$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.Comment: 28 pages, 13 figure

Factorization method for difference equations of hypergeometric type on nonuniform lattices

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.Comment: 21 page

Performance of a plastic scintillator developed using styrene monomer polymerization

This paper presents a newly developed plastic scintillator produced in collaboration with Turkiye Energy, Nuclear and Mineral Research Agency (TENMAK). The scintillator is manufactured using thermal polymerization of commercially available styrene monomer. The absorption spectrum of the scintillator exhibited two absorption bands at 225 nm and 340 nm, with an absorption edge observed at 410 nm. The wavelength of the emitted light was measured in the range of 400-800 nm, with a maximum intensity at 427 nm. Monoenergetic electrons from the 137Cs source were used to evaluate the characteristics of the new scintillator, particularly its light yield. As the light readout the MAPD-3NM type silicon photomultiplier array (4 x 4) with an active area of 15 x 15 mm2, assembled using single MAPDs with an active area of 3.7 x 3.7 mm2, was used. The light yield of the scintillator was determined to be 6134 photons/MeV. In addition, the efficiency of the scintillator for gamma rays with an energy of 662 keV was found to be approximately 1.8 %. A CmBe neutron source was employed to evaluate its fast neutron detection performance. However, neutron/gamma discrimination using pulse shape discrimination (charge integration) method was not observed. The results demonstrate the potential of a newly produced plastic scintillator for various applications, particularly in radiation monitoring and detection systems.Comment: 7 pages, 7 figure