A quantum exactly solvable non-linear oscillator related with the isotonic oscillator

A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is studied. First the general case, that depends of a parameter $a$, is considered and then a particular case is studied with great detail. It is proven that it is Schr\"odinger solvable and then the wave functions $\Psi_n$ and the energies $E_n$ of the bound states are explicitly obtained. Finally it is proven that the solutions determine a family of orthogonal polynomials ${\cal P}_n(x)$ related with the Hermite polynomials and such that: (i) Every ${\cal P}_n$ is a linear combination of three Hermite polynomials, and (ii) They are orthogonal with respect to a new measure obtained by modifying the classic Hermite measure.Comment: 11 pages, 11 figure

Semiclassical wave equation and exactness of the WKB method

The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials.Comment: 13 page

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.Comment: 25 pages, 1 figur

Thermal Radiation from Au + Au Collisions at \sqrt{s} = 200 GEV/A Energy

The transverse momentum distribution of the direct photons measured by the PHENIX collaboration in $Au + Au$ collisions at $\sqrt{s}=200$ GeV/A has been analyzed. It has been shown that the data can be reproduced reasonably well assuming a deconfined state of thermalized quarks and gluons with initial temperature more than the transition temperature for deconfinement inferred from lattice QCD. The value of the initial temperature depends on the equation of state of the evolving matter. The sensitivities of the results on various input parameters have been studied. The effects of the modifications of hadronic properties at non-zero temperature have been discussed.Comment: minor modifications in the text, accepted for publicatio

The systematic study of the influence of neutron excess on the fusion cross sections using different proximity-type potentials

Using different types of proximity potentials, we have examined the trend of variations of barrier characteristics (barrier height and its position) as well as fusion cross sections for 50 isotopic systems including various collisions of C, O, Mg, Si, S, Ca, Ar, Ti and Ni nuclei with $1\leq N/Z < 1.6$ condition for compound systems. The results of our studies reveal that the relationships between increase of barrier positions and decrease of barrier heights are both linear with increase of $N/Z$ ratio. Moreover, fusion cross sections also enhance linearly with increase of this ratio.Comment: 28 pages, 7 figures, 5 Table

One-dimensional fermions with incommensuration

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/ \delta --> 0, the number of states lying inside the q=0 gap is nonzero and equal to 2 \delta /\pi^2. Thus the limit q --> 0 differs from q=0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q --> 0, we find a nontrivial density of states near zero energy. However, the limit q --> 0 and q=0 give the same results near commensurate wave numbers which are different from pi. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in delta.Comment: Revtex, 23 pages including 7 epsf figures; this is a greatly expanded version of cond-mat/981133

Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity

We demonstrate coupling of the zero-phonon line of individual nitrogen-vacancy centers and the modes of microring resonators fabricated in single-crystal diamond. A zero-phonon line enhancement exceeding ten-fold is estimated from lifetime measurements at cryogenic temperatures. The devices are fabricated using standard semiconductor techniques and off-the-shelf materials, thus enabling integrated diamond photonics.Comment: 5 pages, 4 figure

Tensor Coupling and Vector Mesons in Dense Nuclear Matter

The effects of magnetic interaction between vector mesons and nucleons on the propagation (mass and width) of the $\rho$-meson in particular moving through very dense nuclear matter is studied and the modifications, qualitative and quantitative, due to the relevant collective modes (zero-sound and plasma frequencies) of the medium discussed. It is shown that the $\rho$-mesons produced in high-energy nuclear collisions will be longitudinally polarized in the region of sufficiently dense nuclear matter, in the presence of such an interaction.Comment: Plain Latex file. Three figures, not appended, may be obtained on request to [email protected]

Approximate solution of the Duffin-Kemmer-Petiau equation for a vector Yukawa potential with arbitrary total angular momenta

The usual approximation scheme is used to study the solution of the Duffin-Kemmer-Petiau (DKP) equation for a vector Yukawa potential in the framework of the parametric Nikiforov-Uvarov (NU) method. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for arbitrary total angular momentum in closed form. Further, the approximate energy equation and wave function spinor components are also given for case. A set of parameter values is used to obtain the numerical values for the energy states with various values of quantum levelsComment: 17 pages; Communications in Theoretical Physics (2012). arXiv admin note: substantial text overlap with arXiv:1205.0938, and with arXiv:quant-ph/0410159 by other author

Study of in-medium ω\omega meson properties in Ap, pA and AA collisions

We propose to investigate the in-medium properties of vector $\omega$ mesons at the normal nuclear density in Ap(pA) collisions and at higher density in AA collisions at the ITEP accelerator facility TWAC. Using of the inverse Ap kinematics will permit us to study the $\omega$ meson production in a wide momentum interval included the not yet explored range of small meson momenta relative to the projectile nuclei where the mass modification effect in nuclear matter is expected to be the strongest. Momentum dependence of the in-medium $\omega$ meson width will be studied in the traditional pA kinematics. We intend to use the electromagnetic calorimeter for reconstruction of the $\omega$ meson invariant mass by detecting photons from the $\omega \to \pi^{0}\gamma \to 3\gamma$ decay. The model calculations and simulations with RQMD generator show feasibility of the proposed experiment. Available now intensity of the ion beams provides a possibility to collect large statistics and make decisive conclusion about the $\omega$ meson properties at density of normal nuclei. At the second stage of the investigation the $\omega$ meson properties will be studied in AA collisions at higher density. Interpretation of these measurements will be based on the results obtained in Ap(pA) interactions. Further investigation of the in-medium properties of light unflavored and charmed mesons can be performed at ITEP and at GSI(FAIR) where higher ion energies will be accessible in near future.Comment: 26 pages, 10 figures, 2 table