Analytical parametrization of fusion barriers using proximity potentials

Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1$. A comparison with the experimental data is also in good agreement.Comment: 12 pages, 5 figure

Relativistic shape invariant potentials

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected and replaced by two new statement

Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems

For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground state energy in an associated, well-separated, asymmetric double-well-type potential. Our discussion is also relevant for the analysis of the fermion bound state in the kink-antikink scalar background.Comment: revised version, to be pubilshed in PR

Rho-omega mixing in asymmetric nuclear matter via QCD sum rule approach

We evaluate the operator product expansion (OPE) for a mixed correlator of the isovector and isoscalar vector currents in the background of the nucleon density with intrinsic isospin asymmetry [i.e. excess of neutrons over protons] and match it with its imaginary part, given by resonances and continuum, via the dispersion relation. The leading density-dependent contribution to $\rho-\omega$ mixing is due the scattering term, which turns out to be larger than any density dependent piece in the OPE. We estimate that the asymmetric density of $n_n-n_p \sim 2.5 \times 10^{-2} ~{\rm fm^3}$ induces the amplitude of $\rho-\omega$ mixing, equal in magnitude to the mixing amplitude in vacuum, with the constructive interference for positive and destructive for negative values of $n_n-n_p$. We revisit sum rules for vector meson masses at finite nucleon density to point out the numerical importance of the screening term in the isoscalar channel, which turns out to be one order of magnitude larger than any density-dependent condensates over the Borel window. This changes the conclusions about the density dependence of $m_\omega$, indicating $\sim 40$ MeV increase at nuclear saturation density.Comment: 8 pages, Revte

The influence of managerial optimism and self-regulation on learning and business growth expectations within an emerging economic context

This paper examines psychological and behavioral mechanisms that underlie business growth expectations by examining how managerial optimism and self-regulatory focus influence learning behaviors. To empirically examine these relationships, the study situates in a resource-constrained business context by studying managers in two Pacific Island economies. Results indicate that a positive view toward gains encourages exploratory learning in unknown situations; whereas, a less optimistic disposition and avoidance are related to exploitative learning. This finding is consequential as managerial learning that leans toward development of new insights and possibilities is associated with greater business growth expectations versus learning that adheres to familiar and proven ideas and alternatives. The study results have implications for both practice and theory

Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations

SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the oscillator potential by point canonical transformations. We call this class the "oscillator class". A nontrivial graded extension of SO(2,1) is defined and its realization by two-dimensional matrices of differential operators acting in spinor space is given. It turns out that this graded algebra is the supersymmetry algebra for a class of relativistic potentials that includes the Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in fact, the relativistic extension of the oscillator class. A new point canonical transformation, which is compatible with the relativistic problem, is formulated. It maps all of these relativistic potentials into the Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio

Quantum Mechanics of Multi-Prong Potentials

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of $N$ identical prongs exhibit an alternating pattern of non-degeneracy and $(N-1)$ fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in $N$-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is for general values of $N$, the results can be studied in the large $N$ limit. A somewhat surprising result is that a free particle incident on an $N$-prong vertex undergoes continuously increased backscattering as the number of prongs is increased.Comment: 17 pages. LATEX. On request, TOP_DRAW files or hard copies available for 7 figure

Supersymmetric quantum mechanics with nonlocal potentials

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.Comment: 4 pages, REVTeX, Minor revisions for clarificatio

The effects of meson mixing on dilepton spectra

The effect of scalar and vector meson mixing on the dilepton radiation from hot and dense hadronic matter is estimated in different isospin channels. In particular, we study the effect of $\sigma$-$\omega$ and $\rho-a_0$ mixing and calculate the corresponding rates. Effects are found to be significant compared to standard $\pi$-$\pi$ and $K$-${\bar K}$ annihilations. While the mixing in the isoscalar channel mostly gives a contribution in the invariant mass range between the two-pion threshold and the $\omega$ peak, the isovector channel mixing induces an additional peak just below that of the $\phi$. Experimentally, the dilepton signals from $\rho$-$a_0$ mixing seem to be more tractable than those from $\sigma$-$\omega$ mixing.Comment: 10 pages, 9 figure

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev.