17848894
Irreducible Bases in Icosahedral Group Space
The irreducible bases in the icosahedral groupspace are calculated explicitly by reducing the regularrepresentation. The symmetry-adapted bases of the systemwith I or Ih symmetry can becalculated easily and generally by applying those irreduciblebases to wavefunctions of the system, if they are notvanishing. As examples, the submatrices of the HuckelHamiltonians for carbon-60 and carbon-240 arerecalculated by the irreducible bases.
117217126
Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz
Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+λ), the singular one-fraction power one V(r)=ar−1/2+br−3/2 and the singular two-fraction one V(r)=ar2/3+br−2/3+cr−4/3. The latter one is found that the hidden symmetry exists if substituting r→−ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant.
121783508
Quantum states of a sextic potential: hidden symmetry and quantum monodromy
A known terminating polynomial ansatz for a finite sub-set of states of the sextic central potential V(a,b,c;r) = ar2 + br4 + cr6, c>0, subject to integer related parameter constraints, is confirmed to apply in two as well as three dimensions. A hidden symmetry relating the eigenstates of V(a,b,c;r) to those of V(a,-b,c;r) is used to establish the boundary between the ansatz sub-set and the infinite set of higher states. Connections between the radial wavefunctions Rn(a,b,c;r) and Rn'(a,-b,c;r) also provide semiclassical insight into the origin of the parameter constraint. Finally the ansatz eigenvalue dispositions are related to the phenomenon of quantum monodromy.
120777661
ANALYTICAL APPROXIMATIONS TO THE SCHRÖDINGER EQUATION FOR A SECOND PÖSCHL–TELLER-LIKE POTENTIAL WITH CENTRIFUGAL TERM
The bound state solutions of the Schrodinger equation for a second Poschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.
15491159
Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials
By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar2 + br4 + cr6,V(r) = ar + br2 + cr−1,and V(r) = ar2 + br−2+ cr−4 + dr−6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.
119543557
LEVINSON'S THEOREM FOR THE KLEIN-GORDON EQUATION IN TWO DIMENSIONS
The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.
119183924
Chemical evolution of the Galactic bulge as traced by microlensed dwarf and subgiant stars - III. Detection of lithium in the metal-poor bulge dwarf MOA-2010-BLG-285S
Context. To study the evolution of Li in the Galaxy it is necessary to observe dwarf or subgiant stars. These are the only long-lived stars whose present-day atmospheric chemical composition reflects their natal Li abundances according to standard models of stellar evolution. Although Li has been extensively studied in the Galactic disk and halo, to date there has only been one uncertain detection of Li in an unevolved bulge star. Aims. Our aim with this study is to provide the first clear detection of Li in the Galactic bulge, based on an analysis of a dwarf star that has largely retained its initial Li abundance. Methods. We performed a detailed elemental abundance analysis of the bulge dwarf star MOA-2010-BLG-285S using a high-resolution and high signal-to-noise spectrum obtained with the UVES spectrograph at the VLT when the object was optically magnified during a gravitational microlensing event (visual magnification A similar to 550 during observation). The Li abundance was determined through synthetic line profile fitting of the Li-7 resonance doublet line at 670.8 nm. The results have been corrected for departures from LTE. Results. MOA-2010-BLG-285S is, at [Fe/H] = -1.23, the most metal-poor dwarf star detected so far in the Galactic bulge. Its old age (12.5 Gyr) and enhanced [alpha/Fe] ratios agree well with stars in the thick disk at similar metallicities. This star represents the first unambiguous detection of Li in a metal-poor dwarf star in the Galactic bulge. We find an NLTE corrected Li abundance of log epsilon(Li) = 2.16, which is consistent with values derived for Galactic disk and halo dwarf stars at similar metallicities and temperatures. Conclusions. Our results show that there are no signs of Li enrichment or production in the Galactic bulge during its earliest phases. Observations of Li in other galaxies (omega Cen) and other components of the Galaxy suggest further that the Spite plateau is universal. (Less)
18017754
The absolute magnitude of RRC variables from statistical parallax
We present the first definitive measurement of the absolute magnitude of RR Lyrae c-type variable stars (RRc) determined purely from statistical parallax. We use a sample of 242 RRc variables selected from the All Sky Automated Survey for which high-quality light curves, photometry, and proper motions are available. We obtain high-resolution echelle spectra for these objects to determine radial velocities and abundances as part of the Carnegie RR Lyrae Survey. We find that M V, RRc = 0.59 ? 0.10 at a mean metallicity of [Fe/H] = ?1.59. This is to be compared with previous estimates for RRab stars (M V, RRab = 0.76 ? 0.12) and the only direct measurement of an RRc absolute magnitude (RZ Cephei, M V, RRc = 0.27 ? 0.17). We find the bulk velocity of the halo relative to the Sun to be (W ?, W ?, Wz ) = (12.0, ?209.9, 3.0) km s?1 in the radial, rotational, and vertical directions with dispersions . For the disk, we find (W ?, W ?, Wz ) = (13.0, ?42.0, ?27.3) km s?1 relative to the Sun with dispersions . Finally, as a byproduct of our statistical framework, we are able to demonstrate that UCAC2 proper-motion errors are significantly overestimated as verified by UCAC4.
14062967
Probing ~100 AU Intergalactic Mg II Absorbing “Cloudlets” with Quasar Microlensing
Intergalactic Mg II absorbers are known to have structures down to scales ~102.5 pc, and there are now indications that they may be fragmented on scales 10-2.5 pc according to Hao and coworkers. When a lensed quasar is microlensed, the microimages of the quasar experience creation, destruction, distortion, and drastic astrometric changes during caustic crossings. I show that quasar microlensing can effectively probe Mg II and other absorption "cloudlets" with sizes ~10-4.0 to 10-2.0 pc by inducing significant spectral variability on timescales of months to years. With numerical simulations, I demonstrate the feasibility of applying this method to Q2237+0305, and I show that high-resolution spectra of this quasar in the near future would provide a clear test of the existence of such metal-line absorbing "cloudlets."
18317896
Long-term cycling of Kozai-Lidov cycles: extreme eccentricities and inclinations excited by a distant eccentric perturber.
The very long-term evolution of the hierarchical restricted three-body problem is calculated analytically for high inclinations. The Kozai-Lidov Cycles (KLCs) slowly evolve due to the octupole term in the perturber's potential and exhibit striking features, including extremely high eccentricities and the generation of retrograde orbits with respect to the perturber. These features were found in recent numerical experiments of the nonrestricted three-body problem and were attributed inaccurately to the comparable and low masses of the two orbiting companions. Our calculation is done by averaging for the first time the double averaged secular equations of motion over the KLCs and finding a new constant of the motion. These very long-term effects are likely to be important in various astrophysical systems thought to involve KLCs, such as hot Jupiters, irregular moons of planets, and many others.
118316787
An exact integral relation between the Ni56 mass and the bolometric light curve of a type Ia supernova
An exact relation between the Ni56 mass and the bolometric light curve of a type Ia supernova can be derived as follows, using the following excellent approximations: 1. the emission is powered solely by Ni56-> Co56 ->Fe56; 2. each mass element propagates at a non-relativistic velocity which is constant in time (free coasting); and 3. the internal energy is dominated by radiation. Under these approximations, the energy E(t) carried by radiation in the ejecta satisfies: dE/dt=-E(t)/t-L(t)+Q(t), where Q(t) is the deposition of energy by the decay which is precisely known and L(t) is the bolometric luminosity. By multiplying this equation by time and integrating over time we find: E(t)*t=\int_0^t Q(t')t'dt' -\int_0^t L(t')t'dt'. At late time, t>> t_peak, the energy inside the ejecta decreases rapidly due to its escape, and thus we have \int_0^t Q(t')t'dt'=\int_0^t L(t')t'dt'. This relation is correct regardless of the opacities, density distribution or Ni56 deposition distribution in the ejecta and is very different from "Arnett's rule", L_peak ~ Q(t_peak). By comparing \int_0^t Q(t')t'dt' with \int_0^t L(t')t'dt' at t~40 day after the explosion, the mass of Ni56 can be found directly from UV, optical and infrared observations with modest corrections due to the unobserved gamma-rays and due to the small residual energy in the ejecta, E(t)*t>0.