Resonances and adiabatic invariance in classical and quantum scattering theory

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal resonance-width and classical friction has been established with a classically deterministic quantity, the stability exponent of an adiabatically perturbed periodic orbit. This relation can be employed to estimate the rate of energy dissipation in finite quantum systems.Comment: 8 page

Small eta-N scattering lengths favour eta-d and eta-alpha states

Unstable states of the eta meson and the 3He nucleus predicted using the time delay method were found to be in agreement with a recent claim of eta-mesic 3He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the eta-d and eta-4He elastic scattering. The T-matrix for eta-4He scattering is evaluated within the Finite Rank Approximation (FRA) of few body equations. For the evaluation of time delay in the eta-d case, we use a parameterization of an existing Faddeev calculation and compare the results with those obtained from FRA. With an eta-N scattering length, $a_{\eta N} = (0.42, 0.34)$ fm, we find an eta-d unstable bound state around -16 MeV, within the Faddeev calculation. A similar state within the FRA is found for a low value of $a_{\eta N}$, namely, $a_{\eta N} = (0.28, 0.19)$ fm. The existence of an eta-4He unstable bound state close to threshold is hinted by $a_{\eta N} = (0.28, 0.19)$ fm, but is ruled out by large scattering lengths.Comment: 21 pages, LaTex, 7 Figure

Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box

We study the effect of different heating rates of a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the Bose-Einstein condensate fraction.Comment: 7 pages, 8 figure

Evidence of Pentaquark States from K+ N Scattering Data?

Motivated by the recent experimental evidence of the exotic B = S = +1 baryonic state Theta(1540), we examine the older existing data on K+ N elastic scattering through the time delay method. We find positive peaks in time delay around 1.545 and 1.6 GeV in the D03 and P01 partial waves of K+ N scattering respectively, in agreement with experiments. We also find an indication of the J=3/2 Theta* spin-orbit partner to the Theta, in the P03 partial wave at 1.6 GeV. We discuss the pros and contras of these findings in support of the interpretation of these peaks as possible exotics.Comment: 10 pages, 4 figure

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances

Intraurethral Catheter: Alternative Management for Urinary Retention in Patients With Benign Prostatic Hypertrophy

A polyurethane intraurethral catheter (IUC) was used in 27 patients with benign prostatic hypertrophy who were unfit for surgery, or were awaiting surgery. All of them had previously had a periurethral catheter inserted. The IUC was inserted with a cystoscope under fluoroscopic control. Spontaneous voiding through the IUC resumed in 25 patients (93%) in the immediate postprocedure period. At the end of 6 months follow-up, the peak flow rates and the residual volumes estimated in 22 patients were satisfactory. Immediate complications included incontinence due to distal displacement in 2 patients and hematuria in one patient; long-term complications included mild encrustation of the IUC in 2 patients and calculus formation on the IUC in 1 patient. None of the patients had clinically significant urinary tract infection. The presence of the IUC did not compromise the subsequent transurethral resection of the prostate gland. We recommend the use of an IUC for up to 6 months in patients with urinary retention who are awaiting surgery or are unfit for surgery as an alternative to an indwelling urethral catheter

Critical view of WKB decay widths

A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulae for tunneling near the top and the bottom of the barrier are investigated. Though the simple WKB method gives the right order of magnitude of the decay widths, a small number of parameters are often fitted. The need to perform the fitting procedure remaining consistently within the WKB framework is emphasized in the context of the fission model based calculations. Calculations for the decay widths of some recently found super heavy nuclei using microscopic alpha-nucleus potentials are presented to demonstrate the importance of a consistent WKB calculation. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late

Breit Equation with Form Factors in the Hydrogen Atom

The Breit equation with two electromagnetic form-factors is studied to obtain a potential with finite size corrections. This potential with proton structure effects includes apart from the standard Coulomb term, the Darwin term, retarded potentials, spin-spin and spin-orbit interactions corresponding to the fine and hyperfine structures in hydrogen atom. Analytical expressions for the hyperfine potential with form factors and the subsequent energy levels including the proton structure corrections are given using the dipole form of the form factors. Numerical results are presented for the finite size corrections in the 1S and 2S hyperfine splittings in the hydrogen atom, the Sternheim observable $D_{21}$ and the 2S and 2P hyperfine splittings in muonic hydrogen. Finally, a comparison with some other existing methods in literature is presented.Comment: 24 pages, Latex, extended version, title change