Reflection at a complex potential barrier in the semiclassical theory of scattering

The reflection of spherical waves at a complex potential barrier is discussed in the semiclassical approximation. We study the complex WKB method and the Uniform Approximation in the special case of weakly absorptive barriers, typical of surface transparent optical potentials used in heavy-ion reactions. It is found that the complex WKB results lead to a very accuratecross- section despite their inaccuracy in the most importantphase shifts. Thereby, the amazing stamina of the WKB has been confirmed once more. One of us (Y.A.) spent the summer of 1976 at the Max-Planck Institute at Heidelberg where the present work has been done. He would like to thank J. Hüfner and H. Weidenmüller for the hospitality extended to him.     

Synthesis and characterization of titanium nitride, niobium nitride, and tantalum nitride nanocrystals via the RAPET (reaction under autogenic pressure at elevated temperature) technique

TiN, NbN, and TaN nanocrystals have been selectively prepared through a simple, solvent-free, and convenient reaction under autogenic pressure at moderate temperature (RAPET) process at 350 °C for 12 h, reacting transition metal chlorides and sodium azide. The nanostructures obtained are characterized by powder X-ray diffraction (PXRD), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). A reaction mechanism is suggested based on the experimental results. These rapid reactions produce nanocrystals of TiN, NbN, and TaN with average sizes of approximately 30, 28, and 27 nm, respectively (as calculated from X-ray line broadening). An octahedral inorganic fullerene was detected among the various structures of the TiN.     

Designing a call center with an IVR (Interactive Voice Response)

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality and Efficiency Driven) or the Halfin–Whitt regime, which accommodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.     

Semiclassical analysis of edge state energies in the integer quantum Hall effect

Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separately, this problem is equivalent to that of a one dimensional harmonic oscillator centered at x = x_c and an infinite wall at x = 0, and appears in numerous physical contexts. The eigenvalues E_n(x_c) for a given quantum number n are solutions of the equation S(E,x_c)=π[n+ γ(E,x_c)] where S is the WKB action and 0 < γ < 1 encodes all the information on the connection procedure at the turning points. A careful implication of the WKB connection formulae results in an excellent approximation to the exact energy eigenvalues. The dependence of γ[E_n(x_c),x_c] ≡γ_n(x_c) on x_c is analyzed between its two extreme values as x_c ↦-∞ far inside the sample and as x_c ↦∞ far outside the sample. The edge-state energiesE_n(x_c) obey an almost exact scaling law of the form and the scaling function f(y) is explicitly elucidated.     

Measurement of the K(L) charge asymmetry

We present a measurement of the charge asymmetry delta(L) in the mode K(L)-->pi(+/-)e(-/+)nu based on 298 x 10(6) analyzed decays. We measure a value of delta(L) = [3322+/-58(stat)+/-47(syst)]x10(-6), in good agreement with previous measurements and 2.4 times more precise than the current best published result. The result is used to place more stringent limits on CPT and DeltaS = DeltaQ violation in the neutral kaon system.     

Search for the decay KL --> pi(0)e+e-

We report on a search for the decay KL-->pi(0)e+e- carried out by the KTeV/E799 experiment at Fermilab. This decay is expected to have a significant CP violating contribution and the measurement of its branching ratio could support the Cabibbo-Kobayashi-Maskawa mechanism for CP violation or could point to new physics. Two events were observed in the 1997 data with an expected background of 1.06+/-0.41 events, and we set an upper limit B(KL-->pi(0)e+e-)<5.1 x 10(-10) at the 90% confidence level.     

Study of the K(0)(L) --> pi(+)pi(-)gamma Direct Emission Vertex

We have performed studies of the K(0)(L)-->pi(+)pi(-)gamma direct emission ( DE) and inner Bremsstrahlung ( IB) vertices, based on data collected by KTeV during the 1996 Fermilab fixed target run. We find a(1)/a(2) = -0.737+/-0.034 GeV2 for the DE form-factor parameter in the rho-propagator parametrization, and report on fits of the form factor to linear and quadratic functions as well. We concurrently measure gamma(K(0)(L)-->pi(+)pi(-)gamma,E(*)(gamma)>20 MeV)/gamma(K(0)(L)-->pi(+)pi(-)) = (20.8+/-0.3)x10(-3), and a K(0)(L)-->pi(+)pi(-)gamma DE/(DE+IB) branching ratio of 0.683+/-0.011.     

First measurement of form factors of the decay Xi(0) --> Sigma(+)e(-)nu macro(e)

We present the first measurement of the form factor ratios g(1)/f(1) (direct axial vector to vector), g(2)/f(1) (second class current), and f(2)/f(1) (weak magnetism) for the decay Xi(0)-->Sigma(+)e(-)nu macro(e) using the KTeV (E799) beam line and detector at Fermilab. From the Sigma(+) polarization measured with the decay Sigma(+)-->p pi(0) and the e(-)-nu; correlation, we measure g(1)/f(1) to be 1.32+/-(0.21)(0.17)(stat)+/-0.05(syst), assuming the SU(3)(f) (flavor) values for g(2)/f(1) and f(2)/f(1). Our results are all consistent with exact SU(3)(f) symmetry.