Highly Excited States of a Hydrogen Atom in a Strong Magnetic Field

Classical trajectories and semiclassical energy eigenvalues are calculated for an atomic electron in a high Rydberg state in an external magnetic field. With the use of perturbation theory, a classical trajectory is described as a Kepler ellipse with orbital parameters evolving slowly with time. As they evolve, the ellipse rocks, tilts, and flips in space, but the length of its major axis remains approximately constant. Exact numerical calculations verify that perturbation theory is quite accurate for the cases considered (principal quantum number ≃ 30, magnetic field ≲ 6 T). Action variables are calculated from perturbation theory and from exact trajectories, and semiclassical eigenvalues are obtained by quantization of action. Excellent agreement is found with observations

Trajectories of an Atomic Electron in a Magnetic Field

Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength B. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to LzB13). For small values of this parameter there is an elliptical regime in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values of the parameter there is a helical regime in which the electron circles rapidly around a magnetic field line and bounces slowly back and forth along the field. Between these two regimes there is an irregular regime, with chaotic orbits and a transition regime in which the trajectories can be described in oblate spheroidal coordinates. Bound states persist even at energies above the escape energy, provided that the angular momentum (or field strength) is sufficiently large. With use of action-variable quantization, some formulas for semiclassical energy eigenvalues are given for regimes where the trajectories are regular

Excessive gas exchange impairment during exercise in a subject with a history of bronchopulmonary dysplasia and high altitude pulmonary edema

A 27-year-old male subject (V(O2 max)), 92% predicted) with a history of bronchopulmonary dysplasia (BPD) and a clinically documented case of high altitude pulmonary edema (HAPE) was examined at rest and during exercise. Pulmonary function testing revealed a normal forced vital capacity (FVC, 98.1% predicted) and diffusion capacity for carbon monoxide (D(L(CO)), 91.2% predicted), but significant airway obstruction at rest [forced expiratory volume in 1 sec (FEV(1)), 66.5% predicted; forced expiratory flow at 50% of vital capacity (FEF(50)), 34.3% predicted; and FEV(1) /FVC 56.5%] that was not reversible with an inhaled bronchodilator. Gas exchange worsened from rest to exercise, with the alveolar to arterial P(O2) difference (AaD(O2)) increasing from 0 at rest to 41 mmHg at maximal normoxic exercise (VO(2) = 41.4 mL/kg/min) and from 11 to 31 mmHg at maximal hypoxic exercise (VO(2) = 21.9 mL/kg/min). Arterial P(O2) decreased to 67.8 and 29.9 mmHg at maximal normoxic and hypoxic exercise, respectively. These data indicate that our subject with a history of BPD is prone to a greater degree of exercise-induced arterial hypoxemia for a given VO(2) and F(I(O2)) than healthy age-matched controls, which may increase the subject's susceptibility to high altitude illness

Bound State Semiclassical Wave Functions

The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for a two‐dimensional bound state system. We investigate in detail an eigenstate of a coupled anharmonic oscillator system. The primitive semiclassical wave function is obtained from the characteristic function S and the density function J. Each of these functions consists of four branches corresponding to the four possible directions of motion of the classical trajectory through any point. The interference from the four branches determines the basic structure of the wave function. A uniform approximation gives a wave function which is well behaved along each caustic and which is in good agreement with the fully quantal wave function

Semiclassical Theory of Inelastic Collisions I. Classical Picture and Semiclassical

This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, iℏddtdi(t)=Σjhij(t)dj(t), which describe the time dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared

Use of Preclinical Models to Improve Treatment of Retinoblastoma

Dyer and colleagues examine the most promising preclinical models that recapitulate the molecular, genetic, and cellular features of retinoblastoma

Accumulation of driver and passenger mutations during tumor progression

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a novel mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development - providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate, for the first time, the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small, 0.005 +- 0.0005, and has major implications for experimental cancer research

Hydrogen-Helium Mixtures at High Pressure

The properties of hydrogen-helium mixtures at high pressure are crucial to address important questions about the interior of Giant planets e.g. whether Jupiter has a rocky core and did it emerge via core accretion? Using path integral Monte Carlo simulations, we study the properties of these mixtures as a function of temperature, density and composition. The equation of state is calculated and compared to chemical models. We probe the accuracy of the ideal mixing approximation commonly used in such models. Finally, we discuss the structure of the liquid in terms of pair correlation functions.Comment: Proceedings article of the 5th Conference on Cryocrystals and Quantum Crystals in Wroclaw, Poland, submitted to J. Low. Temp. Phys. (2004

Differential cross sections for pion charge exchange on the proton at 27.5 MeV

We have measured pion single charge exchange differential cross sections on the proton at 27.5 MeV incident $\pi^-$ kinetic energy in the center of momentum angular range between $0^\circ$ and $55^\circ$. The extracted cross sections are compared with predictions of the standard pion-nucleon partial wave analysis and found to be in excellent agreement.Comment: ReVTeX v3.0 with aps.sty, 23 pages in e-print format, 7 PostScript Figures and 4 Tables, also available via anonymous ftp at ftp://helena.phys.virginia.edu/pub/preprints/scx.p

Analytically Derived Switching-Functions For Exact H-2(+) Eigenstates

Electron translation factors (ETF\u27s) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical two-center decomposition of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the angle variable of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-∊R22, where ∊ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic optimization scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV