Photodetachment Cross Section of H- in Crossed Electric and Magnetic Fields. II. Quantum Formulas and Their Reduction to the Result of the Closed-Orbit Theory

In this, the second of two papers, we derive general quantum formulas for the photodetachment cross section for H− in perpendicular electric and magnetic fields. The results are valid for any polarization and can be reduced to the semiclassical results of the first paper [A. D. Peters and J. B. Delos, Phys. Rev. A 47, 3020 (1993)]: a smooth background plus oscillatory terms. This connection between the quantum and semiclassical results is made using a stationary-phase approximation and it is shown that each stationary-phase point corresponds to a closed orbit

The Private Costs of Commercial Forestry, Reforestation and Social Forestry

This article is prepared for the Upland Policy Conference on March 14, 1988. It analyzes the private perspective of upland resource management mechanisms by drawing from the salient findings of studies on commercial forestry, reforestation and communal tree farming conducted under PIDS/IDRC upland resources research program.natural resources and environment, forestry sector, environmental issues, farm lands, environmental management, uplands

The Private Costs of Commercial Forestry, Reforestation and Social Forestry

This article is prepared for the Upland Policy Conference on March 14, 1988. It analyzes the private perspective of upland resource management mechanisms by drawing from the salient findings of studies on commercial forestry, reforestation and communal tree farming conducted under PIDS/IDRC upland resources research program.natural resources and environment, forestry sector, environmental issues, farm lands, environmental management, uplands

Grouper culture in floating net cages

The manual describes the culture of groupers (Epinephelus) in floating cages, providing a farming option for grouper growers and also a production alternative to the farmed species being done today, such as shrimp, milkfish and tilapia. The following aspects are covered: species identification for commercially cultured groupers; source of stock; net cage specifications; anchor; hides and shelters; nursery net cage operation; production cages; harvesting; post-harvest; profitability analysis of grouper cage culture; and, cost and return of growing grouper in cages

Half-Cycle Pulse Acting on a One-Dimensional Rydberg Atom: Semiclassical Transition Amplitudes in Action and Angle Variables

In this paper we derive the expression for the transition coefficient used in the preceding paper [C. D. Schwieters and J. B. Delos, Phys. Rev. A 51, 1023 (1995)] for principal-quantum-number transitions in one-dimensional hydrogen caused by half-cycle pulses. We briefly review the methods of Miller [Adv. Chem. Phys. 25, 69 (1974)] and Marcus [Chem. Phys. Lett. 7, 525 (1970); J. Chem. Phys. 54, 3965 (1971)], and then derive the result using the methods of Maslov and Fedoriuk [Semi-Classical Approximation in Quantum Mechanics, (Reidel, Dordrecht, 1981)]. Also, we examine the approximate reduction of hydrogen from three to one dimension and we find a hitherto unknown correction due to the residual motion of one of the ignored degrees of freedom. We discuss the regime of validity of this one-dimensional approximation

Photodetachment Cross Section of H- in Crossed Electric and Magnetic Fields. I. Closed-Orbit Theory

In this, the first of two papers, we obtain a simple analytic formula for the photodetachment cross section of H− in crossed electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and these oscillations are correlated with closed classical orbits. In the following paper [A. D. Peters and J. B. Delos, Phys. Rev. A 47, 3036 (1993)] we derive fully-quantum-mechanical formulas for the cross section in perpendicular electric and magnetic fields and show how these results can be reduced to the semiclassical results of this paper

Bifurcation of the Periodic Orbits of Hamiltonian Systems: An Analysis using Normal Form Theory

We develop an analytic technique to study the dynamics in the neighborhood of a periodic trajectory of a Hamiltonian system. The theory begins with Poincaré and Birkhoff; major modern contributions are due to Meyer, Arnol\u27d, and Deprit. The realization of the method relies on local Fourier-Taylor series expansions with numerically obtained coefficients. The procedure and machinery are presented in detail on the example of the ‘‘perpendicular’’ (z=0) periodic trajectory of the diamagnetic Kepler problem. This simple one-parameter problem well exhibits the power of our technique. Thus, we obtain a precise analytic description of bifurcations observed by J.-M. Mao and J. B. Delos [Phys. Rev. A 45, 1746 (1992)] and explain the underlying dynamics and symmetries. © 1996 The American Physical Society

Organization and Bifurcation of Planar Closed Orbits of an Atomic Electron in Crossed Fields

We describe the patterns of creation and splitting of planar closed orbits of electrons in hydrogen atoms in crossed electric and magnetic fields. These orbits lie in the plane perpendicular to the magnetic field, and they start and end at the nucleus. Using a Poincaré map to study the regular motions, we observe that the bifurcations of planar closed orbits fall into an ordered sequence as energy changes: a “tangent bifurcation” creates one closed orbit that splits into two; subsequently, one of them becomes periodic, and splits by a “pitchfork bifurcation” into two periodic orbits and one closed orbit. Based on these calculations, we classify the closed orbits that are involved in a sequence of bifurcations in a family, and we name the family by the winding ratio of the periodic orbits in the family. To understand this ordered sequence of bifurcations, we create a simple integrable Hamiltonian as a model of the Poincaré map. This model gives a simple interpretation of the sequence of the bifurcations. The model contains only general assumptions, so we expect that such sequences of bifurcations of closed orbits will be commonly found in physical systems

Semiclassical Treatment of a Half-Cycle Pulse Acting on a One-Dimensional Rydberg Atom

The final-state distribution of hydrogen, acted upon by a 1/2-cycle pulse, has been calculated semiclassically for a proposed one-dimensional experiment. This work was motivated by the recent experimental realization of half-cycle pulses by Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] in which preliminary studies of ionization and state redistribution for hydrogenlike atoms were carried out. To simplify the situation theoretically, an experiment is proposed in which an additional weak static electric field is imposed and approximately one-dimensional states are selected. Within this one-dimensional approximation the transition probability to various n states (n is the principal quantum number) has been calculated as a function of the amplitude of the half-cycle pulse, using a semiclassical formula due to Miller [Adv. Chem. Phys. 25, 69 (1974)]. A complete derivation of this formula and a discussion of approximations are made in the following paper. We have found that an even number of trajectories always contributes to the transition probability and leads to observable interference effects. In addition, we find that bifurcations of these trajectories can occur, resulting in resonances and more complicated interference structures

Inner cusps of the first dark matter haloes: Formation and survival in a cosmological context

We use very high resolution cosmological zoom simulations to follow the early evolution of twelve first-generation haloes formed from gaussian initial conditions with scale-free power spectra truncated on small scales by a gaussian. Initial collapse occurs with a diverse range of sheet- or filament-like caustic morphologies, but in almost all cases it gives rise to a numerically converged density cusp with $\rho = Ar^{-3/2}$ and total mass comparable to that of the corresponding peak in the initial linear density field. The constant $A$ can be estimated to within about 10 per cent from the properties of this peak. This outcome agrees with earlier work on the first haloes in cold and warm dark matter universes. Within central cusps, the velocity dispersion is close to isotropic, and equidensity surfaces tend to align with those of the main body of the halo at larger radii. As haloes grow, their cusps are often (but not always) overlaid with additional material at intermediate radii to produce profiles more similar to the Einasto or NFW forms typical of more massive haloes. Nevertheless, to the extent that we can resolve them, cusps survive at the smallest radii. Major mergers can disturb them, but the effect is quite weak in the cases that we study. The cusps extend down to the resolution limits of our simulations, which are typically a factor of several larger than the cores that would be produced by phase-space conservation if the initial power spectrum cutoff arises from free streaming.Comment: 23 pages, 28 figures; to be submitted to MNRA