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Deexcitation rates, lifetimes, and branching ratios are calculated for all the J = 0, J = 1, and J = 2 bound states of the muonic molecular ion td(mu) when it serves as the nucleus of a hydrogen atom. The J = 2 binding energy (E2 = 101.59 eV) is the first reported variational result for this state. It is found that the excited J = 0 state is populated several hundred times as often as the ground state.
The equation of state of cold dense matter in strong magnetic fields is calculated in the Thomas-Fermi and Thomas-Fermi-Dirac approximations. For use in the latter calculation, a new expression is derived for the exchange energy of the uniform electron gas in a strong magnetic field. Detailed calculations of the density profile in the surface region of a neutron star are described for a variety of equations of state, and these show that the surface density profile is strongly affected by the magnetic field, irrespective of whether or not matter in a magnetic field has a condensed state bound with respect to isolated atoms. It is also shown that, as a consequence of the field dependence of the screening potential, magnetic fields can significantly increase nuclear reaction rates.
In the present evaluation of the rate of direct positron annihilation with electrons in the nonrelativistic limit, general analytic expressions are given for the radiative recombination of positrons to form positronium. Formulae are derived for the radiative capture to bound states of atomic hydrogen, and the connection between the two problems is demonstrated. Annihilation from excited states of positronium is considered, and it is estimated that 90 percent of the annihilations occur from the ground 1s state for both ortho and para positronium following radiative capture and cascade. A convenient form is given for the photodissociation cross section of positronium.
The adaptation of the molecular R-matrix method, originally developed for electron-molecule collision studies, to positron scattering is discussed. Ab initio R-matrix calculations are presented for collisions of low energy positrons with a number of diatomic systems including H2, HF and N2. Differential elastic cross sections for positron-H2 show a minimum at about 45 deg for collision energies between 0.3 and 0.5 Ryd. The calculations predict a bound state of positronHF. Calculations on inelastic processes in N2 and O2 are also discussed.
No one likes to see a scattering cross section curve that is too smooth; it is much more interesting to find bumps and wiggles and most interesting if it is possible to understand their cause. Several types of resonances were clearly established in positron-containing systems: those lying just below a degenerate threshold (like 2s-2p in hydrogenic atoms or ions) and those representing Coulomb bound states in a rearranged channel (like Ps + H reversing positron +H(-)). Recently, two new sorts of resonances have been reported for which the resonant mechanism is not clear. The first is a very low lying resonance in the e-Ps system (obtained by an adiabatic expansion method), and the second is a similarly low lying two channel resonance in the positron -H system (obtained by a close-coupling technique.) These developments encouraged the examination of such systems using the standard methods of stabilization and complex rotation. Most of the results are negative; the low lying resonances in either system are verified. Some indication of new resonances in the e(+)-He(+) system is found; this may be caused by the attraction between Ps in the n=2 state and the He(++) nucleus.
Cross sections for positronium formation by capture from the negative hydrogen ion are given. Orthogonalization corrections to the Coulomb (First) Born Approximation (CBA) differential and total cross sections are calculated using approximate H- wave functions of both Lowdin and Chandrasekhar. Various methods of orthogonalizing the unbound projectile to the possible bound states are considered. It is found that treating the atomic nuclei as if they were isotopic spin projections of a single type of nucleon gives cross sections that are an improvement over the CBA.
Close-coupling calculations are carried out for radiative processes in neutral carbon and a number of carbon-like ions; energy levels, oscillator strengths, and photoionization cross sections have been computed for all bound states of the type 2 s(j)2p(k)nl with n not above 10 and 1 not above 3. The R-matrix method is employed to solve the coupled equations with a ten-state eigenfunction expansion for the parent ion C II and an eight-state expansion for the other boron-like target ions. A number of selected results for oscillator strengths are presented and compared with earlier data, as well as for photoionization cross sections with autoionizing resonance structures. Isoelectronic trends are discussed. The present results for the oscillator strengths of C I and N II are found to differ significantly from some earlier theoretical works for a number of transitions. However, the present C I f values are in excellent agreement with recent calculations and experimental results.
It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.
Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
Researchers fabricated and characterized several AlGaAs/GaAs multiple quantum well infrared detectors to evaluate the ultimate performance of these devices for low infrared background applications. The detectors were designed to have a single bound state in the quantum well and the first excited state in the continuum above the AlGaAs conduction band edge. The difference in energy between the two levels, as determined by the quantum well width and aluminum mole fraction in the barrier, was chosen such that peak absorption would occur near 8 microns. The initial structures studied comprised 50 periods with 40 A well widths and 300 A Al(0.28)Ga(0.72)As barriers. The performance of these detectors are summarized. To better interpret these results and design optimized detectors, researchers modeled both the detector noise and tunneling currents. The noise model correctly predicts that multiple quantum well detectors will, indeed, exhibit noise lower than full shot noise. The tunneling current model predicts the dark current versus bias for any choice of design parameters in a multiple quantum well detector. This model predicts a substantially reduced dark current (x 10(exp 04)) for samples with 400 A barriers. To evaluate structures with thicker barriers, researchers fabricated and characterized detectors with 400 A and 500 A barriers; a comparison of detector dark currents is shown. These results are consistent with the predictions of the dark current model.
Amorphous Si:H and amorphous Si sub x, Ge sub (1-x):H solar cells were irradiated with 1.00 MeV proton fluences in the range of 1.00E14 to 1.25E15 cm (exp -2). Annealing of the short circuit current density was studied at 0, 22, 50, 100, and 150 C. Annealing times ranged from an hour to several days. The measurements confirmed that annealing occurs at 0 C and the initial characteristics of the cells are restored by annealing at 200 C. The rate of annealing does not appear to follow a simple nth order reaction rate model. Calculations of the short-circuit current density using quantum efficiency measurements and the standard AM1.5 global spectrum compare favorably with measured values. It is proposed that the degradation in J sub sc with irradiation is due to carrier recombination through the fraction of D (o) states bounded by the quasi-Fermi energies. The time dependence of the rate of annealing of J sub sc does appear to be consistent with the interpretation that there is a thermally activated dispersive transport mechanism which leads to the passivation of the irradiation induced defects.
A finite time, minimum force rate-feedback-threshold controller is developed to bring a system with or without known external disturbances back into an 'allowable' state bound in finite time. The disturbances are assumed to be expandable in terms of Fourier series. The optimal control is defined by a two-point boundary value problem coupled to a set of definite integral constraints. Quasi-closed form solutions are derived which replace the solution of the two-point boundary value problem and definite integral constraints with the solution of algebraic equations and the calculation of matrix exponentials. Examples are provided which demonstrate the threshold control technique and compare the quasi-closed form solutions with numerical and MACSYMA generated exact solutions.
A method has been developed for solving two body relativistic bound state equations in momentum space with a confining interaction. A total of six different three dimensional reductions of the Bethe-Salpeter equations are studied with particular emphasis placed on the competing roles of relativistic kinematics and retardation. The results indicate that these two effects counteract each other and this sheds some light on why nonrelativistic models of meson spectroscopy have been quite successful.
A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.
A typical viscoplastic model will introduce up to three types of internal state variables in order to properly describe transient material behavior; they are as follows: the back stress, the yield stress, and the drag strength. Different models employ different combinations of these internal variables--their selection and description of evolution being largely dependent on application and material selection. Under steady-state conditions, the internal variables cease to evolve and therefore become related to the external variables (stress and temperature) through simple functional relationships. A physically motivated hypothesis is presented that links the kinetic equation of viscoplasticity with that of creep under steady-state conditions. From this hypothesis one determines how the internal variables relate to one another at steady state, but most importantly, one obtains bounds on the magnitudes of stress and back stress, and on the yield stress and drag strength.
A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.