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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Choice of gauge in 2-photon 1s-2s transition in atomic hydrogen and pseudostate expansions

The problem of gauge choice in multiphoton transitions in connection with the proper choice of the unperturbed wave functions require to insure gauge invariance was considered. J. Bassani, J. J. Forney, and A. Quattropani considered the case of 2-photon 1s-2s transition rate for hydrogen, using gauges vector E x vector r and vector A x vector p. Exactly the same results were obtained for the two gauges, but the findings indicate that the vector E x vector r interaction tends to the final result with a small number of intermediate states and is therefore the one to be used in any approximate calculation. Whether the so-called pseudostate expansion method works equally well with either gauge was tested. To accomplish this task, in addition to researching the problem, the FORTRAN programming was learned and a FORTRAN program was constructed for the calculation of the dimensionless 2-photon transition probability amplitude D(v) for 1s-2s transition in Hydrogen as a function as a function of the incident photon frequency v in gauge vector E x vector p at certain values of v, using the pseudostate method. However, some puzzling unresolved difficulties were experienced in the calculation. Then should the pseudostate calculations prove successful for gauge vector E x vector r the method will be applied to gauge vector A x vector p. If successful, then the problem is complete.

Shabazz, Abdulalim A.↗
NASA NTRS1990

The effects of vacuum polarization on thermonuclear reaction rates

Added to the pure Coulomb potential, the contribution from vacuum polarization increases the barrier, reducing the wave function (u) for reacting nuclei within the range of nuclear forces. The cross section and reaction rate are then reduced accordingly by a factor proportional to u squared. The effect is treated by evaluating the vacuum polarization potential as a small correction to the Coulomb term, then computing u in a WKB formulation. The calculation is done analytically employing the small r power-series expansion for the Uehling potential to express the final result in terms of convenient parameters. At a temperature of 1.4 x 10 to the 7th K the (negative) correction is 1.3 percent for the fundamental fusion process p + p yields d + e(+) + nu.

Gould, Robert J.↗
NASA NTRS1991

Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox

The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.

Polchinski, Joseph↗
NASA NTRS1991

The determination of accurate dipole polarizabilities alpha and gamma for the noble gases

Accurate static dipole polarizabilities alpha and gamma of the noble gases He through Xe were determined using wave functions of similar quality for each system. Good agreement with experimental data for the static polarizability gamma was obtained for Ne and Xe, but not for Ar and Kr. Calculations suggest that the experimental values for these latter ions are too low.

Rice, Julia E.↗
NASA NTRS1991

Rotational and vibrational effects in the E 1Sigma(+)g-X 1Sigma(+)g two-photon transitions of H2, HD, and D2

This paper reports a theoretical study of the dependence of the E 1Sigma(+)g v(E) = 0, J-X 1Sigma(+)g, v(X),J transitions in H2, HD, and D2 on the initial vibrational and rotational quantum numbers v(X) and J. The results demonstrate the concerted nature of two-photon transitions. The magnitude of the two-photon transition moment increases with v(X) between 0 and 2, then decreases rapidly at higher v(X). The J dependence of the two-photon transition moment is most strongly affected by the changes in vibrational wave functions caused by centrifugal distortion of the vibrational potential. It is shown that the J variation can be used as a probe of resonant tunneling in the double-well potential of the E,F state.

Huo, Winifred M.↗
NASA NTRS1991

The generation of O(1S) from the dissociative recombination of O2(+)

The multichannel quantum defect theory (MQDT) method and large scale wave functions are applied to the calculation of the cross sections and rates for dissociative recombination of O2(+) along the 1Sigma-u(+) dissociative potential. Indirect dissociative recombination is accounted for by simultaneously including both the vibronic and electronic coupling to the intermediate Rydberg resonances. An enhanced MQDT approach involving a second-order K matrix is described. Cross sections and rates for the lowest three vibrational levels of the ion are reported. The shapes of the cross sections are discussed in terms of Fano's profile index. It is found that, for each of the three ion vibrational levels, the intermediate Rydberg resonances reduce the dissociative recombination rate below the direct recombination rate. Just above threshold, resonances with centers below threshold play an important role.

Guberman, Steven L.↗
NASA NTRS1991

1,3P(0) resonance states in positronium ions

The complex-rotation method was used to calculate doubly excited 1,3P(0) autodetaching resonances in Ps(-). The wave function is of the Hylleraas type with number of terms up to 1330, and Feshbach resonances connected with the positronium n = 4, 5, and 6 thresholds are reported. The study has also identified 1P(0) shape resonances connected with the n = 4 and 6 thresholds and a 3P(0) shape resonance connected with the n = 5 threshold.

Ho, Y. K.↗
NASA NTRS1991

Complex-coordinate calculation of D-(1,3) resonances in two-electron systems

Feshbach-type D-(1,3)resonances in two-electron systems, Z = 2-10, have been investigated using the method of complex rotation. These states lie below the n = 2 and 3 thresholds of hydrogenic systems. Wave functions containing up to 1230 Hylleraas functions have been used, giving accurate results for positions and widths. Comparisons between various calculations are given.

Ho, Y. K.↗
NASA NTRS1990

Time-dependent treatment of scattering - Integral equation approaches using the time-dependent amplitude density

The time-dependent form of the Lippmann-Schwinger integral equation is used as the basis of several new wave packet propagation schemes. These can be formulated in terms of either the time-dependent wave function or a time-dependent amplitude density. The latter is nonzero only in the region of configuratiaon space for which the potential is nonzero, thereby in principle obviating the necessity of large grids or the use of complex absorbing potentials when resonances cause long collision times (leading, consequently, to long propagation times). Transition amplitudes are obtained in terms of Fourier transforms of the amplitude density from the time to the energy domain. The approach is illustrated by an application to a standard potential scattering model problem where, as in previous studies, the action of the kinetic energy operator is evaluated by fast Fourier transform (FFT) techniques.

Hoffman, David K.↗
NASA NTRS1992

Localization of one-photon state in space and Einstein-Podolsky-Rosen paradox in spontaneous parametric down conversion

An experiment on one-photon state localization in space using a correlation technique in Spontaneous Parametric Down Conversion (SPDC) process is discussed. Results of measurements demonstrate an idea of the Einstein-Podolsky-Rosen (EPR) paradox for coordinate and momentum variables of photon states. Results of the experiment can be explained with the help of an advanced wave technique. The experiment is based on the idea that two-photon states of optical electromagnetic fields arising in the nonlinear process of the spontaneous parametric down conversion (spontaneous parametric light scattering) can be explained by quantum mechanical theory with the help of a single wave function.

Penin, A. N.↗
NASA NTRS1992

Going through a quantum phase

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Shapiro, Jeffrey H.↗
NASA NTRS1992

Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Yeon, Kyu Hwang↗
NASA NTRS1992

Confining potential in momentum space

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.

Norbury, John W.↗
NASA NTRS1992

Importance of parametrizing constraints in quantum-mechanical variational calculations

In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.

Chung, Kwong T.↗
NASA NTRS1990

Magnetism and electron pairing in high-Tc superconductors

Correlated wave functions are used for YBa2Cu3O(7-y) where epsilon(d)-epsilon(p) is about 0 for Cu3d- and 02p-electrons. The electrons are delocalized (metallic) for y less than 0.5 with weak and temperature-independent paramagnetism. In contrast, the systems are conventional antiferromagnetic insulators for y greater than 0.6 with a narrow y between 0.5 and 0.6 transition region. These results are in agreement with magnetic and neutron diffraction data.

Tsang, T.↗
NASA NTRS1992

A simple correction for the Born approximation for electron impact excitation of hydrogenic ions

An analytic procedure is developed for obtaining the electron impact excitation cross sections for hydrogenic ions. A simple modification of the Born approximation, in order to include Coulomb focusing of the continuum wave functions, produces the correct energy dependence of the cross section near excitation threshold. This procedure is used to compute the 1s yields 2s and 1s yields 2p excitation cross sections for hydrogenic ions (Z approaches infinity), and compare these modified-Born cross sections with numerical Colomb-Born calculations. The modified-Born cross sections agree well with the Coulomb-Born cross sections and thus provide a reliable generalized analytic expression for electron impact excitation of hydrogenic ions. By treating effective charges, the results in this work can be extended to nonhydrogenic target systems.

Jung, Young-Dae↗
NASA NTRS1993

Wave packet motion in harmonic potential and computer visualization

Wave packet motions of a single electron in harmonic potentials or a magnetic field are obtained analytically. The phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the electron changes its width and central position periodically. These results are visualized using computer animation techniques.

Tsuru, Hideo↗
NASA NTRS1993

Point form relativistic quantum mechanics and relativistic SU(6)

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

Klink, W. H.↗