Net Transition Research Articles

Spin-lattice relaxation in magnetic ion pairs

A new theoretical model of spin-lattice relaxation for magnetic "ion pairs" has been developed in which both the "spin-phonon" and "spin-spin" interactions are jointly effective in producing a net relaxation transition. The Raman-type indirect two-phonon relaxation rate for non-Kramers as well as Kramers ion pairs shows ${T}^{7}$ dependence at low temperatures and ${T}^{3}$ dependence at high temperatures. The ${T}^{3}$ dependence is entirely a new result. The ${T}^{7}$ dependence for Kramers pairs is also a new result as it is not possible in the usual Van Vleck mechanism. Even the ${T}^{7}$ dependence for non-Kramers ion pairs is different from a similar standard result for unpaired ions. It appears that the electronic spin relaxation behavior of ion pairs may be quite different from that of unpaired ions.

A model of enforcement relationships among database access control dependencies

The various kinds of access decision dependencies within a predicate-based model of database protection are classified according to cost of enforcement. Petri nets and some useful extensions are described. Extended Petri nets are used to model the flow of messages and data during protection enforcement within MULTISAFE, a multimodule system architecture for secure database management. The model demonstrates that some of the stated criteria for security are met within MULTISAFE. Of particular interest is the modeling of data dependent access conditions with predicates at Petri net transitions. Tokens in the net carry the intermodule messages of MULTISAFE. Login, authorization, and database requests are traced through the model as examples. The evaluation of complex access condition predicates is described for the enforcement process. Queues of data and queues of access condition predicates are cycled through the net so that each data record is checked against each predicate. Petri nets are shown to be a useful modeling tool for database security.

Gauge-invariant time-dependent perturbation theory. II. degenerate case

For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.

Gauge-invariant time-dependent perturbation theory

A manifestly gauge-invariant time-dependent perturbation theory is developed. The first-order and the second-order net transition rates are obtained for the exact fields. These gauge-invariant transition rates are compared with their conventional counterparts. It is found that the conventional and the gauge-invariant perturbative (only) transitions agree completely.

A MINDO/3 MO study of oxidized flavins

The use of semi-empirical molecular orbital methods for the study of biologically important molecules has increased in recent years. The validity of well-known approximate Hartree-Fock molecular orbital methods such as MINDO/3 and MNDO still remains largely untested for biological molecules. Here we report its first application to the study of the electronic structures of isoalloxazines. Electronic charge distribution, variation of dipole moment, first ionization potential, electron affinity, orbital energies and electronic transitions are examined. Some of these results are compared with experiments. Good correlations with experiments were generally found in net atomic charge distributions, ionization potentials and electronic transitions. As a result of relatively good correlations with experiment application of the MINDO/3 method for extended study of biologically important coenzymes is promising.

Parallel permit grammars and some graph representations of Petri nets

The graph of a set grammar is introduced in such a way that each set rule of the grammar is represented by a cartesian subgraph of it. The correspondence between cartesian subgraphs and transitions of Petri nets (which satisfy the axiom of extensionality) is established. The set grammars with input (initial) and output (terminal) elements are studied in an analogy to Chomsky's string grammars and their strong equivalence. Permit rules and parallel permit rules are introduced in such a way that parallel permit grammars are more general tools than Petri nets themselves, because the equivalence between homogeneous parallel permit grammars and set grammars (and Petri nets) is proved.

Cross Pressures During Socialization for Medicine

Processes of socialization with respect to three principal role components of the competent physician are analyzed by means of turnover tables between contiguous periods observed during a longitudinal study. Summary measures concerning the net turnover, transition probabilities and continuous time transition rates permit an analysis of the overall process of change from a point in time prior to the start offormal socialization all the way to the end of year six when formal socialization ends. Findings show that the process of socialization with respect to the People component is characterized by ambivalence which is expressed in almost balanced positive and negative cross pressures concerning the importance of this component in the role of the competent physician. The process of change with respect to the Status component is an absorbing Markov chain: change is in a positive direction and occurs rather quickly so that by the end of year three virtually all of the population has moved to a positive position on this component and practically no change is evident during subsequent years. With respect to the Science component the data show that pressures are consistently and dominantly negative during the entire process with few counter pressures in a positive direction.

Effect of Caffeine on the Human Small Intestine

Methylxanthines produce intracellular accumulation of cyclic 3'5'-AMP (cAMP) by inhibition of phosphodiesterase and mucosal cAMP accumulation. Cyclic AMP is thought to mediate small intestinal secretion caused by some enterotoxins, hormones, and methylxanthines. These studies were designed to evaluate the effect of caffeine on small intestinal net fluid movement and transit times. The administration of caffeine in amounts ordinarily contained in many beverages and medications (75 to 300 mg) resulted in striking net secretion in the jejunum which lasted at least 15 minutes. This occurred in six of seven studies. Baseline net absorption of 0.5 ml per cm per hr was reversed to net secretion of 6.0 +/- 2.2 ml per cm per hr after oral caffeine ingestion (P less than 0.01). Net secretion also occurred in the ileum in seven of eight studies, but the onset of secretion appeared 35 min later than in the jejunum. These patterns of secretion correlated best with the passage of the intestinal bolus of caffeine rather than plasma caffeine levels. In contrast to other net secretory conditions, which increase the speed of transit, small intestinal transit times, as determined by dye dilution methods, were unchanged by caffeine. It is possible that methylxanthine-induced small intestinal secretion may play a role in the symptoms experienced by some patients with functional diarrhea.

Tunneling between Superconductors in the Vortex State

Superconductor-insulator-superconductor (S-I-S) and S/sub 1/-I-S/sub 2/ tunne l junctions have been studied with the thin-film electrodes in a dilute vortex state, at temperatures such that the tunneling is predominantly due to the vortex-core excitations. We conclude that the vortex cores in the upper film lie on top of those in the lower film, but that the net tunneling transition probability between vortex-core states is very much smaller than usual tunneling probabilities. (auth)

Raman ion-lattice interaction processes and the linewidth problem

The earlier work on harmonic raman ion-lattice interaction processes is extended to systems with an arbitrary number of ionic energy levels. The weisskopf-wigner linewidth-lifetime relation (that the full width is the sum of the inverse lifetimes of the two states) is valid only for those linewidth contributions arising from raman processes in which there is a net electronic transition, that is, processes which contribute to depopulation rates. This includes the usual three level raman processes and the semidiagonal process, but not the self energy raman process; for the latter process, transition probability amplitudes combine coherently.

Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution

The singularities of x-ray absorption or emission in metals are studied by a new "one-body" method, which describes the scattering of conduction electrons by the transient potential due to the deep hole. Using the linked-cluster theorem, the net transition rate in the time representation is expressed as the product of two factors: a one-electron transient Green's function $L$, and the deep-level Green's function $\mathcal{G}$. These factors obey simple Dyson equations, which can be solved asymptotically by using Muskhelishvili's method. The x-ray transition rate is found to behave as $\frac{1}{{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}}$, where $\ensuremath{\epsilon}$ is the frequency measured from the threshold, and $\ensuremath{\alpha}$ an exponent involving the various phase shifts ${\ensuremath{\delta}}_{l}$ which describe scattering by the deep hole. $\ensuremath{\alpha}$ may be >0 (infinite threshold) or 0 (zero threshold). The experimental implications of these results and their relation to the Friedel sum rule are briefly discussed.

Phase Memory in Electron Spin Echoes, Lattice Relaxation Effects in CaWO4: Er, Ce, Mn

The electron-spin-echo phase memory ${T}_{M}$ has been studied both experimentally and theoretically for the specific case in which it is limited by the lattice relaxation processes occurring in the sample. The relevant mechanism is as follows. Lattice relaxation of any spins, whether or not they belong to the species being observed, causes fluctuations in the local fields and so destroys the relations between precessional phases which lead to the generation of echoes. The effect of these fluctuations on the echo amplitude can be calculated by taking an ensemble average for the precessing spins and for all the environmental spins which give rise to significant time variations of the local fields in the sample. The problem reduces to that of finding a time and a space average. The space average has been obtained here by assuming a random distribution of spins in the paramagnetic sample, and by applying the statistical methods of Margenau. In order to obtain the time average, two models have been chosen to represent the time variation of the components ${\ensuremath{\mu}}_{z}$ for the relaxing spins. In one model, the ${\ensuremath{\mu}}_{z}$ are treated as Gaussian random variables (Gauss-Markoff model), and in the other the spins are assumed to make sudden jumps at random times between the "spin-up" and "spin-down" quantum states (sudden-jump model). Different forms of echo envelope are derived for the two models. Further differences in behavior will be observed, according to whether the sample is singly or doubly doped. If the sample contains only one spin species, ${T}_{M}$ becames shorter as the temperature is raised and as the lattice relaxation time ${T}_{1}$ is reduced. Initially, ${T}_{M}$ is limited by local field fluctuations and may be considerably shorter than ${T}_{1}$. Eventually, as the lattice relaxation of the precessing spins themselves becomes the dominant factor, ${T}_{1}$ and ${T}_{M}$ tend to the same value. If the sample contains two species $A$ and $B$, where $B$ relaxes more rapidly than $A$, then ${T}_{M}(A)$ and ${T}_{M}(B)$ both begin by shortening as ${T}_{1}(B)$ is reduced. For very small values of ${T}_{1}(B)$, however, ${T}_{M}(A)$ lengthens again. The rapidly fluctuating local fields due to the $B$-spins produce a diminishing effect on the $A$ spins, the phenomenon being analogous to motional narrowing. The form of the $A$-spin echo envelope in the limit of rapid $B$-spin relaxation does not depend on the model chosen to represent the time variation of ${\ensuremath{\mu}}_{z}$ during the relaxation of the $B$ spins.Experimental results are presented for two-pulse and three-pulse echoes, and are compared with the calculations. The material is CaW${\mathrm{O}}_{4}$ doped with Ce and Er or with Mn and Er. At the lower temperatures, the results are in moderately good agreement with the Gauss-Markoff theory. At higher temperatures, the results can only be explained by assuming that the transition rate between the levels of the Er ground doublet is an order of magnitude higher than the transition rate inferred from ${T}_{1}$ measurements. It is tentatively suggested that this may arise from the fact that ${T}_{M}$ depends on the arithmetic sum of the upward and downward transitions, whereas ${T}_{1}$ merely measures the algebraic sum, i.e., the excess of down-ward over upward transitions. If some form of spin-spin interaction is taking place, or if there is a phonon bottleneck (or any other mechanism causing transfers of energy within the spin system), the absolute and the net transition rates will cease to bear the usual thermodynamic relation to one another. In the present case it is suggested that energy transfer in the Er spin system is accelerated by the exchange of real phonons as soon as there is a significant population of the first excited doublet. The possible effects of spin clustering and of nonmagnetic dipolar interactions on the form of the echo decay envelopes are also briefly discussed.

Interaction of Conduction Electrons with Acoustic Waves in Many-Valley Semiconductors

A semi-classical theory is given for explaining the characteristics of the interaction of conduction electrons with acoustic waves in many-valley semiconductors such as n -Ge. In general, the ultrasonic absorption coefficient can be written as \begin{aligned} \varLambda{=}\varLambda_{P}+\varLambda_{K}, \end{aligned} where \(\varLambda_{P}\) is due to the change of the deformation potential energy of electrons caused by net intervalley transitions. \(\varLambda_{K}\) due to the change of the kinetic energy caused by intravalley transitions. The acousto-electromotive force can be also written as \begin{aligned} F{=}F_{P}+F_{K}. \end{aligned} In the low frequency range the dominant terms are \(\varLambda_{P}\) and F P , but \(\varLambda_{K}\) and F K Predominate in sufficiently high frequency range. For longitudinal waves propagating in the direction and transverse waves propagating in the direction and polarized in the direction, F is identical with the formula of Weinreich-Sanders-White i...

The excitation of chromospheric HeI lines.

Relative intensities of singlet and triplet lines of Hei in the solar chromosphere allow a determination of bn exp E~n/Te~, where ~,` is the ionization energy of the level n and bn is a non- thermodynamic equilibrium factor. We have computed bn'5 for values of Te ranging from 10,0000 to 50,0000 for an idealized helium atom consisting of a continuum and IS level and the levels 25, 2P, and n = 3, 4 and 5 in the excited singlets and triplets. Computed and observed values of b exp E~n/Te~ for the triplets agree for all Te even though b varies with Te. The relative populations of the triplets are determined almost entirely by the radiative transitions, which, because of the low chromospheric opacity in the triplets, are independ~nt of the ambient Te. For the singlets, however, the occupation numbers of the excited levels depend critically upon R~, the net radiative transition rates to the ground state, which are functions of TO, the chromospheric opacity in the first resonance line. Thus, both Te and TO are parameters of the calculations, with TO, in turn, being a function of Te and ne. The electron density, ne, may be estimated from the absolute line intensities. In order to relate Re to TO, we use the source- function computations of Jefferies and Thomas (1959). Computed values of be exp E~n/Te~ and TO for the singlets agree satisfactorily with the empirical be exp E~.~/Te~ for Te 4o,ooo0~5o 0000 Uncertainties in atomic constants and Rn may permit a Te as low as 30,0000, but certainly not as low as 25,0000. At chromospheric densities, helium becomes predominantly Heii at Te 20,000, and predominantly Heiii at Te 55,ooo0. Chromospheric helium is, there- fore, predominantly Heii as suggested earlier by Athay and Menzel (1956). REFERENCES Athay, R. G. and Meuzel, D. H. 1956, Ap. J. 123, 285. Jefferies, J. T. and Thomas, R. N. 1959, Ap. J. 129, 401. National Bureau of Standards and High A ltitude Observatory Boulder, Colorado

Polarization of Resonance Radiation and Hyperfine Structure: the Cadmium Resonance Lines

The cadmium resonance lines $\ensuremath{\lambda}\ensuremath{\lambda}$ 2288 and 3261A excited by unpolarized radiation in a magnetic field parallel to the exciting light beam are found to be 76.3 percent and 86-87 percent polarized respectively. From spectroscopic evidence Sch\"uler has assigned nuclear moments of 0 and $\frac{3}{2}$ to the even and odd isotopes of Cd. Separations in 2288 are small compared to Doppler breadth, while in 3261 the strong component of the $\frac{3}{2}$ isotope pattern merges with the 0 isotope line. If we suppose that the introduction of spin does not change the net transition probabilities between the gross levels concerned these polarization values both yield 2.53 for the ratio of abundance of even and odd isotopes. A recent calculation of C. G. Mitchell leads to other results, but is based on the apparently incompatible assumptions that intensities in the source are proportional to the isotope abundance but in absorption are determined by assigning equal weights to Zeeman levels making absorption by the spin isotope twice that by the non-spin isotope for equal abundance and uniform spectral distribution, conflicting with Kirchhoff's law.