Quantitative investigation of critical slowing down in all-optical bistability

We have observed optical bistability in rubidium vapor enclosed in a Fabry-Perot cavity for λ ～ 7779 Å (two-photon transition) and λ ～ 7800 Å (one-photon transition). We have measured the switching time τ_S as a function of (l?l_c) where l_c is the last value of the length of the cavity for which switching occurs. In all the experimental situations, we have found a similar law τ_S ～ (l?l_c)^-α with α ～ 0.5. This result is in agreement with theoretical predictions.     

Energy splitting betweenT > andT < single particle states in91Nb

The isobaric energy splitting ΔE(n, l, j) betweenT _>- andT _<-single particle states in the shell (2d _5/2, 2d _3/2, 1g _7/2, 3S _1/2) has been experimentally determined for⁹¹Nb from a study of the reaction⁹⁰Zr(³He,d)⁹¹Nb. The splitting of the 1g _7/2-states is found to be about 25% larger than that of the³ s _1/2-states. The observed dependence of the energy splitting ΔE(n, l, j) on the shell model quantum numbers (n, l, j) of the states is reproduced by the expression \(\Delta {\rm E}(n, l, j) = \frac{1}{2}(2T + 1) \left\langle {\phi _ > ^{n l j} | U_1 (r)|\phi _ > ^{n l j} } \right\rangle\) , which is based on approximate solutions of Lane's equations.φ _> ^nlj is the wave function of the parent state in the (nC) system. There is evidence, that only a Lane potentialU ₁(r) of surface type can reproduce the observed strong dependence of ΔE(n, l, j) on the quantum numbers. The depthū ₁ of Lane's potential is found to be 2.0 MeV.     

The15N(p,α 0)12C reaction at stellar energies

The¹⁵N(ρ, α₀)¹²C reaction has been investigated in the energy range ofE _p (lab)=78-810keV. The measurement of the excitation functions and α-particle angular distributions involved solid targets as well as a quasi-point supersonic jet gas target. The determination of absolute cross sections has been carried out with the gas target. The observed energy dependence of the total cross sections can be described in terms of two-level Breit-Wigner shapes including the resonances atE _p (J ^π)=335(1^?) and 1,028(1^?)keV. The data lead to a zero-energy intercept of the astrophysicalS(E) factor ofS(0)= 65±4MeV-b. The angular distributions are asymmetric around 90° and require an additional amplitude in the reaction mechanism, which interferes predominantly with the 335 keV resonance. The origin of this background amplitude is discussed.     

The 19F(p,d)18F reaction studied at Ep = 19.3 MeV

The ¹⁹F(p, d)¹⁸F reaction was used at E_p = 19.3 MeV to study the level properties of ¹⁸F up to 6 MeV excitation energy. Angular distributions were measured over the angular range θ_lab = 10°–70° with an overall resolution of 35 keV. The experimental data were analyzed by DWBA theory to obtain l_n and C²S_l values, which were compared with existent theoretical nuclear structure calculations.     

Unified model of energy transfer for arbitrary Franck-Condon offset and temperature

The Huang-Rhys-Pekar W_p(T, S) function is known to give the thermal-Franck-Condon (FC) weight of single-center radiative and non-radiative transitions for arbitrary energy mismatch p?ω₀, temperature T, and FC offset S. The thermal-FC weight for energy transfer is shown also to be W_p(T, S), with S enlarged to be the sum of the S values of the energy donor and energy acceptor. This result generalizes an earlier result of Miyakawa and Dexter for low-temperature Poisson functions. The W_p function with enlarged S is equivalent to the overlap of the donor emission and acceptor absorption bands in the Förster-Dexter theory. Experimental verification is good except for the p dependence of non-radiative and energy-transfer rates for S small (e.g. 4f → 4f transitions). Here, if the smooth, exponential p dependences (exponential energy-gap laws) that have been drawn through many 4f → 4f transition rates in certain hosts (Y₂O₃, LaF₃) are fitted with a W_p(T, S) function with a single S value, this S value is too large to describe 4f → 4f transitions.     

The riemann surface of a static dispersion model and regge trajectories

The S matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy ω in the plane with cuts (?∞, ?1] and [+1, +∞). In the elastic case, it reduces to N functions S _i(ω) connected by the crossing-symmetry matrix A. The scattering of a neutral pseudoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.     

Effect of temperature on $$\mathbf{In}_{{\varvec{x}}} \mathbf{Ga}_{1-{{\varvec{x}}}} \mathbf{As}/\mathbf{GaAs}$$ quantum dots

Analytical solution of the Dirac equation for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential for spin symmetry is studied using asymptotic iteration method. One-dimensional Dirac equation consisting of the radial and angular parts can be obtained by the separation of variables. By using asymptotic iteration method, the relativistic energy equation and orbital quantum number (l) equation can be obtained, where both are interrelated. Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number n _r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system can be determined by reducing the relativistic energy equation to the non-relativistic energy equation. Thermodynamical properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Coupling of vibration,rotation, and electron spin in multiplet states

The effective Hamiltonian of Van Vleck (1) for energy calculations of rotating molecules in multiplet states, is extended to include the effect of vibrational angular momentum, within a given nondegenerate electronic state. H_C and H_S operators are defined, to account for vibration-rotation (Coriolis) and spin-vibration interactions, respectively. Such interactions are discussed for degenerate E vibrational states of symmetric tops, as well as for the occurrence of vibrational angular momentum involving different vibrational states, with accidentally low energy separation. Following the classification of Hund's case (b) for the spin-rotation wave function (coupled representation), we find that H_C operators do not mix different F components, whereas H_S operators give also matrix elements between F components differing by one unit in the quantum number N, for given J.     

Relaxation times in dissipative heavy-ion collisions

The classical model introduced earlier for analyzing experimental data on dissipative heavy-ion collisions, is generalized to include effects from the gradual dissipation of radial kinetic energy and from the development of fragment deformations during the collision. Relaxation times for the dissipation of radial kinetic energy (τ _R ) and relative angular momentum (τ _l ) as well as for the development of deformations (τ_α) are fitted to the reaction⁸⁶Kr (8.18 MeV/u) +¹⁶⁶Er and applied to three other reactions. A consistent set of relaxation times isτ _R = 0.3 · 10^?21 s,τ _l =1.5 · 10^?21 s andτ _α = 5 · 10^?21 s. Empirical mass transport coefficients are deduced from comparisons with experimental element distributions. Effects from fluctuations in the deflection function are discussed. Evidence is found for the existence of a relaxation time of the order 10^?21 s in the mass-drift coefficient.     

Die Winkelverteilung der Protonen der Reaktion B11 (d,p 0,1 B12 im Energiebereich von 0,7 ... 1,7 MeV

Angular distributions of the protons in this low-energy region have been measured by only few groups for obvious reasons: the energy of the emitted protons is very low. It will be shown that by using non-supported targets of B¹¹ with very little oxygen contamination the angular distributions can be obtained between approximately 5 and 165 degrees (cm.,p ₀-group) and between 20 and 165 degrees (cm.,p ₁) with high accuracy. The Butler-fits givel=1,r _B =5.2 fm forp ₀ andl=1,r _B =4.7 fm forp ₁. All angular distributions seem to exhibit strong participation of non-stripping mechanism.     

Spin autocorrelation of Ni in K2Mn0.975Ni0.025F4 studied by nuclear spin-lattice relaxation

From the nuclear spin-lattice relaxation of the out-of-layer ¹⁹F nuclei in magnetic fields perpendicular to the c-axis the low-frequency component of the autocorrelation function 〈S^z(t)S^z(O)〉 of Ni in ordered K₂Mn_0.975Ni_0.025F₄ is found to be substantially reduced relative to the Mn host. The experimental rates vs temperature are in accord with those for relaxation involving two spin excitations calculated with local Green's functions.     

Elastic <Superscript>16</Superscript>O<Superscript>16</Superscript>O scattering at <Emphasis Type="Italic">E</Emphasis>(<Superscript>16</Superscript>O) = 350 MeV and new method for a model-independent determination of the scattering matrix

A new approach that can be used to extract the scattering matrix S(l) as a complex-valued function of the orbital angular momentum l directly from experimental data on elastic nucleus-nucleus scattering at intermediate energies without resort to additional model assumptions is developed on the basis of the evolutionary algorithm. Owing to the fact that the behavior of the derivatives of S(l) is automatically monitored within this approach, the scattering matrix obtained for ¹⁶O¹⁶O interaction at an energy of 350 MeV is determined by its absolute value and the nuclear phase shift, which are smooth monotonic functions of the orbital angular momentum. Moreover, the result involves no distortions, the form of the quantum deflection function being typical of the nuclear-rainbow pattern. It is shown that the ultimate form of S(l) is independent of input representations of the scattering matrix, which were usually taken on the basis of various phenomenological models.     

Proton-hole states in 115In observed in the 116Sn(d, 3He) reaction

The ¹¹⁶Sn(d, ³He)¹¹⁵In reaction has been investigated at E_d = 50 MeV. Thirteen transitions to states up to 3 MeV excitation energy were studied. The measured angular distributions were compared with DWBA calculations and transferred angular momenta and spectroscopic factors were deduced. Levels at 1.04, 2.23 and 2.52 MeV were found to be excited most likely by l = 3 angular momentum transfer in contrast to previous investigations at lower incident energies in which no l = 3 transitions have been observed.     

Photoluminescence studies of exciton-ionized donor complexes in high pusity epitaxial GaAs

We report the first observation of three radiative transitions associated with excitons bound to three different residual ionized donors in high purity undoped vapor phase epitaxial (VPE) GaAs at liquid helium temperature. The values of the localization energies (E_l) of excitons bounds to these ionized donors were measured. We also determine simultaneously, the ionization energies of these donors using excited state transitions of exciton-neutral donor complexes as reported earlier. The variation of the localization energy (E_l) as a function of the donor binding energy (E_D) is plotted and a linear dependence described by E_l = ? 2.22 + 0.72E_D is observed.     

Resonance structure of strength functions for first-forbidden β +/EC transitions

Experimental data obtained by measuring the fine structure of the strength function S _?? (E) in spherical and deformed nuclei were analyzed. The use of modern nuclear-spectroscopy methods made it possible to reveal the nuclear-deformation-induced splitting of peaks in S _?? (E) for transitions of the Gamow-Teller type. For first-forbidden transitions, the resonance nature of S _?? (E) was proven experimentally both for spherical and for deformed nuclei. It is shown that, at some values of the excitation energy, the intensity of first-forbidden transitions in nuclei can be commensurate with the intensity of Gamow-Teller transitions.     

S-matrix spin and parity decoherence and damping of coherent nuclear rotation: quantum chaos in dissipative heavy-ion collisions?

We extend the statistical reaction with memory approach to study off-diagonal spin and parity S-matrix energy autocorrelation in dissipative heavy-ion collisions. It is suggested that S-matrix spin and parity decoherence results in (i) damping of the coherent nuclear rotation and (ii) is a manifestation of quantum chaos in dissipative heavy-ion collisions.     

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions C_l (t) = <P(cos δθ(t))> were calculated for l = 1 through 4 ; P_l is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.