Adiabatic Wave Research Articles

Analytical calculation of the Smith lifetime Q matrix using a Magnus propagator: Applications to the study of resonances occurring in ultracold inelastic collisions with and without an applied magnetic field

We take advantage of the simple expression of the sector adiabatic wave functions of the Magnus propagator to obtain accurate values of the energy derivative of the S matrix which, in turn, is used to get the Smith lifetime Q matrix. The procedure involves the simultaneous generation of both the R matrix and its energy derivative dR/dE which are propagated along the scattering coordinate. We present a few examples of application to the field free He-N(2)(+) inelastic collisions which we previously studied. This method is then applied to the calculation of the lifetime of tuned zero energy Feshbach resonances using a magnetic field. We give and discuss the law of variation as a function of the magnetic field of the Q matrix eigenvalues across such resonance. Some examples of application are given for the He-N(2)(+) collisions in a magnetic field.

Nonadiabatic effects in D + + H 2 and H + + D 2

Using time-dependent nonadiabatic and adiabatic wave packet methods, we investigate nonadiabatic effects in collisions of D +(H +) with H 2(D 2) for collision energies from 1.7 to 2.5 eV. A new accurate diabatic potential energy surface [L.P. Viegas, A. Alijah, A.J.C. Varandas, J. Chem. Phys. 126 (2007) 74309] of the H 3 + system fitted from full multireference configuration interaction calculations with a cc-pV5Z basis set is incorporated into the quantum calculations of initial state resolved integral cross sections. Comparison with previous calculations and experimental measurements are used to give insight on the nonadiabatic charge transfer process and isotope effect.

Relativistic E×T Jahn–Teller effect in tetrahedral systems

It is shown that (2)E states in tetrahedral systems exhibit a linear ExT Jahn-Teller effect which is of purely relativistic origin (that is, it arises from the spin-orbit-coupling operator). The electrostatic interactions give rise to a Jahn-Teller effect which is quadratic in the T displacements. The 4 x 4 Hamiltonian matrix in a diabatic spin-electron basis is derived by an expansion of the electrostatic electronic Hamiltonian and the Breit-Pauli spin-orbit operator in powers of the Jahn-Teller active normal mode and taking account of symmetry selection rules for the matrix elements. The adiabatic potential-energy functions of the (2)E x T system are doubly degenerate (Kramers degeneracy). For small displacements from the tetrahedral reference geometry, the adiabatic potential-energy surfaces represent a double cone in four-dimensional space, which is a novel topography of Jahn-Teller potential-energy surfaces. The topological phases of the adiabatic electronic wave functions are discussed.

Preparation of nano-size ZrB 2 powder by self-propagating high-temperature synthesis

Preparation of nano-size ZrB 2 powder by SHS has been investigated. Zr and B elemental powders were mixed with 10–50 wt.% NaCl, and prepared pellets were reacted under argon. Adiabatic temperatures were calculated by HSC software. Increasing NaCl content led to a continuous decrease in adiabatic temperatures and reaction wave velocity. Products were subjected to XRD, SEM and FESEM analyses. Average crystallite size of ZrB 2, which was 303 nm without NaCl, decreased to 32 nm with 40% NaCl addition. Distinct decrease in ZrB 2 particle size was also observed from SEM analyses. 30% NaCl addition was found to be optimum for ensuring a stable SHS reaction and providing the formation of nano-size ZrB 2 particles. It was revealed from particle size distribution measurements that ZrB 2 powder obtained by 30 wt.% NaCl addition contained particles mostly finer than 200 nm. A mechanism, similar to solution-precipitation was proposed for the particle size refining effect of NaCl.

Quantum theory of chemical reactions in the presence of electromagnetic fields

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.

Effects of hydration on the elastic properties of olivine

Water, dissolved as hydroxyl (OH)− into the solid silicate minerals of the upper mantle can reduce adiabatic wave speeds through associated defects. Here we report Brillouin spectroscopy measurements of the sound velocities and single‐crystal elastic constants of hydrous forsterite (hy‐Fo100) and hydrous olivine (hy‐Fo97) containing 0.8–0.9 wt% H2O. The samples, synthesized at 12 GPa and 1250°C, represent nearly the maximum storage capacity of water in olivine at conditions of 350–400 km depth. The adiabatic bulk (KS0) and shear (G0) moduli of hy‐Fo100 are 125.7(±0.2) GPa and 79.8(±0.1) GPa, respectively. For hy‐Fo97, we obtain KS0 = 124.4(±0.4) GPa and G0 = 75.3(±0.3) GPa. Compared with anhydrous forsterite, the combined effects of 3 mol% Fe and 0.8 wt% H2O reduce bulk and shear moduli by 3.5(±0.3)% and 7.5(±0.4)% respectively, with greater reductions expected for more iron‐rich Fo90 mantle compositions. Although lattice preferred orientation (LPO) studies have not been carried out under relevant conditions of water or pressure, analysis of idealized single‐crystal anisotropy for various known LPO types predicts up to 3% higher S‐wave splitting anisotropy in hydrous olivine crystals aligned according to A‐type and E‐type fabrics, but no change in S‐wave splitting anisotropy for B‐type and C‐type fabrics.

The 3E × E, 4E × E and 5E × E Jahn–Teller Hamiltonians of trigonal systems

The vibronic Hamiltonians describing linear and quadratic Jahn–Teller coupling as well as spin–orbit coupling in M E states of trigonal systems are derived for the spin multiplicities M = 3 , 4 , 5 , starting from the microscopic Breit–Pauli spin–orbit operator. The 2 M × 2 M Hamiltonian matrices in a diabatic spin-electronic basis are obtained by the expansion of the Hamiltonian in powers of the Jahn–Teller active normal mode. It is shown that the M E × E Jahn–Teller Hamiltonians can be made block-diagonal by the transformation to an alternative diabatic basis which mixes electronic orbital and spin projections. The adiabatic potential-energy surfaces and the adiabatic electronic wave functions are obtained in analytical form. In systems with an odd number of electrons (and thus even spin multiplicity) the Jahn–Teller effect is quenched by strong spin–orbit coupling and the adiabatic potential-energy surfaces are strictly two-fold degenerate (Kramer’s degeneracy). In systems with an even number of electrons (and thus odd spin multiplicity), two of the 2 M adiabatic potentials exhibit an E × E Jahn–Teller effect which is unaffected by the spin–orbit interaction. The geometric phases of the adiabatic electronic wave functions are those of the 2E × E Jahn–Teller effect with and without spin–orbit coupling, respectively.

Quantum Monte Carlo studies of the ground states of heavy atoms in neutron-star magnetic fields

The ``released-phase'' diffusion quantum Monte Carlo method is used to calculate the ground-state energies of atoms with nuclear charges from $Z=2,3,4,\dots{},26$ for magnetic field strengths relevant for neutron stars. The feature of our study is the use of adiabatic approximation wave functions as guiding wave functions to initialize the quantum Monte Carlo procedure. Our calculations are motivated by the discovery of broad features in the thermal spectra of isolated neutron stars, which may be due to heavy atoms. Our results confirm previous results for nuclear charge numbers up to 10, and are the most accurate ones available in the literature to date for $Z>10$.

Smooth light curves from a bumpy ride: relativistic blast wave encounters a density jump

In the standard forward shock model for gamma-ray burst (GRB) afterglow, the observed afterglow emission is synchrotron radiation from a quasi-spherical, adiabatic, self-similar, relativistic blast wave, that propagates into the external medium. This model predicts a smooth light curve where the flux scales as a power law in time, and may at most smoothly transition to a different power law. However, some GRB afterglow light curves show significant variability, which often includes episodes of rebrightening. Such temporal variability had been attributed in several cases to a large enhancement in the external density, or a density ‘bump’, that is encountered by the self-similar adiabatic blast wave. Here we examine the effect of a sharp increase in the external density on the afterglow light curve in this scenario by considering, for the first time, a full treatment of both the hydrodynamic evolution and the radiation. To this end we develop a semi-analytic model for the light curve and carry out numerical simulations using a one-dimensional hydrodynamic code together with a synchrotron radiation code. Two spherically symmetric cases are explored in detail – a density jump in a uniform external medium (which is used to constrain the effect of a density clump) and a wind termination shock. We find that even a very sharp (modelled as a step function) and large (by a factor of a≫ 1) increase in the external density does not produce sharp features in the light curve, and cannot account for significant temporal variability in GRB afterglows in the forward shock model. For a wind termination shock, the light curve smoothly transitions between the asymptotic power laws over about one decade in time, and there is no rebrightening in the optical or X-rays that could serve as a clear observational signature. For a sharp jump in a uniform density profile, we find that the maximal deviation Δαmax of the temporal decay index α from its asymptotic value (at early and late times) is bounded (e.g, Δαmax < 0.4 for a= 10); Δαmax slowly increases with a, converging to Δαmax≈ 1 at very large a values. Therefore, no optical rebrightening is expected in this case as well. In the X-rays, while the asymptotic flux is unaffected by the density jump, the fluctuations in α are found to be comparable to those in the optical. Finally, we discuss the implications of our results for the origin of the observed fluctuations in several GRB afterglows.

Test of Determination of (p,γ) AstrophysicalS-Factors Using the Asymptotic Normalization Coefficients from NeutronTransfer Reactions

The asymptotic normalization coefficients (ANCs) for the virtual decay17O→16O+n are derived from the angulardistributions of the 16O(d,p)17O reaction leading to theground and first excited states of 17O, respectively, using thedistorted wave Born approximation and the adiabatic wave approximation.The ANCs of 17F are then extracted according to charge symmetry ofmirror nuclei and used to calculate the astrophysical S-factors of16O(p,γ)17F leading to the first two states of17F. The present results are in good agreement with those from thedirect measurement. This provides a test of this indirect method todetermine direct astrophysical S-factors of (p,γ) reaction. Inaddition, the S-factors at zero energy for the direct captures to theground and first excited states of 17F are presented, without theuncertainty associated with the extrapolation from higher energies indirect measurement.

Effect of Cu content on the reaction behaviors of self-propagating high-temperature synthesis in Cu–Ti–B4C system

The SHS reaction behaviors of the Cu–Ti–B4C system with various Cu content were investigated. Theoretical calculation of the adiabatic temperatures reveals that the reaction in the Cu–Ti–B4C system is self-sustainable for the presence of 0–72.22 wt.% Cu in the reactants without any preheat. With the increase of Cu content, the adiabatic temperatures, combustion temperatures and wave velocity decrease greatly, while the ignition time shows first a remarkable decrease and then an increase with the minimum value at 20 wt.% Cu. Moreover, with the increase of Cu content, the sizes of the TiC and TiB2 grains decrease considerably.

Guided waves in elastic plates with Gaussian section variation: Experimental and numerical results

Experimental and numerical results are presented on the behavior of guided waves in elastic plates in plane strain that include a Gaussian variation of their section, located between two areas of constant thickness. The area of varying section is wide compared to the used wavelengths, which allows wave propagation inside this area. The experimental results show that an incident Lamb wave is indeed converted into an adiabatic wave inside the varying section domain. A trapped wave in the Gaussian domain is also observed, depending on the incident mode and on the Gaussian maximum height. Outside the varying section domain, conversion into different Lamb waves is observed. This conversion phenomenon is experimentally quantified by the measurement of the Lamb wave normal displacement and of its carried energy. A numerical study, based on the Finite Elements Method is performed, and successfully compared to the experimental results.

Spin-orbit vibronic coupling in Π3 states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.

Decay phases of Swift X-ray afterglows and the forward-shock model

The X-ray flux of the gamma-ray burst (GRB) afterglows monitored by the Swift satellite from January 2005 to July 2006 displays one to four phases of flux power-law decay. In chronological order, they are: the GRB tail, the 'hump', the standard decay and the post-jet-break decay. More than half of the GRB tails can be identified with the large-angle emission produced during the burst (but arriving later at observer). The remaining, slower GRB tails imply that the gamma-ray mechanism continues to radiate after the burst, as also suggested by the frequent occurrence of X-ray flares during the burst tail. The several GRB tails exhibiting a slow unbroken power-law decay until 100ks must be attributed to the forward shock. In fact, the decay of most GRB tails is also consistent with that of the forward-shock emission from a narrow jet. The X-ray light-curve hump may be due to an increase of the kinetic energy per solid angle of the forward-shock region visible to the observer, caused by either the transfer of energy from ejecta to the forward shock or the emergence of the emission from an outflow seen from a location outside the jet opening. The decay following the X-ray light-curve hump is consistent with the emission from an adiabatic blast wave but, contrary to expectations, the light-curve decay index and spectral slope during this phase are not correlated. The X-ray light curves of two dozens X-ray afterglows that followed for more than a week do not exhibit a jet break, in contrast with the behaviour of pre-Swift optical afterglows, which displayed jet breaks at 0.5-2 days. Nevertheless, the X-ray light curves of several Swift afterglows show a second steepening break at 0.4-3 days that is consistent with the break expected for a jet when its edge becomes visible to the observer.

Small-Amplitude Disturbances in a Radiating and Scattering Grey MediumIII. Gravitational Effects on the Solutions of Given Real Wave Number k

We study the fundamental modes of radiation hydrodynamic linear waves that arise from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium by taking into account the gravitational effects. The equation of radiative acoustics is derived from three hydrodynamic equations, Poisson’s equation, and two moment equations of radiation, by assuming a spherical symmetry for the matter and radiation and by using the Eddington approximation. We solve the dispersion relation as a quintic function of angular frequency ω, the wave number k being a real parameter. Numerical results reveal that wave patterns of five solutions are distinguished into three types: the radiation-dominated, type 1, and type 2 matter-dominated cases. In the case of no gravitaional effects (Kaneko et al., 2005), the following wave modes appear: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusions, adiabatic sound wave, cooling-damped and drag-force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. Meanwhile, the gravitaional effects being taken into account, the growing gravo-diffusion mode newly arises from the constant-pressure diffusion at the point that k agrees with Jeans’ wave number specified by the isothermal sound speed. This mode changes to the growing radiation-acoustic gravity mode near the point that k becomes Jeans’ wave number specified by the isentropic radiation-acoustic speed. In step with a transition between them, the isentropic radiation-acoustic wave splits into the damping radiation-acoustic gravity mode and constant-volume diffusion. The constant-volume diffusion emerges twice if the gravitational effects are taken into account. Since analytic solutions are derived for all wave modes, we discuss their physical significance. The critical conditions are given which distinguish between radiation-dominated and type 1 matter-dominated cases, and between type 1 and type 2 matter-dominated cases. Waves in a self-gravitating scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.

Active Carbon and Oxygen Shell Burning Hydrodynamics

We have simulated 2.5$\times10^3$ s of the late evolution of a $23 \rm M_\odot$ star with full hydrodynamic behavior. We present the first simulations of a multiple-shell burning epoch, including the concurrent evolution and interaction of an oxygen and carbon burning shell. In addition, we have evolved a 3D model of the oxygen burning shell to sufficiently long times (300 s) to begin to assess the adequacy of the 2D approximation. We summarize striking new results: (1) strong interactions occur between active carbon and oxygen burning shells, (2) hydrodynamic wave motions in nonconvective regions, generated at the convective-radiative boundaries, are energetically important in both 2D and 3D with important consequences for compositional mixing, and (3) a spectrum of mixed p- and g-modes are unambiguously identified with corresponding adiabatic waves in these computational domains. We find that 2D convective motions are exaggerated relative to 3D because of vortex instability in 3D. We discuss the implications for supernova progenitor evolution and symmetry breaking in core collapse.

Erratum to “Determination of Non–Adiabatic Scattering Wave Functions in a Born–Oppenheimer Model"

instead of ψ(x, t, ,±) = σ=± ψ(x, t, ,±). With this definition, Proposition 4.1 should be replaced by Proposition 4.1′ Assume H1, H2, H3 and C0. Then, for any 0 < β < 1/2, we have the following L(IR)–norm estimate as t → ±∞, ‖ψ(x, t, ) − (ψ−(x, t, ,±) + ψ(x, t, ,∓)) ‖ = O (1/|t|β). In eqn. (4.4), “ψ(x, t, ,−) =” should be replaced by “ψ−(x, t, ,−) ,” and the qualification “for negative x’s” should be added. Similarly, in the next sentence, the stipulation “for positive x’s” should be added. The proof of Proposition 4.1 should be amended as follows: Equation (7.14) should begin with

The relativistic E × E Jahn–Teller effect revisited

The vibronic Hamiltonian describing linear Jahn–Teller coupling as well as spin–orbit coupling in systems of trigonal symmetry is derived in the diabatic spin–orbital representation, employing the microscopic (Breit–Pauli) spin–orbit coupling operator in the single-electron approximation. The analysis generalizes previous treatments based on more phenomenological models of spin–orbit coupling. It is shown that an alternative time-reversal symmetry adapted diabatic representation exists, in which the 4 × 4 Jahn–Teller spin–orbit vibronic Hamiltonian is block-diagonal. The adiabatic electronic wave functions are obtained in explicit form. The topological phases (Berry’s phases) of all four adiabatic electronic basis states are calculated. As found previously for the special case of systems with D 3h symmetry, the topological phases depend on the radius of the loop of integration.

A Complete Set of NMR Chemical Shifts and Spin−Spin Coupling Constants forl-Alanyl-l-alanine Zwitterion and Analysis of Its Conformational Behavior

With the aid of labeling with stable isotopes ((15)N and (13)C) a complete set of chemical shifts and indirect spin-spin coupling constants was obtained for the zwitterionic form of L-alanyl-L-alanine in aqueous solution. Different sensitivities of the NMR parameters to the molecular geometry were discussed on the basis of comparison with ab initio (DFT) calculated values. An adiabatic two-dimensional vibrational wave function was constructed and used for determination of the main chain torsion angle dispersions and conformational averaging of the NMR shifts and coupling constants. The quantum description of the conformational dynamics based on the density functional theory and a polarizable continuum solvent model agrees reasonably with classical molecular dynamics simulations using explicit solvent. The results consistently evidence the presence of a single form in the aqueous solution with equilibrium main chain torsion angle values (psi = 147 degrees, varphi = -153 degrees), close to that one found previously in an X-ray study. Under normal temperature the torsion angles can vary by about 10 degrees around their equilibrium values, which leads, however, to minor corrections of the NMR parameters only. The main chain heavy atom chemical shifts and spin-spin coupling constants involving the alpha-carbon and hydrogen atoms appear to be most useful for the peptide structural predictions.

Review on critical impact velocities in tension and shear

Adiabatic heating, due to conversion of plastic work into thermal energy, substantially changes the boundary value problems in the theory of plastic wave propagation. Besides a systematic review of the subject, the thermal coupling during plastic wave propagation leading to adiabatic wave trapping is the main subject of this study. Two cases are analyzed, the adiabatic wave trapping in tension and also in shear. The case of shear is relatively new. The wave trapping by adiabatic deformation via thermal softening leads to the so called critical impact velocity (CIV). Theory, experiments and numerical analyses of the CIV in tension and shear is the main part of this paper.