Rotational Coupling Effects Research Articles

Asteroseismology of the fast-rotating high-amplitude δ Scuti star V2367 Cygni

ABSTRACT We present the comprehensive analysis of the high-amplitude $\delta$ Sct star V2367 Cygni. First, we perform the frequency analysis for the whole available set of the Kepler and TESS photometry. Most of the frequency peaks are harmonics or combinations of the three known independent frequencies with the highest amplitudes, i.e.$\nu _1=5.661\,06$ d$^{-1}$, $\nu _2=7.14898$ d$^{-1}$, and $\nu _3=7.77557$ d$^{-1}$. The total number of independent frequencies is 26 and 25 from the Kepler and TESS light curve, respectively. Then, using the ${\it UBVRI}$ time-series photometry, we unambiguously identify the dominant frequency $\nu _1$ as the radial mode, whereas in the case of frequencies $\nu _2$ and $\nu _3$ the most probable mode degrees are $\ell =0$ or $\ell =2$. However, only the frequency $\nu _2$ can be associated with a radial mode, and only if higher order effects of rotation are taken into account. Including the rotational mode coupling, we constructed complex seismic models of V2367 Cyg, which fit $\nu _1$ and $\nu _2$ as radial modes, and reproduce the amplitude of bolometric flux variations (the parameter f) for the dominant mode. The empirical values of f are derived from the ${\it UBVRI}$ amplitudes and phases. We rely on the Bayesian analysis based on Monte Carlo simulations to derive constraints on evolutionary stage, mass, rotation, overshooting from the convective core, and efficiency of convective transport in the envelope. Our seismic analysis clearly indicates that V2367 Cyg is in a post-main sequence phase of evolution. This is the first extensive seismic modelling that takes into account the effect of rotational coupling between pulsation modes.

Optimal face-to-face coupling for fast self-folding kirigami.

Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer folding times in the presence of fluctuations. Here, we study the effect of rotational coupling between levels on the self-folding of two-level kirigami designs driven by thermal noise in a fluid. Naturally present due to hydrodynamic resistance, we find that this coupling parameter can significantly impact a structure's self-folding pathway, thus enabling us to assess the quality of a kirigami design and the possibility for its optimization in terms of its folding rate and yield.

Single-electron capture in 3-keV/uAr8+-He collisions

The electron transfer mechanism was investigated for the single-electron-capture process in 3-keV/u ${\mathrm{Ar}}^{8+}$-He collisions with cold target recoil ion momentum spectroscopy. The different state-selective electron capture processes were identified for one $1s$ electron of He capture into $4s$, $4p$, $4d\text{\ensuremath{-}}4f$, and $5s\text{\ensuremath{-}}5p$ states of ${\mathrm{Ar}}^{8+}$. We observed that $1s$ to $4s$ capture mainly happens at small transverse recoil ion momentum, while $1s$ to $4p$ capture mainly happens at large transverse recoil ion momentum. By comparing the measured projectile scattering angle distributions to the theoretical calculations, it is suggested that $1s$ to $4s$ and $1s$ to $4p$ state-selective capture processes are mainly caused by radial and rotational coupling effects, respectively, and the $4{p}_{\ifmmode\pm\else\textpm\fi{}1}$ quantum states are preferred.

Coupled channel effect in elastic scattering and fusion for6,7Li+28Si

The fusion excitation and elastic angular distribution were measured for 6,7 Li+28 Si from below to above Coulomb barrier (≤ 3Vb ) energies. The barrier distribution derived from the fusion data was found to be broad and asymmetric at the sub-barrier region, compared to 1D BPM estimation. Effect of rotational coupling on fusion was found to be not so dominant. Phenomenological optical potential parameters, with surface and volume type imaginary potentials, were obtained from f tting of elastic scattering data and energy dependence of real and imaginary surface strengths were investigated around the barrier. CDCC calculations considering only breakup of projectile were performed for 6,7 Li+28 Si with the elastic scattering data, using the code FRESCO. The effects of breakup of projectile on elastic cross section do not agree with the energy dependence of real and imaginary strength with volume type imaginary potential around the barrier.

Vibrational and rotational coupling effects in the direct scattering of H 2 from Cu(111)

We investigate how the coupling between molecular vibration and rotation affects the direct scattering of H 2 from Cu(111) by performing coupled channel calculations. Our calculation results show that the rotational excitation probability of H 2 scattered (vibrationally elastic) in the first vibrationally excited state ( ν=1) increases more rapidly than that of H 2 scattered (vibrationally elastic) in the vibrational ground state ( ν=0) with increasing translational energy in the low translational energy region. Furthermore, the calculation results for the ratio of the probability of H 2 scattered in ν=1 and rotational state J=2 to the probability of H 2 scattered in ν=1 and J=0 as a function of translational energy qualitatively reproduce the experimental results in the low translational energy region.

Effect of rotational coupling on charge transfer into Coulomb channels

The significance of Coriolis coupling in charge-transfer reactions during collisions of highly charged ions with atoms is studied under conditions where electron correlation effects may be ignored. Reaction amplitudes are expressed in closed form in the case of full Coriolis mixing and parametrized in simple terms when partial mixing is considered. It is shown that Coriolis mixing only plays a minor role in the diabatic wing of the reaction window, i.e. for capture into states with fairly small energy defects. The form of the reaction window is, on the other hand, strongly influenced by rotational coupling in the adiabatic wing corresponding to capture into more deeply lying final states.

Rotational coupling effects on the spin relaxation of free ferromagnetic clusters

A model based on resonant spin-rotation coupling is used to reproduce the magnetization of free iron clusters experimentally observed by Stern-Gerlach deflections. Due to the interaction with the rotating magnetocrystalline anisotropy field, the dynamics of the magnetic moment of the clusters cannot be explained only in terms of thermal relaxation. As in magnetic resonance experiments, modified Bloch equations can describe the interaction of the particle spin with the deflecting field and the rotating anisotropy field. The dependence of the magnetization on the rotational temperature of the clusters and the relaxation time is discussed.

Quantal and thermal zero point motion formulae of barrier transmission probability.

A Green's function method is developed to derive quantal zero point motion formulae for the barrier transmission probability in heavy ion fusion reactions corresponding to various nuclear intrinsic degrees of freedom. In order to apply to the decay of a hot nucleus, the formulae are then generalized to the case where the intrinsic degrees of freedom are in thermal equilibrium with a heat bath. A thermal zero point motion formula for vibrational coupling previously obtained through the use of influence functional methods naturally follows, and the effects of rotational coupling are found to be independent of temperature if the deformation is rigid.

Collision-induced intramultiplet mixing for Ne

We have investigated fine-structure--changing collisions of short-lived (20-ns) ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$ atoms in the {\ensuremath{\alpha}}\ensuremath{\equiv}{(2p${)}^{5}$(3p)} multiplet with ground-state He atoms. A newly designed cross-beam apparatus allows the measurement of accurate polarized cross sections ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}\ensuremath{\Vert}}$ for the {\ensuremath{\alpha}${\mathrm{}}}_{k}$\ensuremath{\rightarrow}{\ensuremath{\alpha}${\mathrm{}}}_{l}$ transition. In the experiment, the initial {\ensuremath{\alpha}${\mathrm{}}}_{k}$ state is prepared with a well-defined asymptotic orientation ${M}_{k}$ of its electronic angular momentum J, through excitation of metastable ${\mathrm{Ne}}^{\mathrm{*}}$ atoms with a polarized laser. The reported transitions are mainly between states in the {\ensuremath{\alpha}${\mathrm{}}}_{4}$,5,6,7 group (Paschen numbering), at approximately 100 meV center-of-mass energy. Some of these exhibit very strong polarization effects, with differences between ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}\ensuremath{\Vert}}$ and ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}^{\mathcal{'}}\ensuremath{\Vert}}$ of up to a factor 4. Fully quantum-mechanical coupled-channel calculations on a diabatic basis, with the ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-He model potentials of Hennecart and Masnou-Seeuws as input, prove successful in reproducing experimental results. Cross-section behavior may be qualitatively understood from the presence of avoided crossings between the adiabatic potentials, indicative of strong radial coupling. The restraint of reflection symmetry is strongly felt here. In addition, the effects of rotational coupling can be readily identified.

Charge transfer in low-energy Al3+-H and Ti4+-H collisions: effect of rotational coupling in three-state crossings

A theoretical investigation of charge transfer in collisions of Al3+ and Ti4+ ions with atomic H is carried out for the energy range 1-1000 eV amu-1. An adiabatic molecular basis set, with the inclusion of appropriate translation factors, is used to describe the collision dynamics. In both the Al3+-H and Ti4+-H systems, the influence of rotational coupling proves to be considerable and depends quite critically on the correlation to the principal electron capture channel of the asymptotic energy splitting of the Sigma and Pi states.

Dynamics of molecular stereochemistry via oriented molecule scattering

Crossed-beam reactive scattering experiments employing electrostatic hexapole fields to control the initial collision geometry of chemical reactions are described. New results are presented on the reactions of oriented NO with ozone and oriented N/sub 2/O with Ba. Preliminary results are also given for the oriented CH/sub 3/F + Ca* ..-->.. CaF* + CH/sub 3/ reaction. Recent technical advances in state selection and product detection are detailed. They discuss the effects of rotational coupling and nonzero impact parameters in changing the molecular precollisions orientation selected by the hexapole fields to a different in-collision orientation at the moment of impact with the reaction partner. Uncoupling of l doubling in N/sub 2/O at strong orientation fields is demonstrated via the observed reactive anisotropy. Steric effects are found to govern many aspects of the reactions investigated thus far. Strong correlations are observed of the reactivity, product recoil, and rotational angular momentum distributions with the collisional orientation. These correlations ultimately provide information on the anisotropic part of the reaction potential energy surface. They conclude with a brief outline of possible future directions in oriented molecule scattering.

Effect of rotational coupling on emission probabilities of Lyman and Werner band systems of the vacuum ultraviolet spectrum of H2

Ratios of emission probabilities of rotational lines of the Lyman and Werner band systems, B 1∑+u →X 1∑+g and C 1∏u →X1∑+g, respectively, are calculated by different methods. These theoretical ratios are compared to the experimental intensity ratios of about a hundred lines selected from a vacuum ultraviolet emission spectrum whose intensity is investigated for the first time at high resolution. The computation permits to compare two ways of solving a system of two coupled equations with discrete eigenvalues. In most cases the effect of the mutual rotational perturbation between B and C states is found significant on the ratio of P and R line intensities. Ambiguity in labeling a few B and C levels is discussed.

Use of an approximate diabatic molecular representation in He + -He charge transfer collision

A single-configuration “frozen-orbital” molecular basis set has been used as an approximation to the “standard” radial diabatic representation defined by Smith. The usefulness of this approximate representation has been demonstrated in an eight-state close-coupled treatment of the He + -He resonant transfer collisions in the impact parameter approximation. Apart from the Σ-Σ potential couplings the two Σ-Π rotational couplings at short range have been considered. Generally satisfactory agreement with the experimental data of Nagy ., together with a significant improvement in the estimate of the rotational coupling effects toward the region of large EO (≳ 3-4 keV deg) as compared to the earlier theoretical work of McCarroll and Piacentini is obtained.

Fine-structure excitation of ground-state C+ions by hydrogen atoms

Cross sections are computed for the low-energy fine-structure excitation of singly ionized carbon (2P electronic ground state) by atomic hydrogen (2S electronic ground state) in a close-coupling formulation; recent accurate potential energy curves are employed. The effects of rotational coupling and of the fine-structure energy defect are investigated. The excitation cross section is found to be larger than previously computed. The cooling function is calculated for temperatures of astrophysical interest.

Prediction of Jump Phenomena in Roll-Coupled Maneuvers of Airplanes

An easily computerized analytical method is developed for identifying critical airplane maneuvers in which nonlinear rotational coupling effects may cause sudden in the response to pilot's control inputs. Fifth- and ninth-degree polynomials for predicting multiple pseudosteady states of roll-coupled maneuvers are derived. The program calculates the pseudosteady solutions and their stability. The occurrence of jump-like responses for several airplanes and a variety of maneuvers is shown to correlate well with the appearance of multiple stable solutions for critical control combinations. The analysis is extended to include aerodynamics nonlinear in angle of attack. HILLIPS'! original analysis of the roll-coupling problem considered the rotational coupling effects of constant roll rate on the stability of the short-period longitudinal and lateral oscillations. Although the constant rolling constraint is artificial, it is physically realistic for well-behaved airplanes with good damping in roll. Phillips' analysis predicted that divergence-like motions would be expected at certain critical roll rates, when the usual linearized stability analysis predicted perfectly acceptable behavior. This dangerous coupling effect of rapid rolling, leading to large deviations in incidence angles and tail loads, was confirmed in many nonlinear computerized simulations and in flight. In con- nection with these simulation studies, there were many at- tempts to extend Phillips' analysis. The main objective of these studies was to obtain a simplified method for predicting the peak motions in roll-coupled maneuvers. Pinsker2 and Rhoads and Schuler3 showed that Phillips' critical roll rates also could be obtained as steady-state (autorotational) solutions of the approximate equations of motion used by Phillips. This method has the advantages that it also predicts steady-state solutions for the other variables, is more readily generalized, and permits the use of control input values as independent parameters, instead of roll rate. However, attempts to use this method to predict peak disturbances reliably in coupled maneuver were not suc- cessful. In the present study we have returned to this method of calculating the steady states of the approximate equations of motion, which we shall call the pseudosteady-state (PSS) method, because it neglects the effects of varying weight components in body axes. However, instead of trying to predict the magnitudes of response peaks, the method will be used to predict those control input combinations that may cause sudden jumps in the response as the motion is attracted to a new stable pseudosteady-state.

Rotational coupling and laser dynamics in TE CO2 lasers

A model of the gain−switched TE CO2 laser is presented which explicitly includes rotational relaxation within the sublevels of the 10.4−μ laser band. Careful comparison with experiment is made employing a Q−switched cavity, and it is shown that rotational coupling dominates the laser dynamics at pressures below 150 Torr. Calculations demonstrate that the effect of rotational coupling is very significant even at atmospheric pressure, and its inclusion in the laser dynamical equations accounts for most of the difficulties obtained with previous models.

Close coupling calculations for massive ion-hydrogen atom collisions in the linear trajectory model

The Wilets and Gallaher (1966) formulation for H+-H collisions has been generalized to the heavy ion-atomic hydrogen collision. The resulting coupled differential equations have been solved and a corresponding computer program has been constructed to extract numerical results. Four-state calculations have been carried out for the specific example of He2+-H collisions using both eigenfunction and pseudo-state expansion bases. Charge transfer, excitation and ionization cross sections as well as 2p polarization fractions are presented and compared with other theoretical calculations and experimental measurements where these are available. The computations encompass the range of He2+ energies from 6.3 keV-4 MeV. It has been found that: the neglect of rotational coupling effects underestimate charge transfer cross sections at impact energies of the He2+ ion less than about 15 keV; at high velocities of encounter the charge transfer cross section to the He+(1s) state predominates over that to the He+(2s) or He+(2p) state and is confined to a small range of impact parameters; excitation cross sections are sensitive to the choice of pseudostates. It is further shown that an eigenfunction expansion basis is unlikely to reproduce the 1.2 degrees total charge transfer probability experiment of Keever and Everhart (1966) in a calculation employing a four-state approximation.

Ionization processes in He-He collisions

Differential scattering measurements of ionization in He-He collisions are made in the keV energy range using the energy loss technique. Combining the results with those obtained from the ejected electron spectra measurements of Gerber et al., the ionization process is discussed in the framework of the quasimolecular picture of the collision. Two-step mechanisms are proposed involving a primary radial or rotational coupling either to a molecular state which autoionizes during the collision or to a state which leads on dissociation to the formation of He- in an auto-ionizing state. Calculations taking account of rotational coupling effects between the 1 Sigma g, 1 Pi g and 1 Delta g states of He2 are in satisfactory agreement with experiment for energy E and scattering angle theta when E theta exceeds 3 keV deg.

Rotational coupling effects on the differential elastic and inelastic cross sections He+-He collisions

The He+-He collision is investigated using a molecular expansion which takes account of rotational coupling between the 2 sigma u and 2 Pi u states and between the 2 Sigma g, 2 Pi g and 2 Delta g states of the He2+ quasimolecule. Differential cross sections for elastic scattering, resonant charge transfer, direct and exchange excitation of He(1s, 2p) 1,3P, He+(2p) and of the autoionizing state He(2p2) 1S, 1D have been computed for a range of energies from 300 eV to 1.5 keV and for a range of scattering angles from 0 to 24 degrees (in centre of mass system). The agreement with experiment is satisfactory. For E theta >or approximately=3 keV deg, it is seen that rotational coupling is the dominant mechanism for the excitation of inelastic transitions. The consequences on the determination of potential energy curves from scattering data are briefly discussed.

Molecular perturbations

The interaction between rotation and electronic motion in a diatomic molecule is investigated by giving the direct wave mechanical form of the components of angular momenta. In order to get a suitable form of the interaction a reference system connected with the nuclei and independent from the electrons is used, defined by the Eulerian angles, in which the rectangular components of both total angular momentum and electronic angular momentum can be given. The adventage of this way of description in comparison with other used reference systems is emphasised. Observed perturbations are connected with a part of the effect of rotational coupling called here accidental, while there may be a considerable coupling between rotation and electronic motion without manifesting itself in irregularities. This is still more the case with respect to the coupling between vibration and electronic motion, since the nuclear motion may affect also the electronic part of the wave function with respect to which the averaging of the interactions of the particles leads to the potential curve characterising the regular sequence of energy levels. The fact that this electronic part of the wave function cannot be identified in general with an eigenfunction of the two center problem, yields a term which can play essential role in homogeneous perturbations. The analogous and different features of homogeneous and heterogeneous perturbations are discussed.