Mutual Angle Research Articles

Planetary Systems in Binaries. I. Dynamical Classification

Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20% of the known extrasolar planetary systems are associated with one or more stellar companions. The orbits of stellar binaries hosting planetary systems are typically wider than 100 AU and often highly inclined with respect to the planetary orbits. The effect of secular perturbations from such an inclined binary orbit on a coupled system of planets, however, is little understood theoretically. In this paper we investigate various dynamical classes of double-planet systems in binaries through numerical integrations and we provide an analytic framework based on secular perturbation theories. Differential nodal precession of the planets is the key property that separates two distinct dynamical classes of multiple planets in binaries: (1) dynamically-rigid systems in which the orbital planes of planets precess in concert as if they were embedded in a rigid disk, and (2) weakly-coupled systems in which the mutual inclination angle between initially coplanar planets grows to large values on secular timescales. In the latter case, the quadrupole perturbation from the outer planet induces additional Kozai cycles and causes the orbital eccentricity of the inner planet to oscillate with large amplitudes. The cyclic angular momentum transfer from a stellar companion propagating inward through planets can significantly alter the orbital properties of the inner planet on shorter timescales. This perturbation propagation mechanism may offer important constraints on the presence of additional planets in known single-planet systems in binaries.

Resonant triple-differential cross-section measurements on atomic strontium

Resonant triple-differential cross-section (TDCS) measurements were performed on atomic strontium on the 4p → 4d resonance. A variety of energy sharings were examined with the experimental arrangement in the coplanar geometry. The angle of detection of one electron, relative to the direction of the vector of the fully linear polarized incident photon beam, was set to −90o. The mutual angle between the two electrons had a range just short of 90o → 270o. These experimental data are presented with comparisons made to similar data from West et al (2001 J. Phys. B: At. Mol. Phys. 34 4169–81) and to the theoretical characterization as derived by Malegat et al (1997 J. Phys. B: At. Mol. Phys. 30 251–61) using the parametrization of Cvejanović and Reddish (2000 J. Phys. B: At. Mol. Phys. 33 4691–709). All of the present TDCS measurements display unexpected lobes at a mutual emission angle of 180o, possible explanations for these lobes are explored.

Induced Kozai Migration and Formation of Close-in Planets in Binaries

AbstractMany recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20%, and presumably a larger fraction, of the known extrasolar planetary systems are associated with one or more stellar companions. These stellar companions normally exist at large distances from the planetary systems (typical projected binary separations are 102–104AU) and are often faint (ranging from F to T spectral types). Yet, secular cyclic angular momentum exchange with these distant stellar companions can significantly alter the orbital configuration of the planets around the primaries. One of the most interesting and fairly common outcomes seen in numerical simulations is the opening of a large mutual inclination angle between the planetary orbits, forced by differential nodal precessions caused by the binary companion. The growth of the mutual inclination angle between planetary orbits induces additional large-amplitude eccentricity oscillations of the inner planet due to the quadrupole gravitational perturbation by the outer planet. This eccentricity oscillation may eventually result in the orbital decay of the inner planet through tidal friction, as previously proposed as Kozai migration or Kozai cycles with tidal friction (KCTF). This orbital decay mechanism induced by the binary perturbation and subsequent tidal dissipation may stand as an alternative formation channel for close-in extrasolar planets.

Anisotropic magnetoresistance in Fe/MgO/Fe tunnel junctions

The ballistic conductance of Fe/MgO/Fe magnetic tunnel junctions depends significantly onthe direction of the magnetization in the leads, as is investigated by relativistic first-principleselectronic structure and transport calculations. The rotation of the parallel aligned leadmagnetizations from in-plane to perpendicular orientation with respect to the interfaces, thatis tunnel anisotropic magnetoresistance (TAMR), increases the zero-bias conductance by about30%. The effect originates from both the Rashba spin–orbit interaction at the interfaces andfrom resonant tunneling. Spin–orbit induced band gaps in the leads show no considerableeffect on the anisotropic magnetoresistance. The tunnel magnetoresistance (TMR), i.e. thedependence of the conductance on the mutual angle between the lead magnetizations, isalso addressed.

Double-blind test program for astrometric planet detection with Gaia

We use detailed simulations of the Gaia observations of synthetic planetary systems and develop and utilize independent software codes in double-blind mode to analyze the data, including statistical tools for planet detection and different algorithms for single and multiple Keplerian orbit fitting that use no a priori knowledge of the true orbital parameters of the systems. 1) Planets with astrometric signatures $\alpha\simeq 3$ times the single-measurement error $\sigma_\psi$ and period $P\leq 5$ yr can be detected reliably, with a very small number of false positives. 2) At twice the detection limit, uncertainties in orbital parameters and masses are typically $15%-20%$. 3) Over 70% of two-planet systems with well-separated periods in the range $0.2\leq P\leq 9$ yr, $2\leq\alpha/\sigma_\psi\leq 50$, and eccentricity $e\leq 0.6$ are correctly identified. 4) Favorable orbital configurations have orbital elements measured to better than 10% accuracy $> 90%$ of the time, and the value of the mutual inclination angle determined with uncertainties $\leq 10^{\degr}$. 5) Finally, uncertainties obtained from the fitting procedures are a good estimate of the actual errors. Extrapolating from the present-day statistical properties of the exoplanet sample, the results imply that a Gaia with $\sigma_\psi$ = 8 $\mu$as, in its unbiased and complete magnitude-limited census of planetary systems, will measure several thousand giant planets out to 3-4 AUs from stars within 200 pc, and will characterize hundreds of multiple-planet systems, including meaningful coplanarity tests. Finally, we put Gaia into context, identifying several areas of planetary-system science in which Gaia can be expected to have a relevant impact, when combined with data coming from other ongoing and future planet search programs.

Single-Molecule Spectroscopic Characterization of Light-Harvesting 2 Complexes Reconstituted into Model Membranes

The spectroscopic properties of the light-harvesting 2 complexes (LH2) from the purple bacterium Rhodopseudomonas acidophila (strain 10050) in detergent micelles and reconstituted into lipid membranes have been studied by single-molecule spectroscopy. When LH2 complexes are solubilized from their host biological membranes by nondenaturing detergents, such as LDAO, there is a small 2-nm spectral shift of the B850 absorption band in the ensemble spectrum. This is reversed when the LH2 complexes are put back into phospholipid vesicles, i.e., into a more native-like environment. The spectroscopic properties on the single-molecule level of the detergent-solubilized LH2 complexes were compared with those reconstituted into the lipid membranes to see if their detailed spectroscopic behavior was influenced by these small changes in the position of the B850 absorption band. A detailed analysis of the low-temperature single-molecule fluorescence-excitation spectra of the LH2 complexes in these two different conditions showed no significant differences. In particular, the distribution of the spectral splitting between the circular k = ±1 exciton states of the B850 absorption band and the distribution of the mutual angle between the k = ±1 exciton states are identical in both cases. It can be concluded, therefore, that the LH2 complexes from Rps. acidophila are equally stable when solubilized in detergent micelles as they are when membrane reconstituted. Moreover, when they are solubilized in a suitable detergent and spin coated onto a surface for the single-molecule experiments they do not display any more structural disorder than when in a phospholipid membrane.

Hard axis magnetic field dependence on current-induced magnetization switching in MgO-based magnetic tunnel junctions

We conducted a detailed study of hard axis magnetic field (Hhard) dependence on current-induced magnetization switching (CIMS) in MgO-based magnetic tunnel junctions (MTJs) with various junction sizes and various uniaxial anisotropy fields. The decreases in critical current density (Jc) and the intrinsic critical current density (Jc0) estimated from the pulse duration dependence on Jc in CIMS are observed when applying Hhard for all MTJs. The decrease in energy barrier of CIMS is also observed except for the largest sample. These results indicate that the reduction of Jc is attributable to both the increase of spin-transfer efficiency and the decrease in energy barrier in the case of applying Hhard. The Jc0 decreases with increase in the mutual angle between the direction of magnetization and the easy axis (θf), which is consistent with the theoretical prediction proposed by Slonczewski. The degree of the reduction of Jc0 for the same value of Hhard decreases with decreasing size of MTJs. This behavior is considered to be related to not only decrease in θf due to the increase in anisotropy field in MTJs, but also to the increase in the variance of the initial angle of magnetization due to the thermally activated magnon excitation. The stable switching endurance related to CIMS was observed in a wide range of MTJ sizes when applying Hhard. Moreover, we proposed a new architecture and a new switching method considering write disturbance. These results would be useful for application to spin memory and other spin-electronic devices.

Fabrication of three-dimensional periodic microstructures in photoresist SU-8 by phase-controlled holographic lithography

Three-dimensional (3D) periodic dielectric structures were recorded in a commercial photoresist SU-8 by exposure to intensity patterns created by five interfering coherent femtosecond Ti : sapphire laser pulses. Periodic symmetry of these patterns was controlled by the choice of mutual convergence angles of the beams as well as their phases. The fabricated structures are mechanically and chemically stable, well-connected frameworks of SU-8 regions in air; the smallest dimensions of SU-8 features are in the sub-micrometre range. The structures exhibit a high degree of long-range order across areas as large as 1 mm in cross-section.

Crystal Structures of Lanthanide(III) Complexes with Cyclen Derivative Bearing Three Acetate and One Methylphosphonate Pendants

A series of lanthanide(III) complexes formulated as M[Ln(Hdo3ap)].xH(2)O (M = Li or H and Ln = Tb, Dy, Er, Lu, and Y) with the monophosphonate analogue of H(4)dota, 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic-10-methylphosphonic acid (H(5)do3ap), was prepared in the solid state and studied using X-ray crystallography. All of the structures show that the (Hdo3ap)(4-) anion is octadentate coordinated to a lanthanide(III) ion similarly to the other H(4)dota-like ligands, i.e., forming O(4) and N(4) planes that are parallel and have mutual angle smaller than 3 degrees . The lanthanide(III) ions lie between these planes, closer to the O(4) base than to the N(4) plane. All of the structures present the lanthanide(III) complexes in their twisted-square-antiprismatic (TSA) configuration. Twist angles of the pendants vary in the range between -24 and -30 degrees, and for each complex, they lie in a very narrow region of 1 degree. The coordinated phosphonate oxygen is located slightly above (0.02-0.19 Angstroms) the O(3) plane formed with the coordinated acetates. A water molecule was found to be coordinated only in the terbium(III) and neodymium(III) complexes. The bond distance Tb-O(w) is unusually long (2.678 Angstroms). The O-Ln-O angles decrease from 140 degrees [Nd(III)] to 121 degrees [Lu(III)], thus confirming the increasing steric crowding around the water binding site. A comparison of a number of structures of Ln(III) complexes with DOTA-like ligands shows that the TSA arrangement is flexible. On the other hand, the SA arrangement is rigid, and the derived structural parameters are almost identical for different ligands and lanthanide(III) ions.

Quasi-binary incident electron—centre of mass collision in (e, 3e) process on He and He-like ions

We present in this communication the results of our first Born calculation in the three-Coulomb (3C) wave approach for the (e, 3e) process on He and He-like ions at an incident electron energy 5599 eV in the coplanar constant θ12 as well as out-of-plane constant φ12 modes. These two geometrical modes are such that the quasi-binary collision between the incident electron and centre of mass of the ejected electrons is in the scattering plane. The theoretical formalism has been developed using plane waves, Le Sech wave function and approximated BBK-type wave function respectively for the incident and scattered, bound and ejected electrons to calculate five-fold differential crosssection (FDCS) of the (e, 3e) process. We emphasize on the similarities and dissimilarities (asymmetries) in the angular profile of the FDCS in two modes as well as the effects of post-collision interaction (between the ejected electrons) and nuclear chargeZ on the angular profile of the FDCS. We observe that with the increment of nuclear charge the two quasi-binary collisions approach towards identical behaviour at larger mutual angles and thus bringing less asymmetry in FDCS for higherZ target.

Electrostatic Interactions Between Glycosaminoglycan Molecules

The electrostatic interactions between nearest-neighbouringchondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains areobtained on the bottle brush conformation of proteoglycan aggrecanbased on an asymptotic solution of the Poisson-Boltzmann equation theCS-GAGs satisfy under the physiological conditions of articularcartilage. The present results show that the interactions areassociated intimately with the minimum separation distance and mutualangle between the molecular chains themselves. Further analysisindicates that the electrostatic interactions are not only expressed tobe purely exponential in separation distance and decrease with theincreasing mutual angle but also dependent sensitively on the salineconcentration in the electrolyte solution within the tissue, which isin agreement with the existed relevant conclusions.

(e,3e)process on a quantum dot

The exact initial state wave function of an interacting electron pair in a quantum dot under parabolic confinement and neutralization of the dot by the substrate after ejection of electrons is exploited to obtain the fivefold differential cross section $(X)$ of the $(e,3e)$ process on the dot. The reflections of the center-of-mass (c.m.) motion and relative motion on $X$ are decoupled if the incident and scattered electrons are energetic and the ejected electrons are slow. The results are studied in fixed mutual angle (with zero c.m. momentum $K$) and Bethe ridge modes which allow the ``cleanest'' analysis of the contribution of the relative motion. The Coulomb interaction between the emitted electrons is found to qualitatively change the angular distribution of $X$. In the mode in which the magnitude of $K$ is equal to the momentum transfer $q$, the angular distribution of $X$ with respect to ${\ensuremath{\theta}}_{Kq}={\mathrm{cos}}^{\ensuremath{-}1}(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{K}∙\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q})$ leads to a mapping of the initial c.m. wave function of the ejected pair. However, the c.m. motion is found to be best studied in the kinematics where the relative momentum $\stackrel{P\vec}{k}$ of the ejected pair is equal to $\stackrel{P\vec}{q}$.

Quasiperiodic structures via atom-optical nanofabrication

We deposit a laser-collimated chromium beam onto a substrate through a quasiperiodic laser standing-wave (SW) tuned above the atomic resonance at the ${}^{52}\mathrm{Cr}$ transition ${}^{7}{\stackrel{\ensuremath{\rightarrow}}{{S}_{3}}}^{7}{P}_{4}^{o}$ at 425.55 nm. This SW is created by interference of five laser beams crossing in one point at mutual angles of $72\ifmmode^\circ\else\textdegree\fi{}.$ The resulting chromium pattern on the substrate surface mimics the geometry of the SW and it is thus itself quasiperiodic. On a surface area of $0.2\ifmmode\times\else\texttimes\fi{}0.2{\mathrm{mm}}^{2}$ the spatial Fourier spectrum of the measured patterns is decagonal. Besides being of fundamental interest, this quasiperiodic nanofabrication via atom optics can find its applications in photonics.

Perturbative analysis of the triply differential cross section and circular dichroism in photo-double-ionization of He

We extend application of our lowest-order perturbative approach (in electron-electron correlation ) for analysis of photo-double-ionization (PDI) of He [A.Y. Istomin et al., J. Phys. B 35, L543 (2002)] to excess energies up to 450 eV and to analysis of circular dichroism. We find that account of electron correlation in the final state to first order provides predictions for the triply differential cross section and circular dichroism that are in reasonable agreement with absolute data for excess energies up to 80 eV. For an excess energy of 450 eV, account of electron correlation in both initial and final states is necessary and the predicted triply differential cross sections are in agreement with absolute data only for large mutual ejection angles. We find that at excess energies of a few tens of eV, the PDI is dominated by the “virtual” knock-out mechanism, while the “direct” (on-shell) knock-out process gives only small contributions for large mutual ejection angles. As a result, we conclude that the circular dichroism effect at these energies originates from the nonzero electron Coulomb phase shifts.

Study of wedge-adjusted Talbot interferometer for writing fiber gratings with variable inscribed Bragg wavelengths

A wedge-adjusted Talbot interferometer is presented to change the inscribed Bragg wavelength of fiber Bragg gratings. In this system, the grating is written by UV interference stripes of 193 nm derived from two combined mirrors, where a phase mask is used as a beamsplitter of ±1 order of diffraction light. It is noteworthy that the adjustor transforms the shift of wedge into the rotation of the two mirrors, and alters the mutual angle of two interfering beams in writing fiber Bragg gratings.

Shape-amplitude representation of N-particle photofragmentation processes.

The general form of the multiparticle photofragmentation matrix element in dipole approximation is derived. Using two noncolinear momentum vectors to create a coordinate system enables the extraction of shape amplitudes depending only on lengths and mutual angles of the momentum vectors, i.e., on body fixed quantities, defining the fragmentation configuration. This is in contrast to previous parametrizations and, in particular, allows selection rules to be derived in a simpler and more transparent way.

Azimuthal Frustration and Bundling in Columnar DNA Aggregates

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the interaxial separation of two DNA molecules, but also on their azimuthal orientation. The optimal mutual azimuthal angle is a function of the DNA-DNA interaxial separation, which leads to azimuthal frustrations in an aggregate. On the basis of the pair potential, the positional and orientational order in columnar B-DNA assemblies in solution is investigated. Phase diagrams are calculated using lattice sums supplemented with the entropic contributions of the counterions in solution. A variety of positionally and azimuthally ordered phases and bundling transitions is predicted, which strongly depend on the counterion adsorption patterns.

Coplanar (e, 3e) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ12 mode

Angle-dependent postcollisional interaction and interference effects in resonant double photoionization of neon

The resonant double photoionization of Ne has been studied via an electron-electron coincidence experiment. A complete set of measurements was performed at different mutual angles when the photoelectron and Auger-electronpairs have nearly equal energy. The overall experimental energy resolution, narrower than the natural linewidth of the intermediate state, has allowed us to observe interference effects due to the indistinguishability of the two electrons. The observed energy and angular distribution exhibit a strong interplay of postcollisional interaction and interference effects. Calculations based on the model developed by Sheinerman and Schmidt [J. Phys. B 30, 1677 (1997)] describe the main trend of the experimental observations.

Single-molecule study of the electronic couplings in a circular array of molecules: light-harvesting-2 complex from Rhodospirillum molischianum.

Applying single-molecule spectroscopic techniques allowed us to determine the mutual angles between the transition-dipole moments associated with optical transitions of the eight bacteriochlorophyll a molecules which form the so-called B800 ring of the light-harvesting-2 complex from Rhodospirillum molischianum. The orientation of the transition-dipole moment is a sensitive probe for the strength of the local intermolecular interactions because of the well-defined arrangement of the individual molecules within the B800 ring. Our data reveal that the strength of the electronic coupling between individual molecules in the ring is subjected to spatial as well as temporal variations.