Planetary migration in evolving planetesimals discs

In the current paper, we further improved the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi (2002). In the current study, the assumption of Del Popolo and Eksi (2002), that the surface density in planetesimals is proportional to that of gas, is released. In order to obtain the evolution of planetesimal density, we use a method developed in Stepinski and Valageas (1997) which is able to simultaneously follow the evolution of gas and solid particles for up to 10^7 yrs. Then, the disk model is coupled to migration model introduced in Del Popolo et al. (2001) in order to obtain the migration rate of the planet in the planetesimal. We find that the properties of solids known to exist in protoplanetary systems, together with reasonable density profiles for the disk, lead to a characteristic radius in the range 0.03-0.2 AU for the final semi-major axis of the giant planet.Comment: IJMP A in prin

Orbital Configurations and Magnetic Properties of Double-Layered Antiferromagnet Cs3_3Cu2_2Cl4_4Br3_3

We report the single-crystal X-ray analysis and magnetic properties of a new double-layered perovskite antiferromagnet, Cs$_3$Cu$_2$Cl$_4$Br$_3$. This structure is composed of Cu$_2$Cl$_4$Br$_3$ double layers with elongated CuCl$_4$Br$_2$ octahedra and is closely related to the Sr$_3$Ti$_2$O$_7$ structure. An as-grown crystal has a singlet ground state with a large excitation gap of $\Delta/k_{\rm B}\simeq 2000$ K, due to the strong antiferromagnetic interaction between the two layers. Cs$_3$Cu$_2$Cl$_4$Br$_3$ undergoes a structural phase transition at $T_{\rm s}\simeq330$ K accompanied by changes in the orbital configurations of Cu$^{2+}$ ions. Once a Cs$_3$Cu$_2$Cl$_4$Br$_3$ crystal is heated above $T_{\rm s}$, its magnetic susceptibility obeys the Curie-Weiss law with decreasing temperature even below $T_{\rm s}$ and does not exhibit anomalies at $T_{\rm s}$. This implies that in the heated crystal, the orbital state of the high-temperature phase remains unchanged below $T_{\rm s}$, and thus, this orbital state is the metastable state. The structural phase transition at $T_{\rm s}$ is characterized as an order-disorder transition of Cu$^{2+}$ orbitals.Comment: 6pages. 6figures, to appear in J. Phys. Soc. Jpn. Vol.76 No.

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Simulations of the Population of Centaurs I: The Bulk Statistics

Large-scale simulations of the Centaur population are carried out. The evolution of 23328 particles based on the orbits of 32 well-known Centaurs is followed for up to 3 Myr in the forward and backward direction under the influence of the 4 massive planets. The objects exhibit a rich variety of dynamical behaviour with half-lives ranging from 540 kyr (1996 AR20) to 32 Myr (2000 FZ53). The mean half-life of the entire sample of Centaurs is 2.7 Myr. The data are analyzed using a classification scheme based on the controlling planets at perihelion and aphelion, previously given in Horner et al (2003). Transfer probabilities are computed and show the main dynamical pathways of the Centaur population. The total number of Centaurs with diameters larger than 1 km is estimated as roughly 44300, assuming an inward flux of one new short-period comet every 200 yrs. The flux into the Centaur region from the Edgeworth-Kuiper belt is estimated to be 1 new object every 125 yrs. Finally, the flux from the Centaur region to Earth-crossing orbits is 1 new Earth-crosser every 880 yrsComment: 15 pages, 2 figures, MNRAS in pres

Structure and rotations of the Hoyle state

The excited state of the 12C nucleus known as the "Hoyle state" constitutes one of the most interesting, difficult and timely challenges in nuclear physics, as it plays a key role in the production of carbon via fusion of three alpha particles in red giant stars. In this letter, we present ab initio lattice calculations which unravel the structure of the Hoyle state, along with evidence for a low-lying spin-2 rotational excitation. For the 12C ground state and the first excited spin-2 state, we find a compact triangular configuration of alpha clusters. For the Hoyle state and the second excited spin-2 state, we find a "bent-arm" or obtuse triangular configuration of alpha clusters. We also calculate the electromagnetic transition rates between the low-lying states of 12C.Comment: 4 pages, 3 figures, 4 tables, version to be published in Physical Review Letter

Theory and applications of atomic and ionic polarizabilities

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.Comment: Review paper, 44 page

The effects of supernovae on the dynamical evolution of binary stars and star clusters

In this chapter I review the effects of supernovae explosions on the dynamical evolution of (1) binary stars and (2) star clusters. (1) Supernovae in binaries can drastically alter the orbit of the system, sometimes disrupting it entirely, and are thought to be partially responsible for `runaway' massive stars - stars in the Galaxy with large peculiar velocities. The ejection of the lower-mass secondary component of a binary occurs often in the event of the more massive primary star exploding as a supernova. The orbital properties of binaries that contain massive stars mean that the observed velocities of runaway stars (10s - 100s km s$^{-1}$) are consistent with this scenario. (2) Star formation is an inherently inefficient process, and much of the potential in young star clusters remains in the form of gas. Supernovae can in principle expel this gas, which would drastically alter the dynamics of the cluster by unbinding the stars from the potential. However, recent numerical simulations, and observational evidence that gas-free clusters are observed to be bound, suggest that the effects of supernova explosions on the dynamics of star clusters are likely to be minimal.Comment: 16 pages, to appear in the 'Handbook of Supernovae', eds. Paul Murdin and Athem Alsabti. This version replaces an earlier version that contained several typo

Toward Understanding Massive Star Formation

Although fundamental for astrophysics, the processes that produce massive stars are not well understood. Large distances, high extinction, and short timescales of critical evolutionary phases make observations of these processes challenging. Lacking good observational guidance, theoretical models have remained controversial. This review offers a basic description of the collapse of a massive molecular core and a critical discussion of the three competing concepts of massive star formation: - monolithic collapse in isolated cores - competitive accretion in a protocluster environment - stellar collisions and mergers in very dense systems We also review the observed outflows, multiplicity, and clustering properties of massive stars, the upper initial mass function and the upper mass limit. We conclude that high-mass star formation is not merely a scaled-up version of low-mass star formation with higher accretion rates, but partly a mechanism of its own, primarily owing to the role of stellar mass and radiation pressure in controlling the dynamics.Comment: 139 pages, 18 figures, 5 tables, glossar

Dynamical Jahn-Teller Effect and Berry Phase in Positively Charged Fullerene I. Basic Considerations

We study the Jahn-Teller effect of positive fullerene ions $^2$C$_{60}^{+}$ and $^1$C$_{60}^{2+}$. The aim is to discover if this case, in analogy with the negative ion, possesses a Berry phase or not, and what are the consequences on dynamical Jahn-Teller quantization. Working in the linear and spherical approximation, we find no Berry phase in $^1$C$_{60}^{2+}$, and presence/absence of Berry phase for coupling of one $L=2$ hole to an $L=4$/$L=2$ vibration. We study in particular the special equal-coupling case ($g_2=g_4$), which is reduced to the motion of a particle on a 5-dimensional sphere. In the icosahedral molecule, the final outcome assesses the presence/absence of a Berry phase of $\pi$ for the $h_u$ hole coupled to $G_g$/$H_h$ vibrations. Some qualitative consequences on ground-state symmetry, low-lying excitations, and electron emission from C$_{60}$ are spelled out.Comment: 31 pages (RevTeX), 3 Postscript figures (uuencoded

Frequency of Solar-Like Systems and of Ice and Gas Giants Beyond the Snow Line from High-Magnification Microlensing Events in 2005-2008

We present the first measurement of planet frequency beyond the "snow line" for planet/star mass-ratios[-4.5<log q<-2]: d^2 N/dlog q/dlog s=(0.36+-0.15)/dex^2 at mean mass ratio q=5e-4, and consistent with being flat in log projected separation, s. Our result is based on a sample of 6 planets detected from intensive follow-up of high-mag (A>200) microlensing events during 2005-8. The sample host stars have typical mass M_host 0.5 Msun, and detection is sensitive to planets over a range of projected separations (R_E/s_max,R_E*s_max), where R_E 3.5 AU sqrt(M_host/Msun) is the Einstein radius and s_max (q/5e-5)^{2/3}, corresponding to deprojected separations ~3 times the "snow line". Though frenetic, the observations constitute a "controlled experiment", which permits measurement of absolute planet frequency. High-mag events are rare, but the high-mag channel is efficient: half of high-mag events were successfully monitored and half of these yielded planet detections. The planet frequency derived from microlensing is a factor 7 larger than from RV studies at factor ~25 smaller separations [2<P<2000 days]. However, this difference is basically consistent with the gradient derived from RV studies (when extrapolated well beyond the separations from which it is measured). This suggests a universal separation distribution across 2 dex in semi-major axis, 2 dex in mass ratio, and 0.3 dex in host mass. Finally, if all planetary systems were "analogs" of the Solar System, our sample would have yielded 18.2 planets (11.4 "Jupiters", 6.4 "Saturns", 0.3 "Uranuses", 0.2 "Neptunes") including 6.1 systems with 2 or more planet detections. This compares to 6 planets including one 2-planet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.Comment: 42 pages, 10 figure