Three-Dimensional Simulations of Mixing Instabilities in Supernova Explosions

We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 solar-mass blue supergiant star. The outgoing supernova shock is followed from its launch by neutrino heating until it breaks out from the stellar surface more than two hours after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant asphericity, which triggers the growth of Rayleigh-Taylor (RT) instabilities at the composition interfaces of the exploding star. Deep inward mixing of hydrogen (H) is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the H-envelope of the star as observed, e.g., in the case of SN 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 0.001 solar masses) are obtained in some models. The metal core of the progenitor is partially turned over with Ni-dominated fingers overtaking oxygen-rich bullets and both Ni and O moving well ahead of the material from the carbon layer. Comparing with corresponding 2D (axially symmetric) calculations, we determine the growth of the RT fingers to be faster, the deceleration of the dense metal-carrying clumps in the He and H layers to be reduced, the asymptotic clump velocities in the H-shell to be higher (up to ~4500 km/s for the considered progenitor and an explosion energy of 10^{51} ergs, instead of <2000 km/s in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries. (abridged)Comment: 15 pages, 8 figures, 30 eps files; significantly extended and more figures added after referee comments; accepted by The Astrophysical Journa

Thin Ice Target for 16^{16}O(p,p') experiment

A windowless and self-supporting ice target is described. An ice sheet with a thickness of 29.7 mg/cm$^2$ cooled by liquid nitrogen was placed at the target position of a magnetic spectrometer and worked stably in the $^{16}$O$(p,p')$ experiment at $E_{p}=392$ MeV. Background-free spectra were obtained.Comment: 14 pages, 4 figures, Nucl. Instr. & Meth. A (in press

Anomalous Spin Dynamics observed by High Frequency ESR in Honeycomb Lattice Antiferromagnet InCu2/3V1/3O3

High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while it tends to decrease as the temperature in a conventional three-dimensional antiferromagnet decreases. In general, a honeycomb lattice antiferromagnet is expected to show a simple antiferromagnetic order similar to that of a square lattice antiferromagnet theoretically because both antiferromagnets are bipartite lattices. However, we suggest that the observed anomalous spin dynamics below TN is the peculiar feature of the honeycomb lattice antiferromagnet that is not observed in the square lattice antiferromagnet.Comment: 5 pages, 5 figure

Neutron Scattering study of Sr_2Cu_3O_4Cl_2

We report a neutron scattering study on the tetragonal compound Sr_2Cu_3O_4Cl_2, which has two-dimensional (2D) interpenetrating Cu_I and Cu_{II} subsystems, each forming a S=1/2 square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the inter-subsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the Cu_{II} subsystem. Due to quantum fluctuations a dramatic increase of the Cu_I out-of-plane spin-wave gap is also observed. The temperature dependence and the dispersion of the spin-wave energy are quantitatively explained by spin-wave calculations which include quantum fluctuations explicitly. The values for the nearest-neighbor superexchange interactions between the Cu_I and Cu_{II} ions and between the Cu_{II} ions are determined experimentally to be J_{I-II} = -10(2)meV and J_{II}= 10.5(5)meV, respectively. Due to its small exchange interaction, J_{II}, the 2D dispersion of the Cu_{II} SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a novel dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the Cu_{II} SLQHA is obtained up to a very high temperature, T/J_{II}\approx 0.75. This result is compared with several theoretical predictions as well as recent experiments on the S=1/2 SLQHA.Comment: Figures and equations are rearrange

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions. Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.Comment: 20 pages, 10 figure

Electron affinities of the first- and second- row atoms: benchmark ab initio and density functional calculations

A benchmark ab initio and density functional (DFT) study has been carried out on the electron affinities of the first- and second-row atoms. The ab initio study involves basis sets of $spdfgh$ and $spdfghi$ quality, extrapolations to the 1-particle basis set limit, and a combination of the CCSD(T), CCSDT, and full CI electron correlation methods. Scalar relativistic and spin-orbit coupling effects were taken into account. On average, the best ab initio results agree to better than 0.001 eV with the most recent experimental results. Correcting for imperfections in the CCSD(T) method improves the mean absolute error by an order of magnitude, while for accurate results on the second-row atoms inclusion of relativistic corrections is essential. The latter are significantly overestimated at the SCF level; for accurate spin-orbit splitting constants of second-row atoms inclusion of (2s,2p) correlation is essential. In the DFT calculations it is found that results for the 1st-row atoms are very sensitive to the exchange functional, while those for second-row atoms are rather more sensitive to the correlation functional. While the LYP correlation functional works best for first-row atoms, its PW91 counterpart appears to be preferable for second-row atoms. Among ``pure DFT'' (nonhybrid) functionals, G96PW91 (Gill 1996 exchange combined with Perdew-Wang 1991 correlation) puts in the best overall performance. The best results overall are obtained with the 1-parameter hybrid modified Perdew-Wang (mPW1) exchange functionals of Adamo and Barone [J. Chem. Phys. {\bf 108}, 664 (1998)], with mPW1LYP yielding the best results for first-row, and mPW1PW91 for second-row atoms. Indications exist that a hybrid of the type $a$ mPW1LYP + $(1-a)$ mPW1PW91 yields better results than either of the constituent functionals.Comment: Phys. Rev. A, in press (revised version, review of issues concerning DFT and electron affinities added

Polarization transfer in the 16^{16}O(p,p′)(p,p') reaction at forward angles and structure of the spin-dipole resonances

Cross sections and polarization transfer observables in the $^{16}$O$(p,p')$ reactions at 392 MeV were measured at several angles between $\theta_{lab}=$ 0$^\circ$ and 14$^\circ$. The non-spin-flip (${\Delta}S=0$) and spin-flip (${\Delta}S=1$) strengths in transitions to several discrete states and broad resonances in $^{16}$O were extracted using a model-independent method. The giant resonances in the energy region of $E_x=19-$27 MeV were found to be predominantly excited by ${\Delta}L=1$ transitions. The strength distribution of spin-dipole transitions with ${\Delta}S=1$ and ${\Delta}L=1$ were deduced. The obtained distribution was compared with a recent shell model calculation. Experimental results are reasonably explained by distorted-wave impulse approximation calculations with the shell model wave functions.Comment: 28 pages RevTex, including 9 figures, to be published in Phys. Rev. C.; a typo in Eq. (3b) was correcte

Multi-channel analog of the effective-range expansion

Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the S-matrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.Comment: 33 pages, 10 figure