Improved Laboratory Transition Probabilities for Ce II, Application to the Cerium Abundances of the Sun and Five r-process Rich, Metal-Poor Stars, and Rare Earth Lab Data

Recent radiative lifetime measurements accurate to +/- 5% using laser-induced fluorescence (LIF) on 43 even-parity and 15 odd-parity levels of Ce II have been combined with new branching fractions measured using a Fourier transform spectrometer (FTS) to determine transition probabilities for 921 lines of Ce II. This improved laboratory data set has been used to determine a new solar photospheric Ce abundance, log epsilon = 1.61 +/- 0.01 (sigma = 0.06 from 45 lines), a value in excellent agreement with the recommended meteoritic abundance, log epsilon = 1.61 +/- 0.02. Revised Ce abundances have also been derived for the r-process-rich metal-poor giant stars BD+17 3248, CS 22892-052, CS 31082-001, HD 115444 and HD 221170. Between 26 and 40 lines were used for determining the Ce abundance in these five stars, yielding a small statistical uncertainty of 0.01 dex similar to the Solar result. The relative abundances in the metal-poor stars of Ce and Eu, a nearly pure r-process element in the Sun, matches r-process only model predictions for Solar System material. This consistent match with small scatter over a wide range of stellar metallicities lends support to these predictions of elemental fractions. A companion paper includes an interpretation of these new precision abundance results for Ce as well as new abundance results and interpretations for Pr, Dy and Tm.Comment: 84 pages, 8 Figures, 14 Tables; To appear in the Astrophysical Journal Supplemen

The Hitting Times with Taboo for a Random Walk on an Integer Lattice

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x, the hitting state y and the taboo state z. We find the probability that these passages times are finite and analyze the tails of their cumulative distribution functions. In particular, it turns out that for the random walk on Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the tail decrease is specified by dimension d only. In contrast, for a simple random walk on Z, the asymptotic properties of hitting times with taboo essentially depend on the mutual location of the points x, y and z. These problems originated in our recent study of branching random walk on Z^d with a single source of branching

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in $\R^d$ is supported on a set of Hausdorff dimension strictly less than $d$ \cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of $\Z ^d$, $d\geq 2$. By refining the argument, we prove that for all \b>0 there exists \rho (d,\b)N(d,\b), any $x \in \Z^d$, and any $A\subset \{1,..., n\}^d$ | \{y\in\Z^d\colon \nu_{A,x}(y) \geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where $\nu_{A,x} (y)$ denotes the probability that $y$ is the first entrance point of the simple random walk starting at $x$ into $A$. Furthermore, $\rho$ must converge to $d$ as \b \to \infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne

Atomic Transition Probabilities for Transitions of Si I and Si II and the Silicon Abundances of Several Very Metal-Poor Stars

We report new measurements of branching fractions for 20 UV and blue lines in the spectrum of neutral silicon (Si I) originating in the 3$s^{2}$3$p$4$s$ $^{3}$P$^{\rm o}_{1,2}$, $^{1}$P$^{\rm o}_{1}$ and 3$s$3$p^{3}$ $^{1}$D$^{\rm o}_{1,2}$ upper levels. Transitions studied include both strong, nearly pure LS multiplets as well as very weak spin-forbidden transitions connected to these upper levels. We also report a new branching fraction measurement of the $^{4}$P$_{1/2}$ - $^{2}$P$^{\rm o}_{1/2,3/2}$ intercombination lines in the spectrum of singly-ionized silicon (Si II). The weak spin-forbidden lines of Si I and Si II provide a stringent test on recent theoretical calculations, to which we make comparison. The branching fractions from this study are combined with previously reported radiative lifetimes to yield transition probabilities and log($gf$)s for these lines. We apply these new measurements to abundance determinations in five metal-poor stars.Comment: Accepted for publication in the Astrophysical Journal Supplement Series (26 pages, 6 figures, 5 tables; machine-readable versions of Tables 3 and 4 will be available from the publisher

On harmonic measure of critical curves

Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure have been computed by B. Duplantier [Phys. Rev. Lett. {\bf 84}, 1363 (2000)] by relating the problem to boundary two-dimensional gravity. We present a simple argument that allows us to connect harmonic measure of critical curves to operators obtained by fusion of primary fields, and compute characteristics of fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with $c\leqslant 1$.Comment: Some more correction

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Evidence of Multiple r-Process Sites in the Early Galaxy: New Observations of CS 22892-052

First results are reported of a new abundance study of neutron-capture elements in the ultra-metal-poor (UMP; [Fe/H] = -3.1) halo field giant star CS 22892-052. Using new high resolution, high signal-to-noise spectra, abundances of more than 30 neutron-capture elements (Z>30) have been determined. Six elements in the 40<Z<56 domain (Nb, Ru, Rh, Pd, Ag and Cd) have been detected for the first time in a UMP star. Abundances are also derived for three of the heaviest stable elements (Os, Ir, and Pb). A second transition of thorium, Th{4086}, confirms the abundance deduced from the standard Th{4019} line, and an upper limit to the abundance of uranium is established from the absence of the U{3859} line. As found in previous studies, the abundances of the heavier (Z>=56) stable neutron-capture elements in CS 22892-052 match well the scaled solar system r-process abundance distribution. From the observed Th abundance, an average age of ~= 16 +/- 4 Gyr is derived for cs22892-052, consistent with the lower age limit of ~= 11 Gyr derived from the upper limit on the U abundance. The concordance of scaled solar r-process and CS 22892-052 abundances breaks down for the lighter neutron-capture elements, supporting previous suggestions that different r-process production sites are responsible for lighter and heavier neutron-capture elements.Comment: To be published in the Astrophysical Journal Letter