BVI Photometry and the Luminosity Function of the Globular Cluster M92

We present new BVI ground-based photometry and VI space-based photometry for the globular cluster M92 (NGC 6341) and examine luminosity functions in B, V, and I containing over 50,000 stars ranging from the tip of the red giant branch to several magnitudes below the main sequence turn off. Once corrected for completeness, the observed luminosity functions agree very well with theoretical models and do not show stellar excesses in any region of the luminosity function. Using reduced chi squared fitting, the new M92 luminosity function is shown to be an excellent match to the previously published luminosity function for M30. These points combine to establish that the "subgiant excess" found in previously published luminosity functions of Galactic globular clusters are due to deficiencies in the stellar models used at that time. Using up to date stellar models results in good agreement between observations and theory. Several statistical methods are presented to best determine the age of M92. These methods prove to be insensitive to the exact choice of metallicity within the published range. Using [Fe/H]=-2.17 to match recent studies we find an age of 14.2 plus or minus 1.2 Gyr for the cluster.Comment: 22 pages, 13 figures, 3 tables, accepted for publication in A

Bound States and Critical Behavior of the Yukawa Potential

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp(-\alpha r)/ r$, using different algorithms: solving the Schr\"odinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $\alpha=\alpha_C$, above which no bound state exists. We study the relation between $\alpha_C$ and $\lambda$ for various angular momentum quantum number $l$, and find in atomic units, $\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in China

Phenomenological Lambda-Nuclear Interactions

Variational Monte Carlo calculations for ${_{\Lambda}^4}H$ (ground and excited states) and ${_{\Lambda}^5}He$ are performed to decipher information on ${\Lambda}$-nuclear interactions. Appropriate operatorial nuclear and ${\Lambda}$-nuclear correlations have been incorporated to minimize the expectation values of the energies. We use the Argonne $\upsilon_{18}$ two-body NN along with the Urbana IX three-body NNN interactions. The study demonstrates that a large part of the splitting energy in ${_{\Lambda}^4}H$ ($0^+-1^+$) is due to the three-body ${\Lambda}$ NN forces. $_{\Lambda}^{17}O$ hypernucleus is analyzed using the {\it s}-shell results. $\Lambda$ binding to nuclear matter is calculated within the variational framework using the Fermi-Hypernetted-Chain technique. There is a need to correctly incorporate the three-body ${\Lambda}$ NN correlations for $\Lambda$ binding to nuclear matter.Comment: 18 pages (TeX), 2 figure

Anisotropic softening of magnetic excitations in lightly electron doped Sr2_2IrO4_4

The magnetic excitations in electron doped (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with $x = 0.03$ were measured using resonant inelastic X-ray scattering at the Ir $L_3$-edge. Although much broadened, well defined dispersive magnetic excitations were observed. Comparing with the magnetic dispersion from the parent compound, the evolution of the magnetic excitations upon doping is highly anisotropic. Along the anti-nodal direction, the dispersion is almost intact. On the other hand, the magnetic excitations along the nodal direction show significant softening. These results establish the presence of strong magnetic correlations in electron doped Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with close analogies to the hole doped cuprates, further motivating the search for high temperature superconductivity in this system