Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of {\mathcal O}(N) \to \CP^m and, in an asymptotic sense, for those of line bundles over general K\"ahler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.Comment: 14 pages, corrected typo

The retarding ion mass spectrometer on dynamics Explorer-A

An instrument designed to measure the details of the thermal plasma distribution combines the ion temperature-determining capability of the retarding potential analyzer with the compositional capabilities of the mass spectrometer and adds multiple sensor heads to sample all directions relative to the spacecraft ram directions. The retarding ion mass spectrometer, its operational modes and calibration are described as well as the data reduction plan, and the anticipated results

Mirror Energy Differences at Large Isospin Studied through Direct Two-Nucleon Knockout

The first spectroscopy of excited states in 52Ni (Tz=2) and 51Co (Tz=-3/2) has been obtained using the highly selective two-neutron knockout reaction. Mirror energy differences between isobaric analogue states in these nuclei and their mirror partners are interpreted in terms of isospin nonconserving effects. A comparison between large scale shell-model calculations and data provides the most compelling evidence to date that both electromagnetic and an additional isospin nonconserving interactions for J=2 couplings, of unknown origin, are required to obtain good agreement.Comment: Accepted for publication in Physical Review Letter

Spectroscopy of 54^{54}Ti and the systematic behavior of low energy octupole states in Ca and Ti isotopes

Excited states of the $N=32$ nucleus $^{54}$Ti have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from $^{55}$Ti by a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array. Inelastic proton-scattering cross sections and deformation lengths have been determined. A low-lying octupole state has been tentatively identified in $^{54}$Ti for the first time. A comparison of $(p,p')$ results on low-energy octupole states in the neutron-rich Ca and Ti isotopes with the results of Random Phase Approximation calculations demonstrates that the observed systematic behavior of these states is unexpected.Comment: 7 pages, 8 figure