Looking Toward the Future: A Review of Western New York\u27s Early Childhood System

In 2017, Liftoff--Western New York Early Childhood Funders for Change--wanted to better understand how the region serves its youngest residents, how other communities structure systems to improve life and learning for young children and their families, and how stakeholders across the system could come together to affect change. Together with partners across Western Yew York (including Allegany, Cattaraugus, Chautauqua, Genesee, Erie, Niagara, Orleans, and Wyoming Counties), Liftoff engaged Public Sector Consultants to provide an outside, objective review of early childhood systems and programs in the region. We hope this report will be the foundation for many conversations in the months and years to come

Public Sector Safety Report, Winter 2002

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates $Z_{\rm eff}$ and annihilation gamma spectra for positron collisions with the hydrogen-like ions He$^+$, Li$^{2+}$, B$^{4+}$ and F$^{8+}$. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the r\^ole of the positron-ion repulsion, the annihilation rate is also estimated analytically in the Coulomb-Born approximation. It is found that the energy dependence and magnitude of $Z_{\rm eff}$ is governed by the Gamow factor that characterizes the suppression of the positron wave function near the ion. For all of the H-like ions, the correlation enhancement of the annihilation rate is found to be predominantly due to corrections to the annihilation vertex, while the corrections to the positron wave function play only a minor r\^ole. Results of the calculations for $s$, $p$ and d-wave incident positrons of energies up to the positronium formation threshold are presented. Where comparison is possible, our values are in excellent agreement with the results obtained using other, e.g., variational, methods. The annihilation vertex enhancement factors obtained in the present calculations are found to scale approximately as $1+(1.6+0.46\ell)/Z_i$, where $Z_i$ is the net charge of the ion and $\ell$ is the positron orbital angular momentum. Our results for positron annihilation in H-like ions provide insights into the problem of positron annihilation with core electrons in atoms and condensed matter systems, which have similar binding energies.Comment: 26 pages, 25 figure