Model space truncation in shell-model fits

We carry out an interacting shell-model study of binding energies and spectra in the $sd$-shell nuclei to examine the effect of truncation of the shell-model spaces. Starting with a Hamiltonian defined in a larger space and truncating to the $sd$ shell, the binding energies are strongly affected by the truncation, but the effect on the excitation energies is an order of magnitude smaller. We then refit the matrix elements of the two-particle interaction to compensate for the space truncation, and find that it is easy to capture 90% of the binding energy shifts by refitting a few parameters. With the full parameter space of the two-particle Hamiltonian, we find that both the binding energies and the excitation energy can be fitted with remaining residual error about 5% of the average error from the truncation. Numerically, the rms initial error associated with our Hamiltonian is 3.4 MeV and the remaining residual error is 0.16 MeV. This is comparable to the empirical error found in $sd$-shell interacting shell model fits to experimental data\cite{br06}.Comment: 10 pages, 3 figure

Calibration of a gamma-ray telescope using tagged position annihilation photons

Measurements of detection efficiency, angular resolution, and energy resolution properties of a gamma ray telescope used to study celestial gamma rays from balloon flight altitudes are described. Nearly monochromatic photons produced at the National Bureau of Standards tagged photon facility were used for the calibration. Details of the photon beam configuration and properties and results of the measurements made at photon energies of 15.1 and 31.1 MeV are presented. Finally, the data are compared with a Monte Carlo analysis of the instrument properties

How harmonic is dipole resonance of metal clusters?

We discuss the degree of anharmonicity of dipole plasmon resonances in metal clusters. We employ the time-dependent variational principle and show that the relative shift of the second phonon scales as $N^{-4/3}$ in energy, $N$ being the number of particles. This scaling property coincides with that for nuclear giant resonances. Contrary to the previous study based on the boson-expansion method, the deviation from the harmonic limit is found to be almost negligible for Na clusters, the result being consistent with the recent experimental observation.Comment: RevTex, 8 page

The information content of a new observable: the case of the nuclear neutron skin

We address two questions pertaining to the uniqueness and usefulness of a new observable: (i) Considering the current theoretical knowledge, what novel information does new measurement bring in? (ii) How can new data reduce uncertainties of current theoretical models? We illustrate these points by studying the radius of the neutron distribution of a heavy nucleus, a quantity related to the equation of state for neutron matter that determines properties of nuclei and neutron stars. By systematically varying parameters of two theoretical models and studying the resulting confidence ellipsoid, we quantify the relationships between the neutron skin and various properties of finite nuclei and infinite nuclear matter. Using the covariance analysis, we identify observables and pseudo-observables that correlate, and do not correlate, with the neutron skin. By adding the information on the neutron radius to the pool of observables determining the energy functional, we show how precise experimental determination of the neutron radius in $^{208}$Pb would reduce theoretical uncertainties on the neutron matter equation of state.Comment: 5 pages, 3 figure