Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation

The dynamical symmetries of the Fermion Dynamical Symmetry Model are used as a principle of truncation for the spherical shell model. Utilizing the usual principle of energy-dictated truncation to select a valence space, and symmetry-dictated truncation to select a collective subspace of that valence space, we are able to reduce the full shell model space to one of manageable dimensions with modern supercomputers, even for the heaviest nuclei. The resulting shell model then consists of diagonalizing an effective Hamiltonian within the restricted subspace. This theory is not confined to any symmetry limits, and represents a full solution of the original shell model if the appropriate effective interaction of the truncated space can be determined. As a first step in constructing that interaction, we present an empirical determination of its matrix elements for the collective subspace with no broken pairs in a representative set of nuclei with $130\le A \le 250$. We demonstrate that this effective interaction can be parameterized in terms of a few quantities varying slowly with particle number, and is capable of describing a broad range of low-energy observables for these nuclei. Finally we give a brief discussion of extending these methods to include a single broken collective pair.Comment: invited paper for J. Phys. G, 57 pages, Latex, 18 figures a macro are available under request at [email protected]

Continuum radiative transfer Modeling of Sagittarius B2

We present results from radiative transfer modeling of the continuum emission towards Sagittarius B2 (hereafter Sgr B2). We have developed a radiative transfer framework – Pandora – that employs RADMC-3D (Dullemond 2012) for a self-consistent determination of the dust temperature. With this pipeline, we have set-up a single model that consistently reproduces the thermal dust and free-free continuum emission of Sgr B2 spanning four orders of magnitude in spatial scales (0.02–45 pc) and two orders of magnitude in frequency (20–4000 GHz)

The physical and chemical structure of Sagittarius B2. I. Three-dimensional thermal dust and free-free continuum modeling on 100 au to 45 pc scales

Context. We model the dust and free-free continuum emission in the high-mass star-forming region Sagittarius B2. Aims. We want to reconstruct the three-dimensional density and dust temperature distribution, as a crucial input to follow-up studies of the gas velocity field and molecular abundances. Methods. We employ the three-dimensional radiative transfer program RADMC-3D to calculate the dust temperature self- consistently, provided a given initial density distribution. This density distribution of the entire cloud complex is then recursively reconstructed based on available continuum maps, including both single-dish and high-resolution interferometric maps covering a wide frequency range (ν = 40 GHz - 4 THz). The model covers spatial scales from 45 pc down to 100 au, i.e. a spatial dynamic range of 105. Results. We find that the density distribution of Sagittarius B2 can be reasonably well fitted by applying a superposition of spherical cores with Plummer-like density profiles. In order to reproduce the spectral energy distribution, we position Sgr B2(N) along the line of sight behind the plane containing Sgr B2(M). We find that the entire cloud complex comprises a total gas mass of 8.0 × 106 M within a diameter of 45 pc. This corresponds to an averaged gas density of 170 M pc−3. We estimate stellar masses of 2400 M and 20700 M and luminosities of 1.8 × 106 L and 1.2 × 107 L for Sgr B2(N) and Sgr B2(M), respectively. We report H2 column densities of 2.9 × 1024 cm−2 for Sgr B2(N) and 2.5 × 1024 cm−2 for Sgr B2(M) in a 40 ′′ beam. For Sgr B2(S), we derive a stellar mass of 1100 M , a luminosity of 6.6 × 105 L and a H2 column density of 2.2 × 1024 cm−2 in a 40 ′′ beam. We calculate a star formation efficiency of 5 % for Sgr B2(N) and 50 % for Sgr B2(M). This indicates that most of the gas content in Sgr B2(M) has already been converted to stars or dispersed. Key words. radiative transfer – radio continuum