Surface Symmetry Energy

Binding energy of symmetric nuclear matter can be accessed straightforwardly with the textbook mass-formula and a sample of nuclear masses. We show that, with a minimally modified formula (along the lines of the droplet model), the symmetry energy of nuclear matter can be accessed nearly as easily. Elementary considerations for a macroscopic nucleus show that the surface tension needs to depend on asymmetry. That dependence modifies the surface energy and implies the emergence of asymmetry skin. In the mass formula, the volume and surface and (a)symmetry energies combine as energies of two connected capacitors, with the volume and surface capacitances proportional to the volume and area, respectively. The net asymmetry partitions itself into volume and surface contributions in proportion to the capacitances. A combination of data on skin sizes and masses constrains the volume symmetry parameter to 27 MeV < alpha < 31 MeV and the volume-to-surface symmetry-parameter ratio to 2.0 < alpha/beta < 2.8. In Thomas-Fermi theory, the surface asymmetry-capacitance stems from a drop of the symmetry energy per nucleon S with density. We establish limits on the drop at half of normal density, to 0.57 < S(rho_0/2)/S(rho_0) < 0.83. In considering the feeding of surface by an asymmetry flux from interior, we obtain a universal condition for the collective asymmetry oscillations, in terms of the asymmetry-capacitance ratio.Comment: 29 pages, 16 figures; final version - Nuclear Physics A, in pres

Symmetry Energy II: Isobaric Analog States

Using excitation energies to isobaric analog states (IAS) and charge invariance, we extract nuclear symmetry coefficients, from a mass formula, on a nucleus-by-nucleus basis. Consistently with charge invariance, the coefficients vary weakly across an isobaric chain. However, they change strongly with nuclear mass and range from a_a~10 MeV at mass A~10 to a_a~22 MeV at A~240. Following the considerations of a Hohenberg-Kohn functional for nuclear systems, we determine how to find in practice the symmetry coefficient using neutron and proton densities, even when those densities are simultaneously affected by significant symmetry-energy and Coulomb effects. These results facilitate extracting the symmetry coefficients from Skyrme-Hartree-Fock (SHF) calculations, that we carry out using a variety of Skyrme parametrizations in the literature. For the parametrizations, we catalog novel short-wavelength instabilities. In comparing the SHF and IAS results for the symmetry coefficients, we arrive at narrow (+-2.4 MeV) constraints on the symmetry energy values S(rho) at 0.04<rho<0.13 fm^-3. Towards normal density the constraints significantly widen, but the normal value of energy a_a^V and the slope parameter L are found to be strongly correlated. To narrow the constraints, we reach for the measurements of asymmetry skins and arrive at a_a^V=(30.2-33.7) MeV and L=(35-70) MeV, with those values being again strongly positively correlated along the diagonal of their combined region. Inclusion of the skin constraints allows to narrow the constraints on S(rho), at 0.04<rho<0.13 fm^-3, down to +-1.1 MeV. Several microscopic calculations, including variational, Bruckner-Hartree-Fock and Dirac-Bruckner-Hartree-Fock, are consistent with our constraint region on S(rho).Comment: 101 pages, 27 figures, 2 tables; submitted to Nuclear Physics

Un fragment de Séleucus de Séleucie conservé en version arabe

Pinès S. Un fragment de Séleucus de Séleucie conservé en version arabe. In: Revue d'histoire des sciences et de leurs applications, tome 16, n°3, 1963. pp. 193-209

An Arabic version of the testimonium flavianum and its implications

Jerusalem87 p.; 22 c

Une Notice sur les Rech Galuta chez un écrivain arabe du IXe siècle

Pines Shlomo. Une Notice sur les Rech Galuta chez un écrivain arabe du IXe siècle. In: Revue des études juives, tome 100 bis, n°199-200, janvier-juin 1936. pp. 71-73

The Jewish Christians of the early centuries of Christianity according

Jerusalem74 p.; 23 c

Études sur Awhad al-Zamân Abu'l Barakât al-Baghdâdî [II et fin]

Pines Shlomo. Études sur Awhad al-Zamân Abu'l Barakât al-Baghdâdî [II et fin]. In: Revue des études juives, tome 4 (104), juillet-décembre 1938. pp. 1-30

Études sur Awhad al-Zamân Abu'l Barakât al-Baghdâdî [I]

Pines Shlomo. Études sur Awhad al-Zamân Abu'l Barakât al-Baghdâdî [I]. In: Revue des études juives, tome 3 (103), janvier-juin 1938. pp. 3-64

Un fragment inconnu d'Aristote en version arabe

Pinès Shlomo. Un fragment inconnu d'Aristote en version arabe. In: Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres, 99ᵉ année, N. 3, 1955. pp. 387-395