Surface properties for Ne, Na, Mg, Al and Si isotopes in the Coherent Density Fluctuation Model using the relativistic mean field densities

We have systematically studied the surface properties, such as symmetry energy, neutron pressure, and symmetry energy curvature coefficient for Ne, Na, Mg, Al, and Si nuclei from the proton to neutron drip-lines. The Coherent Density Fluctuation Model (CDFM) is used to estimate these quantities taking the relativistic mean-field densities as inputs. The Br ¨uckner energy density functional is taken for the nuclear matter binding energy and local density approximation is applied for its conversion to coordinate space. The symmetry energy again decomposed to the volume and surface components within the liquid drop model formalism to the volume and surface parts separately. Before calculating the surface properties of finite nuclei, the calculated bulk properties are compared with the experimental data, whenever available. The NL3* parameter set with the BCS pairing approach in an axially deformed frame-work is used to take care of the pairing correlation when needed. The deformed density is converted to its spherical equivalent with a two Gaussian fitting, which is used as an input for the calculation of weight function in the CDFM approximation. With the help of the symmetry energy for the recently isotopes ²⁹F, ²⁸Ne, ^29,30Na and ^31,35,36Mg are considered to be within the island of inversion emphasized [Phys. Lett. B 772, 529 (2017)]. Although we get large symmetric energies corresponding to a few neutron numbers for this isotopic chain as expected, an irregular trend appears for all these considered nuclei. The possible reason behind this abnormal behavior of symmetry energy for these lighter mass nuclei is also included in the discussion, which gives a direction for future analysis.

A Study on the Blue Coloration of Ao-ike Pond, Aomori Prefecture, Japan: Formulation of a Physical Model in Terms of Radiance and Image Analyses

The blue coloration model of a closed pond, Ao-ike Pond, Aomori Prefecture, Japan, was formulated in terms of radiance by applying a theory of observation devices proposed by Szirmay-Kalos (2008) and Hanaishi’s reverse ray tracing method. In this model, three potential contributions to the coloration were considered; irregular reflection at the Lambertian pond bottom, density fluctuation scattering by water, and Mie scattering by suspended solids. By utilizing model formulas for these mechanisms, some parameters were determined in order to duplicate the images of the pond surface without solar shading by tree leaves above the pond surface, in addition to the images with sunbeam trajectories by solar radiations passing through tree leaves, which are emitted from the water and visible on the surface. Simulating the pictures of the pond surface and the sun-beam-image analyses revealed that the blue colorations of Ao-ike Pond are mainly produced (1) by the density fluctuation scattering of water itself and the white Mie scattering by suspended solids and (2) by the red-light absorption by water in the optical paths before and after the two scatterings. Then, the density fluctuation scattering of water and the Mie scattering by suspended solids exhibited contributions of almost equal magnitude. The contribution of irregular reflections at the pond bottom was judged to be relatively small.