The nuclear surface as a collective variable

Abstract

In heavy nuclei where the thickness of the diffused edge is relatively small, a certain sharp effective surface can be defined which characterizes the shape of the nucleus, and it can be considered as a collective dynamic variable. It is shown that the problem of fluid dynamics can be simplified by reducing it to simple linearized equations for the dynamics in the nuclear interior and boundary conditions set at the effective dynamic sharp surface of the density distribution. These conditions are derived from the fluid dynamical equations. Transitional densities obtained from this simple model are compared with the numerical solution of fluid dynamical equations.

Nuclear asymmetry energy and isovector stiffness within the effective surface approximation

“…It is related to the fundamental constant C − of the energy density (2). For the parameter set T6 (C − = 0) one finds k S = 0.…”

“…The analytical solutions will be obtained approximately up to the order of A 2/3 in the binding energy. To satisfy the condition of particle number conservation with the required accuracy, we account for relatively small surface corrections (∝ a/R ∼ A −1/3 at the first order) to the leading terms in the Lagrange multipliers [2,3,5] (Appendixes B and C).…”

“…[1][2][3]. It exploits the saturation properties of nuclear matter in the narrow diffuse-edge region in finite heavy nuclei.…”

Asymmetry and Spin-Orbit Effects in Binding Energy in the Effective Nuclear Surface Approximation

“…1) through the curvature H = (1/R 1 + 1/R 2 )/2 in terms of the main ES curvature radii [1,3] (13) compared to the isoscalar one w(x) (11) as a function of x = ξ/a within the approximation (6) to ǫ(w) calculated for the same SLy7 forces (left) and w − (x) for several Skyrme forces [7] (right).…”

“…In the present work, we extend the ES approach [4] taking into account the spin-orbit and the asymmetry effects in nuclei. [1,3]; a is the parameter of the nuclear diffuse edge.…”