Influence of different proton and neutron deformations on fission barriers

The response of the nuclear energy with respect to relative changes of proton versus neutron distributions is investigated. Contrary to most macroscopic–microscopic approaches, different multipole deformations of both distributions are admitted. The average part of the total energy is evaluated using the Yukawa-folded model, while microscopic energy corrections are obtained within the Strutinsky and BCS methods. PACS numbers: 21.10.Dr, 21.10.Ma, 21.60.Cs, 21.60.Jz, 25.85.Ca One of the most fundamental problems in nuclear structure is a proper description of nuclear shapes. A very successful nuclear-surface description was proposed in [1]. We use here a slightly modified version thereof describing the nuclear shape in cylindrical coordinates as ρ2s (z)= R20 c f (a, B) (1 − u 2) (1 +α u − B e−a2u2), (1) where the factor f (a, B) ensures volume conservation, R0 is the radius of the corresponding spherical nucleus, z0 = cR0 the elongation and u = (z − zsh)/z0 a dimensionless parameter, with the end point of the nuclear shape at zsh ± z0 with zsh = − 45 αz0 / f (a, B). The deformed nucleus is characterized by the set of parameters {c, B, α} respon-sible respectively for elongation, neck formation and left– right asymmetry [1], where B is related to the neck parameter h of [1] through B = h(3c − 1). Since the energy of the deformed nucleus depends only weakly on the width of the neck, the parameter a is chosen to be constant a = 2.5. The nuclear energy can be separated into a dominant macroscopic (liquid-drop type) contribution (see [2]) and a quantum (shell+pairing) correction. We use the folding procedure of [3] to estimate the macroscopic energy coming from different types of nucleons (q = {p, n}