By Hans J. Krappe, Krzysztof Pomorski

This ebook brings jointly quite a few elements of the nuclear fission phenomenon came across via Hahn, Strassmann and Meitner nearly 70 years in the past. starting with an old advent the authors current numerous types to explain the fission means of scorching nuclei in addition to the spontaneous fission of chilly nuclei and their isomers. The function of shipping coefficients, like inertia and friction in fission dynamics is mentioned. The influence of the nuclear shell constitution at the fission chance and the mass and kinetic power distributions of the fission fragments is gifted. The fusion-fission strategy resulting in the synthesis of recent isotopes together with super-heavy parts is defined. The ebook will hence be important for theoretical and experimental physicists, in addition to for graduate and PhD students.

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36) extended to such states. We will restrict the discussion in the following to time-reversal invariant systems with pairs of degenerate states (Kramers degeneracy). In particular rotating systems are not time-reversal invariant. 7 of Ref. [108]. The BCS Hamiltonian is ˆ = H ˆ+ ˆi ia i a + i≶0 1 V iı,jj a ˆ+ ˆ+ ˆj a ˆj . ) The transformation to quasiparticle operators simpliﬁes in the BCS theory compared to the HFB deﬁnition, Eqs. 16). 38) with real ui and vi . With this deﬁnition we follow the convention of Ref.

70), the kinetic energy densities τq , Eq. 69), and spin-orbit densities Jq = −i ϕi (r, σ, q)[∇ϕi (r, σ , q) × σ|σ|σ ] . 105) where ρ = ρp + ρn , τ = τp + τn , and ECoul is the Coulomb energy-density. The latter can be written as sum of a direct and an exchange contribution. The exchange contribution is usually approximated by the Slater form [162, 172] (cf. Eq. 142) below) ECoul (r) = e2 ρp (r) 2 d3 r 3 ρp (r ) − e2 |r − r | 4 3 π 1/3 ρ4/3 p (r) . 106) For systems whose ground-state wave-function is not time-reversal invariant, for example, for odd systems, the energy density has additional terms [115, 173].

The ﬁrst sections of this chapter are therefore devoted to the calculation of nuclear ground-state properties. With parameters ﬁtted to these properties, the construction of energy surfaces as functions of shape parameters is presented in the last section with a particular emphasis on secondary minima and saddle points. 1 Mean ﬁeld theories Many attempts have been made to obtain ground-state binding energies and radii on an a priori basis from empirical nucleon-nucleon potentials by solving the many-body Schr¨ odinger equation in the self-consistent Brueckner-HartreeFock approximation.