Boost-invariant mean field approximation and the nuclear Landau-Zener effect

We investigate the relation between time-dependent Hartree-Fock (TDHF) states and the adiabatic eigenstates by constructing a boost-invariant single-particle Hamiltonian. The method is numerically realized within a full three-dimensional TDHF which includes all the terms of the Skyrme energy functional and without any symmetry restrictions. The study of free translational motion of a nucleus demonstrates the validity of the concept of boost-invariant and adiabatic TDHF states. The interpretation is further corroborated by the test case of fusion of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$. As a first application, we present a study of the nuclear Landau-Zener effect on a collision of ${}^4\mathrm{He}+{}^{16}\mathrm{O}$.

Figure 1

Time evolution of boost-invariant and adiabatic observables for a central ${}^{16}\mathrm{O}$+${}^{16}\mathrm{O}$ collision at 25 MeV. The dashed lines with error bars show the boost-invariant single-particle energies ${\varepsilon }_{\alpha }^{(\mathrm{inv})}$ and their variances $\Delta {\varepsilon }_{\alpha }^{(\mathrm{inv})}$ for the lowest ($1s_{1/2}$) proton states, and solid lines the adiabatic energies ${\varepsilon }_i^{(\mathrm{adia})}$ for comparison.

Figure 2

Time evolution of higher lying proton states for a central collision of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ with a center-of-mass energy of 25 MeV. The upper panels show the boost invariant single-particle energies ${\varepsilon }_{\alpha }^{(\mathrm{inv})}$ (dashed) and the adiabatic energies ${\varepsilon }_i^{(\mathrm{adia})}$ (full lines). The lower panels show the corresponding adiabatic occupation probabilities. The arrows pointing from the upper panels to the lower ones indicate the level crossings where occupation changes rapidly. The labels of the single-particle states at $t=0$ are indicated near the left axis.

Figure 3

Time evolution of the central collision of ${}^4\mathrm{He}+{}^{16}\mathrm{O}$ with c.m. energies of 75 and 125 MeV. (a) rms radius for the colliding system as a function of time; (b) adiabatic occupation probability $P_i$ of the last occupied neutron state; and (c) interacting single-particle adiabatic states. The labels of the single-particle states at $t=0$ are near the left axis.