Deformation effects in the12C-12C system

Abstract

The quantized adiabatic time dependent Hartree-Fock (quantized ATDHF) theory is applied to the 12C-~2C-system. Especially the intrinsic oblate ground state deformation of this nucleus is considered. For four relevant mutual orientations of the two nuclei the optimal, i.e. maximally decoupled collective paths, associated to relative motion, are evaluated by solving a coupled set of nonlinear differential equations on three dimensional grids in coordinate and momentum space. In a second step, the constituents of the corresponding collective Hamiltonian are calculated. Besides the collective potentials this includes the evaluation of the appropriate mass parameters, of the quantum corrections with regard to rotation, translation and collective relative motion and of the centrifugal potentials, all of which are shown to be important. By means of generalized WKB methods, subbarrier fusion cross sections are evaluated for different assumptions on the reaction process and compared with experimental data. Finally, the collective Hamiltonian is calculated for a head-on-collision of two 12C_chains" PACS: 21.60 Jz

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

“…The equilibrium parameters (β, γ, ∆, λ) are found to agree with Table 2 of the same paper. The ground states of 146,148 Sm are spherical (β = 0) and the others have prolate shapes (β > 0, γ = 0).…”

“…The equilibrium parameters (β, γ, ∆, λ) are found to agree with Table 2 of the same paper. The ground states of 146,148 Sm are spherical (β = 0) and the others have prolate shapes (β > 0, γ = 0). Figure 40 shows the excitation energies (RPA frequencies) of β and γ vibrations, obtained by the RPA and projected RPA calculations.…”

“…Basically they have shown that if one applies the generator coordinate method to the space of Slater determinants that contains both even and odd members, parameterized by pairs of canonical coordinates, then by a suitable expansion in powers of the momentum one essentially reaches the results obtainable from TDHF by a momentum expansion. There is an additional bonus that zero point fluctuations associated with the collective coordinates can be computed; these were incorporated in the applications to which we have previously alluded [142][143][144][145][146][147][148].…”

The effect of nuclear and Coulomb interactions on the nuclear shapes of two colliding208Pb nuclei

“…In order to describe such a smooth transition, one has to employ a time dependent treatment like the time dependent Hartree Fock approach. A similar deformation effect in the 12C-12C system has been studied in the quantized adiabatic TDHF approach by Niklas et al [12]. They calculated the interaction potential and subbarrier fusion cross sections.…”

Solving the Two-Center Nuclear Shell-Model Problem with Arbitrarily Oriented Deformed Potentials

“…The molecular sp spectra are useful to microscopically obtain collective potentials and mass surfaces for a molecular reaction dynamical calculation [29]. It is worth mentioning that other studies [31,32,33,34] have also argued the importance of the non-axial symmetric configurations for effects of molecular resonances on reaction processes for 12 C + 12 C.…”