Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique

A particle-number projection technique is used to calculate transfer probabilities in the ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.

Figure 1

Density evolution for the central collision of a ${}^{16}\mathrm{O}$ (initially on the right side) with a ${}^{208}\mathrm{Pb}$ (left) at $E_{c.m.}=74.44\mathrm{MeV}$. The snapshots run from $t=7.5$ to 37.5 zs by steps of 7.5 zs.

Figure 2

Neutron (circles) and proton (squares) number probability distributions of the lightest fragment in exit channel of a head-on ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ collision at $E_{c.m.}=74.44\mathrm{MeV}$ (solid lines) and 65 MeV (dotted lines).

Figure 3

Proton number probability distribution as function of the distance of closest approach obtained with TDHF (lines). Experimental data (squares) are adapted from Ref. 26 using $E_{c.m.}=74.3\mathrm{MeV}$ data and show the sum of the one and two-proton transfer channels.