Importance of the wave function tail in computing the pre-emission probability for the halo neutron from 11 Be fusion with light and heavy targets

In this work, an improved method for the estimation of the neutron pre-emission probability in a fusion process is given, taking into account a more realistic halo neutron distribution with an extreme long tail. It has been demonstrated that core and halo densities can be separated in: ρ(r) = ρc (r) + ρh (r). 11 Be, the only one neutron halo nucleus has two bound states, both of halo type, with one neutron separation energies 0.5 MeV and 0.2 MeV, respectively. The 2s1/2 state is the main component (77%) of the ground state of 11 Be. The density distribution of the halo neutron was determined by solving Schroedinger equation for a separation energy of Sn = - 0.504 MeV using a Woods-Saxon potential. The halo neutron is considered to be on 2s1/2 state. The root mean square radius of 10 Be is taken as 2.90 fm. All the following steps in our estimation are parameter free for the neutron pre-emission probability method. A sharp cut-off approach for the fusion process was used. After computing the volume distribution, we calculated the superficial distribution of the halo neutron on a surface which is perpendicular on the beam direction. The volume was divided in spherical shells with step equal to 0.1 fm in which we considered the probability distribution to be constant. These shells were projected on that surface. After that, the same method was applied for three energies: E1 near the Coulomb barrier, E2 near the energy of an expected experiment and E3 near that value when the compound nucleus explodes. The results are given in a Table. The pre-emission probability is dependent on target radius. For a smaller size target (12 C, Si), the probability is larger than for a large size target nucleus (209 Bi). All these results are thought as an upper limit for the neutron pre-emission probability, due to the fact that the applied model corresponds to a r.m.s. radius of 5.2 fm for 11 Be neutron halo. We want to thank M. Fukuda, I. Bulboaca and F. Carstoiu for help and discussions. (authors)