Quantum tunneling under the influence of an environment with nearly degenerate spectrum is considered. It is shown that the finite excitation energy of the environment reduces the tunneling probability estimated in the limit of sudden tunneling. Some applications to heavy-ion fusion reactions are discussed. H(R,~) = TR + U(R) + Ho(~) + V(R,~).(1)Here TR is the kinetic energy of the macroscopic motion, U ( R) the potential in the absence of the coupling, Ho(~) the Hamiltonian for the internal motion, and V(R, ~) by guest on July 14, 2015 http://ptps.oxfordjournals.org/ Downloaded from

Sub-barrier fusion has often been studied by linearizing couplings to nuclear structure for calculational convenience. Using a Green s function technique and the interacting boson model, we are able to include couplings to all orders. After renormalizing the coupling strengths, we find that couplings to all orders lead to improved agreement with data for the fusion cross section and distribution of barriers, compared to the linear couplings.PACS number(s): 25.70.Jj, 24.10.Eq, 21.60.Fw

The interacting boson model with s and d bosons has been used to describe the nuclear structure effects in sub-barrier fusion. We generalize the previous formalism to include arbitrary kinds of bosons in the target nucleus and investigate whether g bosons have any discernible effect on fusion reactions. In particular, we compare the fusion cross sections, barrier distributions, and the average angular momentum of the compound nucleus in the sd and sdg boson models.PACS number(s): 21.60.Fw, 25.70. Jj, 24.10.Eq

Quantum tunneling under the influence of an environment with nearly degenerate spectrum is considered. We first give a general derivation of the zero point motion formula in the sudden tunneling limit. The eAects of a finite excitation energy of the environment are then considered by a perturbation method. Examples of linear oscillator coupling and rotational coupling show that the finite excitation energy can be represented by a dissipation factor and reduces the tunneling probability estimated in the limit of sudden tunneling. These examples clearly show that the applicability of the sudden tunneling approximation is governed by the details of the coupling as well as the relative time scales of the tunneling and the environmental degrees of freedom. We discuss some applications to heavy-ion fusion reactions. PACS number(s): 25.70.Jj, 03.65. Sq, 21.10.Re, 74.50.+r I. INTRGDUCTIGNQuantum tunneling in systems with many degrees of &eedom has attracted much interest during the past decade in many fields of physics and chemistry [1,2]. This problem is often called macroscopic quantum tunneling.One of the major interests in this area is to assess the effects of the environment on the tunneling rate of a macro-