Breakup/Transfer Channel Couplings in Sub-barrier Fusion Reactions, C. Beck, Institut Pluridisciplinaire Hubert Curien IN2P3/CNRS and University of Strasbourg, FRANCE − Heavy-ion fusion reactions with colliding stable and/or weakly bound nuclei at bombarding energies at the vicinity and below the Coulomb barrier have been widely studied [1-9].  The specific role of multi-step neutron-transfers and/or breakup in sub-barrier fusion enhancement still needs to be investigated in detail both experimentally [2,3,7,8] and theoretically [4-6].  In a complete description of the fusion dynamics the transfer channels in standard coupled-channel (CC) calculations [1,5,9] have to be taken into account accurately in reactions induced by stable nuclei. Similarly, the breakup channel is included in the Continuum-Discretized Coupled Channel (CDCC) approach [4,6] applied for weakly bound and/or halo nuclei.


It is known that neutron transfers may induce a neck region of nuclear matter in-between the interacting nuclei favoring the fusion process to occur.  In low-energy fusion reactions, the very simple one-dimensional barrier-penetration model (1D-BPM) is based upon a real potential barrier resulting from the attractive nuclear and repulsive Coulomb interactions.  For light- and medium-mass nuclei, one only assumes that the di-nuclear system fuses as soon as it has reached the region inside the barrier i.e. within the potential pocket.  If the system can evolve with a bombarding energy high enough to pass through the barrier and to reach this pocket with a reasonable amount of energy, the fusion process will occur after a complete amalgation of the colliding nuclei forming the compound nucleus.  On the other hand, for sub-barrier energies the di-nuclear system has not enough energy to pass through the barrier. In this case, neutron pick-up processes can occur when the nuclei are close enough to interact each other significantly, if the Q-values of neutron transfers are positive. It was shown that sequential transfers can lead to the broad distributions characteristic of many experimental fusion cross sections.  Finite Q-value effects can lead to neutron flow and a buildup of a neck between the target and projectile. The situation of this neck formation of neutron matter between the two colliding nuclei could be considered as a ”doorway state" to fusion. In a basic view, this intermediate state induced a barrier lowering. As a consequence, it will favor the fusion process at sub-barrier energies and enhance significantly the fusion cross sections. Experimental results have already shown such enhancement of the sub-barrier fusion cross sections due to neutron transfer with positive Q-values [2].


In order to investigate the role of neutron transfers we studied 32S+90,96Zr as benchmark reactions. The analysis of the quasi-elastic barrier distributions [7] showed the significant role played by neutron transfers in the fusion processes.  We present the analysis of fusion excitation functions recently measured for these reactions [10]. For this purpose we develop a new computer code named NTFus [11] by taking the neutron transfer channels into account within the model of Zagrebaev [5].  The effect of neutron transfers yield a fair agreement with the present data of sub-barrier fusion for 32S+96Zr [10].   This was initially expected from the positive Q-values of the neutron transfers as well as from the failure of previous CC calculation of quasi-elastic barrier distributions without coupling of the neutron transfers [7].  With the agreement obtained by fitting the present experimental fusion excitation function and the CC calculation at sub-barrier energies, we conclude that the effect of the neutron transfers produces a significant enhancement of the sub-barrier fusion cross sections for 32S+96Zr as compared to 32S+90Zr.


Finally. an experimental overview of reactions induced by the stable, but weakly-bound nuclei 6Li, 7Li and 9Be, and by the exotic, halo nuclei  6He, 8B, 11Be and 17F on medium-mass targets, such as 58Ni, 59Co or 64Zn, is presented.  Existing data on elastic scattering, total reaction cross sections, fusion, breakup and transfer channels will be discussed in the framework of a CDCC approach taking into account the breakup degree of freedom.


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[5] V. I. Zagrebaev, Phys. Rev. C 67, 061601 (2003).

[6] C. Beck, N. Keeley and A. Diaz-Torres, Phys. Rev. C 75, 054605  (2007).

[7] F. Yang et al., Phys. Rev. C 77, 014601 (2008).

[8] F. A. Souza et al., Eur. Phys.J. A 44, 181 (2010).

[9] Sunil Kalkal et al., Phys. Rev. C 81, 044610 (2010).

[10] H. Q. Zhang it et al., Phys. Rev. C 82, 054609 (2010).

[11] A. Richard et al., EPJ Web of Conf. 17, 08005 (2011).