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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[4] A. Diaz-Torres, I. J. Thompson and C. Beck, Phys. Rev. C 68, 044607 (2003).

[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).