Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 48 (2015)

Origin of fusion hindrance in heavy systems
K. Washiyama∗1

∗1100
100

Mo ++XXMo1010Energy [MeV]In fusion reactions in heavy systems whose charge
product ZP ZT is larger than 1600, it has been observed1) that the formation of a compound nucleus isstrongly hindered around the Coulomb barrier energy,
compared with ZP ZT < 1600 systems. In such heavy
systems, an additional energy is needed to achieve
fusion, which is called the extra-push energy.2) Themost probable reason behind the fusion hindrance phenomenon is the occurrence of the quasi-fission process,which involves reseparation without the formation of acompound nucleus after two nuclei touch each other, inheavy systems. A macroscopic fluctuation–dissipation
model using a Langevin equation has been developed3)
to analyze quasi-fission and fusion dynamics especiallyin the synthesis of superheavy elements. Recently,
the quasi-fission process was analyzed using the microscopic time-dependent Hartree-Fock (TDHF) model.4)
The aim of this study is to analyze in detail theorigin of fusion hindrance in heavy systems by using
the microscopic TDHF model. To this end, we employ
our method5) to extract nucleus–nucleus potential andone-body energy dissipation from the relative motionof colliding nuclei to internal degrees of freedom in theentrance channel of fusion reactions from TDHF evolutions. We reported in Ref.6) that the nucleus–nucleus
potential extracted from TDHF in the 96 Zr + 124 Sn
system monotonically increases as the relative distancedecreases, and that the potential shows no ordinary
barrier. In this report, we present results of our systematic study for fusion in heavy systems and discussa possible origin of fusion hindrance.
First, we perform systematic calculations for estimating the extra-push energy by TDHF for several
heavy systems. We define the extra-push energy using TDHF as the difference between the fusion threshold energy and the potential barrier obtained from thefrozen density approximation, Eextra = Ethres − VFD .
The frozen density potential is estimated while keeping the projectile and target densities frozen to theirrespective ground-state densities. We confirm that theobtained extra-push energies agree well with those deduced from experimental observations. Then, we extract the nucleus–nucleus potential V (R) and friction
coefficient γ(R) as a function of the relative distance
between two nuclei R for those systems. We find thatthe property of the extracted potentials is similar tothat in the 96 Zr + 124 Sn system,6) i.e., monotonic increase and no barrier structure in the potential. Finally, we analyze the fusion hindrance in heavy systems. We extract V (R) and γ(R) at the fusion threshold energy. We stop the extraction at Rmin where the9696

Zr ++XXZr�V∆VEdissEdiss8866
44
2200

92
92

100
104110124132136
Mo 100Mo
Mo 104Ru
Ru 110Pd
Pd 124Sn
Sn 132Sn
Sn 136Xe
XeMoFig. 1. Increase in potential ∆V (red circle) and accumulated dissipation energy E diss (blue diamond) for the100
Mo + 92,100 Mo, 104 Ru, 110 Pd and 96 Zr + 124,132 Sn,136
Xe systems.

remaining kinetic energy reduces as much as possible
in the TDHF simulations. At R min, we can identify
the extra-push energy as a sum of the remaining kinetic energy, accumulated dissipation energy estimatedfrom γ(R)5) , and increase in potential due to the frozen
density barrier, denoted by ∆V = V (Rmin ) − VFD . InFig. 1, the increase in potential ∆V and dissipated energy Ediss are plotted for the 100 Mo + 92,100 Mo, 104 Ru,110
Pd (left panel) and 96 Zr + 124,132 Sn, 136 Xe (rightpanel) systems. It is clear that the contribution fromthe increase in potential to the extra-push energy islarger than that from the dissipated energy. From thisfinding, we conclude that the dynamical increase inpotential energy is the main contribution to the extrapush energy.
References
1) C.-C. Sahm et al.: Nucl. Phys. A 441, 316 (1985).
2) W. J. Swiatecki: Nucl. Phys. A 376, 275 (1982).
3) Y. Aritomo, K. Hagino, K. Nishio, and S. Chiba: Phys.
Rev. C 85, 044614 (2012).
4) C. Simenel: Eur. Phys. J. A 48, 152 (2012); L. Guo andT. Nakatsukasa: EPJ Web Conf. 38, 09003 (2012); V.
E. Oberacker, A. S. Umar, and C. Simenel, Phys. Rev.
C 90, 054605 (2014).
5) K. Washiyama and D. Lacroix: Phys. Rev. C 78, 024610(2008); K. Washiyama, D. Lacroix and S. Ayik: Phys.
Rev. C 79, 024609 (2009).
6) K. Washiyama: RIKEN Accel. Prog. Rep. 47, 67(2013).

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