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3. Recent HRIBF Research - The 132Sn + 96Zr Reaction: A Study of Fusion Enhancement/Hindrance
(W. Loveland, spokesperson)

In fusion reactions induced by neutron-rich radioactive nuclei, one expects to observe a lowering of the fusion barrier, relative to that observed in reactions induced by stable nuclei with smaller neutron to proton ratios. This is simply a geometrical effect due to the greater size of the n-rich projectile. In addition, in the synthesis of heavy nuclei with n-rich projectiles, one expects a higher survival probability of the completely fused system due to its lower fissility and the lower excitation energies.

In the systems investigated to date, one does not generally expect significant fusion hindrance because ZpZt < 1600. For ZpZt > 1600, it is believed that fusion hindrance effects become prominent. Fusion hindrance generally takes the form of an extra energy that must be supplied to the fusing system to drive it from the contact point inside the fission saddle point. This energy is loosely referred to as the "extra-push" energy although the formal definition of this energy is that it is the "extra-extra push energy". Evaporation residue (ER) cross section measurements with massive projectiles (A ~ 100) have clearly established the occurrence of fusion hindrance with an extra energy needed to cause fusion. This fusion hindrance was explained successfully by the extra push model developed by Swiatecki et al. [1].

Studies by Sahm et al. for the 90-96Zr + 124Sn reactions showed an unexpected result. As the fusing system became more neutron-rich (decreasing fissility), the fusion hindrance, as measured by the extra push energy, increased in contradiction to predictions of most theoretical models. (See Fig. 3-1) If this trend were confirmed, it would reduce the attractiveness of fusion using very n-rich projectiles as a pathway to the heaviest elements. We have carried out, over a period of several years, a set of measurements of the capture-fission excitation functions for the 124,132Sn + 96Zr system to try to define this effect. The results of these investigations have been published [2,3].

Figure 3-1: Extra push as determined from the mean fusion barrier height EB and the barrier height calculated with the Bass potential, VB, versus the effective entrance channel fissility. The experimental points are taken from Sahm, et al., with 124Sn+96,94,92,90Zr systems selected. The theoretical prediction by Bjornholm and Swiatecki is shown by a line.

Figure 3-2: Comparison of the capture fission excitation functions for the 132Sn+96Zr (solid squares and line) and 124Sn+96Zr reactions (open circles and dashed line). The lines are to guide the eye through the data points.

The measured capture-fission excitation functions for the two systems are shown in Fig.3-2. Clearly the interaction barrier is shifted to lower energies for the more n-rich system.

We have measured capture cross sections in this work. The direct measurement of fusion cross sections requires the separation of the quasi-fission and fusion-fission components of the capture cross sections, which is not feasible with the current generation of radioactive beam facilities. However, for many purposes, such as heavy element syntheses, we need to know the properties of the fusion cross sections in these collisions. What should we do?

We have chosen to extrapolate from the capture cross sections to the fusion cross sections, which, at least, involves cross sections of similar magnitude. We do this extrapolation using the dinuclear system (DNS) model. This model was successful in reproducing evaporation residue cross sections for 16O+204Pb and 124Sn+96Zr systems.

Figure 3-3: Excitation function for 132Sn+96Zr capture-fission reaction. The one dimensional barrier penetration model prediction is shown as a dashed line. The predicted capture, and fusion cross sections predicted by the DNS model are shown by solid, and dotted lines, respectively. See text for details.

Calculations by Giardina et al. using the DNS model for capture cross sections in the 132Sn+96Zr reaction are shown in Fig. 3-3 as a solid red line. The predictions of this model for the fusion cross sections for this reaction are shown as a dotted line. Since the DNS model calculations agree reasonably well with the observed capture cross sections for the 132Sn+96Zr and 124Sn+96Zr reactions [2] and the evaporation residue cross sections for the 124Sn+96Zr reaction, it is reasonable to speculate that the interaction and fusion barrier heights for these reactions are those predicted by the DNS model. For the 132Sn+96Zr reaction, the deduced (DNS) interaction barrier height is 192.3 MeV while the fusion barrier height is 201.8 MeV. Similarly, for the 124Sn+96Zr reaction [2], the deduced interaction barrier height is 204.4 MeV while the fusion barrier height is 208.9 MeV. The Bass barrier heights for these reactions are 213.8 and 216.3 MeV, respectively.

One immediately comes to several conclusions. The deduced fusion barrier heights from the DNS model for the reactions induced by neutron-rich radioactive beams (201.8 and 208.9 MeV) are substantially below the Bass barrier heights. We take the definition that "extra-push" energy is the difference between the interaction barrier height and the fusion barrier height. Both the 124Sn+96Zr and 132Sn+96Zr reactions show positive extra push energies (fusion hindrance) of 4.5 and 9.5 MeV, respectively, as deduced from the DNS model. (Refs. [2,4] would have estimated these energies as 10 and 7 MeV, respectively). Some but not all of the advantage of using neutron-rich radioactive beams is predicted by the DNS model to be lost due to fusion hindrance in the Sn + Zr system.

[1]W. J. Swiatecki, Physica Scripta 24, 113 (1981); Nucl. Phys. A 376, 275 (1982).
[2]A. M. Vinodkumar, W. Loveland, P.H. Sprunger, D. Peterson, J. F. Liang, D. Shapira, R. L. Varner, C. J. Gross and J. J. Kolata, Phy. Rev. C 74, 064612 (2006).
[3]A.M. Vinodkumar, et al., Phys. Rev. C 78, 054608 (2008).
[4]S. Bjoernholm and W. J. Swiatecki, Nucl. Phys. A 391, 471 (1982).

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