Fusion is a process of merging two nuclei into one. To make it possible projectile and target need to overcome a barrier for fusion, which arises due to the competition between Coulomb force, which is long-ranged and repulsive and nuclear force, which is short-ranged and attractive. The sum of Coulomb and nuclear potentials is, in the simplest approximation, the total potential, which maximum value is called barrier height.
When both nuclei - the projectile and the target - are spherical, we see a single barrier (of height indicated with the blue arrow), but due to quantal tunneling the barrier is smeared and we obtain a distribution about 2-3 MeV wide.
If at least one of the nuclei is deformed, the barrier height depends on the orientation of target versus projectile during the impact. Actually we have to average over all possible orientations in space of the colliding system. This is the classical interpretation of arising of the distribution of fusion barrier heights. Quantally, the distribution is generated by couplings of many reaction channels.
How to extract the distribution experimentally?
One of methods uses data from backward angles quasi-elastic and Rutherford scattering. As quasi-elastic we define the sum of elastic, inelastic and transfer processes. Then the distribution is given by the following formula:
where σqe is quasi-elastic scattering cross section and σR is Rutherford cross section. So essentially, the measurements consist in registering the ratio of number of particles scattered backwards divided by number of particles scattered forward, where we observe pure Rutherford scattering.
Using this method we have extracted fusion barrier distributions in the 20,22Ne + natNi and 118Sn systems. The Barrier Collaboration involves physicists from Warsaw University, HIL, University in Bialystok, IReS in Strasbourg, Tohoku University in Japan and Jyvaskyla University in Finland. The experiments have been performed at the Warsaw Cyclotron U200P. The detecting system was arranged inside the CUDAC scattering chamber. The experimental setup is extremely simple. 30 semiconductor detectors are set at angles between 130 to 150 degrees to register backscattering, 2 detectors are set at 35 degrees to measure Rutherford scattering and beam energy. Additionally we put up to 4 E-ΔE telescopes to learn about light charged particles transfer.
Scattering chamber.
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The data from 20Ne + natNi were compared to coupled channels calculations performed using the CCQUEL code. The experimental distribution is a little bit asymmetric (red points). The calculation performed using CCQUEL code shows clear structure (blue line, deformation parameters taken from other sources, experimental resolution taken into account). The black dotted curve is a result of calculation obtained assuming no couplings between reaction channels, so-called inert case. We can improve the agreement with data reducing the value of a β4 hexadecapole deformation parameter of 20Ne by a factor of 2 (green line), but...
...no set of parameters lets us discribe the experimental distribution for 20Ne + 118Sn which, at variance with calculated results, is completely structureless. We suspected that the smoothing of the distribution could be caused by strong α-particle transfer, so...
...we have made the same measurements with 22Ne beam, but again in the experimental distribution we failed to get any structure. We checked experimentally that α-transfer and break-up are in this case very weak, so these reaction channels cannot be blamed for smoothing the distribution. The disagreement between experiment and theory remains a puzzle to solve.
We have also published the results on 16O + 116,119Sn systems [1,2] and 20Ne + 112,116,118Sn [3].
[1] E. Piasecki et al., Acta Phys. Pol. B33 (2002) 397.
[2] E. Piasecki et al., Phys. Rev. C65 (2002) 054611.
[3] L. Swiderski et al., Int. Journ of Mod. Phys. E13 (2004) 315.
The Barrier Collaboration:
E.Piasecki (a), T.Krogulski (b), Ł.Świderski (a), T. Czosnyka (c), J. Jastrzębski (c), A. Kordyasz (c), M. Kisieliński (d), M. Kowalczyk (a), K. Piasecki (a), C.Marchetta (e), A.Pagano (f), M.Mutterer (g), S. Khlebnikov (h), W.H. Trzaska (i), K. Hagino (j), N.Rowley (k)