Concluding remarks

Before starting on some remarks summarizing the meeting we have just completed, I would like to say a few words about one of the organizers. As we heard at the conference, Jack Leigh of the Australian National University has decided to retire in the very near future. Jack was a student of John Newton's at Manchester and then a postdoc in Berkeley before coming to Canberra where he has remained ever since. Jack's work has been characterized by an attention to detail and a critical examination of the physics, of which we have seen many examples at this meeting. This thorough approach has led us to a re-evaluation of many of the basic ideas of nuclear dynamics, an area which still holds some surprises and new aspects. I am sure we all wish him well in his retirement and, although he claims otherwise, I find it hard to believe that he will be away from the lab for long!

The meeting started with a brief history of measurements of fusion of heavy ions and we were reminded of the first calculations of the fusion of ₁₄N+₁₄N prompted by the (unfounded) concern that the first nuclear explosions could ignite and consume the atmosphere. As we know, the fusion of heavy ions at low energies is dominated by penetration of the barrier which exists between the two colliding ions. In fact, such studies have a much earlier, and peculiarly antipodean origin - starting with the passage through the Great Barrier Reef by Captain Cook in 1770. Shortly thereafter, the incoming wave boundary condition was discovered when it was found that, once in Australia, it was difficult to return to one's point of origin. This important observation encouraged the powers in England at that time to issue many one-way tickets to Australia. Whether or not this has anything to do with the long and fruitful connection of Australia and New Zealand to nuclear physics is not known, but our field was largely defined by a native of one of these countries.

As mentioned, heavy-ion fusion at low energies is dominated by penetration through the barrier which separates the two ions and much of what has been discussed here concerns the shape and other properties of this barrier. Barrier penetration is one of the fundamental manifestations of quantum physics and nuclear physics can rightfully lay claim to the first phenomenon displaying this feature - nuclear α-decay. Following this, of course, nuclear physics contains many other such examples, such as heavy-ion fusion and nuclear reactions in the stellar environment. Barrier penetration plays an essential role in a wide range of physical problems from chemical reactions, phase transitions and symmetry breaking to quantum well devices and perhaps even such problems as protein folding.

The essential point under discussion at this meeting relates to the influence of coupling of other degrees of freedom on the barrier penetration problem. It has long been realized that such couplings will always have the effect of enhancing the barrier penetration probability at energies below the classical barrier and of reducing the penetration at energies above the barrier. In the case of heavy-ion fusion, we have the opportunity through variation of the shape and vibrational degrees of freedom of the colliding nuclei as well as the Q-value for mass transfer to study this physics in detail over a wide range of parameter values.

The key to the recent renewed interest in this problem comes from the realization that the fusion cross section in the vicinity of the classical barrier is much more sensitive to the specific nature of the coupling to non-elastic channels than was originally thought. This realization comes in large part from the suggestion by Rowley of a new way to plot the fusion data which, in certain approximations, shows the `fingerprints' of these couplings. Such clever ways of plotting data, suggested by theoretical models, have always played an important role in nuclear physics. It is often the case, however, that such plots illuminate particular aspects of the data while masking others. For example, the famous Geiger - Nuttall plot in which the logarithm of the α-decay half-life is plotted against Qα shows the essential dependence of the barrier penetration probability on energy but hides, as small deviations, important nuclear structure effects. Similarly, the Kurie plot for β-decay shows the dominance of phase space in the determination of the shape of the β spectrum but hides, perhaps, the neutrino mass in the details of the endpoint behaviour.

Heavy-ion fusion cross sections have suffered similarly. As the measured cross sections in the vicinity of the barrier vary extremely rapidly with energy, it was initially conventional to plot the logarithm of the cross section against energy which, in itself, is not particularly informative except when data for different systems are compared. Later, it became fashionable to plot the data against 1/E, whereby simple theory led us to expect that the intercept of the resulting straight line was the inverse of the fusion barrier (1/V_B) and the slope of the line, . This latter plot, however, disguises the effects of barrier penetration in the behaviour of the cross section near the intercept with the 1/E axis. The suggestion of Rowley was to plot d²(Eσ)/dE² versus E which, according to a simple model, should reflect the `distribution of barriers' produced by the coupling of the elastic channel to non-elastic channels. This approach has proved very illuminating and, indeed, is the major focus of much of the work presented here. Following the above suggestion, the ANU group pioneered the measurement of fusion excitation functions in fine enough energy steps and with enough precision to meaningfully extract the second derivative. The results of these and other similar studies have shown an unexpected richness and sensitivity of the fusion data to nuclear structure effects and demonstrate the benefits of pushing the precision of measurements to new levels.

A potential trap, in my view, which has been successfully avoided is the literal interpretation of d²(Eσ)/dE² as the set of effective barriers resulting from diagonalization of the coupled channels in the fusion problem. The speakers here have avoided this connection and it now seems generally recognized that the experimental values must still be compared with the results of full calculations - also plotted in the same way. Here, it is worth noting that barrier distributions extracted from other channels (elastic, quasi-elastic ^...) or using other methods should also be compared with the results of the appropriate theoretical calculations. There is no reason to assume a priori that these distributions should be the same for each channel or method and, in fact, the information contained may rather reflect different aspects of the scattering problem and therefore be complimentary to the fusion data.

The many excellent talks at this meeting were very stimulating and raise many interesting questions. The use of the latest generation of 4π γ-ray arrays to probe fusion is particularly attractive. Of course, γ-rays have long been used to study the distribution of cross section as a function of angular momentum through measurements of γ-ray multiplicities, isomer ratios and the population pattern of ground-state rotational bands. At this meeting, we heard of studies of the population of superdeformed bands as a probe of the fusion angular momentum distribution. This sensitivity to very high angular momentum raises the possibility of addressing one of the crucial approximations made in many models of fusion. Namely, that the fusion barrier is independent of spin except for the trivial dependence of the barrier on angular momentum arising from the centrifugal energy. This approximation seems to me to be rather suspect in that the space of available couplings (reaction channels) must be considerably larger at high spin than for s-wave collisions. One possible probe of this is through careful measurements of fusion - fission cross sections for compound systems for which fission only occurs at relatively high angular momentum. The measured fusion - fission cross section then reflects the properties of the fusion barriers for these angular momenta convoluted with the energy and angular momentum dependence of the fission process. Experiments some years ago on the fusion - fission of ³²S+Sm did indeed show a similar dependence on target deformation as had been observed for fusion evaporation measurements near the s-wave barrier. Perhaps more detailed measurements will allow a quantitative assessment of the validity of the angular momentum independence assumption.

This question can also be addressed through γ-ray measurements using the characteristic gamma rays to identify the yield arising from those evaporation residues fed by the highest angular momenta. Thus, an excitation function measurement for these channels will probe the fusion barriers at high angular momentum much as in the fusion - fission measurements. The high efficiency of the new arrays will allow these measurements to be carried out with high statistical precision in a short time.

Another important question relates not so much to the spin distribution itself but rather to the methods by which it is determined - γ-ray multiplicity and fission fragment angular distribution measurements. The first of these two methods seems to produce quite acceptable results despite the complexity and assumptions involved in turning a measured γ-ray fold distribution into the spin distribution. To date there is no independent test of the method but it is possible to do so recognizing that, plausibly, the fusion process depends only on the orbital angular momentum of the colliding nuclei and not on their intrinsic spin. In some cases, it is possible to find combinations of target and projectile which will produce the same compound system but with quite large and different values of the intrinsic angular momentum in the entrance channel (e.g. ¹⁶O+³⁰⁸Pb, ¹⁵N+³⁰⁹Bi, ¹⁴N+²¹⁰Bi). Measurements of the compound nucleus spin distributions for these systems can check if the expected effects of the coupling of intrinsic to orbital angular momentum are indeed observed.

The second, fission fragment angular distribution measurements, have long been known to produce average angular momenta in the vicinity of the barrier which are too large, reflecting anisotropies which are larger than predicted by the standard transition state model. This result has led to a questioning of the validity of the assumptions which go into this standard, but old, theory and it now appears that some venerable concepts regarding the nature of the fission process must be challenged. Our improved understanding of fusion leads us to new aspects of nuclear dynamics. What has been especially important in this is the necessity, recognized by the ANU group, of a consistent analysis of all aspects of the data - fusion, fission and evaporation - not just a satisfactory description of isolated examples.

Similarly, in the case of the theoretical calculations, we have seen the importance of including, in a consistent way, all reaction channels. This in turn requires the use of models to describe the nature and strengths of the couplings. This is particularly important in cases where important coupling parameters may not be available from other sources (e.g. electromagnetic decays) and we must therefore rely on the predictions of nuclear structure models. In the comparison between data and experiment, we are now reasonably confident that we know how to recognize the signatures of various degrees of freedom in the data - surface vibrations, static deformation and transfer. This being the case it might now be possible to turn the problem around and use high-precision fusion data to determine spectroscopic quantities of interest. This is especially interesting in cases where the information is not available from other sources, such as high multipoles in the nuclear shape or collective vibrations. If this is to be carried out to any significant degree, it is then clear that we must have some standard way of analysing the data such that everyone understands precisely how the experimental observations were related to the spectroscopic quantities. This would be similar to the situation of obtaining spectroscopic information from light-ion transfer reactions via DWBA codes or using Coulomb excitation to determine multipole matrix elements.

One question which must always arise is whether or not all the important channels have been included in the coupled-channel calculation. We saw several examples where the agreement between experiment and theory actually worsened as the calculation was nominally improved. Another issue relates to channels which although intrinsically weak have large effects on fusion simply because their couplings are large near the radial position of the barrier - multi-nucleon transfer channels may be such an example.

We have seen some beautiful new results on pair and multi-pair transfer for several systems in which the parallel between neutron pair transfer and the Josephson effect was drawn. We should recall that the latter relates to the tunnelling of Cooper pairs through a potential barrier which in the nuclear case corresponds to ground-state to ground-state neutron pair transfer. The transfer probability corresponds to the Josephson current and the reaction Q-value to the junction voltage. So what is eventually required is a study of ground-ground transitions over a wide range of isotopes where the variation of transfer probability can be studied as a function of Q-value. Sn+Sn is the obvious choice, but the experimental obstacles are formidable.

Some of the very first measurements of fusion of weakly bound `halo' nuclei were presented. These experiments are clearly in their very early stages and the data are still of low precision. It is worth recalling that in the history of measurements of fusion with stable beams, the errors on the early data were typically 30 - 50% but have now, routinely, been reduced to the 1% level. Perhaps this is too much to expect, but progress can often be very fast, particularly with the strong theoretical motivations for measuring these cross sections.

Other than coupled channels, developments in `transport' type models of reaction processes seem to have made significant progress and are producing interesting insights into the possibilities of producing the very heaviest nuclei. Classical models of scattering show very strong energy dependences which mimic the behaviour of resonances but are rather interpreted as a transition between closed and chaotic trajectories. The reconciliation of such different views of the same physical process has always taught us new and significant things - we must do this. Similar remarks apply to the discussion of the fluctuations observed in the energy dependence of deeply inelastic scattering in some systems. Are these resonances or fluctuations or perhaps something quite different? - we should understand this.

In general, we see that the data become better and better and the theoretical treatments become more and more realistic and start to have real predictive power. It is interesting to note that, in this time of a transition of nuclear physics into `big' science, these experiments are suited to the `small' laboratories. The exciting and fundamental physics that they address provides ammunition for a compelling case to continue support for such facilities of which the ANU is an outstanding example.

Finally, I should express my own thanks and also those of the participants for the tremendous meeting organized by Andy, Brian, David, Jack, Nanda and Sirdar. They did a wonderful job of ensuring that we all were well treated and especially allowing us the opportunity to witness the `Miracle of the Bottomless Wine Bottles' every evening.

This work was supported by the US Department of Energy Nuclear Physics Division.