I very vividly remember the day the Chernobyl accident was announced at the Italian TV, and the news of a few days later when the authorities asked people to stop consuming “wide-leaf vegetables” because of the risk of accumulation of radioactive dust. That same afternoon we had been camping in a mountain place near our home, in Umbria, surrounded by nice grass fields sparkling with wildflowers, and those 8pm news instilled more than just a passing apprehension in our minds. It was the early days of May 1986, and just a few days later, the 10th of May, a huge popular rally in Rome attended by almost half-million people would mark the first step towards the referendum, which the following year would lead to abandoning nuclear energy in Italy. My job as a nuclear physicist working at the European Fast Reactors program, which I had started just less than one year before, was officially at risk.

The 1980s were exciting years to work in reactor physics at the Cadarache Research Center, run by the French CEA (Commissariat à l’Energie Atomique). There were two operational fast power reactors, RAPSODIE and PHENIX, for which the physics team had to solve any problems that arose during operation of, and one new large-sized fast prototype reactor, SUPERPHENIX, for which we had to calculate the neutronic design, then develop the strategy and follow its start-up. Moreover, we had available two fast-flux zero-power facilities, MASURCA for the study of reactor core configurations, HARMONIE for neutron and gamma-ray propagation and shielding, where nuclear and radiation physics experiments were conceived and carried out, thanks to the modular structure with small rodlets that allowed any reactor geometry to be simulated, with a resolution of a few centimeters. We also developed new methods and code systems, and investigated new nuclear fuel cycles strategies. The personnel in the Physics Division were extremely heterogeneous. Indeed, following the 1974 oil crisis, the European agreement for developing the Fast Reactors Program brought to Cadarache a wave of Italian researchers, followed by German and Belgian researchers, and finally by a small group of British researchers. Computations went hand in hand with experiments and, with the hindsight of 35 years later, both were plagued by the technological limits of that time. It is just amazing to think back, and recall what one could do with such limited resources: the IBM-4381 that we used in Cadarache, with 64 MB of memory and a peak power of less than 100 MFLOPs, was as powerful as a 2013 Motorola cell phone!

During the golden age of reactor design, in the 1960’s, it was common to build *mockups* of reactor systems, followed by hundreds of *integral* *measurements* to characterize the reactor system as a whole, and its feedback coefficients. Neutronics designs had become increasingly complex (with the advent of fast reactors, molten salt systems, thorium systems, accelerator driven systems etc.) and mockups determined the applicability of the simulation tools that were used in the design of the real thing. Validation of basic nuclear data was (and still is) a big business, and the methods to optimize the whole process, starting from basic nuclear cross sections up to the macroscopic control of reactor operation, were of the utmost economic importance. Nuclear reactor perturbation theory had benn

outlined by Eugene Wigner, in an obscure paper he wrote for the Manhattan Project in 1945, and had been extensively developed, expanded, and applied by Lev Usachev in Obninsk, who used these methods to improve experimental design. As perturbation theory methods were increasingly adopted in the 1970s and 80s, with our director Augusto Gandini in Rome as a prominent developer of the mathematical foundations of the method, the theory was widely applied to improve interpolation and extrapolation of experimental results, based on similarity of mockups to the reactors being designed. This was the concept known as *representativity*. What makes perturbation theory very special in the case of neutronic calculations (that is, the numerical solution of Boltzmann transport equation in the uber-complicate geometry of the nuclear reactor) is the multiplicating neutron source from fission: your theoretical problem has just one singular point as its steady state solution, and can *explosively* (both mathematically and physically!) diverge if a small perturbation moves it away from that point. This is what Wigner announced in his report CP-G-3048, “Effect of Small Perturbations on Pile Period” of June 13, 1945, that the discretized Boltzmann equations for the neutron flux (plural is in order, since we deal with a system of coupled equations, one for each neutron discrete energy) are not self-adjoint. To the ears of the “modern” quantum physicist, who requires all its operators to be self-adjoint for the expectation values to be real, this sounds like heresy. In fact, the correct weighting function in nuclear reactor perturbation theory must be the product of the *adjoint* and the *direct* neutron flux, which both have a *different* spectrum of eigenvalues. Today the adjoint flux is calculated routinely, and non-self-adjoint perturbation theory is applied in many problems of particle transport far removed from nuclear reactors – for example in climate forecast models.

Chernobyl-related dangers and popular growing disdain notwithstanding, we (including my minuscule contribution) were anyway pushing hard for the start-up of the SUPERPHENIX fast breeder reactor, the largest in the World with its steel double-wall vessel (the “cuve”), the biggest piece ever built by a forge factory, holding a Plutonium-239/Uranium-238 oxide core immersed in 700 tons of liquid sodium flowing at 550 ^{o}C. In the hall of the Building 220 in Cadarache there was a large paper billboard hanging, with the loading plan of the reactor. Every day a few new fuel elements were loaded in the reactor core, and control rods were slightly moved up and down, and this was reported by stickers attached to the billboard. On the side, there was a betting contest in which each research group formulated its own prediction of the n-th fuel element that would make the giant reactor to reach criticality: each weekend some precious computer time was secretly spent, by readjusting the calculations with slightly improved nuclear data, or with a more refined numerical approximation, and the next Monday new predictions would appear on the billboard. The Italian group, led by Massimo Salvatores (at the time, head of the Physics Laboratory of the Fast Reactors Department) and Pino Palmiotti, won the final contest by getting right the criticality event, with an error of only 3 fuel elements out of about 1,000.

The computer codes and methods we used could be judged, by today’s standards, quite primitive. The energy spectrum was divided into 22, but more often just 6 bins (“groups”) between 0 and 14 MeV, and that was quite an improvement with respect to Wigner’s two-group theory; basic nuclear data were used in a first step, to produce homogeneized values, further adjusted by a wealth of correction coefficients, to be used in the spatial integration routines; equations were then integrated in space by discrete-ordinates grids, with a coarse-grained angular distribution that stopped at the 5th, but more often at the 3rd order of Legendre polynomials. (Today, all this cumbersome machinery is replaced by elegant and accurate Monte Carlo codes, that can simultaneously track neutrons, photons and electrons with continuous energy distributions, over the most complex geometries.) After the Chernobyl accident, we set up a joint team to re-analyze with our “western” methods the development of the accident, from the point of view of neutronic runaway of the core. The Soviets had traditionally been very spare in opening to their data, until the official IAEA Report of the Post-Accident Meeting disclosed some important data, in August 1986. The realization that the RBMK reactors of the Chernobyl type had their key reactivity coefficients *positive* by design, was a shock to us. When you ride a bicycle, the worst that can happen is that you hit something, you fall down, and the bicycle stops running. This is an example of negative feedback. All safety systems in a nuclear reactor are usually designed so as to contribute *negatively* to the reactivity: whatever happens, the bicycle stops. Instead, we nuclear scientists in the West realized that the RBMK bicycle was designed to accelerate indefinitely in the case of an accident. In particular, the “void coefficient” was positive, that is, in case of increase of the temperature, the water coolant would vaporize in the core, thereby reducing the neutron absorption rate. (Actually, the RBMK is a boiling-water reactor, so there is always a fraction of vapor in the core; the rise in temperature would increase the vapor fraction.) Once started, this bicycle would never stop, but would accelerate downhill until inevitably exploding.

Because of the large uncertainties in the computer codes and basic nuclear data, error estimation and “sensitivity analysis” (that is: *what would happen if our calculations were wrong by some X%* ?) were the main concern in reactor safety. At some point, by the end of 1987, it occurred that the SUPERPHENIX control rod measurements during the operation of the reactor were lingering just at the lower boundary (that is, the dangerous one at which the Boron control rods would be ineffective in stopping the chain reaction) of the announced 13% maximum uncertainty. Because of that, the French safety authority threatened to stop the reactor operations. The physics team at Cadarache quickly found out that the problem was coming from the fact that the core design teams (mind you… engineers!) were using a simple diffusion theory model for their calculations, by attaching crude corrective factors for transport and heterogeneity effects for the control rods. With a sharp decision, Salvatores immediately diverted our BALZAC experimental campaign at the MASURCA test reactor, in that moment oriented at the investigation of the reactivity loss by fuel depletion, to the study of the transport and heterogeneity effects attached to control rods. In just a few weeks, several configurations with many different heterogeneity arrangements were carried out, measured, and analyzed with new methodologies, to show our capability to correctly calculate these effects. Besides working at the numerical analysis of neutron reaction rates and coupled neutron-photon flux distributions, that was also my only experimental contribution to the fast reactor program, for which I designed and realized a series of measurements of gamma-ray energy deposition by placing thermoluminescent detectors at various locations of the central MASURCA channel.

I wish to close this personal recollection motivated by the “Chernobyl times”, by honoring the memory of Massimo Salvatores, whom I mentioned several times already, and who passed away on March 26 of last year, after hitting his head in a sudden fall while visiting a temple in India. Massimo was a very special scientist and manager, who made his career with seminal contributions to the field of generalized perturbation theory and to nuclear data adjustment using integral experiments, for which he contributed the first cross-section capability and a full-scale computational code system for the Italian fast reactor design. After positions as visiting scientist at Argonne, Oak Ridge and Georgiatech, he entered the CEA Fast Reactors Department in 1977, where he became director of the Physics Division in 1983, leading a number of experimental and theory programs. After retiring from CEA, Massimo was called as member of countless organizations for the development of nuclear reactors in the world, such as the Scientific Advisory Board of the Paul Scherrer Institute in Switzerland, the Karlsruhe Institute of Technology, the TRIGA Accelerator Driven Experiment in Rome, which he conceived together with Nobel Prize recipient Carlo Rubbia, the scientific advisory board at Idaho National Laboratory, and the proposal for the “Versatile Test Reactor” VTR that he designed, and was selected by the US-DOE for the Generation-IV Nuclear Program.

I consider myself lucky to have worked and co-authored papers with him, but the greatest pleasure was to know Massimo as a friend and passionate intellectual. To cheer up the younger colleagues, he used to tell this story about his start of career as a scientist. After obtaining his degree in physics in Turin, 1964, he had received two job offers: one from the Italian CNEN, to work at the Casaccia Research Centre in Rome, and the other from the UK, to be part of the team for the international DRAGON nuclear reactor program. He had decided to take the position abroad, but then a ”Sliding Doors” movie-type event happened. The English sent him a notification with the date and a time for a taxi that would pick him up to go to the airport, and fly him to London to discuss the last details of his contract. However, the taxi never showed up. Newly married and in need of money, he quickly changed his mind and accepted the CNEN offer, and went to work in the group lead by Prof. Augusto Gandini (under which direction I too ended up, when I entered the CNEN in 1985). Massimo used to wonder at the alternate-universe idea, of how different the UK nuclear program would look today if that taxi had arrived. The UK’s loss turned out to be an enormous gain for the Italian and French nuclear programs, and for all of us who knew him as a friend and had him as a guide.