Eur. Phys. J. A (2020) 56:212https://doi.org/10.1140/epja/s10050-020-00219-4

Regular Article - Experimental Physics

Jacques Raynal: memories of a physicist

Nicolas Alamanosa

IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France

Received: 30 June 2020 / Accepted: 9 August 2020 / Published online: 25 August 2020© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020Communicated by Maria Borge

Abstract This text is dedicated to the memory of JacquesRaynal. I recall some of the interactions I had with Jacquesfrom 1975 up until his death. I first met Jacques as a youngstudent at Saclay in the mid 1970s and from then on we col-laborated frequently. Jacques initiated me into elastic andinelastic scattering calculations in the coupled channels for-malism. Within this formalism we calculated the excitation ofGiant Resonance by light- or heavy-ion projectiles. We col-laborated on the Coulomb corrections implemented in ECISand later we tested numerically the Incoming Wave BoundaryCondition, which is an important assumption when calculat-ing sub-Coulomb fusion cross sections. He was among thefirst to understand the origin of what we would call the 3-excitation hindrance and suggest solutions.

1 The early years

I met Jacques Raynal for the first time in 1975 or 1976 whenas a young student at Saclay I was finishing my postgraduatethesis (thèse de troisième cycle). At that time Jacques, at theage of 40, was recognized as one of the best specialists inelastic and inelastic scattering calculations. His code ECIS1

was authoritative.2 However, he had published very little.Even today, his most important contributions are part of CEAinternal reports. He is one of the promotors of the modernoptical model. As early as the 1960s he had studied deuteronelastic scattering [1] or the discretization of the continuum[2], a notion to which I will return later in this article. Paul

1 (ECIS) “Equations Couplées Itérations Séquentielles” is a coupled-channels code using a sequential iteration method for solving the cou-pled differential equations.2 For the collection of Jacques’ codes see: http://www.oecd-nea.org/tools/abstract/detail/nea-0850/.

a e-mail: nicolas.alamanos@cea.fr (corresponding author)

Bonche3 introduced me to Jacques to help me with my thesiscalculations. Jacques had a large beard and a pipe which neverleft him. He looked at me intently, filled his pipe, lit it andturning to me said, “What do you want me to do?” He wastalking into his beard. One had to be very attentive to hearhim. That was Jacques. For many years, Jacques tutored myscientific career by giving precious advice when the analysisof our experiments needed scattering calculations.

The end of the 1970s and the beginning of the 1980s wasa special time for nuclear physics in France. Several accel-erators were still operating in the Paris region: the ALICEaccelerator at Orsay, the SATURNE accelerator at Saclay,the linear accelerator at Saclay (ALS), the tandem post-accelerator at Saclay, the tandem at Orsay ... but their fatehad been decided a few years previously. At that time areal infatuation with heavy ion physics appeared. CNRS andthe CEA decided to build a new machine which, like theGerman (UNILAC) and American (Super-HILAC) projectswould accelerate all possible heavy ions, from the lightestcarbon to uranium. The lightest ions would have an energyof ~100A MeV, i.e. ten times higher than that of the ionsaccelerated by ALICE or the UNILAC project. Finally, thefuture machine would deliver beams 100 times more intensethan those of ALICE. This was the GANIL project.

In order to have the work force and the financial resourcesneeded to build GANIL, but also to continue contribut-ing to the construction of accelerators and detectors atCERN, the French community had to make difficult choices.ALICE, SATURNE, ALS and, a little later, the tandem post-accelerator at Saclay, had to be closed.

During the construction of GANIL, experiments on GiantResonances (GR), one of the subjects of predilection at thetime, continued with light probes at ALICE and with light but

3 Paul Bonche worked from 1972 to 2006 as a theorist in the NuclearTheory Division (SPhT) of CEA-Saclay.

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higher energy probes, essentially protons and alpha particles,at SATURNE.

At the end of the 1970s and in parallel to my new thesis(thèse d’état) that I was pursuing with the Tandem at Saclay,I participated under the aegis of Mrs. Henriette Faraggi4 inexperiments at Saturne on the study of Giant Resonances withthe SPES spectrometer. We measured the inelastic scatteringof α particles of energy 85A MeV and 120A MeV incidenton 58Ni, 116Sn and 208Pb nuclei up to 60 MeV of excita-tion energy. The coherent background subtraction and multi-pole analysis performed by B. Bonin5 provided the multipolestrength distributions for these nuclei [3]. The analysis con-firmed the properties of the already known low-lying giantresonances and highlighted possible new states at higherexcitation energy. My closeness to Jacques had marked meout as the physicist who was to calculate the excitation ofthese modes. I worked with Jacques to deepen my under-standing of the subtleties of ECIS and to initiate myself inthese calculations. Jacques was always very courteous andpatient in his explanations. I remember that in using the com-puter terminal Jacques was a fan of VI, which caused me realproblems when I needed to change the program parameters.

The planned shutdown of the ALICE and SATURNEaccelerators had prompted us to consider the continuation ofthe GR experiments at GANIL. However, to perform this typeof experiment a high-energy resolution magnet was manda-tory. The community was divided. Many senior physiciststhought that it was impossible in the “molasses” of the heavyion collision products to identify and study reaction chan-nels of relatively low cross section. I had been designatedto champion a program for investigating giant resonances atGANIL and to advocate the construction of a magnet. Byanalogy with the SPES magnet at SATURNE it was to becalled the SPEG magnet at GANIL.

2 ECIS and sub-Coulomb barrier fusion

While awaiting the completion of GANIL, experiments werecontinuing at Saclay at the Tandem Van de Graaff, theaccelerator of the Low Energy Nuclear Physics Division(DPhN/BE).

4 Henriette Mathieu-Faraggi was the Director of the Department ofNuclear Physics (DPhN) at Saclay from 1972 to 1978. At that time theDPhN consisted of several divisions, the DPhN/BE, the LNS, the MFthe HE, the ALS .... She was also President of the Nuclear Physics Com-mittee of the International Union of Pure and Applied Physics (IUPAP).At the end of her tenure at DPhN and until her death in 1985 she workedat Saturne conducting experiments on the study of the properties of giantresonances in nuclei.5 This was Bernard Bonin’s thesis work. Bernard subsequently had abrilliant career at the CEA; he was Deputy Scientific Director of theNuclear Energy Directorate.

One of the topics that interested physicists at that time wassub-Coulomb barrier fusion. A physical process present fromprimordial nucleosynthesis to energy production in the starsand eventually energy production on earth at future fusionreactors whose technical feasibility is being tested today bythe ITER project.

A student of the division, Dalva Maria de Castro Rizzo,was working in this field and she had obtained data on sub-Coulomb barrier fusion for the 18O + 44Ca and 12C + 48Tisystems. Out of interest, I plunged into the understanding ofthe subject.

The sub-Coulomb barrier fusion of two nuclei is classi-cally forbidden. It can only be achieved by quantum tunnel-ing. A very popular formula, widely used at the time, allow-ing either calculation of the sub-Coulomb barrier fusion crosssection or the value of the fusion barrier, is the Wong formula[4]. It allows the different physical parameters that come intoplay during the fusion process to be visualized:

σ f us (E) = h̄ωR2b

2Eln

(1 + exp

(2π

h̄ω(E − Vb)

))(1)

where Vb = V(Rb) is the height of the s-wave barrier, Rb isthe radius corresponding to the maximum of the barrier, andh̄ω is the curvature of the barrier.

Very quickly, it became clear that sub-Coulomb barrierfusion depends on the microscopic structure of the collidingnuclei. However, the structure of colliding heavy nuclei istoo complex to be described simply by two rigid spheres.For this reason, theoretical attempts to reproduce the fusioncross sections have taken into account various aspects of thenuclear structure of the reaction partners such as static defor-mations, dynamical deformations, neck formation betweenreactants, or even inelastic scattering or transfer reactions.

These aspects of a collision, i.e. inelastic scattering andtransfer reactions, are part of the arsenal of coupled channelscalculations. Therefore, ECIS, Jacques’ code, could play animportant role in describing sub-barrier fusion. Nevertheless,what is the relationship between a coupled channels (CC)calculation and sub-barrier fusion?

Here, I would like to recall our thoughts and hesitationsat the time. With ECIS, it is possible to calculate the part ofthe incident flux escaping from inelastic scattering or transferreactions and crossing the Coulomb barrier. That is, the partof the flux leading to fusion. A very intuitive procedure tovisualize the effects of coupled channels on fusion consists ofdiagonalizing the CC in order to reduce the coupled-equationproblem to a set of uncoupled equations. This is possible,although rigorously not exact, only when: (i) the differentcoupling matrix elements have the same radial form, (ii) thereorientation couplings are zero and (iii) the energy of theexcited states is neglected. In this case, let us take as anexample the fusion of two nuclei of spin zero with one ofthem having a low-lying 2+ vibrational state, the coupled

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equations can be reduced to two uncoupled equations withtwo central potentials, V(R)+F(R) and V(R)−F(R), whereF(R) is the usual coupling potential [5]. The fusion crosssection is then given by the average of the two uncoupledchannels, and can be approximated by the following formula:

σ f us (E) = 1

2(σ f us (E, (Vb + Fb))

+ (σ f us (E, (Vb − Fb))

)(2)

where Fb = F (Rb) and σ f us(E, (Vb ± Fb) are given byEq. (1) with Vb replaced by (Vb ± Fb). Couplings can loweror enhance the fusion barrier. Equation (2) gives a qualita-tive picture of the effect of coupling to a vibrational excitedstate on the fusion cross section. For energies well above thes-wave Coulomb barrier Vb, the values obtained by Eqs. (1)and (2) are very close. However, the predictions of the twoequations are considerably different for energies near andbelow Vb, since the fusion cross-section depends exponen-tially on the term (E − (Vb ± Fb). In other words, a singlefusion barrier could be thought of as splitting into a distribu-tion of barriers when couplings to other channels are present.

Intuitively, sub-Coulomb barrier fusion corresponds towave functions crossing the barrier without being reflectedback, that is crossing the barrier in the opposite way. Thisis the incoming wave boundary condition (IWBC).6 In sub-Coulomb barrier fusion calculations, the IWBC is simulatedby using an imaginary potential with a radius smaller thanRb, a short-ranged imaginary potential.

I discussed this issue with Jacques and I expressed mydoubts concerning this procedure. He agreed to modify ECISin order to introduce numerically the IWBC and checkwhether an imaginary potential with a radius smaller than Rb

does correctly simulate the IWBC in the case of CC calcula-tions. The result was positive. Later, when performing sub-Coulomb barrier fusion calculations myself, I also adoptedthe short-ranged imaginary potential recipe in order to facil-itate the calculations.

At that time, I got closer to Jacques. I learned to appreciatehis silences. He had been in Japan and he loved Japaneseculture, especially the Kabuki theatre. When he was young,during the fifties, he used to ride his bicycle a lot. He hadtravelled through almost all of Europe by bicycle. He leftParis to visit Greece and arrived in Constantinople. I laterlearned from a text by Jacques that Eric Bauge confided tome that Jacques had taken up the habit of cycling when hewas young, “There was no school transport and we used togo to school by bike. I was fond of long trips. It started withvisits to my maternal grandparents, a hundred kilometersthrough the mountains; then the Alps from South to North

6 Quantum mechanically the wave function is written as a superpo-sition of ingoing and outgoing waves. The Incoming Wave BoundaryCondition (IWBC) consist of imposing only ingoing waves.

and North to South sleeping in the woods and buying bread,ham and fruit”. My closeness to Jacques was well known andseveral physicists asked me at the time to help them in theirexchanges with Jacques. I thus found myself doing ECIScalculations for other groups.

Let us return to the sub-Coulomb barrier fusion of 18O +44Ca and 12C + 48Ti, which motivated us to undertake thesestudies. With the guidance of Jacques, we made detailed cal-culations within the coupled-channels formalism in order tostudy the fusion and inelastic excitation functions for thesesystems. The form factors for the inelastic scattering cal-culations were generated by deforming the real, imaginaryand Coulomb parts of the entrance channel potential. TheCoulomb corrections included at that time in ECIS made a~14 fm matching radius sufficient for the convergence of thecalculations (see chapter 2). The calculations allowed us toreproduce the experimental inelastic excitation functions ofthe 2+ excited state of both 44Ca and 48Ti. However, thecalculated enhancement of the fusion excitation functionsat energies below the Coulomb barrier, even if couplingsto higher excited states were considered, was insufficient toreproduce the experimental data. We attributed this to the factthat the colliding nuclei have a rather weak collective nature.Nevertheless, we obtained rather good agreement with theexperimental results by including an extra inelastic chan-nel mimicking the contribution of transfer reactions [5]. Weunderstood that transfer reactions could play an importantrole in sub-barrier fusion.

Indeed, sub-Coulomb barrier fusion measurements for58Ni + 58Ni and 64Ni + 58Ni showed a strong dependenceon the neutron excess of the projectile. These intriguingresults for the Ni + Ni systems measured using the MIT-BNL Velocity Selector in conjunction with a gas telescopecalled for an independent confirmation of the experimentaldata [6]. The measurements were performed using 58Ni and64Ni beams provided by the Stony Brook superconductingLINAC. With an entirely different experimental setup, were-measured the sub-Coulomb barrier fusion for these sys-tems. Our data were in good agreement with the previousmeasurements. In agreement with the earlier investigationsin this domain, ECIS calculations showed that by consis-tently taking into account the excitation of low-lying collec-tive levels, although it was possible to account qualitativelyfor fusion data at sub-barrier energies, they over-predicted thehigh energy data7 by approximately a factor of 2. The pos-sible presence of equilibrium fission at these energies wasinvestigated by calculating the fission probability. For thesecalculations we used the spin distribution for the compoundnucleus as predicted by ECIS. This yields a negligible con-tribution from fission at all energies [6].

7 A similar conclusion was drawn for sub-Coulomb barrier fusioninduced by exotic nuclei in the CDCC scheme [10].

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Throughout my scientific career I have retained a spe-cial interest in sub-Coulomb barrier fusion. This interest wasrenewed with the advent of beams of exotic nuclei. I amtaking a leap in time to comment on our current understand-ing of sub-Coulomb barrier fusion induced by exotic nucleiand discuss the expected improvements in coupled channelscodes to deal with such reactions.

Since Isao Tanihata’s famous experiment in 1985 at Berke-ley, which highlighted the phenomenon of the neutron halo,the physics of radioactive or exotic nuclei has had a mete-oric development. Probably one of the most overpoweringeffects of reactions induced by weakly bound nuclei is theimportance of breakup effects. Before, breakup was a curios-ity, with the advent of weakly bound nuclei it is everywhere.The most accurate method for taking into account breakupin nuclear reactions is certainly the Continuum DiscretizedCoupled Channels approach (CDCC). ECIS was developeda long time before the emergence of radioactive beams. Atthe beginning of his scientific career Jacques had workedon approaches related to the discretization of the contin-uum. He was familiar with the subject. However, despitethe exchanges we had, Jacques never introduced this formal-ism into ECIS. At that time, in the early 1990s, Jacques wasapproaching his retirement – he retired in 1996 – and hewanted to get ECIS easily accessible to a larger part of thenuclear physics community. Indeed, the different versions ofECIS are available today in the NEA data bank2.

Let us return to sub-Coulomb barrier fusion calculations.In many cases, it is possible to calculate with ECIS sub-Coulomb barrier fusion cross sections for stable nuclei with-out any adjustable parameter. However, for weakly boundnuclei the situation is more subtle. It becomes necessaryeither to use CDCC calculations or a potential taking intoaccount coupling effects to the continuum. In other words,a reduced real potential, which is a local representation (notexact) of the discretized CC calculations, in the sense thatby solving the one-channel Schrödinger equation with thatreduced potential, the same results are obtained as those withCDCC calculations.8 Obviously, in this second case, sub-Coulomb barrier fusion calculations in the coupled channelsformalism have to be considered with caution.

I will give an example of this type of investigation for thesystems: (i) 4He + 238U, 4He + 209Bi and (ii) 6He + 238U,6He+ 209Bi, 11Be+ 209Bi, the left- and right-hand panels ofFig. 1 respectively. Here I should note that later on, in 2004,the two low energy points for the 6He + 238U system were

8 However, one has to keep in mind that coupling to the continuummay not be fully represented by a simple reduction of the depth ofthe entrance channel potential, since the real part of the Dynamicalpolarization potential (DPP) may not have the same radial shape as thefolded one.

assigned to the two-neutron transfer reaction [7] and not tothe fusion process [8].

The real part of the entrance channel optical model poten-tial was computed within the double folding model approach.For a complete description of these calculations, see ref-erence [9]. As expected, the experimental results for both4He + 238U and 4He + 209Bi were equally well reproduced,without any reduction of the potential (N = 1) and withoutany adjustable parameter.

For the weakly bound projectiles, the right-hand panelof Fig. 1, calculations for two normalization factors of theentrance potential, N = 1 and N = 0.6, are presented. Thedata are compatible with the calculations with a normaliza-tion factor of N = 0.6. This is not surprising since accordingto the general trend of analyses of elastic scattering data forweakly bound systems a reduction of N = 0.6 seems tobe required to reproduce the data. An important conclusiondrawn from these results is that there is no strong evidence ofany sub-barrier fusion enhancement. It is a conclusion that Ibelieve is still valid.

However, this type of investigation is not intellectu-ally satisfying. It is not a completely consistent calculationthat simultaneously describes elastic and inelastic scatter-ing, breakup and fusion.9 This consistency was achieved byCDCC calculations in a remarkable paper published in 2007[10]. In this publication, our understanding of reaction pro-cesses involving light unstable nuclei at energies around theCoulomb barrier was reviewed. It was found that the dataare consistent with an above-barrier suppression and possi-bly a sub-barrier enhancement of the fusion cross section,although the latter remains to be confirmed. In that sensethe calculations made within the CDCC formalism justify aposteriori the conclusions drawn concerning the sub-barrierfusion of 6He + 238U, 6He + 209Bi and 11Be + 209Bi.

Considering the importance of breakup in reactionsinduced by weakly bound nuclei, codes like Ian Thompson’sFRESCO are more and more frequently used to the detrimentof ECIS. However, the story is not over. These new codes alsoneed to evolve. I let Nick Keeley10 take up the discussion.

9 Conceptually, sub-barrier fusion CC calculations should use onlygeneric optical potentials that do not necessarily reproduce elastic scat-tering data a priori. Coupled channels effects may modify elastic scatter-ing data and the deduced elastic scattering potentials may indirectly con-tain coupled channels effects. When calculating CC sub-barrier fusionwith potentials that reproduce elastic scattering the same couplings canbe considered, unintentionally, more than once! Completely satisfac-tory calculations are those that simultaneously describe all the coupledchannels as well as the elastic scattering a posteriori. In the case of ourpaper, couplings other than the breakup (simulated by the potential) didnot modify the sub-barrier fusion calculations. It is this last point thatgave us confidence in our conclusions.10 I first met Nick Keeley in 2003. Since then we have developed astrong friendship and a common perception of priorities in physics,

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Fig. 1 Left: Fusion crosssection measurements for stablenuclei compared with thecalculations. Right: Fusion crosssection for weakly boundsystems compared with thecalculations with a non-reduced(N = 1) optical potential (solidline) and a reduced (N = 0.6)optical potential (dashed line)

“A major part of the problem in any calculation of thefusion of a weakly bound projectile is in the fundamentalmatter of what is meant by “fusion” in this context. This isnot the trivial question that it may seem, since for weaklybound projectiles it is, at least in principle, possible for theprojectile to break up into two or more fragments and for onlyone of these to fuse with the target, giving rise to a so-called“partial fusion” or “incomplete fusion” event. Depending onthe system, these may be difficult or impossible to distinguishexperimentally from the usual or “complete” fusion eventsfollowed by evaporation of particles. Thus the first problemis to ensure that the quantity calculated as “fusion” equatesto what has actually been measured. Simply applying theingoing wave boundary condition to a CDCC code – CDCCwas developed to analyse elastic scattering and breakup,i.e. direct reactions – is not sufficient. Further complicationsarise in the interpretation of “partial fusion” events, sincethey are often difficult to distinguish from a classic transferreaction, leading as they do to the same final states. Muchwork has been done along these lines but further experimen-tal and theoretical developments are required before we canbe said to understand the fusion of weakly bound projectileswith heavy targets.”

I would like to close this excursion back in time by recall-ing a story that Valérie Lapoux reminded me of. One day, I donot remember exactly when, Jacques arrived in our laboratorywith a diskette that contained a subroutine on discretizationfor ECIS. Unfortunately we never managed to test this partof the code which I think is lost forever.

3 Elastic and inelastic scattering at GANIL

Let us go back to the thread of our story, to the events ofthe late 1970s and early 1980s. After the release of the firstelastic and inelastic scattering code MAGALI Jacques had

important problems to deal with, and others that are just a waste oftime.

been working for a few years on a new approach, the coupledequations – sequential iterations method, which is the basisof a new generation of codes, the ECIS codes. I participatedin the first tests of one of the ECIS codes; I think it wasECIS78, lost today, or probably an even older version. One ofthe problems we had at that time was the length of time it tookto do CC calculations. With the then available computers wewould submit a calculation in the evening and get the resultthe next morning.

In 1975 or 1976, employing the Saclay QDDD magneticspectrometer, we measured with a 16O beam elastic andinelastic scattering angular distributions for the 148,150,152Smisotopes at incident energies near the Coulomb barrier [11].The elastic scattering angular distributions showed importantdeviations from the Fresnel-like angular distribution shapeand they could not be reproduced by optical-model calcu-lations using standard optical potentials. The origin of thiseffect was attributed to the excitation of low-lying excitedstates of the targets. In other words, the effect was producedby the removal of flux from the elastic channel due to thestrong Coulomb excitation of low-lying states. A long com-puter time was needed to perform this type of coupled chan-nels calculation, which was hard to obtain in many labs. AtSaclay, we had the necessary computer resources to repro-duce the data with CC. I performed these calculations underJacques’ supervision using matching radii of the order of300 fm. To accelerate the calculations less time consum-ing calculational approaches were introduced, such as forinstance the addition to the usual optical-model potential ofa long-range imaginary potential simulating coupled chan-nels effects. N. Keeley and collaborators wrote a very nicereview article on these strong coupling effects in near-barrierheavy-ion elastic scattering [12], see also [13].

In the same context, another of the groups of our divisionhad measured the elastic and inelastic scattering of 16O and18O on a 28Si target at 56 MeV. The data were also analyzedin terms of coupled channels calculations [14]. It was real-ized that numerical problems linked to Coulomb inelasticexcitations might arise whenever charged projectiles bom-

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bard a heavy-ion target. These numerical problems may alsobe present for proton and alpha particle inelastic scattering,but they are dramatically enhanced for inelastic scatteringinduced by heavy ions. For instance, in the case of the exci-tation of the low energy 2+ state of 28Si, to obtain convergedresults a matching radius of 60 fm and an angular momentumup to 300 J were needed. This led Jacques to introduce newnumerical methods to speed up CC calculations. In his paperon “Recurrence relations for distorted-wave Born approx-imation Coulomb excitation integrals and their use in cou-pled channel calculations”, [15] he introduced Coulomb cor-rections for alleviating the CC calculations for heavy ioninelastic scattering dominated by the Coulomb interaction.An interesting example taken from [15] is the analysis of16O inelastic scattering on 74Ge. The results of calculations,without Coulomb corrections and with matching radii of 40,60, and 100 fm are shown in Fig. 2. The computation stopsat J = 205, 310, and 525 for a precision of 10−5. The com-putation with Coulomb corrections using a nuclear matchingradius of 15 fm, that is the potential radius plus 12 times thediffuseness, agrees quite well with the conventional calcu-lations using a matching radius of 100 fm, except between5◦ and 10◦, where the curve is sensitive to very high partialwaves. The dashed curve is the DWBA result and shows thatcoupled channels effects are mostly nuclear in origin.

The elastic cross section depends slightly on the match-ing radius. The maximum of the cross section divided bythe Rutherford cross section at 54◦ decreases from 1.1690to 1.1325 when the matching radius is changed from 15to 100 fm without Coulomb corrections; these values are1.1269, 1.1310, and 1.1320 with Coulomb corrections andmatching radii of 15, 20, and 25 fm respectively [15].

The Coulomb corrections were implemented in the codesECIS78 and ECIS79 and since then in all new versionsof ECIS. Coulomb corrections associated with momentuminterpolation methods made heavy ion inelastic scatteringcalculations feasible in terms of time. We also used Coulombcorrections in the sub-barrier fusion calculations.

GANIL delivered its first beam in 1982. It was 40Ar at anenergy of 44A MeV. For about a year this was the only avail-able projectile, but it allowed the various teams to familiarizethemselves with the new national laboratory and the asso-ciated experimental equipment. The first experiments tookplace in January 1983.

In January or February 1983, we carried out one of the veryfirst experiments at GANIL [16]. We measured very preciselythe elastic scattering of 40Ar on 60Ni, 120Sn and 208Pb nuclei.The aim of the experiment was precisely to study the energydependence of the optical potential. The main observation ofthe analysis of the experimental results was that for all targetsthe real part of the potentials which reproduced best the datahad a radius (the only fitted parameter of the real potential)0.2–0.3 fm smaller than that of a general empirical potential

Fig. 2 The solid curve was obtained with Coulomb corrections at amatching radius of 15 fm. The others were obtained without Coulombcorrections; the dashed-dot one with a matching radius of 40 fm, thedotted one with 60 fm and the dashed one with 100 fm. For the latter thedifference with the solid curve might come from long-range integration.For large angles, the dashed line shows the effects of coupled channels

extracted from an ensemble of lower energy elastic scatteringstudies. This deepening was attributed to the reduction of thePauli blocking with increasing energy.

The paper was published in 1984, one year after the exper-iment. We were rather happy with this paper, until a telephonecall from the United States. A telephone call by Ray Satch-ler.11 Ray had called my collaborator and friend Jean Barretteto tell him that he was sorry but that he could not reproduceour results with the code PTOLEMY.

I first met Ray in 1983 at Oak Ridge. He was a real gentle-man. From that time up until his death I kept in good contactwith Ray with periodic exchanges of letters. In Fig. 312 I

11 Ray Satchler, born in London, England in 1926, was an internation-ally influential and respected nuclear theorist. In the 1980s he publishedtwo major books - An Introduction to Nuclear Reactions and DirectNuclear Reactions. The latter is the definitive book on the topic and isstill frequently cited. In 1977, for his seminal work on the theory andapplications of direct nuclear reactions, he was awarded the Tom W.Bonner Prize by the Division of Nuclear Physics of the American Phys-ical Society and in 1989 he was awarded a prestigious Doctor of Sciencedegree by Oxford University for particularly outstanding contributionsto his field of research. He died in Seattle, Washington, on March 28,2010. https://physicstoday.scitation.org/do/10.1063/pt.4.1886/full/.12 ....Thank you for your letter just arrived. I can suggest pp. 599 etseq. of my book “Direct Nuclear Reactions and the enclosed paper.Confusion often arises because people do not define their S.R. ! I thinkPitthan in referring to the “proton” S R, needed for B(El), and con-cerning the operator Q p (eq.(14.63), p.600), rather than the “I S” and“I V” operators Q0 and Q1 of (14.62), p. 599. Although there are lin-

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Fig. 3 Letter from Ray Satchler from 1989. I reproduce Ray’s text below because it is an historical document, despite the fact that it was written30 years ago, it brings a particularly interesting light on the definition of sum rules, always of actuality

reproduce a letter by Ray and our exchange concerning theexcitation of GR.

After Ray’s call, Jean was devastated. I was displeased.I had taken a good look at the ECIS inputs and I could notfind a flaw. I spoke with Jacques. Jacques, without lookingvery carefully at the ECIS inputs – or at least that was myimpression – said to me: He is wrong! It was a heart-warminganswer, but it did not reassure me. A few days later came afurther telephone call from Ray. Could we send him the ECISinputs? Jean and I promised each other a good restaurant if

early related, Q p = 1/2(Q0 + Q1), etc., the sum rules concern thesquares of their matrix elements . : There are interference terms. As anexample of the complication this can lead to, I can suggest what Pitthanmay mean. Suppose there is a state, which exhausts the “I S” SR,

∑0

of (14.66). The contribution of this to the proton sum rule, is (Z/A)2∑0, (if �n/�p = N/Z etc.), while the proton sum rule, (14.68), is∑p = Z/A∑0 This leaves the remainder [Z/A − (Z/A)2]∑0 as

contribution to the∑p from other states (which I suppose one might

call “I V” !) But this is just [N/Z x(Z/A)2]∑0, or N/Zx contributionfrom the postulated I S state. I think this a confusing way to look at it!For example if we were postulate an “out-of-phase”, or I V , giant reso-nance which enhances the I V sum the

∑I, (= ∑0

)....its contributionto the proton sum will also be (Z/A)2 ∑0. Thus the two states do notexhaust the proton sum rule

∑P : there is still a fraction (N − Z)/A of∑P to be found elsewhere. I hope I have not succeeded in confusingyou further......

our calculations were correct. Having Jacques’ blessing wasvery important.

I was impressed by the scientific stature of Jacques andRay. They had never met. I remember that at the time Idreamed of a meeting between Ray and Jacques, a little likethe meeting between Maimonides and Averroes imagined byIli Gorlizki.13 Alas, it never took place.

One month later, we received a preprint from Ray onthe effects of using relativistic kinematics in the analy-sis of heavy-ion elastic scattering. Both calculations, byPTOLEMY and ECIS were correct. At the beginning ofRay’s paper was written [17] : “During the initial stage ofan analysis of the elastic scattering of 40Ar at E= 44AMeV,we observed an apparent discrepancy between our calcula-tions and those published by Alamanos et al. The discrep-ancy was resolved when we realized that those authors hadused the relativistic transformation between laboratory (L)and center-of-mass (CM) coordinate systems.” Indeed, thedifference arose from the fact that in performing the calcu-lations with ECIS we had used the relativistic kinematicsoption. This difference may apply an “apparent” change inthe potential strength larger than 20% for 40Ar scatteringfrom 208Pb at an energy as low as 44A MeV. Today, as far

13 Maïmonide - Averroès : Une correspondance rêvée by Ili Gorlizki(2004-04-22).

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as I know, ECIS is the only code offering the possibility touse relativistic kinematics.14 Beware; this may be importantwhen analyzing high-energy experimental results.

From 1985 onwards the range of experiments at GANILwas broadened with the commissioning of the spectrome-ter SPEG, which gave access to experiments requiring high-energy resolution. In 1985, we restarted the GR excitation andde-excitation experiments at GANIL. These experiments,carried out over a period of about ten years, often in thecontext of international collaborations, have considerablyenriched our knowledge of the excitation and decay prop-erties of these modes. Of this scientific adventure, I wouldlike to recall the results of the first experiments that weconducted, on the Coulomb excitation of GR in 208Pb by84A MeV 17O projectiles in collaboration with groups fromOak Ridge National Laboratory, the “Centre de RecherchesNucléaires in Strasbourg” and, of course, physicists fromGANIL [18,19]. The second topic I would like to discuss isthe excitation of modes with multipolarities L ≥ 3. Theircomputation by ECIS-type codes is even today a trap intowhich many physicists continue to fall [17–19]. During theseyears I continued to discuss very frequently with Jacquesproblems related to ECIS and other physics questions.

i) Coulomb excitation of GR in 208Pb: At that time therewere few measurements of GR excitation using inelastic scat-tering of heavy ion projectiles and most of these were per-formed at beam energies lower than 30A MeV. We thoughtthat heavy ions, by providing higher cross sections, a largerpeak-to-continuum ratio due to a decrease of knockout reac-tions, and the possibility of selectively excitation of reso-nances of high angular momentum, would enhance thesestudies.

The left-hand panel of Fig. 4 shows a 208Pb(17O, 17O′)spectrum from the GANIL measurements (solid line) at84A MeV and a spectrum from the same reaction at 22A MeV.The lower energy spectrum is normalized to the 84A MeVdata at 40 MeV excitation energy. It is apparent that the exci-tation energy of the centroid of the GR peak is higher inthe GANIL data than in the 22A MeV energy data. This isbecause Coulomb excitation of the Isovector giant dipole res-onance (IVGDR) provides the largest single contribution tothe GR region at the higher bombarding energy.

We quickly learned how to deal with the excitation of theIsovector Giant Dipole Resonance (IVGDR). For this mode,the d2σ

d�dE excitation cross section is given by:

d2σ

d�dE=

[dσ

d�

]E

βE1 (E) (3)

14 The most recent version of Ian Thompson’s code FRESCO, FRES-COX, now includes options for relativistic kinematics. However, as oneof the referees of this paper pointed it out, ECIS is the only one thatincludes the possibility of solving directly the Dirac equation.

where[ dσ

d�

]E is the DWBA cross section evaluated at exci-

tation energy E for unit E1 excitation strength {B (E1) ↑=1 e2 fm2} and βE1 (E) = d B(E1)↑

d E is the distribution of E1reduced matrix element per unit energy, which is related tothe photonuclear cross section σpn(E) by:

βE1 (E) = 9�c

16π3

σpn (E)

E

e2 fm2

MeV. (4)

The double differential cross section, d2σd�dE for Coulomb

excitation of the IVGDR was calculated as a function ofthe scattering angle and excitation energy as discussed pre-viously. The excitation energy cross section distribution ofthe IVGDR depends quite sensitively on the scattering angle.For each experimental scattering angle, the calculated doubledifferential cross section was integrated over the solid anglecorresponding to that defined by the cuts used to constructthe experimental spectra. In the right-hand panel of Fig. 4calculated shapes for the IVGDR for two scattering anglesare shown along with the photonuclear strength function. Tounderstand qualitatively this behaviour we have to note that,for each scattering angle, the cross section for Coulomb exci-tation of a dipole state decreases exponentially as a functionof the excitation energy of that state. This exponential depen-dence results in an enhancement of the low-energy part ofthe IVGDR strength distribution and shifts the position of itsmaximum from 13.5 to 12.7 MeV, right-hand panel of Fig. 4.

I think that one of the most important lessons we learnedfrom the analysis of this experiment is that when the photonu-clear cross-section is known, the contribution of the IVGDRto the scattering spectrum can be calculated without param-eters and subtracted.

Inelastic spectra obtained at three different scatteringangles are shown in the left-hand panel of Fig. 5. In the mid-dle spectrum, obtained at the angle where the cross section ofthis structure is maximum, the ratio is 6 to 1! At θlab = 2.56◦the giant resonance structure is largely dominated by the peakcorresponding to the IVGDR. At this angle, the small nar-row peak observed at 11.3 MeV is consistent with a similarstructure observed on the IVGDR strength function in pho-tonuclear reactions.

The measured experimental angular distributions for theIVGDR and the Isoscalar quadrupole Giant Resonance(ISGQR) are presented in the right-hand panel of Fig. 5.Special note should be made of the dramatically large valuesof the differential cross sections; of the order of a few b/sr.The two angular distributions also have distinctly differentshapes; that for the ISGQR being broader and flatter. Alsoshown in Fig. 4 are calculations assuming only Coulomb andonly nuclear interactions, respectively. Coulomb excitationdominates in the angular region 2◦−4◦. Hence, the experi-mental cross section in this vicinity is a sensitive and almostmodel independent measure of the B (E2)↑.

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Fig. 4 Left: Spectra from inelastic scattering of 84 and 22A MeV 17Ofrom 208Pb. The two spectra are normalized in the unstructured con-tinuum near 40 MeV. Right: Isovector giant dipole resonance shapesversus scattering angle. The solid curve is the IVGDR from photonu-clear reactions. The dashed and dotted curves are, respectively, the 2◦

and 3◦ distributions of excitation cross section for the IVGDR resultingfrom Coulomb excitation in the 208Pb(17O,17 O′) reaction at 84A MeV.For display purposes these curves are normalized to have unit energyintegrals [19]

Fig. 5 Left: Inelastic scatteringspectra at θlab = 1.86◦, 2.56◦,and 3.98◦ from the208Pb(17O, 17O′) reaction at1428 MeV (84A MeV). Thesolid curves show thedecomposition of the spectrainto resonance peaks includingthe ISGQR and IVGDRcentered at 10.6 and 12.7 MeVrespectively. Right:Experimental and calculatedangular distributions for theisovector giant dipole resonance(upper part) and the isoscalargiant quadrupole resonance(lower part) in 208Pb. For theISGQR, the calculated Coulomband nuclear contributions to thecross section are also shown(dashed lines). The error barsreflect the estimated uncertaintyin the fitting process and do notinclude the error on the absolutenormalization [18]

Since the electromagnetic strength was explicitly deter-mined in this analysis it was possible to obtain the distribu-tion of B(E2)↑ strength and compare the results with thoseobtained by other probes. The integrated B(E2)↑ strengthfrom the present data and for the entire ISGQR region (∼8–13 MeV) shown in Fig. 6 is 5120 + / − 800 e2 fm4, ingood agreement with the corresponding value 5400 e2 fm4

reported from (e, e′n) experiments. It is also clear from Fig. 6that not only is the integrated B(E2)↑ consistent with the (e,

e′n) results but also the distribution of B(E2)↑ strength is inexcellent agreement over the bulk of the 10.6 MeV ISGQR.

For the first time it was possible to obtain with hadronicprobes not only the percentage of the energy-weighted sumrule exhausted by the excitation of the ISGQR but also itsstrength distribution. Furthermore, for the first time a quan-titative comparison between the E2 GR strength distribu-tion from hadronic excitation with that from electron scat-tering was provided and an excellent agreement, both qual-

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Fig. 6 The distribution of B(E2)↑ in the giant resonance region asobtained from the present measurements (solid curve) and (e, e′n) mea-surements (points with error bars). The contributions of the 8.8- and9.3-MeV states and the 10.6-MeV state are shown separately as dashedcurves

itatively and quantitatively, between the two measurementswas found.

These results, combined with the burgeoning interest inthe physics of weakly bound nuclei, led us to think aboutstudying at GANIL GR for weakly bound nuclei. For this, itis important to reaccelerate the nuclei to be studied at ener-gies of the order of ~60A MeV. At the origin of the SPIRAL2-Phase2 project, the re-acceleration of radioactive beams wasforeseen with the CIME cyclotron, but the energy of CIMEis somewhat too low to measure giant resonance properties.The ISOLDE-CERN, SPES-Italy or ARIEL-Canada facili-ties today are limited to accelerated beam energies of less than10A MeV. Only a new accelerator at GANIL would coverthis energy range in Europe, pending the construction of theRAON facility in South Korea.

(ii) Excitation of modes with multipolarity L ≥ 3: Thesecond topic I would like to discuss is the excitation ofmodes with multipolarity L ≥ 3.15 After the first successfulexperiment concerning the study of GR modes for 208Pb,we decided to extend this type of measurement to othernuclei. We measured the elastic and inelastic scattering ofan 84A MeV 17O beam from 208Pb, 120Sn, 90Zr and 60Ni.

On this occasion, I wrote a code called “Form Factors” thatgenerated the input for ECIS specially for calculating giantresonance excitations with different types of folded poten-tials. It was an interface between the user and ECIS. Thedevelopment of this code and the definition of sum rules and

15 The transition probability B(EL↑) can be obtained by many meth-ods such as Coulomb excitation measurements, lifetime measurementsand electron scattering. Coulomb excitation and (e, e′) measurementsare sensitive to the properties of charge deformation. On the contrary,light- and heavy-ion inelastic scattering is sensitive to both the mass andcharge deformation in a ratio which depends on the incident energy, thecharge product of the colliding nuclei and the multipolarity of the tran-sition.

transition potentials for the different multipolarities led tointeresting exchanges with Jacques.

Inelastic-scattering angular distributions are currentlyanalyzed in the framework of coupled-channels calculationswith a transition potential containing a nuclear FL ,n (r) anda Coulomb FL ,c (r) term:

FL ,n (r) = δL ,ndV (r)

dr(5)

where V(r) is the entrance channel nuclear potential. Thisapproach is often justified by arguing that the potential V (r)

follows the shape of the density distribution when the latteris deformed:

FL ,c (r) = 3δL ,c ZT Z P e2

2L + 1

RL−1c

r L+1 if r ≥ Rc (6a)

FL ,c (r) = 3δL ,c ZT Z P e2

2L + 1

r L

RL+2c

if r � Rc (6b)

where δL ,n and δL ,c are the nuclear and Coulomb deforma-tions respectively. For more details, see [20,21].

In this second series of experiments we also wished toobtain good quality data for several well-known low-lyingstates and test the transition potentials FL ,n (r) , FL ,c (r)

widely used for calculating the excitation of these transitions.To our mind, those tests were also important since the sameform factors are currently used for the analysis of L ≥ 2isoscalar GR modes.

The B(E2↑) values obtained from our data analysis werein rather good agreement with the results of electromagneticexcitation measurements [20]. On the other hand, the B(E3↑)

values were consistently smaller than the adopted ones by atleast 30% or more. This result came as a surprise to us. Wehad to understand the origin of this difference. It was discred-iting the analyses of isoscalar GR excitations with multipo-larity L ≥ 2. We rapidly realized that this “hindrance” wasnot new. Several authors had observed this type of behaviourwithout really understanding the origin. L=3 states excitedby inelastic scattering of light ions were frequently weakerthan would be expected from the electromagnetic measure-ments. Even in articles providing compilations of B(E3↑)

values, empirical correction factors were applied in order tocorrect the B(E3↑) values obtained by inelastic scattering oflight projectiles [20].

After many hesitations, we decided to publish the resultsof this analysis with a rather provocative abstract. “Elasticand inelastic scattering of 1435 MeV 16O ions on 208Pb,120Sn, 90Zr and 60Ni have been measured. Hindrance in theexcitation of the first 3− states is observed. Parameters ofthe isoscalar giant monopole and quadrupole resonancesare obtained .... ”

I had discussed our results with Jacques. We were bothamazed by the structure of Eqs. 5 and 6. The nuclear transitionpotential does not depend on the multipolarity of the transi-

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Fig. 7 Transition potentials for17O +208 Pb at E = 84A MeV.Left: curves from the foldingmodel for l = 2−5. The solidcurve corresponds to thedeformed potential (DP) model.Right: logarithmic plot of thepotentials in the surface regionto which the scattering issensitive

tion while the electromagnetic transition potential dependson it. One of the arguments in favor of Eq. 5 is that the poten-tial follows the shape of the density distribution when thelatter is deformed. However, a more direct and consistentapplication of this view would be to obtain both optical andtransition potentials by folding an effective (and complex)nucleon-nucleon interaction over the density of the projec-tile and the deformed density of the target. Jacques suggestedusing microscopic transition potentials to study this effect.

Ray Satchler has ascribed this hindrance to the use ofdeformed optical model potentials. With his collaborators,he published a paper demonstrating that a more sophisti-cated analysis using folding model transition potentials couldremove this apparent discrepancy [21].

In following the discussion concerning this topic I willrely on a review article on elastic and inelastic scatteringthat I wrote together with Patricia Roussel-Chomaz [22]. Itcorresponds to the lectures I gave at the third “Euroschoolon Exotic Beams” held in Leuven in September 1995. Thearticle was published in 1996, the year of Jacques’ officialretirement.

As noticed by Ray, there is a fundamental differencebetween the standard deformed transition potential G D P

l(FL ,n (r), also Eq. 5) and the explicitly folded transitionpotentials.

A very simple density distribution for folding model cal-culations used in both [21] and [22] is given by:

gil (r) = −αlr

l−1 dρi (r)

dr(7)

where ρi (r) is the ground state density distribution and αl

a parameter related to the deformation of the state (i). Thevarious transition potentials are compared to the standardtransition potential in Fig. 7. Although the various transi-tion potentials have similar shapes, the folded ones dependon the multipolarity and their magnitudes decreases as themultipolarity increases, Fig. 7.

Since the inelastic cross sections are proportional to thesquare of the transition potential in the region of strong

Fig. 8 Comparison of the theoretical differential cross sections withthe measured ones for 17O +208 Pb and 17O + 90Zr at E = 84A MeV.The B(EL↑) values are compatible with the adopted ones

absorption, which is ~11 fm for 17O + 208Pb (cf. The right-hand panel of Fig. 7), it is clear that the cross sections pre-dicted by the folding model are smaller than those predictedby the deformed potential model calculations. This differenceincreases with the multipolarity. A reanalysis of the inelas-tic scattering data within the folding model showed that theapparent hindrance was removed, Fig. 8.

I am still skeptical of this type of analysis. The foldingmodel we used in our calculations was a very simple one[23]. Various aspects could be treated more realistically.

These may include different radial distributions for thetarget neutrons and protons, more realistic forms for the tran-sition densities, such as those obtained from shell model orRPA calculations, etc. Even today I am not completely con-vinced that we can extract unambiguously B(EL↑) valuesfrom inelastic scattering experiments using hadronic probes.

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After 2002, although I was more and more absorbed byadministrative duties, I stayed in touch with Jacques byexchanging messages and meeting him from time to time.I know that at that time he was particularly interested bythe treatment of the spin-orbit term in CC calculations. Heexpressed his ideas in 2005 in what is probably his last sci-entific article [24].

While writing these lines about Jacques, I have oftenwondered if I was not writing about my own experience inphysics, at least in the domain of CC calculations, rather thanabout Jacques. I think this is one of the pitfalls of this typeof exercise. I knew Jacques through the different problemsof physics. Even if with time we became close, ECIS andphysics always guided our discussions. I wish Jacques couldhave read these lines. The Italian author Andrea Camilleri16

dedicated one of his books to friends who would not be ableto read it. Likewise, I know that Jacques will never read thistext. That is how it is. That is life the shadow of a fleetingdream.

I would like to end this very personal contribution toJacques’ memory by recalling that Jacques was a personof very great sensitivity and kindness. Many years afterhis retirement he was still working with experts, releasingupdates of his codes. His depth of knowledge, passion andcommitment to our field were remarkable. He will certainlyleave his mark on nuclear physics for a very long time tocome. That was Jacques.

Data Availability Statement This manuscript has no associated dataor the data will not be deposited. [Authors’ comment: The article is areview article with not new data.]

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