An ISR Discovery : The Rise of the Proton – Proton Cross-Section

The Intersecting Storage Rings (ISR) were the first hadron collider ever built, providing proton–proton collisions at centre-of-mass energies as high as 62 GeV, almost five times larger than any previous accelerator. When in 1971 the ISR began operation the Reggepole approach dominated and the proton–proton total cross-section was expected to have already reached a finite asymptotic value. However, ISR experiments found that the cross-section was rising by 10% between 22 and 62GeV, while the interaction radius was increasing by 5%, a trend that continues up to the hundred times larger energies available at the Large Hadron Collider. In order to accurately measure the total and elastic cross-sections, new experimental methods — uniquely adapted to the environment of a hadron collider — had to be developed; they are described in the central part of this paper, which closes with a review of the data obtained at the LHC since they put in a wider perspective the forty years old ISR results.

(ii) The "shrinking" of the forward differential cross-sections when the collision energy was increasing, 2 which meant that the forward proton-proton differential elastic cross-section at small centre-of-mass angles θ cm (i.e. at small momentum transfers q = cp cm sin θ cm , usually measured in GeV) is proportional to exp(−Bq 2 ), with a slope parameter B that increased with the centre-of-mass energy, indicating, through the uncertainty principle, that the proton-proton interaction radius increased as √ B.
The regime in which all the total cross-sections would become energy independent was called "asymptopia", and theorists and experimentalists alike were convinced that the ISR would demonstrate that the total proton-proton crosssection, which slightly decreases in the Serpukhov energy range (Fig. 1), would tend to a constant of about 40×10 −27 cm 2 (40 mb), thus confirming the mainstream interpretation of all hadronic phenomena, the Regge model.

The Theoretical Framework
In the 1960s the forward differential cross-sections had found a universally accepted interpretation in terms of the collective effect of the exchanges of all the particles,   which, in the mass 2 -spin plane, lay on a "Regge trajectory".The present knowledge of the ρ trajectory is represented in Fig. 2. 3 The exchange of the ρ trajectory dominates the charge-exchange cross-section of Fig. 3(a).By using the usual parameter s = E 2 cm , where E cm is the centre-of-mass energy, the recipes of the Regge model give a cross-section that varies as s α(t=0)−1 (Fig. 3).
In the 1960s, the experimental confirmation of this prediction -see for instance Ref. 4 -was one of the strongest arguments in favour of the Regge description of the scattering of two hadrons.Such a description is still used because these phenomena cannot be computed with quantum chromodynamics.
As shown in Fig. 3(b), in the Regge approach the proton-proton elastic scattering process was also described by the exchange of a trajectory, the "pomeron",  which -given the fact that σ tot is proportional to s α(t=0)−1 -had to have an "intercept" α P (t = 0) = 1 to be consistent with an energy-independent total cross-section.For this reason, at the beginning of the 1970s, the so often heard "asymptopia" and "the pomeron intercept is equal to 1" were used as different ways of saying the same thing.
Since there were no particles belonging to the pomeron trajectory, its slope could be fixed only by measuring the t dependence of the forward elastic proton-proton cross-section, which could be described by the simple exponential exp(−B|t|) with a "slope" B that increased with the centre-of-mass energy.The accepted slope of the pomeron trajectory was α P (0) ≈ 0.25 GeV −2 .
In parallel with this "t-channel" description, other theorists, working on the "s-channel description", were deriving rigorous mathematical consequences from the fundamental properties of the S-matrix, which describes the scattering processes: unitarity, analyticity and crossing.
Unitarity of the S-matrix implies that one can compute the imaginary part of the forward scattering amplitude Im f (t) by taking the product of a scattering amplitude and its conjugate and summing them over all possible intermediate states, as graphically depicted in Fig. 4.
The sum is made up of two contributions, which are called "elastic and inelastic overlap integrals" G el (t) and G in (t).In the forward direction, i.e. for t = 0, the overlap integrals reduce to the elastic and inelastic cross-sections, and the unitarity relation gives the "optical theorem", which states that the imaginary part of the forward scattering amplitude equals the total cross-section σ tot , except for a factor k/4π, which depends on the definition chosen for the amplitude itself.
The figure and the formulae indicate that hadron-hadron forward elastic scattering (t = 0) is determined by the amplitudes of both elastic and inelastic reactions.When the collision energy is large, there are many open inelastic channels, the incoming wave is absorbed and the elastic scattering amplitude is dominated by its imaginary part, which is the "shadow" of the elastic and inelastic processes.In such a diffraction phenomenon, the ratio ρ = Re(f )/Im(f ) between the real and imaginary parts of the elastic amplitude is small, so that, in the expression for the forward elastic cross-section deduced from the optical where the term ρ 2 is of the order of a few percent.
The unitarity equation expressed in term of the variable q = (−t) 1/2 can also be written as a function of the complementary variable, the impact parameter a in the plane perpendicular to the momenta of the colliding particles.By applying the transformation written in Fig. 5 to the scattering amplitude f (q), one can compute the "profile function" Γ(a) as a function of a.
By applying the transformation of Fig. 5 to the three terms of the unitarity relation of Fig. 4, one obtains This equation shows how, in the diffraction limit, i.e. when the scattering amplitude is essentially imaginary because ρ is small, the "profile function" Γ (a) is real and the "inelastic overlap integral" G in (a) determines the elastic "profile function", , and vice versa.The two inequalities to the right express the limits imposed by unitarity.
If for a ≤ R the absorption is complete, i.e.G in (a ≤ R)] = 1 and Γ (a ≤ R)] = 1 − σ el = σ in = πR 2 and σ tot = σ el + σ in = 2πR 2 .Thus a ratio σ el /σ tot = 0.50 is a clear sign of the fact that the "black disk" model has to be adopted.
Combining unitarity with analyticity and crossing, in the 1960s three important theorems had been demonstrated.
• According to the Froissart-Martin theorem 6, 7 the total cross-section must satisfy the bound where the numerical value C = π( /m π ) 2 is determined by the mass of the pion, which is the lightest particle that can be exchanged between the two colliding hadrons, and s 0 is usually taken equal to 1 GeV 2 .• Finally, the Khuri-Kinoshita theorem 8 relates the energy dependence of ρ with the energy dependence of the total cross-section by stating that, if σ tot increases with energy, ρ passes from small negative values to positive values.This is a consequence of the "dispersion relations", which connect the real part of the forward elastic amplitude with some appropriate energy integrals of the total cross-section.Khuri and Kinoshita showed that, if σ tot follows the Froissart-Martin bound and increases proportionally to ln 2 s, for s → ∞ the ratio ρ is positive and tends to zero from above as (ln s) −1 .

Three ISR Proposals
In March 1969, the ISR Committee received three proposals that are relevant to the subjects discussed in this paper.
The title of the proposal by the Pisa group (signed by G. Bellettini, P. L. Braccini, R. R. Castaldi, C. Cerri, T. Del Prete, L. Foà, A. Menzione and G. Sanguinetti) was "Measurements of the p-p total cross-section". 9Giorgio Bellettini presented orally the proposal to the ISR Committee.
Two of the figures of the proposal are reproduced in Fig. 6.The very large scintillator hodoscopes would detect the outgoing particles and count the total number of events.Moreover, small-angle telescopes would detect forward elastic events in order to estimate the number of elastic events not recorded because the protons, scattered at small angles, would be lost in the ISR vacuum chamber.At a collider, in order to measure any cross-section it is necessary to determine the "luminosity" L. In the case of a beam of parallel particles that cross at an angle Φ, the only important spatial variable is the vertical one y.Given the normalised vertical distributions of the two beams, ρ 1 (y − y o ) and ρ 2 (y), which are displaced vertically by y 0 , the luminosity is proportional to the two currents and depends upon the crossing angle of the beams according to the formula: To obtain the luminosity, the Pisa group proposed to measure ρ 1 and ρ 2 separately with the two sets of spark chambers indicated in Fig. 6 with the letters M o , M a and M b , and then to compute numerically the beam overlap integral.
The problem of measuring the ISR luminosity was amply debated during 1968 and various proposals to do so by separated measurements of the vertical distributions were put forward by Darriulat and Rubbia, 10 Rubbia, 11 Schnell, 12 Steinberger 13 and Onuchin. 14Another method proposed in different forms by Cocconi, 15 di Lella 16 and Rubbia and Darriulat 17 was based on the detection of the two protons scattered at angles smaller than about 1 mrad, where the known Coulomb elastic scattering cross-section dominates.
All the proposals requiring the separate measurements of the vertical distributions of the two beams were superseded by a very simple observation made by Simon Van der Meer. 18He remarked that the cross-section σ M of a particular type of event (detected by a set of monitor counters surrounding the interaction region) can be obtained by measuring the rate of the monitor events R M (y 0 ) as a function of the distance y 0 between the centres of the two beams, which are moved vertically in small and precisely known steps.
Since in the integral I VdM = ∫ R M (y 0 )dy 0 the double integral over dy 0 and dy -implicit in R M (y 0 ) -equals 1, because ρ 1 and ρ 2 are normalised, the crosssection of the monitor counters is given by σ M = I VdM /K and the cross-section σ corresponding to any other rate R is simply obtained as The magnets needed to precisely displace the two beams vertically were installed in the ISR, and since then the Van der Meer method has been used to measure proton-proton luminosities at all colliders.
Figure 7 shows the apparatus built by what became the Pisa-Stony Brook Collaboration after the Pisa group joined with the Stony Brook group led by Guido Finocchiaro and Paul Grannis.
Coulomb scattering and its interference with nuclear scattering was the focus of the proposal "The measurement of proton-proton differential cross-section in the   angular region of Coulomb scattering at the ISR" 19 presented by Giorgio Matthiae on behalf of the Rome-Sanità group.The proposal was signed by U. Amaldi, R. Biancastelli, C. Bosio, G. Matthiae and P. Strolin; Strolin, at the time was an ISR engineer.The apparatus (shown in Fig. 8) required a modification of the ISR vacuum pipe, with new magnets to be installed on each beam.A few months later, in an addendum to the proposal, the authors wrote: "In discussions with the specialists of the machine (R. Calder and E. Fischer) we found a simple way for allocating the detectors near the beam, which does not imply a modification of the standard parts of the vacuum chamber."The proposal (Fig. 9) foresaw getting the bottoms of the movable sections as close as 10 mm to the beam with the bottom of the movable sections, as described many years before by Larry Jones. 20This was a daring operation and many people worried so much that, in an ISR meeting, Carlo Rubbia said: "Your scintillators will give light as bulbs!" To counter the criticisms, in 1970 a test was performed at the CERN PS to check whether one could install scintillation counters very close to a circulating proton beam (Fig. 10).Eifion Jones participated in the planning and in the testsin which the PS beam was moved towards the scintillators.Previously Hyams and Agoritsas had performed similar measurements.The memorandum sent to the ISR Committee 22 concluded that, down to a few millimetres from the beam, the rate to be found at the ISR would have been sufficiently low to allow the Coulomb experiment (Fig. 11).
The ISR movable sections of the vacuum chamber soon became known as "Roman pots", which was the translation of the expression "les pots de Rome" invented by the French draftsman whom we visited, regularly travelling from Rome to Geneva and who, under the direction of Franco Bonaudi, transformed our rough sketches into construction drawings.
In October 1970, the ISR Committee took various decisions on pending experiments.Following it, the CERN group of Giuseppe Cocconi, Alan Wetherell, Bert Diddens and Jim Allaby wrote the Committee a memorandum, which said: "At the meeting of the ISRC on 14 October, it was concluded that there is no way to fit the proposed experiment on deep inelastic scattering into the present ISR experimental programme.As a result we have decided, on their invitation, to collaborate with the Rome group (U.Amaldi et al.) on the small-angle scattering experiment." For the final experiment, the newly formed CERN-Rome Collaboration decided to retain only the four movable sections located in front of the first ISR magnet, a decision that simplified the experiment and its interactions with the accelerator.
In the same ISR Committee meeting in which the Pisa and the Rome experiments were presented, Carlo Rubbia described the third proposal by the CERN-Genoa-Torino group (P.Darriulat, C. Rubbia, P. Strolin, K. Tittel, G. Diambrini, I. Giannini, P. Ottonello, A Santroni, G. Sette, V. Bisi, A. Germak, C. Grosso.The title of the proposal was "Measurement of the elastic scattering crosssection at the ISR". 23The apparatus of Fig. 12 was made of two parts such that "the whole angular range from 1 mrad to about 100 mrad can be covered.The very  small-angle events (in the Coulomb region) are detected by a two-arm spectrometer sharing the first four magnets with the storage ring system.The larger-angle events are momentum-analysed with a pair of magnets that do not perturb the circulating beams." After many discussions, the ISR Committee decided to approve only the system made of two septum magnets installed in the intersection regions and to leave the detection of elastic scattering in the Coulomb region to the scintillators mounted in the Roman pots.Since then, Carlo Rubbia has described the ISR experimental programme as "key-hole physics".
After the approval, Rubbia's Collaboration was joined by the Aachen and Harvard groups and became the Aachen-CERN-Harvard-Genoa-Torino (ACHGT) Collaboration.
The two elastic scattering experiments were mounted in interaction regions I6 of the ISR (Fig. 12), while interaction region I8 was assigned to the total cross-section experiment.

First Results on Elastic Scattering and Total Cross-Sections
The slope of the forward elastic cross-section was the easiest measurement to perform.The 1971 results, 24,25 reported in Fig. 13, confirmed the behaviour first found at the PS and confirmed at Serpukhov: in the range 30 ≤ s ≤ 3000 GeV 2 , the elastic slope B is linear in ln s, in agreement with the description based on pomeron exchange, and in the ISR energy range (23 ≤ √ s ≤ 62 GeV, i.e. 550 ≤ s ≤ 3800 GeV 2 ) B increases by about 10%, which corresponds to a 5% increase of the proton-proton interaction radius.
In the Regge description B = B 0 + 2 α P (0) ln s s 0 and the dashed line of Fig. 11 corresponds to α (0) = 0.28 GeV −2 , confirming what was already known from lower-energy data: the pomeron slope at t = 0 is definitely smaller than the slope α ρ (0) ≈ 1 GeV −2 of the ρ trajectory (Fig. 2).Fig. 13.The data available in 1971 for −t ≤ 0.12 GeV 2 and the results of the measurement performed in 1972 at NAL (Fermilab). 26The dashed line shows that, over a very large energy range, the t-width (which is equal to 1/B) of the forward elastic peak decreases as the inverse of (a + b ln s).
In 1972, the ACHGT Collaboration reported the experimental distributions plotted in Fig. 14, which show that (i) The forward elastic cross-section has a variation of slope at |t| ≈ 0.16 GeV 2 ; 27 (ii) The deep diffraction minimum located at |t| ≈ 1.4 GeV 2 is the energy-dependent deepening of the structure observed at lower energies. 28wever, the real surprise came with the measurements of the total cross-section done by the Pisa-Stony Brook Collaboration, with the apparatus of Fig. 7, and by the ACHGT and the CERN-Rome Collaborations, by measuring the forward elastic cross-section and using the optical theorem.
This method, which, as far as I know, was not considered before the ISR start-up, was pioneered in 1971 by ACHGT: 29 the hadron-hadron forward elastic crosssection (measured outside the Coulomb peak with the Van der Meer method) is extrapolated to zero angle to obtain (dσ/dt) 0 and the optical theorem is applied to obtain In the autumn of 1972 the three collaborations were competing to be the first to measure the total proton-proton cross-section.I remember very vividly that period, because I was the one performing the analysis of the CERN-Rome data.The confusing status of the measurements in October 1972 is presented in Fig. 15, which I prepared for the invited talk I gave in September 1973, at the II Aix en Provence International Conference on Elementary Particles. 30he Conference session of September 12, 1973 -in which I presented the rising cross-section data -was the most momentous one I ever contributed to.Daniele Amati gave the first talk on "Strong interaction theory"; he started the presentation by placing on the overhead projector a transparency with a hand-made Chilean flag because the night before the Pinochet coup d'état had overthrown Allende's government.Then Alan Mueller spoke on "High multiplicity reactions", I presented "Elastic scattering and low multiplicities" and Steven Weinberg discussed "Recent progress in gauge theories of weak, electromagnetic and strong interactions".Finally Paul Musset described -in "Neutrino interactions" -the neutral current events discovered at CERN by Gargamelle; the applause never ended.In his Nobel speech Abdus Salam said, "At the Aix-en-Provence meeting, that great and modest man, Lagarrigue, was also present and the atmosphere was that of a carnival -at least this is how it appeared to me." Figure 15 shows that in fall 1972 the Pisa-Stony Brook and CERN-Rome Collaborations had an indication of the rising cross-section, while AGHGT was   finding no energy dependence; this negative result was publicised in many seminars and for many months the difference with the other two was hotly debated.
In February 1972, the CERN-Rome Collaboration had published the first measurement of the ratio ρ between the real and imaginary parts of the forward scattering amplitude and of the total cross-section using Coulomb scattering as normalisation. 31The measurement could only be performed at the two lowest ISR energies because, with the apparatus of Fig. 16, the minimum scattering angle was fixed at about 2.5 mrad by the background rate due to the beam halo.Thus at the highest ISR energies, after completion of the stacking process in the two ISR rings,   The t-dependence of the Coulomb amplitude is well known, because it is due to large-impact-parameter collisions of two point-like charges, is essentially real and decreases proportionally to 1/t.In the t range indicated by the dashed ellipse, the nuclear amplitude varies little and its (small) real part interferes with the Coulomb amplitude, which is well known, being due to an electromagnetic phenomenon.The ratio ρ can thus be obtained by a fit to the very precise data.
The results of this first experiment are shown as full dots in Fig. 17(c).The two data points indicated that ρ was becoming positive in the ISR energy range which, because of the Khuri-Kinoshita theorem, was a signal of the rise of the total proton-proton cross-section.The error bars are large, but within the Collaboration we knew that the indication was stronger than it appeared because, after many discussions, the experimental errors were doubled to be on the safe side in the first paper reporting the result of a new delicate experiment.
The CERN-Rome and Pisa-Stony Brook data -presented at CERN in my 1973 seminar and published shortly after 32, 33 -definitely demonstrated that (i) The proton-proton total cross-section increases by about 10% in the ISR energy range (Fig. 18(a)), (ii) The elastic cross-section (computed by integrating the measured differential cross-section) increases by the about same amount, so that in the full ISR energy range the ratio is σ el /σ tot ≈ 0.17, while it decreases monotonically at lower energies.Since our final paper was ready before the one of the Pisa-Stony Brook Collaboration, we waited a couple of weeks so that the two papers could be published one below the other in the same issue of Physics Letters.
The constant ratio σ el /σ tot ≈ 0.17 and the 10% increase of the proton-proton forward slope are easily attributed to the combination of an energy-independent value of the inelastic overlap integral G in (0) and of the profile function Γ (0) = 1− [1 − G in (0)], with an interaction radius that increases by 5% in the ISR energy range.In this simple model -called "geometrical scaling" -the shape of G in (a) does not change with the collision energy.
The inelastic cross-section is four times larger than the elastic cross-section and increases roughly proportionally to s 0.04 from about 50 MeV/c to the maximum ISR energy (Fig. 18(b)).Looking at the three curves of this figure, it appears that the shallow minimum of the total proton-proton cross-section σ tot = σ in + σ el around s = 100 GeV 2 is a consequence of the continuously rising inelastic cross-section which, through unitarity, seems to drive the increase of the elastic cross-section.
If the energy dependence of the high-energy total cross-section is fitted with the formula of the Froissart-Martin bound, one obtains where √ s 0 = 140 GeV. 32Since the coefficient 0.5 mb is much smaller than the limiting value predicted by the Froissart-Martin bound, the very good fit obtained with ln(s/s 0 ) 2 is probably uncorrelated with the bound itself.As I said, at the time most experts were convinced of the constancy of the cross-sections at high energies, with two important exceptions.In 1952, Werner Heisenberg had published a paper that described pion production in proton-proton collisions as a shock wave problem governed by a non-linear equation and deduced a ln 2 s dependence of the cross-section. 34The model proposed H. Cheng and T. T. Wu 35 is much more sophisticated because it is based on quantum field theory, specifically on a massive version of quantum electrodynamics.After the announcement of the ISR results, the model was reconsidered and fitted to the experimental data by Cheng, Walker and Wu. 36he CERN seminar of March 1973 and, soon after, the two publications made a certain impression also outside the physics community, so much so that I was invited to write an article for Scientific American.In spring and summer 1973 this took me a lot of time since the editor was following very closely the writing of the text and the production of the figures.The article was published in September 1973 37 after a drastic cut of the part of the article containing the impact parameter description of the ISR collision.As a replacement, I introduced the quantity "average opaqueness" O = 2σ el /σ tot , which in wave mechanics is O = 1 for a black disk, and showed with a figure how O decreases at low energies and becomes roughly constant (O ≈ 0.35) in the whole ISR energy range.
I may add that letters and telex exchanges were needed to convince the editor to insert the 29 names of the members of the CERN-Rome and Pisa-Stony Brook Collaborations, a request that in the past Scientific American -as they told mehad always refused because "they are too many and the readers are not interested".At that time a collaboration of 20 scientists were considered to be very large and papers in molecular biology were signed by 2-3 authors.

Second-Generation Experiments
In the years 1974-1978, three experiments brought more precise data.The first one was performed by the Annecy-CERN-Hamburg-Heidelberg-Vienna Collaboration that used the Split Field Magnet to accurately measure the elastic cross-section up to −t = 12 (GeV/c) 2 . 38It was observed that the minimum at −t = 1.4 (GeV/c) 2 deepens around E CM = 30 GeV and fills up at larger energies (Fig. 19(a)).It was interesting to remark that the deepest minimum happens at the same energies at which the forward real part is practically zero (Fig. 21(b)), possibly indicating that the fill-up at higher energy is due to a non-zero real part of the large-angle scattering amplitude.
In 1973 the CERN-Rome and Pisa-Stony Brook Collaborations proposed to the ISR Committee a joint experiment that would be done in new Roman pots installed -with more precise hodoscopes -in intersection region I8 where the Pisa-Stony Brook apparatus was located.Figure 20 shows the overall apparatus.As the inset Fig. 20 shows, the four pots -two per side -had very thin and flat windows, which allowed the pots -and the new systems of "finger" scintillators they contained -to be moved much closer to the circulating proton beams than in the previous experiment, once the beam stacking process was completed.The set-up also allowed a much more accurate measurement of the distance between the edges of the two hodoscopes located one on top of the other.I well remember Giuseppe Cocconi and the NIKHEF PhD student Jheroen Dorenbosch spending long hours to improve -through accurate position measurements -the knowledge of the momentum transfer q.(It can be mentioned that in 1977 one of the CERN-Rome scintillation hodoscope was requested by the National Museum of History and Technology in Washington to be shown to the public.) The combination of the two detectors opened the way to the application of the new method for measuring total cross-sections.This is based on the measurement of (i) the total number of inelastic events N in , measured by the Pisa-Stony Brook detector in a given run, which is, after small corrections due to the unavoidable losses, proportional to σ tot and (ii) the extrapolated forward rate (dN/dt) 0 , measured by the CERN-Rome hodoscopes, which is proportional to σ 2 tot .Because of the optical theorem, σ tot is proportional to the ratio (dN el /dt) 0 /N tot , where (dN/dt) 0 is the extrapolated forward number of events and N tot = N in + N el is the total number of inelastic and elastic events, computed by integrating the differential rate dN el /dt.
The combined results of the three methods are plotted in Fig. 21(a). 40(It is worth noting that the ratio ρ is small and contributes a negligible error to σ tot ).
The CERN-Rome measurements of the real part of the forward amplitude 41, 42 -obtained with the improved Roman pots of Fig. 20 -are plotted in Fig. 21(b).The curves of the two figures have been obtained by taking into account the dispersion relation that connects the forward real parts to energy integrals of the total cross-sections.The physical content of the complicated mathematics can be understood by stating that, at high energies, ρ becomes roughly proportional to the logarithmic derivative of the total cross-section, dσ tot /d(ln s).This fits with the Khuri-Kinoshita theorem, which states that ρ → π ln s for a cross-section that increases proportionally to ln 2 s -and explains why precise measurements of ρ at √ s ≈ 50 GeV determine the total cross-section up to about 500 GeV.(A discussion of this rough argument can be found in Ref. 43.)This was the first experiment in which the measured ratio ρ was used to obtain information on the energy dependence of the total cross-section at energies much larger than those available.
The CERN-Rome fit 41 gives a total cross-section that increases as ln(s/s 0 ) γ with γ = 2.1 ± 0.1 and s 0 = 1 GeV.As in the first generation experiments, the exponent coincides, with a smaller error, with the limiting value of the Froissart-Martin bound.This fact was confirmed by a second experiment performed just before the demise of the ISR, when the availability of the CERN Antiproton Accumulator allowed a measurement of the real part of the antiproton-proton forward scattering amplitude. 44The CERN-Louvain-la-Neuve-Northwestern-Utrecht Collaboration used the apparatus of the CERN-Rome Collaboration and inherited its techniques: I remember Jheroen Dorenbosch and myself passing to Martin Bloch the codes that we had developed over the years.

Overlap Integrals in the ISR Energy Range
To understand the significance of these results, let us step back the definition of the profile function Γ (a) and the inelastic overlap integral G in (a).In 1980, from all the measured elastic differential elastic cross-sections Klaus Schubert and myself have computed these quantities in a much-quoted article. 45igure 22(a) shows that the profile function is Gaussian-like and completely different from that of Fig. 22(b), 43 which describes a "black disk" having a radius  proportional to ln(s/s 0 ) and a grey periphery of constant width, as needed to saturate the Froissart-Martin bound. In the already quoted original works of the 1960s, 6,7 C was proven to be equal to π( /m π ) 2 ≈ 60 mb, but in a 2009 paper 46 André Martin derived for the inelastic cross-section the new limit C = π( /2m π ) 2 , which is four times smaller and corresponds to d = /[(2 √ 2)m π ] ≈ 0.5 fm.Still the new constant is thirty times larger than the best fit to the experimental data.
I now consider the increase ∆G in (a) of the inelastic overlap integral over the ISR energy range.In 1973 I presented such an analysis in Aix en Provence, concluding that the increase of the proton-proton cross-section is a peripheral phenomenon, 30 a conclusion reached at the same time by others. 47,48 is is confirmed by Fig. 23(a), which is the result of the analysis performed with Klaus Schubert. 45The novelties brought by this analysis were the direct calculation of G in (a) from the experimental data in the ISR energy range (23 GeV ≤ √ s ≤ 62 Gev) and the careful estimates of statistical and systematic errors.
It is worth mentioning that the physical origin of the bump of ∆G in (a) at a = 2.3 fm, first noted in Ref. 45, is not yet known.
Figure 23(b) displays the results of the analysis by Henzi and Valin, 49 who used a different approach by first fitting the differential cross-sections with analytical functions and then computing G in (a).
We can see that the shadow of the inelastic channels increases by ∆G in = 0.04 at 1 fm, which confirms the peripheral nature of the phenomenon.At a = 0 the two analyses are compatible when the errors are properly taken into account and indicate that ∆G in (0) is less than three times smaller than ∆G in (a = 1 fm).It could even be zero, since small impact parameters imply large momentum transfers, and in this region the analytical fits to the cross-section 49 are not perfect, a problem that is not encountered when the experimental data are used directly, as done in Ref. 45.As mentioned above, the fitted exponent of the logarithmic increase of σ tot is 2, with a very small error.We can now answer the question: is this fact connected with the exponent 2 predicted by the Froissart-Martin bound?The answer must be negative, because the overlap integral of Fig. 22(a) is very different from that of Fig. 22(b), but the coincidence is so puzzling that, without understanding, the expression "qualitative saturation of the Froissart-Martin bound" was introduced and much used.
In synthesis, the ISR measurements of elastic scattering, total cross-section highlighted an unexpected state of affairs: with increasing collision energy, the proton-proton opacity at zero impact parameter does not decrease -as predicted by the "classical" pomeron exchange model -but remains roughly constant.

The ISR "Small-Angle Physics" Seen from Higher Energies
In forty years, the energy of hadron-hadron colliders has passed from √ s = 30 GeV, the ISR minimum value, to the √ s = 8000 GeV available at the LHC in 2012.A review of the results obtained at this high-energy frontier is beyond the scopes of this paper; however, before closing, some remarks concerning the energy evolution of the main phenomena discussed in the previous sections may be useful.
Figure 24 reproduces the data obtained at the CERN antiproton-proton collider, at the Tevatron and, recently, at the Large Hadron Collider by the TOTEM Collaboration. 50,51 TLAS and CMS have published similar data. 52,53 t is seen that the low energy trend continues and the rough cosmic ray data (see, for instance, Ref. 54) are in agreement with the precise results obtained at LHC.
To detect the protons scattered at very small angles the TOTEM collaboration has located its Roman pots at hundreds of meters from the interaction point, in a high-beta interaction region, used -as proposed for the ISR by Darriulat and Rubbia in Ref. 17 -as a magnifying lens.
The slope of the forward elastic cross-section continues to increase up to 2000 GeV (Fig. 25(a)).
However the TOTEM value (in red) is surprisingly larger than the prediction of the fit to lower energy data.By excluding it from the fit, the slope of the pomeronslope of the pomeron trajectory is in agreement with the value obtained at lower energies: α P (0) = 0.25 GeV −2 .
An overall fit to the total cross-section of Fig. 24 and to the ρ-parameter of Fig. 25    By comparing the error bars of Fig. 25(b) with the one-sigma band -defined by a fit to the lower energy data -one can conclude that the precision of the measurement has to be improved by at least a factor of 3 in order to derive useful constraints on the behaviour of the total cross-section at energies much larger than the one available at LHC, as it was done in the 1970s at the ISR (Fig. 21).
Figure 26 shows that the constant value σ el /σ tot ≈ 0.175 -an indication of what was called "geometrical scaling" -is valid only in the ISR energy range.
Approximate geometrical scaling implies that in this energy region the central inelastic overlap integral G in (0) is almost constant while the effective proton-proton interaction radius increases so that the total cross-section increases.Before 1973, in the framework of the Pomeron model with intercept equal 1, most theorists were instead predicting a decreasing G in (0) so to exactly compensate the increasing proton-proton radius and produce an energy independent total cross-section.This is the physical content of the unexpected result obtained at the ISR.
Since the ratio σ el /σ tot increases above 100 GeV, it does not come as a surprise that the central inelastic overlap integral G in (0), in passing from the ISR to the CERN proton-antiproton collider, increases, as shown by Henzi and Valin, 56 at variance from what happens in the ISR energy range (Fig. 27).
In summary, the s-channel description based on a purely peripheral increase of the inelastic overlap integral may be valid in the ISR energy range but certainly it is not at higher energies.From this wider point of view the much discussed "geometrical scaling" of the 1970s is a transition regime of the restricted energy region where the total proton-proton cross-section begins its rise.
I conclude this discussion of the s-channel description of high-energy scattering by recalling that Henzi and Valin gave a descriptive title to their 1983 paper:    Landshoff to the bestmeasured total cross-sections. 3The intercept of the Reggeon trajectory (α R (0) = 0.45) is in good agreement with the value derived from the masses of the particles belonging to it (Fig. 2).
"Towards a blacker, edgier and larger proton".Moreover in 2015, to summarise their overall fit to all the available data, in Ref. 57 Martin Block et al. wrote: "The cross-sections approach a black disk limit asymptotically.The approach to the limit is, however, very slow: A 'black disk' of logarithmically growing radius is supplemented by a soft 'edge' whose properties are in invariant with energy."This vision is contrasted by the t-channel descriptions of the energy dependence of hadron-hadron cross-sections.In 1992, Donnachie and Landshoff wrote all the hadron-hadron total crosssections as the sum σ tot = Xs ε + Y s −η of two powers, the first due to pomeron exchange and the second to the exchange of the trajectory of Fig. 2. 3 Figure 28 shows the experimental points and the fitted curves for the four best-measured channels.They state their conclusion in the following terms: "The fact that all cross-sections rise with energy at the same rate s ε makes it unnatural to attribute the rise to some intrinsic property of the hadrons involved.It is unhelpful to adopt a geometrical approach and to talk of hadrons becoming bigger and blacker as the energy increases.Rather the rise is a property of something that is exchanged, the pomeron, and this is why the rise is universal.Our conclusions are in accord with the recent important results from UA8 at the CERN collider, which indicate that the pomeron does have a rather real existence: it can hit hadrons hard, break them up and knock most of their fragments sharply forward." In the fit of Fig. 28 the standard pomeron intercept is at α(0) = 1.08 but the authors warn the reader that the exponent ε = 0.08 (appearing in the energy dependence s ε of the total cross-sections) is a little less than α(0) − 1 because of multiple pomeron exchange.
This shows that twenty years ago a debate between the followers of the s-channel and the t-channel approaches was going on.And it is still alive, as indicated by a paper by Donnachie and Landshoff 58 who in 2011 -forty years after the first ISR physics runs -have analysed the data produced at the LHC by the TOTEM Collaboration coming to the conclusion that their picture is still valid but a term has to be added due to the "hard pomeron" observed in electron-proton collisions at HERA by ZEUS and H1. 59n 1973 Daniele Amati could not accept a pomeron intercept above 1, even if his Aix en Provence talk started with the following words: "Despite of the title of this session, there is no theory of strong interactions.Our hadron world is complex and we lack a dynamical theory that could allow us to understand and calculate its properties". 60Forty years later an analysis of all hadron-hadron cross-sections lead to the conclusion that the soft pomeron intercept is at 1.0926 ± 0.0016, 61 a very precise number; still we are not able to compute it from quantum chromodynamics, the well-established fundamental theory of strong interactions.

Concluding Remarks
It is often said that the ISR did not have the detectors needed to discover fundamental phenomena made accessible by its large and new energy range.This is certainly true for "high-momentum-transfer physics", which, since the end of the 1960s, became a main focus of research, but the statement does not apply to the field that is the subject of this paper -elastic and total cross-sections -and to diffraction dissociation, for which the interested reader is referred to Ref. 62.
In fact, looking back to the results obtained at the ISR by the experiments aimed at measuring total cross-sections and small-angle scattering and particle production, one can safely say that the detectors were very well suited to the tasks and performed much better than foreseen.
As far as the results are concerned, in this particular branch of hadronhadron physics, very precise measurements were performed, new phenomena were discovered, unexpected scaling laws were found and the first detailed studies of that still elusive concept which goes under the name "pomeron", were performed.
Moreover, some precision techniques and methods have had a lasting influence: since then all colliders had and have their Roman pots, and the different methods developed at the ISR for measuring the luminosity are still in use.
"Small-angle physics" is not very fashionable today but it gives a lot of satisfaction to those who accurately labour around it and, in addition, has a great merit: it requires a very close collaboration among machine physicists and experimentalists, an invaluable gift that as experimentalists we enjoyed for the first time at a wonderful collider, the Intersecting Storage Rings.

Fig. 1 .
Fig. 1.The total cross-sections σtot (measured in the early 1970s at the Serpukhov 70 GeV synchrotron and at lower-energy accelerators) plotted versus the laboratory momentum p of the proton. 1

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Fig. 2 .
Fig. 2. The present situation of the Chew-Frautschi plot shows that the Regge trajectory containing the ρ meson (mass = 770 MeV) is practically linear up to very large masses.

Fig. 3 .
Fig. 3. (a) The main contribution to the pion charge-exchange phenomenon is the exchange of the ρ trajectory.(b) In the Regge model, the exchange of a pomeron trajectory is the dominant phenomenon in all high-energy elastic collisions.

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Fig. 4 .
Fig. 4. The graphical representation of the unitarity relation, at a given s and for t ≤ 0, explains the definition of the elastic and inelastic overlap integrals G el (t) and G in (t) with k = p/ .

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Fig. 5 .
Fig.5.A Gaussian real elastic profile function corresponds to an imaginary scattering amplitude that decreases exponentially with q 2 = |t|.(In the integral, J 0 is the Bessel function of order zero.)

Fig. 6 .
Fig. 6.The initial proposal by the Pisa group to measure the proton-proton total cross-section.60 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.

Fig. 7 .
Fig. 7.In the final detector built by the Pisa-Stony Brook Collaboration, forward telescopes were used to measure elastic scattering events at small angles.

Fig. 8 .
Fig.8.In the first proposal, two quadrupoles and one magnet focused the protons and bent them so as to measure protons scattered down to 1.5 mrad.

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Fig. 9 .
Fig.9.In the 1969 proposal there were four movable sections on each beam and the forwardscattered protons were detected by a coincidence between counters located upstream and downstream of the first ISR magnet.

Fig. 10 .
Fig. 10.Special section of the PS that allowed the measurement (a) of the rate detected by scintillators placed very close to a circulating beam formed by 5 × 10 11 protons (b).

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Fig. 12 .
Fig. 12.The two septum magnets of the ACHGT Collaboration have been used to measure the forward elastic cross-section.

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Fig. 14 .
Fig. 14.First measurements by the ACHGT Collaboration of proton-proton elastic scattering (a) in the forward region 28 and (b) at large momentum transfer.29

Fig. 15 .
Fig.15.Status of the total cross-section measurements in October 1972.31The points by the CERN-Rome Collaboration were obtained with the luminosity measured with both the Van der Meer method and Coulomb scattering.

Fig. 16 .
Fig. 16.The 1972 telescope systems of the CERN-Rome Collaboration 32 were used (i) to obtain the ISR luminosity using the Coulomb scattering events and (ii) to measure ρ.

Fig. 17
Fig.17.The first measurements of the real part of the forward scattering amplitude were performed at the two lowest ISR energies.32 Fig.17.The first measurements of the real part of the forward scattering amplitude were performed at the two lowest ISR energies.32

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Fig. 19 .
Fig. 19.(a) The elastic differential cross-sections at large momentum transfers plotted on different vertical scales. 38(b) The elastic cross-section is energy independent and decreases as 1/t 8 . 39

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Fig. 21 .
Fig. 21.The curves are fitted to the energy dependence of the total cross-sections and the forward real part, and are based on the analyticity properties of the scattering matrix. 45, 4660 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.

Fig. 22 .
Fig. 22.At ISR energies the profile function is far from saturating the unitarity and analyticity constraints that define the Froissart-Martin bound.The length d, which is determined by the pion mass, fixes the constant C that multiplies ln 2 (s/s 0 ) in the Froissart-Martin bound.60 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.

Fig. 23 .
Fig. 23.The impact parameter dependence of variation of the inelastic overlap integral in the ISR energy range is the best way to understand the significance of the rising p-p cross-sections.
(b) gives for the exponent of ln(s) the value γ = 2.23 ± 0.15, 55 in agreement with the value obtained in Ref. 45: γ = 2.1 ± 0.1.This is a confirmation of the fact that the ISR value has nothing to do with the Froissart-Martin bound.60 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.

Fig. 24 .
Fig. 24.Summary of the available data on the total, inelastic and elastic cross-sections.The TOTEM points are in black.

Fig. 25 .
Fig. 25.The slope B of forward elastic cross-section shrinks in an enormous energy range: 30 ≤ √ s ≤ 7000 GeV and the ratio between the imaginary and real part of the forward amplitude has a shallow maximum around 1000 GeV.The TOTEM results are in red.60 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.

Fig. 26 .
Fig. 26.Above the ISR energies the ratio σ el /σtot is a linear function of the centre-of-mass energy.

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Fig. 28 .
Fig.28.The figure shows the fits obtained by A. Donnachie and P. Landshoff to the bestmeasured total cross-sections.3The intercept of the Reggeon trajectory (α R (0) = 0.45) is in good agreement with the value derived from the masses of the particles belonging to it (Fig.2).

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60 Years of CERN Experiments and Discoveries Downloaded from www.worldscientific.comby EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) on 11/17/15.For personal use only.
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