FERMI, Enrico.; AMALDI, Edoardo.; RASETTI, Franco.

Sull’assorbimento dei neutroni lenti I–III. [With:] Sul cammino libero medio dei neutroni lenti nella paraffina. [With:] Sui gruppi di neutroni lenti. [With:] Sulle proprietà di diffusione dei neutroni lenti. [With:] Sopra l’assorbimento e la diffusione dei neutroni lenti. [With:] Sul moto dei neutroni nelle sostanze idrogenate. [With:] Un generatore artificiale di neutroni. [With:] Azione del boro sui neutroni caratteristici dello iodio. [With:] Recenti risultati della radioattività artificiale.

Rome: Consiglio Nazionale delle Ricerche, 1935–38.

First editions, the complete run of the ten papers in which Fermi and his last two collaborators in Rome turned the slow neutron from an accident with a block of paraffin into a measured branch of physics — the set descending from the library of the American Society for Testing Materials in Philadelphia, whose dated accession stamps show the issues arriving from Rome between January 1936 and December 1938. Each paper is here in the complete original fortnightly issue of the journal of Italy’s National Research Council, in the printed wrappers, as the Society received it. Between November 1935 and October 1938 these papers sorted the neutrons leaving a block of paraffin into groups by the sheet of cadmium that stopped one of them, and identified that group as the neutrons in thermal equilibrium with the hydrogen. They measured the four constants of their diffusion — mean free path, number of collisions, reflection coefficient, lifetime — and the probability that a proton captures one, and read the widths and energies of the resonances Bohr had just predicted. The forty-page theoretical memoir at the centre of the run derived the slowing-down calculation, the extrapolation length and the delta-function potential that still carry Fermi’s name. Fermi restated these results as the substance of his Nobel lecture in December 1938; four years later they were the working constants of the pile under the Chicago stands. The December 1935 issue also prints the text of the lecture Fermi gave at Palermo on 12 October 1935, one of his earliest published accounts in his own voice of how the paraffin discovery was made, a text his collected papers do not reprint.

The first two papers created the vocabulary. Amaldi and Fermi had been measuring the absorption of slow neutrons by one element with another element as detector, and in November 1935 they reported that a thin sheet of cadmium, about a quarter of a gram to the square centimetre, removed one component of the radiation entirely while leaving the rest almost untouched, and that each element absorbed most strongly the neutrons that activated itself. In the second letter, dated in the middle of December and in print by the end of the month, they gave the components names: the neutrons stopped by cadmium became group C, from the initial of the metal, the others groups A, B and D, distinguished by the silver and rhodium that absorbed them. Amaldi later explained that the letters were chosen precisely to say nothing: he had wanted to call the groups energy bands at once, and Fermi had refused to let a plausible interpretation into the laboratory before the data forced it. The same December letter measured how many neutrons of each group left the paraffin, found that group C was reflected back from a paraffin surface with a coefficient of about 0.8 while the others were hardly reflected at all, and showed that a group-C neutron wandered more than three centimetres through the paraffin before it was caught. The two men were working alone. Segrè had taken the chair at Palermo, Rasetti was spending the academic year at Columbia, Pontecorvo was on his way to the Joliot-Curies in Paris and D’Agostino had left for the Council’s chemistry institute; Italy was at war in Ethiopia and under the sanctions of the League of Nations; and Amaldi remembered the winter as a matter of working, in his phrase, ‘con un’ostinazione incredibile’, from eight in the morning until six or seven at night and beyond, on measurements of a few minutes that were repeated for hours and, when it was necessary, for days.

By the following June the two of them had put numbers on everything a thermal neutron does in hydrogen. The third letter, in January 1936, solved the diffusion equation for a neutron that can be captured, and measured the distance a group-C neutron diffuses before capture, two centimetres, against four millimetres for the faster groups. The fourth, in March, measured the mean free path of the thermal neutrons directly, and noticed at its close that a hydrogen atom bound in paraffin scatters a slow neutron four times more strongly than a free proton would — the chemical-binding effect that the theoretical memoir would explain. The sixth, in May, built an ionisation chamber filled with oxygen at seventy-five atmospheres to remeasure the mean free path, and reconciled four independently measured quantities at a single pair of values: a thermal neutron in paraffin travels about three millimetres between collisions, makes about a hundred and fifty of them, is reflected from a surface with an albedo of 0.82, and lives about a sixth of a millisecond before a proton absorbs it; the cross-section for that capture, 0.32 × 10⁻²⁴ cm², is within four per cent of the value in the tables today. The long report of June 1936, fifty pages under the rubric of the Council’s National Committee for Physics, gathered all of this into thirteen sections with an absolute standard of neutron intensity, and closed on the picture that every later treatment of neutron transport has kept: a neutron’s life in a moderator falls into a slowing-down phase and a thermal-diffusion phase, and the two obey different laws.

Between the third letter and the long report the interpretation Fermi had forbidden was forced on him from Copenhagen. In February 1936 Bohr proposed in Nature that a slow neutron entering a nucleus forms a compound system with closely spaced levels, so that an element absorbs strongly the neutrons whose energy matches a level; the lettered groups were resonance bands. The fifth paper, dated 13 April, six weeks after Bohr’s, opens by naming him and then measures what his model required and no one else could yet supply: the logarithmic widths of the bands for rhodium, silver and iodine, the width of the silver band as about six per cent of its energy, and the energies of the groups from the mean-square distance at which each is found in the paraffin, in the ratio 1 : 11 : 400. The June report records the verdict, that the whole body of results agrees qualitatively with Bohr and with the resonance formula of Breit and Wigner. The fifth paper closes with its printed dateline, Rome, 13 April 1936, above both names, and ends on the page after next.

The memoir of July 1936 is the paper Fermi would not translate. It opens with the rule that every collision with a hydrogen nucleus lowers the logarithm of a neutron’s energy by one unit on average, so that some twenty collisions bring a neutron from millions of volts to thermal energy, and from that rule derives the mean-square distance a neutron has travelled by the time its energy has fallen to a given value — the calculation that Fermi would later teach as the age equation. It treats the diffusion of the thermal neutrons in a one-dimensional model from which the neutron density extrapolates to zero a mean free path beyond the surface of the moderator, computes the albedo in three dimensions and matches the exact result of Wick, and in its second half turns to the collision of a neutron with a proton that is free, fixed or bound, replacing the true interaction by a point potential whose strength is fixed by a single length. Gould and Sharapov, who traced the history of that device, found that it becomes a delta function for the first time in this paper. Amaldi tried to persuade Fermi to put the memoir into English, and remembered the answer as a refusal to waste the time on it: anyone who wanted to study slow neutrons would have to read Italian. Temmer eventually translated it for the collected papers. When Gregory Breit went back over the calculation after the war he found that Fermi’s point-potential shortcut gave the scattering of slow neutrons by bound protons to within about three parts in a thousand. That shortcut, from a forty-page article in an Italian research bulletin, is still the working tool of neutron optics.

The December 1935 issue carries something the run of letters could not: Fermi telling the story. The Italian Society for the Progress of the Sciences met at Palermo in October 1935, and the issue prints the congress addresses in sequence, Fermi’s among them under the style of an Academician of Italy. He describes how the paraffin effect was noticed by chance, when pieces of lead lying near the apparatus disturbed the measurements by increasing them, how a block of paraffin raised the activity by forty per cent and surrounding everything with paraffin multiplied it forty- or fiftyfold, and how the explanation followed: a neutron’s energy is divided on average by the number e at each collision with a hydrogen nucleus, so that some twenty collisions bring it down to the energy of the thermal agitation around it. Then, in a sentence standing on its own in the middle of the page, he gives the image that carried the idea: paraffin presents itself as ‘una specie di soluzione di neutroni lenti’, a kind of solution of slow neutrons. Goldoni and Stefanini, who brought the lecture back to notice in 2025, read that sentence as the first form of the thought that led, seven years later in Chicago, from the chain reaction to a pile moderated by graphite. Towards its end the lecture ventures a prediction, for a future Fermi calls probably not distant: the neutron source will be a beam of heavy-hydrogen ions accelerated through two hundred thousand volts onto a heavy-hydrogen target. Twenty-one months later, in the July 1937 issue of this same set, Amaldi, Fermi and Rasetti describe exactly that machine, built in the physics institute’s new quarters at the Città Universitaria: a two-stage tube of two hundred kilovolts with an ion source of Oliphant’s type, an oil diffusion pump made in the laboratory to Sloan’s drawings and a target of heavy-water ice cooled with liquid air, yielding neutrons at the rate of a two-and-a-half-curie radon source, three times the strongest they had used. The lecture was printed twice, here and in the congress’s own proceedings, and then dropped from sight: Fermi’s collected papers list it as their number 111 but do not print it, and Goldoni and Stefanini record that the translation the United States Atomic Energy Commission made of it has not been traced.

That the whole programme should appear in this journal was a matter of money and of speed. The Consiglio Nazionale delle Ricerche subsidised the Rome group through its National Committee for Physics, and the June report says so in its acknowledgment; the Council’s fortnightly bulletin, whose masthead promised technical progress in the national economy, was where the Council’s grantees reported, and Segrè later said plainly that the group published everything there because it was the Council’s official journal and the Council subsidised them. The first six papers run in the letters column, between a note on the iron content of vineyard soils and one on pancreatic tissue, and were in type within a fortnight of their datelines; the three longest carry the Committee’s name as a rubric above the title. The arrangement was already dying as the papers appeared. Corbino, the group’s protector, died in January 1937 and the directorship passed over Fermi; Marconi, the Council’s president, died that July; in May 1938 the Council refused Fermi’s proposal for a national institute of radioactivity, in which he had warned that Italy, until then pre-eminent in the field, was decisively losing ground to laboratories equipped with accelerators. The racial laws of the summer of 1938 decided the rest: Laura Fermi was Jewish, the family resolved in September to leave, and the tenth paper, a two-page note of October 1938 in which Fermi and Rasetti confirm and explain an anomaly in the absorption of neutrons by iodine and boron that Michiels had reported from Imperial College in Nature at the beginning of September, is the last piece of original research Fermi published in Italy. The Nobel announcement reached him on 10 November; he collected the prize at Stockholm on 10 December and sailed for New York.

What the run contains, then, is the physics of the pile written before the pile was thinkable, and the papers say so themselves in the names they cite. The fourth reference of the June report is Leo Szilard, who had noticed the same anomaly in cadmium-filtered neutrons in London and whose observation, Amaldi and Fermi wrote, made them suspect narrow absorption bands; six years later Szilard and Fermi built the first reactor together, its control a rod of the cadmium these papers had made the standard thermal filter, and shared the patent for it. The report of the Chicago experiment defines its reproduction factor in terms of the mean free path of thermal neutrons in graphite, the mean free path for absorption and ‘the age of nascent thermal neutrons’, and records that the top and sides of the piles were covered with cadmium sheet to keep out neutrons scattered back from the surroundings — the quantities of the third, fourth and sixth letters and the memoir, transposed from paraffin to graphite. The number that made the transposition necessary is in the sixth letter: the cross-section for capture by hydrogen measured there is the quantity that decides whether water, the obvious moderator, would eat a chain reaction; when Anderson, Fermi and Szilard remeasured it at Columbia in 1939 they found the capture by hydrogen too large to trust water with the chain, and the moderator that replaced it was graphite. The lecture Fermi gave at Stockholm walks through the set in order, the twenty collisions, the rotating wheel that timed the neutrons’ residence in paraffin, the three-millimetre mean free path, the capture of a neutron by a proton through their magnetic moments, cadmium as the thermal filter, and the absorption bands below a hundred volts.

Provenance: the American Society for Testing Materials, Philadelphia, the standards body founded in 1898 and housed in these years at 260 South Broad Street, with its red three-line accession stamp on each front wrapper but two, each dated on receipt: the November 1935 issue on 9 January 1936, the December issue on 8 February, the January issue on 17 March, and so on to the October 1938 issue received on 6 December 1938, four days before Fermi stood in Stockholm. A society of engineers testing steel and cement had subscribed to the Council’s bulletin for its reports on materials and standards, and took delivery, issue by issue, of the foundations of nuclear engineering; how and when the run left the Society’s custody is not recorded, and no mark of withdrawal was added. Runs of the journal in institutional libraries were bound by the half-year and lost their wrappers in the binding; the ten issues here keep both wrappers throughout, each with its printed title-leaf and table of contents, so that the papers stand as the profession received them, between advertisements for aluminium and the Council’s own list of publications. No complete issue containing any of the ten papers has been traced at auction in more than two decades of sale records; two of the papers have appeared as loose offprints, within a mixed lot of Fermi separates, and the house that handled offprints of the same two in 2017 could trace no other copy of either, in the union catalogues or at auction.

The intellectual line from these pages runs in two directions. Bohr, cited in the fifth paper for the compound nucleus, wrote with Wheeler in 1939 The Mechanism of Nuclear Fission, the model that carried the compound nucleus, whose resonances these papers had first measured, into the theory of the splitting of the uranium nucleus by the slow neutrons these papers had characterised. Breit, in The Scattering of Slow Neutrons by Bound Protons of 1947, gave Fermi’s point potential the test that made it permanent, and the scattering length, a quantity Fermi had first written down in an atomic-physics paper of 1934 and put to work again here, is the quantity in which the physics of ultracold atoms is written today. And Fermi himself, who had told Amaldi that anyone who wanted the theory would have to read it in Italian, taught it in English at Los Alamos in 1945, chapter by chapter from the slowing-down of neutrons through the age equation to the chain reaction, to the men who were building the reactors that the paraffin had first suggested to him as a kind of solution of slow neutrons.

References: Printing and the Mind of Man 422 (the 1934–35 slow-neutron patent) — Fermi, Note e Memorie (Collected Papers), vol. I (Rome and Chicago, 1962), nos. 111–117, 118a, 119, 121, 124 — Amaldi, ‘From the discovery of the neutron to the discovery of nuclear fission,’ Physics Reports 111 (1984), pp. 1–331 — Bonolis, ‘Cronologia dell’opera scientifica di Enrico Fermi,’ in Conoscere Fermi (Società Italiana di Fisica, 2001) — Gould & Sharapov, ‘Fermi’s favorite figure: the history of the pseudopotential concept in atomic physics and neutron physics,’ European Physical Journal H 47 (2022), art. 10 — Goldoni & Stefanini, ‘Slow neutrons in Palermo: a forgotten conference by Enrico Fermi,’ arXiv:2507.16928 (2025) — Esposito & Pisanti, ‘Enrico Fermi and the physics and engineering of a nuclear pile,’ arXiv:0803.1145 (2008) — Fermi, ‘Experimental production of a divergent chain reaction,’ American Journal of Physics 20 (1952), pp. 536–558 — Segrè, ‘Fermi, Enrico,’ Dizionario Biografico degli Italiani 46 (1996) — Turchetti, ‘For slow neutrons, slow pay,’ Isis 97 (2006), pp. 1–28.

Ten complete fortnightly issues of La Ricerca Scientifica ed il progresso tecnico nell’economia nazionale (Rome, Consiglio Nazionale delle Ricerche): Anno VI, vol. II, nos. 9–10 (15–30 November 1935) and 11–12 (15–31 December 1935); Anno VII, vol. I, nos. 1–2 (January 1936), 5–6 (March), 7–8 (April), 9–10 (May) and 11–12 (June 1936), and vol. II, nos. 1–2 (July 1936); Anno VIII, vol. II, nos. 1–2 (July 1937); Anno IX, vol. II, nos. 7–8 (October 1938). The ten papers occupy pp. 344–347, 443–447, 56–59, 223–225, 310–313, 393–395, 454–503, 13–52, 40–43 and 472–473 of their issues, the Palermo lecture pp. 399–402 of the December 1935 issue; text figures, the accelerator note with a diagram of the tube and a photograph of the plant. Large 8vo (242 × 170 mm). Each issue with its printed title-leaf (masthead, Sommario) and in the original printed wrappers, front and rear present throughout; the spine strips worn, several with losses at head or foot, the front wrapper of the June 1936 issue loose and frayed at the spine, the corners of a few wrappers chipped, a few pencil marks on the wrappers. Red three-line accession stamps of the American Society for Testing Materials (‘Received … A.S.T.M.’, dated between 9 January 1936 and 6 December 1938) on eight of the ten front wrappers.

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Item #6758

Price: $6,500.00