Frisch–Peierls Memorandum
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The Frisch–Peierls memorandum was the first technical exposition of a practical
nuclear weapon A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear exp ...
. It was written by expatriate German-Jewish physicists
Otto Frisch Otto Robert Frisch (1 October 1904 – 22 September 1979) was an Austrian-born British physicist who worked on nuclear physics. With Otto Stern and Immanuel Estermann, he first measured the magnetic moment of the proton. With his aunt, Lise M ...
and
Rudolf Peierls Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied ...
in March 1940 while they were both working for Mark Oliphant at the
University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...
in Britain during
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
. The memorandum contained some of the first calculations about the size of the
critical mass In nuclear engineering, critical mass is the minimum mass of the fissile material needed for a sustained nuclear chain reaction in a particular setup. The critical mass of a fissionable material depends upon its nuclear properties (specific ...
of
fissile In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal Nuclear chain reaction#Fission chain reaction, chain reaction can only be achieved with fissil ...
material needed for an
atomic bomb A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear expl ...
. It revealed that the amount required might be small enough to incorporate into a bomb that could be delivered by air. It also anticipated the strategic and moral implications of nuclear weapons. It helped send both Britain and America down a path which led to the MAUD Committee, the
Tube Alloys Tube Alloys was the research and development programme authorised by the United Kingdom, with participation from Canada, to develop nuclear weapons during the Second World War. Starting before the Manhattan Project in the United States, the Bri ...
project, the
Manhattan Project The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada. From 1942 to 1946, the ...
, and ultimately the
atomic bombings of Hiroshima and Nagasaki On 6 and 9 August 1945, the United States detonated two atomic bombs over the Japanese cities of Hiroshima and Nagasaki, respectively, during World War II. The aerial bombings killed between 150,000 and 246,000 people, most of whom were civili ...
.


Background


Rudolf Peierls

Rudolf Peierls Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied ...
was born in
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
in 1907. He studied
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
at the
University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...
, at the
University of Munich The Ludwig Maximilian University of Munich (simply University of Munich, LMU or LMU Munich; ) is a public university, public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke ...
under
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and ...
, the
University of Leipzig Leipzig University (), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Electo ...
under
Werner Heisenberg Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II. He pub ...
, and
ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...
under
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
. After receiving his
DPhil A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
from Leipzig in 1929, he became an assistant to Pauli in Zurich. In 1932, he was awarded a Rockefeller Fellowship, which he used to study in Rome under
Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian and naturalized American physicist, renowned for being the creator of the world's first artificial nuclear reactor, the Chicago Pile-1, and a member of the Manhattan Project ...
, and then at the
Cavendish Laboratory The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the School of Physical Sciences. The laboratory was opened in 1874 on the New Museums Site as a laboratory for experimental physics and is named ...
at the
University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
under
Ralph H. Fowler Sir Ralph Howard Fowler (17 January 1889 – 28 July 1944) was an English physicist, physical chemist, and astronomer. Education Ralph H. Fowler was born at Roydon, Essex, Roydon, Essex, on 17 January 1889 to Howard Fowler, from Burnham-on-Sea, ...
. Due to
Adolf Hitler's rise to power The rise to power of Adolf Hitler, dictator of Nazi Germany from 1933 to 1945, began in the newly established Weimar Republic in September 1919, when Hitler joined the ''German Workers' Party, Deutsche Arbeiterpartei'' (DAP; German Workers' Par ...
in Germany, he elected not to return home in 1933, but to remain in Britain. He worked with
Hans Bethe Hans Albrecht Eduard Bethe (; ; July 2, 1906 – March 6, 2005) was a German-American physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics and solid-state physics, and received the Nobel Prize in Physi ...
at the
University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
, then at the Mond Laboratory at Cambridge. In 1937, Mark Oliphant, an Australian and newly appointed professor of physics at the
University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...
, recruited him for a new chair there in applied mathematics.


Otto Frisch

Otto Robert Frisch was born in
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
in 1904. He studied physics at the
University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...
, from which he received his
DPhil A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
in 1926. He worked at the Physikalisch-Technische Reichsanstalt in Berlin until 1930, when he obtained a position at the
University of Hamburg The University of Hamburg (, also referred to as UHH) is a public university, public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('':de:Allgemeines Vorlesungswesen, ...
under the
Nobel Prize The Nobel Prizes ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...
-winning scientist
Otto Stern :''Otto Stern was also the pen name of German women's rights activist Louise Otto-Peters (1819–1895)''. Otto Stern (; 17 February 1888 – 17 August 1969) was a German-American physicist. He is the second most nominated person for a Nobel Pri ...
. As non-Aryans, Stern and Frisch were dismissed after Hitler's accession. Stern found Frisch a position in Britain with Patrick Blackett at
Birkbeck College Birkbeck, University of London (formally Birkbeck College, University of London), is a public research university located in London, England, and a member institution of the University of London. Established in 1823 as the London Mechanics' ...
at the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...
, and a grant from the Academic Assistance Council. He followed this with a five-year stint at the
Niels Bohr Institute The Niels Bohr Institute () is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics, and biophysics. Overview The institute was foun ...
in
Copenhagen Copenhagen ( ) is the capital and most populous city of Denmark, with a population of 1.4 million in the Urban area of Copenhagen, urban area. The city is situated on the islands of Zealand and Amager, separated from Malmö, Sweden, by the ...
with
Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...
where he increasingly specialised in
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...
, particularly the physics of
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
s, which had been discovered by
James Chadwick Sir James Chadwick (20 October 1891 – 24 July 1974) was an English nuclear physicist who received the Nobel Prize in Physics in 1935 for his discovery of the neutron. In 1941, he wrote the final draft of the MAUD Report, which inspired t ...
in 1932. Oliphant invited Frisch to come to the University of Birmingham in the summer of 1939. When the outbreak of the
Second World War World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
in September 1939 prevented his return to Copenhagen, Oliphant found him a position at the University of Birmingham.


Nuclear fission

During the Christmas holiday in 1938, Frisch visited his aunt
Lise Meitner Elise Lise Meitner ( ; ; 7 November 1878 – 27 October 1968) was an Austrian-Swedish nuclear physicist who was instrumental in the discovery of nuclear fission. After completing her doctoral research in 1906, Meitner became the second woman ...
in
Kungälv Kungälv () is a cities of Sweden, city and the seat of Kungälv Municipality in Västra Götaland County, Sweden. It is also a part of Greater Gothenburg Metropolitan Area. It had 22,768 inhabitants in 2010. In 2021, the main Kungälv - Ytterby - ...
in Sweden, where she had relocated after Germany's annexation of Austria. While there she received the news that her former colleagues
Otto Hahn Otto Hahn (; 8 March 1879 – 28 July 1968) was a German chemist who was a pioneer in the field of radiochemistry. He is referred to as the father of nuclear chemistry and discoverer of nuclear fission, the science behind nuclear reactors and ...
and Fritz Strassmann in Berlin had discovered that the collision of a neutron with a
uranium Uranium is a chemical element; it has chemical symbol, symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Ura ...
nucleus produced
barium Barium is a chemical element; it has symbol Ba and atomic number 56. It is the fifth element in group 2 and is a soft, silvery alkaline earth metal. Because of its high chemical reactivity, barium is never found in nature as a free element. Th ...
as one of its byproducts. Frisch and Meitner hypothesized that the uranium nucleus had split in two. They estimated the energy released at around 200 MeV, and Frisch appropriated the term fission from
biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
to describe it. Hahn's paper described the experiment and the finding of the barium byproduct. Meitner and Frisch's paper, dated 16 January 1939, explained the physics behind the phenomenon. Frisch went back to Copenhagen, where he was able to isolate the fragments produced by fission reactions. Frisch later recalled that: The news of the discovery of fission was brought to America by Bohr in January 1939. Bohr and John A. Wheeler set to work applying the liquid drop model developed by Bohr and Fritz Kalckar to explain the mechanism of nuclear fission. George Placzek, who was skeptical about the whole idea of fission, challenged Bohr to explain why uranium seemed to fission with both very fast and very slow neutrons. Bohr had an epiphany that the fission at low energies was due to the
uranium-235 Uranium-235 ( or U-235) is an isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope that exists in nat ...
isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...
, while at high energies it was due mainly to the more abundant
uranium-238 Uranium-238 ( or U-238) is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, it i ...
isotope. The former makes up just 0.7% of natural uranium; while the latter accounts for 99.3%. On 16 April, Bohr, Placzek, Wheeler,
Eugene Wigner Eugene Paul Wigner (, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of th ...
and Leon Rosenfeld discussed whether it would be possible to use a
nuclear chain reaction In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series or "positive feedback loop" of thes ...
to make an
atomic bomb A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear expl ...
, and concluded that it was not. Bohr observed that "It would take the entire efforts of a country to make a bomb."


British response

In Britain, scientists also considered whether an atomic bomb was practical. At the
University of Liverpool The University of Liverpool (abbreviated UOL) is a Public university, public research university in Liverpool, England. Founded in 1881 as University College Liverpool, Victoria University (United Kingdom), Victoria University, it received Ro ...
, Chadwick and the Polish refugee scientist Joseph Rotblat tackled the problem, but their calculations were inconclusive. At Cambridge,
Nobel Prize in Physics The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
laureates George Paget Thomson and
William Lawrence Bragg Sir William Lawrence Bragg (31 March 1890 – 1 July 1971) was an Australian-born British physicist who shared the 1915 Nobel Prize in Physics with his father William Henry Bragg "for their services in the analysis of crystal structure by ...
wanted the government to take urgent action to acquire
uranium ore Uranium ore deposits are economically recoverable concentrations of uranium within Earth's crust. Uranium is one of the most common Chemical element, elements in Earth's crust, being 40 times more common than silver and 500 times more common than ...
to keep it out of German hands. The Secretary of the Committee for Imperial Defence, Major General Hastings Ismay asked Sir
Henry Tizard Sir Henry Thomas Tizard (23 August 1885 – 9 October 1959) was an English chemist, inventor and Rector of Imperial College, who developed the modern "octane rating" used to classify petrol, helped develop radar in World War II, and led the fir ...
for an opinion. Tizard was sceptical of the likelihood of an atomic bomb being developed, reckoning the odds of success at 100,000 to 1. Even at such long odds, the danger was sufficiently great to be taken seriously. It was not considered worthwhile to immediately acquire the uranium, but Tizard's Committee on the Scientific Survey of Air Defence was directed to conduct research into the feasibility of atomic bombs. Thomson, at
Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...
, and Oliphant, at the University of Birmingham, were tasked with carrying out a series of experiments on uranium. By February 1940, Thomson's team had failed to create a chain reaction in natural uranium, and he had decided that it was not worth pursuing.


Memorandum

As enemy aliens, at least until Peierls'
naturalisation Naturalization (or naturalisation) is the legal act or process by which a non-national of a country acquires the nationality of that country after birth. The definition of naturalization by the International Organization for Migration of the ...
papers came through in February 1940, Frisch and Peierls were excluded from the most important—and secret—war work being done by Oliphant's team at Birmingham, that on
radar Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
. However, Oliphant would ask Peierls a theoretical question about, say, the solution to
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
in a hemispheric cavity. Peierls knew that questions of this nature related to the work on microwave radar, and Oliphant was doubtless aware of this too, but the façade of secrecy was maintained. The nuclear investigation was not yet secret, so Frisch was available to work on it. He began experimenting with
uranium enrichment Enriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (23 ...
through thermal diffusion, a process first demonstrated in Germany by Klaus Clusius. Progress was slow; the required equipment was not available, and the radar project had first call on the available resources. Francis Perrin had defined a
critical mass In nuclear engineering, critical mass is the minimum mass of the fissile material needed for a sustained nuclear chain reaction in a particular setup. The critical mass of a fissionable material depends upon its nuclear properties (specific ...
of uranium to be the smallest amount that could sustain a chain reaction. He calculated the value for triuranium octoxide with natural isotopic ratio i.e. unenriched. However, he greatly overestimated the "average number of neutrons produced per fission" value for natural uranium at 3, compared to a modern value of 1.18 due to absorption. This yielded a critical mass of about . He reckoned that if a
neutron reflector A neutron reflector is any material that reflects neutrons. This refers to elastic scattering rather than to a specular reflection. The material may be graphite, beryllium, steel, tungsten carbide, gold, or other materials. A neutron reflect ...
were placed around it of materials such as iron or lead which did not greatly impede fast neutrons, this might be reduced to . Peierls also attempted to simplify the problem by using the fast neutrons produced by fission, thus omitting consideration of moderator. He then calculated the critical mass of a sphere of uranium metal in a theoretical paper written in 1939. He later recalled that the size of the critical mass "was of the order of tons. It therefore appeared to me that the paper had no relevance to a nuclear weapon." However, Bohr had argued that the uranium-235 isotope was far more likely to capture neutrons, so fissile even using neutrons of low energy. Frisch wondered what would happen if he were able to produce a sphere of pure uranium-235. When he used Peierls' formula to calculate this, he received a startling answer. Peierls later observed that: Realising the sensitive nature of the document, Peierls typed it himself. One carbon copy was made. Today the original is in the
Bodleian Library The Bodleian Library () is the main research library of the University of Oxford. Founded in 1602 by Sir Thomas Bodley, it is one of the oldest libraries in Europe. With over 13 million printed items, it is the second-largest library in ...
at
Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...
.


Non-technical

The memorandum was written in two parts. The first was an elegant and comprehensive outline of the implications of their calculations. It included a proposal that the best defence against such a weapon would be to develop one before Germany did so. In a few short pages these two scientists anticipated the policies of deterrence which would shape
Cold War The Cold War was a period of global Geopolitics, geopolitical rivalry between the United States (US) and the Soviet Union (USSR) and their respective allies, the capitalist Western Bloc and communist Eastern Bloc, which lasted from 1947 unt ...
geopolitics Geopolitics () is the study of the effects of Earth's geography on politics and international relations. Geopolitics usually refers to countries and relations between them, it may also focus on two other kinds of State (polity), states: ''de fac ...
. The second was an explanation of the science supporting their conclusions. The memorandum opens with: This section also contains an early description of the possibility of fizzles caused by predetonation, and dismisses concerns about enemy reverse engineering as even such fizzles would destroy the weapon.


Calculations

Peierls' starting point was a paper by Francis Perrin, in which he had derived
critical mass In nuclear engineering, critical mass is the minimum mass of the fissile material needed for a sustained nuclear chain reaction in a particular setup. The critical mass of a fissionable material depends upon its nuclear properties (specific ...
calculations in terms of nuclear constants. The physicists considered a sphere, which has the minimum surface area for a given volume. A critical mass occurs when the number of neutrons produced equals the number that escape. Perrin assumed that the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
was much larger than the radius of the sphere. Peierls did not agree, and commenced his own calculations. A key insight came from Frisch, who wondered what would happen if, instead of natural uranium, a sphere of the uranium-235 isotope was used. By definition, the mean free path is: :\ell = 1/\sigma n , where is the mean free path, is the number of target particles per unit volume, and is the effective fission cross section area. Peierls did not perform the calculation, leaving this task to Frisch. The chemistry of uranium was not well known at the time, and Frisch believed that its density was ; the true value is approximately . The fission cross section value was more problematic. For this, Frisch turned to a 1939 ''Nature'' article by L. A. Goldstein, A. Rogozinski and R. J. Walen at the Radium Institute in Paris, who gave a value of . This was too large by an
order of magnitude In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are ...
; a modern value is about . Using the values he had, Frisch calculated the value of the mean free path for uranium-235 using the
Avogadro constant The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where th ...
: :\ell = 1 / (1 \times 10^\ \mathrm)(15\ \mathrm)(6 \times 10^\ \mathrm / 235\ \mathrm) = 235/90\ \mathrm = 2.6\ \mathrm . Peierls and Frisch claimed that the critical radius was about 0.8 times the mean free path. From this, Frisch could calculate the volume of the sphere from the well-known equation: :V = \frac\pi r^3 = \frac\pi (2.6 \times 0.8\ \mathrm)^3 \approx 38\ \mathrm . The mass then comes out to be: :38\ \mathrm \times 15 \mathrm = 570\ \mathrm \approx 600\ \mathrm . Frisch and Peierls then considered the speed of a uranium fission chain reaction, exponential in nature, where "''τ'' is the time required for the neutron density to multiply by a factor ''e''." The available data was very approximate, but their central point – that a bomb was possible using fast (~2 MeV) neutrons – remains. Jeremy Bernstein remarked of this effort: "Let me make the same point by asking a somewhat different question but using the correct numbers. How much time does it take to fission a kilogram of 235U using fast neutrons?" Using modern values he found that to be "equal to about a microsecond, which makes the point about the rapidity of fission with fact icneutrons". In the original memorandum, if the neutrons had velocities of 109 cm/s, then they would have an average time between fission collisions of . Therefore, Bernstein's time for a kilogram of uranium-235 to fission is found by solving: :1000 \times (6 \times 10^ /\ 235) = e ^ , where was the mean time for fission neutron density to increase by ''e''. Given the doubling time :t^ = 2.6 \times 10^ \mathrm , this implied a mean fission exponential folding time of :\tau = t^ / ln(2) \approx 4.0 \times 10^\ \mathrm . This led to a calculation of the energy released, which Peierls reckoned as approximately: : E = 0.2 M (r^2/\tau^2) (\sqrt - 1) , where ''M'' is the mass of the sphere, ''r'' is the radius, and ''r''0 is the critical mass radius. The conclusion drawn was that a few kilograms would explode with the energy of thousands of tons of dynamite.


Inaccuracies

In a 1967 interview, Frisch described the selection of the Radium Institute's fission cross section value, and thus low critical mass and radius, as an intentional overestimate: Additionally, they assumed the complete bomb assembly to rely on triggering via
cosmic rays Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar ...
. This was thought to be the inevitable activation method of bombs and critical-state reactors, as the discovery of
spontaneous fission Spontaneous fission (SF) is a form of radioactive decay in which a heavy atomic nucleus splits into two or more lighter nuclei. In contrast to induced fission, there is no inciting particle to trigger the decay; it is a purely probabilistic proc ...
in uranium would only be made later in July 1940.


Influence

The memorandum was given to Oliphant, who passed it on to Tizard in his capacity as the chairman of the Committee for the Scientific Survey of Air Warfare (CSSAW). He in turn passed it to Thomson, the chairman of the committee to which the CSSAW had delegated responsibility for uranium research. Thomson's committee was about to disband. It had studied nuclear reactions in uranium, and the use of
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
as a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, ideally without capturing any, leaving them as thermal neutrons with only minimal (thermal) kinetic energy. These thermal neutrons are immensely ...
in a
nuclear reactor A nuclear reactor is a device used to initiate and control a Nuclear fission, fission nuclear chain reaction. They are used for Nuclear power, commercial electricity, nuclear marine propulsion, marine propulsion, Weapons-grade plutonium, weapons ...
, but its results had been negative, and it had concluded that the rate of capture of neutrons by the graphite was too great to make such a reactor a practical proposition. The Frisch–Peierls memorandum caused Thomson to reconsider. After discussions between Cockcroft, Oliphant and Thomson, CSSAW created the MAUD Committee to investigate further. As enemy aliens, Peierls and Frisch were initially excluded from its deliberations, but they were later added to its technical subcommittee. The research from the MAUD committee was compiled in two reports, commonly known as the MAUD reports in July 1941. The first report, "Use of Uranium for a Bomb", discussed the feasibility of creating a super-bomb from uranium, which they now thought to be real. The second, "Use of Uranium as a Source of Power" discussed the idea of using uranium as a source of power, not just a bomb. The MAUD Committee and report helped bring about the British nuclear program, the
Tube Alloys Tube Alloys was the research and development programme authorised by the United Kingdom, with participation from Canada, to develop nuclear weapons during the Second World War. Starting before the Manhattan Project in the United States, the Bri ...
project. Not only did it help start a nuclear project in Britain but it helped jump-start the American project. Without the help of the MAUD Committee the American program, the
Manhattan Project The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada. From 1942 to 1946, the ...
, would have started months behind. Instead they were able to begin thinking about how to create a bomb, not whether it was possible. Historian Margaret Gowing noted that "events that change a time scale by only a few months can nevertheless change history." In August 1941, Oliphant was sent to the US to assist the Americans with microwave radar. He took the initiative to enlighten the scientific community there of the ground-breaking discoveries of the MAUD Committee. He travelled to Berkeley to meet with his friend
Ernest Lawrence Ernest Orlando Lawrence (August 8, 1901 – August 27, 1958) was an American accelerator physicist who received the Nobel Prize in Physics in 1939 for his invention of the cyclotron. He is known for his work on uranium-isotope separation for ...
, who soon caught his enthusiasm. Oliphant convinced the Americans to move forward with nuclear weapons, and his lobbying resulted in
Vannevar Bush Vannevar Bush ( ; March 11, 1890 – June 28, 1974) was an American engineer, inventor and science administrator, who during World War II, World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almo ...
taking the report directly to the president. Leo Szilard later wrote: "if Congress knew the true history of the atomic energy project, I have no doubt but that it would create a special medal to be given to meddling foreigners for distinguished services, and that Dr Oliphant would be the first to receive one."


Notes


References

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External links


Memorandum on the Properties of a Radioactive "Super-bomb"
:* Enclosure
On the Construction of a "Super-bomb" based on a Nuclear Chain Reaction in Uranium
{{DEFAULTSORT:Frisch-Peierls memorandum Nuclear history of the United Kingdom Science and technology during World War II Classified documents World War II documents 1940 documents Memoranda Collection of the National Archives (United Kingdom)