Fission and Chain Decay of Uranium

Ya. B. Zeldovich and Yu. B. Khariton, Leningrad

1. BASIC PHENOMENA

A careful radiochemical analysis of the radioactive elements formed as a result of the irradiation of uranium and thorium by neutrons led, as is known, Hahn and Strassmann,^1 in clarifying a number of interesting features discovered by Curie and Savitch,^2 to a remarkable result. They were able to prove beyond doubt that one of the products obtained when uranium is irradiated with neutrons is barium, whereas, according to the scheme generally accepted at that time, proposed by Fermi and his collaborators,^3 transuranium elements should have been formed under these conditions.

Proceeding from the facts described in the cited works, Meitner and Frisch^4 suggested that, as a result of the capture of a neutron by the nucleus of uranium or thorium, what occurs is not the emission of a β-particle, as Fermi^3 had assumed, but the fission (or splitting) of the compound nucleus into two approximately equal parts. On the basis of Bohr’s theory of heavy nuclei,^5 they present the mechanism of fission in the following way. Because of their large charge, the surface energy^6 of heavy nuclei will, as a very rough calculation shows, be quite small. It is therefore possible that the uranium nucleus is not very stable with respect to changes of shape, and that, as a result of the onset of oscillations of the nucleus excited upon neutron capture, it may split into two nuclei of approximately equal size. The electrostatic repulsion of these two nuclei will cause them to receive kinetic energy of the order of 200 MeV. A value of the same order may be obtained if, for the calculation, one uses the values of the mass defects of uranium and of elements from the middle part of the periodic system.

Experimental confirmation of this supposition was published by Frisch^7 in the English journal Nature of 18/II 1939 (the note—a letter to the editor—was dated 16 I). In an ionization chamber coated inside with a layer of uranium and irradiated with neutrons from a 300 mCu radium-beryllium source, powerful ionization pulses appeared. A linear amplifier connected

to the chamber, was in turn connected to a thyratron, adjusted so that it responded only to pulses corresponding to no fewer than \(5\cdot 10^5\) ion pairs. When the source was placed at a distance of \(1\ \text{cm}\) from the chamber, the number of pulses was about 15 per minute.

Surrounding the neutron source, placed at a distance of \(4\ \text{cm}\) from the chamber, with paraffin doubled the effect.

By changing the adjustment of the thyratron it was possible to establish that the largest pulses corresponded to approximately two million ion pairs, for a path length of the ionizing particle equivalent to no more than \(0.8\ \text{cm}\) of air. Assuming a reasonable relation between atomic weight and effective charge, these figures give for the atomic weight of the fragment a value not less than 70.

Similar results were obtained with thorium. In this case, however, surrounding with paraffin did not increase the effect but, on the contrary, slightly diminished it.

Frisch notes yet another experiment proposed by Meitner, which it was intended to carry out in the near future: on a metal plate placed in front of a layer of uranium bombarded by neutrons, an active deposit of light atoms formed in the fission of uranium should be obtained.

Almost simultaneously with the papers of Meitner and Frisch, a paper similar in content by Joliot appeared.^8 This work was reported at a meeting of the French Academy of Sciences on 30/I 1939. The argument proceeds from the same experimental facts. Joliot gives the following possible fission scheme:

\[ {}^{233}_{92}\mathrm{U}+{}^{1}_{0}n={}^{93}_{37}\mathrm{Rb}+{}^{141}_{55}\mathrm{Cs}. \]

From fragments having a considerable excess of neutrons in comparison with stable nuclei of the same atomic number, as a result of a series of \(\beta\)-emissions, one may expect the final products to be \({}^{141}_{59}\mathrm{Pr}\) and \({}^{93}_{42}\mathrm{Mo}\).

Joliot’s experiment was carried out as follows. A neutron source (700 mCu of radon with beryllium) was placed inside a brass cylinder \(20\ \text{mm}\) in diameter and \(5\ \text{cm}\) high; a layer of uranium oxide was applied to the outer surface of the cylinder. All this was placed in a bakelite cylinder with an internal diameter of \(26\ \text{mm}\). When either the neutron source or the cylinder coated with uranium oxide was placed separately inside the bakelite cylinder, no activity was detected on the surface (of course, the inner surface) of the bakelite. Their combined action, however, resulted in the appearance of activity on the bakelite. By placing between the surface of the brass and the bakelite a layer of mica with different stopping powers, it was possible to verify that the range in air of the particles ejected from the uranium was about \(3\ \text{cm}\).

Knowing the amount of uranium oxide applied to the brass cylinder, the intensity of the neutron source, and the magnitude of the activity appearing on the bakelite, it was possible to estimate the effective cross section

of a uranium nucleus for neutrons causing the fission process. It proved to be of the order of \(10^{-25}\ \text{cm}^2\).

Joliot observed similar phenomena also in the case of thorium. The fission of heavy nuclei under neutron irradiation was also confirmed by Jentschke and Prankl\(^9\), Droste, and Thibaud and Moussa\(^ {11}\).

It should be noted that the possibility of fission of heavy nuclei had been indicated, on the basis of general considerations regarding the stability of various nuclei, by Ida Noddack\(^ {12}\) as early as 1934. However, her remark went unnoticed; none of the experimentalists attempted—or, if anyone did, then apparently without success—to find the phenomenon she had predicted.

Bohr, who at the beginning of 1939 was in America, was informed by telephone of the interpretation of the data of the Hahn–Strassmann experiments proposed by Meitner and Frisch, and acquainted American physicists with this idea. Within a few days, experiments were carried out in a number of American laboratories possessing powerful neutron sources; these likewise confirmed the hypothesis of Meitner and Frisch and revealed some essential details of the phenomenon.

Roberts, Meyer, and Hafstad\(^ {13}\), working with neutrons from a lithium target bombarded by deuterium ions of energy \(1\ \text{MeV}\), and using an ionization chamber to detect the decay products, obtained a positive result for uranium and thorium; for bismuth and lead, thallium, mercury, gold, tin, and silver the effect was at least a thousand times weaker than for uranium. Under the action of \(\gamma\)-rays (\(3\ \mu\text{A}\) of protons of energy \(1\ \text{MeV}\), bombarding a target containing lithium or fluorine), no fission was observed.

By surrounding uranium or thorium with paraffin to slow down the bombarding neutrons, and by using a cadmium screen (which, as is known, absorbs slow neutrons) to exclude slow neutrons, Roberts, Meyer, and Hafstad showed that in the case of uranium fission can occur either under the action of fast neutrons (with a limiting energy not less than \(0.5\ \text{MeV}\), but less than \(2.5\ \text{MeV}\)), or under the action of slow neutrons. In the case of thorium, however, only fast neutrons can cause disintegration.

Similar results were obtained by Fowler and Dodson\(^ {14}\), and also by Green and Alvarez\(^ {15}\). The latter also showed that no more than \(3\cdot 10^{-3}\ \text{s}\) elapses between the moment at which neutrons enter uranium and the moment at which fission occurs.

Abelson\(^ {16}\) showed, using chemical methods and analysis of the emitted X-rays, that iodine is present among the products of irradiation of uranium by neutrons—this also confirms the correctness of the fission hypothesis. Fezer\(^ {17}\), having observed an asymmetry in the distribution of the fragments, showed that between the moment at which the neutron enters the uranium nucleus and the moment of fission there elapses a time shorter than that required for the nucleus, acquiring a certain velocity as a result of capture of the fast neutron that caused the fission, to be slowed down, i.e., no more than \(10^{-12}\ \text{s}\).

D. Corson and R. Thornton^18 observed the fission of uranium in a Wilson chamber containing a mixture of air and vapors of alcohol and water at a total pressure of 15 cm Hg. Uranium in the form of UO₃ was placed in the chamber on thin films of collodion. In the stereoscopic photograph reproduced in the article by Corson and Thornton (Fig. 1), it is noticeable that, as a result of fission, two strongly ionizing particles flew out in opposite directions. The photograph is very interesting because of the presence of a fork (near the lower end of the track), which makes it possible to estimate the mass of the fragment produced in fission. The density of the lateral branch of the fork is so great that it cannot have been caused by a proton and, consequently, is the track of a carbon, nitrogen, or oxygen ion. The fact that the main branch of the fork is practically not deflected from the initial direction leads to a value of the fragment mass not less than 75.

In some photographs there seemed to be more than two particles; however, the authors do not consider the material sufficiently reliable.

The investigation of the fission process in a Wilson chamber was also carried out by Perfilov^19. In one of the photographs he found a fork which cannot be ascribed to the elastic collision of two particles, since the branch of the fork makes an angle of more than 90° with the main track. The author points out that, perhaps, what we have here is a further fission of the fragment itself.

Fig. 1
Photograph by D. Corson and R. Thornton

Zhdanov, Mysovskii, and Mysovskaya^20 observed the fission of uranium by means of tracks produced by fragments in a special photographic emulsion.

It may be assumed that fission events may proceed nonuniformly, i.e., that the masses and charges of the fragments obtained from uranium may vary within certain limits. E. McMillan^21 made an attempt to separate the various possible types of fragments, using the possible difference in ranges. In front of uranium irradiated with neutrons were placed several layers of thin cigarette paper (the air equivalent of one layer was about 1 cm). After exposure, activity was detected in the first three layers of paper. The curves of the change of activity with time for the second and third layers proved to be identical within the accuracy of the experiment. The activity of the irradiated uranium itself, however, was substantially different; in it there was strong activity with a half-life of 25 min., corresponding, as McMillan believes, to an isotope of uranium forming—

... occur in the resonant capture of a neutron by uranium[^22]. An activity with a period of about two days was likewise detected.

Thus, during the first months of 1939, in a number of laboratories the correctness of the hypothesis of the fission of uranium and thorium nuclei under the action of neutrons was established beyond doubt, and the principal characteristics of this process were clarified.

Somewhat later (July 1939), Grosse, Booth, and Dunning[^23] investigated the behavior of protactinium under neutron bombardment and, just as in the case of thorium, found the presence of fission only by fast neutrons.

We shall give here numerical values characterizing the physical phenomena associated with the process of uranium fission (methods for determining a number of these quantities will be set forth below).

The energy of the fragments (total) proved, in accordance with theoretical ideas, to be about 150–200 MeV.

The fission cross section for radon–beryllium neutrons is \(\sim 0.1 \cdot 10^{-24}\ \mathrm{cm}^2\)[^8],[^24]. For monochromatic neutrons with an energy of 2.4 MeV, the fission cross section of uranium is \(0.5 \cdot 10^{-24}\ \mathrm{cm}^2\) (for thorium, \(0.1 \cdot 10^{-24}\ \mathrm{cm}^2\))[^25].

The fission cross section of uranium for thermal neutrons is \(2 \cdot 10^{-24}\ \mathrm{cm}^2\)[^24]. The radiative-capture cross section of uranium for thermal neutrons (with formation of \(U^{239}\) and subsequent \(\beta\)-emission with formation of eka-rhenium) is \((1.3 \pm 0.45)\cdot 10^{-24}\ \mathrm{cm}^2\)[^26] or \(1.2\cdot 10^{-24}\ \mathrm{cm}^2\)[^65] (the error is not indicated).

The energy of the neutrons (relative to the fragment of the nucleus from which the neutron was emitted) released in the fission of a uranium nucleus under the action of slow neutrons is \(\sim 2\) MeV[^61]. Since a neutron may be emitted at any angle to the direction of motion of the nuclear fragment, the neutron energies lie within the limits from 1 to 3 MeV[^61].

The number of neutrons emitted in a fission event resulting from the capture of a slow neutron is characterized by the following figures: \(3.5 \pm 0.7\)[^62], \(2.3\)[^61], \(2.4\)[^64].

Both the energy and the number of neutrons emitted in a fission event caused by a fast neutron have not been determined with any precision, although fairly detailed investigations have been carried out in this direction[^27].

2. MECHANISM OF FISSION

The general theory of phenomena occurring in heavy nuclei upon interaction with neutrons was given by Bohr[^28] and by Bohr and Wheeler[^29]. The theory of fission proper was also independently developed by Frenkel[^30] and by Flügge and Droste[^31]. In the present section we shall confine ourselves to setting forth the qualitative side of the question.

Bohr considers the process of nuclear fission, like the earlier known nuclear reactions, as proceeding in two stages. “First, from uranium and a neutron a compound nucleus is formed, in which the energy associated with the capture of the neutron is in a form resembling the thermal motion of a liquid or a solid. The second stage ...”

is either the emission of this energy or else its transition into such a form as can lead to the disintegration of the compound nucleus. In the case of ordinary reactions, consisting in the emission of a proton, neutron, or $\alpha$-particle, we are dealing with the concentration of a considerable part of the excitation energy on one of the particles located near the surface, which is similar to the evaporation of molecules from a drop of liquid. In the case of the phenomenon of fission, a considerable part of the energy must pass into a special kind of motion of the entire nucleus as a whole, producing such a deformation of the nuclear surface as may lead to the rupture of the nucleus “in the manner of the formation of two drops of liquid from one” (quotation from $^{28}$). Bohr shows that, for sufficiently large nuclear charges, the probability of fission is indeed of the same order as the probability of emission (radiative capture of a neutron) or the probability of reverse evaporation of a neutron (equivalent to inelastic scattering of a neutron).

Bohr believes that the entire complex set of phenomena observed in the bombardment of uranium (or thorium) by neutrons reduces to two basic processes: radiative capture of a neutron, leading to the formation of a $\beta$-radioactive isotope of uranium, and fission, which may proceed along various paths, i.e., with the formation of fragments having different masses and charges.

Meitner, Hahn, and Strassmann$^{22}$ showed that, in the case of uranium and thorium, neutron capture with the formation of a radioactive isotope has a resonance character. Uranium has been studied more thoroughly in this respect; for it the resonance energy of the neutrons is approximately $25\ \mathrm{eV}$. Near the resonance, the effective cross section of uranium for neutron capture is approximately $10^{-21}\ \mathrm{cm}^2$; this number makes it possible to ascribe radiative neutron capture only to the principal isotope of uranium (with atomic weight 238), since the light isotope, whose abundance is $0.007$, would, in order to provide an effective cross section of $10^{-21}\ \mathrm{cm}^2$, have to possess a cross section exceeding the upper limit allowed by theory. Since, however, the increased capture of neutrons near $25\ \mathrm{eV}$ does not entail an increase in the number of fissions, it may be asserted that for the excited nucleus $^{239}_{92}\mathrm{U}$ produced in this case the probability of emission is considerably higher than the probability of fission. The unexcited nucleus $^{239}_{92}\mathrm{U}$ obtained after emission is unstable only with respect to $\beta$-decay (as a result of which the only “surviving” transuranium, Eka-Re$_{93}^{239}$, is obtained).

In the capture of fast neutrons, for both uranium and thorium the probability of fission, increasing (according to Bohr’s ideas) with increasing excitation energy faster than the probability of emission, reaches sufficiently large values. The cross sections for fast neutrons, according to the theory, should be of the order of nuclear dimensions, which is in fact observed.

There remains the question of the nature of fission under the action of slow neutrons. Bohr assumes that this process is due to the capture of slow neutrons by uranium of mass 235. The fact that the products

decay under the action of slow neutrons are the same as in the case of fast ones is explained by the possibility of obtaining a whole spectrum of fragments both from \(U_{92}^{239}\) and from \(U_{92}^{235}\). Since the binding energy of a neutron in a nucleus with an even atomic number is considerably greater in the case of an even atomic weight than in the case of an odd one, the excitation energies of the compound nucleus \(U_{92}^{236}\) are considerably greater than those of \(U_{92}^{239}\). Therefore even slow neutrons can provide a large probability of fission (as compared with the probability of emission). Owing to the large probability of decay, a spreading of the levels will occur, whose density will be very large because of the high excitation energy. Even a continuous spectrum may occur. As a result, the cross section for the capture of slow neutrons (leading to fission) will be inversely proportional to the velocity, which is also observed experimentally\(^{24}\). Correspondingly, at “intermediate” neutron energies (from 1 to \(10^6\) eV), fission will not be observed, since for isotope 235 their velocity will be too large, and for isotope 238 too small.

3. FISSION PRODUCTS OF URANIUM AND THORIUM

As a result of the work of Hahn and Strassmann\(^{1}\) and the subsequent discovery of uranium fission\(^{4,7,8}\), the schemes proposed by Hahn and Strassmann themselves together with Meitner for artificial radioactive families—transuraniums arising under neutron bombardment of uranium\(^{22}\)—were completely swept away. It became obvious that all the accumulated material had to be reconsidered in the light of the new fact—the fission of heavy nuclei—and further investigations were directed toward the detection of elements from the middle part of the periodic system of elements.

The fact that substances thought to be “transuraniums” are in reality representatives of the middle of the periodic system was demonstrated very clearly by Meitner and Frisch\(^{32}\). They showed that the radioelement extracted from irradiated uranium together with platinum coincides, in its decay time, with the radioelement extracted by them with the same platinum from water over which, at a distance of 1 mm, the irradiated layer of uranium had been placed. Consequently, the “transuraniums” are produced in the fission of the uranium nucleus, since neutron capture itself, with emission of a light particle, could not impart to the nucleus enough energy to carry it from the irradiated layer through the air into the water.

Khlopin, Passvik-Khlopina, and Volkov\(^{33}\) found a certain difference in the character of the decay of fragments collected on the surface of glass (after extraction with platinum) and of the same kind of precipitate obtained directly from irradiated uranium. In the first case, after 30–40 hours a complete drop in activity is observed; in the second, after this time, activity with a long decay period, about 70 hours, is observed.

A number of essential data on the nature of the fission products were obtained by Abelson\(^{34}\). Along with chemical separation Abelson

For identification of the nature of the carriers of the activity, he made use of the possibility of observing the X-rays emitted by them. Before the discovery of uranium fission, Abelson supposed that the radiation he observed was the $L$-rays of “trans-uranium,” with a decay period of 72 hours. Some discrepancies in the values of the absorption coefficient of this radiation were attributed to unsatisfactory geometrical conditions of measurement.

Having reviewed and refined the method in connection with the discovery of uranium fission, Abelson first established with complete certainty that the radiation he observed corresponds to the $K$-group of iodine. Further analysis revealed the presence of a number of radioactive isotopes of antimony, tellurium, and iodine.

Let us consider the path by which the genetic relationships in one of the “families” obtained by Abelson were clarified. After irradiation, an active precipitate with tellurium was separated from uranium. After a week (during which all telluriums with short periods had practically completely decayed), tellurium was separated from the precipitate. The activity of this tellurium increased over approximately 10 hours after separation, which indicates the formation of a daughter substance with a period of about 2.5 hours, which, judging by all chemical properties and by the X-rays, is iodine. An accurate measurement of the decay time of this iodine, obtained from long-period tellurium, gave a value of 2.4 hours. For the tellurium itself a half-life of 77 hours was obtained, which corresponds to the period of 66 hours described by Meitner, Hahn, and Strassmann^22. The difference is apparently connected with the presence of active tellurium with a half-life of 30 hours, which noticeably distorts the decay curve during the first two or three days. According to Meitner, Hahn, and Strassmann^22, the substance with a half-life of 66(77) hours is obtained from a substance with a half-life of 59 min. Abelson, carrying out a series of tellurium separations from irradiated uranium at 10-minute intervals (100 mg of tellurium was introduced into the solution for each separation) and measuring the activity of the precipitates obtained, found a very strong decrease in the activity of the subsequent precipitates in comparison with the preceding ones, by approximately a factor of 3.5. It follows from this that the 77-hour tellurium is produced from approximately 5-minute antimony (or else from 5-minute tin and antimony with an even shorter period). Since among the products formed in uranium there is 5-minute antimony, it is probably the precursor of the 77-hour tellurium.

Abelson supposes that the 2.4-hour iodine is transformed into one of the stable isotopes of xenon with atomic weight 132, 134, or 136. In the case of this antimony–tellurium–iodine–xenon family considered by us, it is not possible to make an exact identification, i.e., to determine, along with the atomic numbers, the atomic weights. In some other cases, however (70-minute and 10-hour tellurium and 8-day iodine), it is possible to determine the atomic weight as well, namely when data are available on artificially radioactive isotopes of the corresponding elements obtained by irradiation with slow neutrons. •

We present a summary of Abelson’s data on the radioactive isotopes of antimony, tellurium, and iodine discovered among the products of uranium fission.

¹) Isomers.

By a similar method, Feather and Bretscher^35 detected iodine in fission products.

Khlopin, Passvik-Khlopina, and Volkov^36 obtained for the half-periods of iodine the values 3.7 and 28 hr. The authors believe that the difference between their figures and the figures obtained by other authors is due to the fact that they (Khlopin et al.) used more refined methods for separating the halides. For tellurium, Khlopin, Passvik-Khlopina, and Volkov^37 obtained a half-period of 56 hr. (Abelson—77 hr.).

Hahn and Strassmann further showed^38 that the 66-hour substance in fact consists of two substances, namely, in addition to tellurium there is also 66-hour molybdenum. This molybdenum is apparently identical with the molybdenum obtained by Seaborg and Segrè^39 by irradiating molybdenum with slow neutrons.

Hahn and Strassmann^40 discovered isotopes of strontium among the decay products, as well as noble gases. In particular, the presence of xenon is indicated by the fact that, when air was blown through an irradiated vessel containing a solution of uranium salt into a cooled vessel with an absorbing substance, through which the air then passed, active isotopes of cesium were detected.

Heyn, Aten, and Bakker^41, by a similar method, found an isotope of rubidium with a half-period of \(16 \pm 2\) min., which makes it necessary to assume the presence of krypton among the products of uranium fission. Krypton with a half-period of 3 hours, transforming into an 18-minute isotope of rubidium, was also found by Langsdorf^42 among the products of thorium fission. Since an 18-minute half-period appears in neutron bombardment of rubidium^43, and since krypton with atomic weight 86 is stable, the 18-minute half-period should apparently be assigned to an isotope of rubidium with atomic weight 88, and not 86. Three-hour krypton was also observed in fission products by Hahn and Strassmann^44. Heyn, Aten, and Bakker^41 found that xenon has a half-period of about 1 min., and established that 12-minute barium is obtained only from primary fragments and not from the gas. This indicates that 12-minute barium either is a primary product of fission, or is formed from an extremely rapidly decaying xenon, or else is formed from cesium produced directly in fission and not from xenon.

On the basis of the indicated facts, Hahn and Strassmann^45 consider that one of the possible fission schemes is the following:

\[ \mathrm{U}_{92}+n_0=\mathrm{Kr}^{88}_{36}+\mathrm{Ba}_{56}, \]

\[ \mathrm{Kr}^{88}_{36}\xrightarrow[\text{3 hours}]{\beta}\mathrm{Rb}^{88}_{37} \xrightarrow[\text{17 min.}]{\beta}\mathrm{Sr}^{88}_{38}, \]

\[ \mathrm{Ba}_{56}\xrightarrow[\text{14 min.}]{\beta}\mathrm{La}_{57} \xrightarrow[\sim 2.5\ \text{hours}]{\beta}\mathrm{Ce}_{58}. \]

We shall also give, without entering into a detailed examination of the sources, the most probable schemes of the families encountered among the products of uranium fission (according to Hahn and Strassmann^45):

\[ \mathrm{Xe}^{139}_{54}\xrightarrow[?]{\beta}\mathrm{Cs}^{139}_{55} \xrightarrow[\text{6 min.}]{\beta}\mathrm{Ba}^{139}_{56} \xrightarrow[\text{86 min.}]{\beta}\mathrm{La}^{139}_{57}, \]

\[ \mathrm{Xe}_{54}\xrightarrow[\sim 15\ \text{min.}]{\beta}\mathrm{Cs}_{55} \xrightarrow[\text{33 min.}]{\beta}\mathrm{Ba}_{56} \xrightarrow[\text{300 hours}]{\beta}\mathrm{La}_{57} \xrightarrow[\sim 36\ \text{hours}]{\beta}\mathrm{Ce}_{58}, \]

\[ \mathrm{Sr}_{38}\xrightarrow[\text{7 min.}]{\beta}\mathrm{Y}_{39}, \]

\[ \mathrm{Kr}_{36}\xrightarrow[\text{very short}]{\beta}\mathrm{Rb}_{37} \xrightarrow[\text{80 sec.}]{\beta}\mathrm{Sr}_{38} \xrightarrow[\text{6 hours}]{\beta}\mathrm{Y}_{39} \xrightarrow[\text{3.5 hours}]{\beta}\mathrm{Zr}?, \]

\[ \mathrm{Kr}^{88}_{36}\xrightarrow[\text{3 hours}]{\beta}\mathrm{Rb}^{88}_{37} \xrightarrow[\text{17 min.}]{\beta}\mathrm{Sr}^{88}_{38}. \]

Thibaud and Moussa^46, Dodson and Fowler^47, Bretscher and Cook^48, Hahn and Strassmann^44, as well as Khlopin, Passvik-Khlopina and Volkov^36, found bromine among the products of uranium fission, which indicates the possibility of an even more asymmetric fission of the uranium nucleus than the one already considered. Hahn and Strassmann^44 regard the half-lives of the two bromine isotopes discovered by them as equal to 35 and 230 min.

Among the products of thorium fission, a number of products have been found which are observed in the case of uranium [Ba—300 hours^49 and 86 min.^50, Mo and Te—77(66) hours^49, J—2.4 hours^49, Rb—18 min.^50, Cs—10 and 33 min.^50].

Nishina, Yazaki, Ezoe, Kimura and Ikawa^51, in studying the products of fission of thorium and uranium, found activity in precipitates obtained with a large number of metals; however, the note is only preliminary in character.

Meitner^52, in analyzing the products of thorium fission, obtained results seemingly indicating the presence of certain products not observed in the case of uranium; namely, in obtaining the active precipitate with the aid of \(\mathrm{H_2S}\), periods of 40 min. and 14 hours were obtained which were not observed in the case of uranium.

Let us also note that, according to Joliot^53, in the case of uranium irradiation by slow neutrons favors the appearance of long-period activities more than irradiation by fast neutrons. Conversely, Bohr, Brostrøm and Koch^54 obtained completely identical activity-decay curves when uranium was irradiated by fast and slow neutrons.

4. EMISSION OF NEUTRONS AND γ-RAYS IN FISSION

Prompt and delayed emission. The strong excitation both of the compound nucleus (associated with neutron capture) and of the fragments produced in fission gives every reason to suppose that the fission process is accompanied by the emission of neutrons. Neutrons may “evaporate” from the compound nucleus or from the fragments; they may “spray out” during the act of fission—analogously to the formation of small droplets in the interval between the main drops into which a jet of liquid breaks up^29; finally, neutron radioactivity of the fragments may occur—the emission of neutrons over a comparatively long time after the act of fission (associated with excitation of the nucleus as a result of β-decay).

Experimental study of the time of neutron emission in fission has indeed shown^55–57 that there is an almost instantaneous emission of nearly the entire number of neutrons emitted, alongside which, however, a certain number of delayed neutrons is also observed.

A direct measurement of the upper limit of the delay time of the fission process was carried out, as we have already indicated above, by Green and Alvarez^15, who obtained for the upper limit of the delay of the fission process \(3 \cdot 10^{-3}\) sec. However, there is no reason to reject the possibility that the main mass of neutrons is emitted not simultaneously with the act of fission, but as a result of disintegration of the fragments. Starting from this consideration, Gibbs and Thomson^57 experimentally investigated whether neutron emission occurs after some interval of time following fission. Using an intermittent neutron source^58 with a period of 0.005 sec, they showed that the main mass of neutrons is emitted no later than 0.001 sec after the arrival of the neutron causing fission.

Delayed neutrons. The emission of neutrons by uranium with a delay was discovered by Roberts, Meyer, and Wang^55. A boron-lined ionization chamber was placed at a distance of several centimeters from a lithium target bombarded by deuterons. Both the target and the counter were surrounded by paraffin. Under these conditions, pulses in the ionization chamber ceased as soon as the deuteron bombardment ceased. If, however, a vessel containing 100 mg of uranium nitrate was placed between the chamber and the target, then ionization pulses could be observed for about \(1 \tfrac{1}{2}\) min after the bombardment stopped, with roughly one neutron per second initially being detected in the chamber. This neutron activity decreased with a period of \(12.5 \pm 3\) sec. A γ-activity with approximately the same period was also detected. It was therefore necessary to establish whether the observed delayed neutrons are photoneutrons or are emitted directly by fission products (primary or secondary). Roberts, Hafstad, Meyer, and Wang^56, having somewhat improved the experimental technique, showed with complete certainty that,

that direct emission of neutrons takes place. They also showed that, in addition to the aforementioned approximately 12-second γ-radiation, there are at least three more γ-radiations with longer periods. Both the delayed neutrons and all the observed γ-radiations were observed (like the fission process itself) under the action of either fast or thermal neutrons, and were not detected under the action of neutrons of intermediate energies (from carbon). In the case of the action of fast neutrons (lithium–deuterium), the effective cross section of uranium for producing delayed neutrons was \(4 \cdot 10^{-26}\ \text{cm}^2\).

The energy of the delayed neutrons, determined from the tracks of atoms in a Wilson chamber, was about 0.5 MeV. Thorium gave a picture similar to uranium, but the number of neutrons was approximately four times smaller than in the case of uranium.

Muon, Park, and Richardson\(^{59,60}\) analyzed, with the aid of a Wilson chamber in a magnetic field, the γ-radiation in the fission of uranium. Chamber expansions were carried out alternately: during irradiation and \(1 \frac{1}{2}\) sec after the irradiation was stopped. The energy distribution of the γ-quanta in both cases was approximately the same, but the number of quanta during irradiation was considerably larger. Quanta with energies up to 9–10 MeV were observed.

5. YIELD AND ENERGY DISTRIBUTION OF NEUTRONS FROM URANIUM UNDER THE ACTION OF SLOW NEUTRONS

The most direct method, and the one providing the greatest reliability, for determining the number of neutrons emitted in fission should be considered the method developed by Zinn and Szilard\(^{61}\). The valuable feature of this method is that, in order to determine the number of neutrons released in fission, it is not necessary to know any effective cross sections; moreover, the conditions for converting fast neutrons into slow ones are quite inessential. Owing to this, naturally, the relative accuracy of the results is probably greater than in the experiments described below by Galban, Joliot, and Kowarski\(^{62}\), Anderson, Fermi, and Hanstein\(^{63}\), or Anderson, Fermi, and Szilard\(^{64}\).

The essence of the Zinn and Szilard method consists in determining, with the aid of a spherical ionization chamber, the number of fast neutrons arising in a certain cell filled with uranium under the action of radium–beryllium photoneutrons slowed down by paraffin, and the number of fission events occurring in a layer of uranium (containing a certain quantity of uranium) deposited on the inner walls of a flat ionization chamber placed in the position of the cell with uranium. The ratio of these two quantities gives, after allowing for the difference in the amounts of uranium and for a few other corrections, the number of neutrons emitted in one fission event.

Zinn and Szilard obtain 2.3 neutrons per fission event. Taking into account that the fission cross section is \(2 \cdot 10^{-24}\ \text{cm}^2\) and the radiative-capture cross section\(^{65}\) is \(1.2 \cdot 10^{-24}\ \text{cm}^2\), one obtains the value 1.4 neutrons per neutron captured by uranium located in a well-

agrees with the value 1.5 obtained by Anderson, Fermi, and Szilard^64, but is somewhat smaller than the value obtained by Halban, Joliot, and Kowarski^62 (3.5 neutrons per fission event, or 2.2 neutrons per capture event).

The neutron energies, according to measurements carried out by Zinn and Szilard^61, lie in the range from 1 to 3 MeV, which corresponds to neutron energies of about 2 MeV relative to the fragment from which they are emitted. The maximum value of the neutron energy is obtained when the neutron is emitted in the direction of motion of the fragment; the minimum, when the neutron is emitted in the direction opposite to that of the fragment.

The emission of fast neutrons in the fission of uranium was first established by Dole, Halban, Joliot, and Kowarski^66 by means of a very elegant experiment. A source of photoneutrons having energies not exceeding 0.1 MeV was surrounded by a layer of uranyl nitrate. This system was placed in a vessel with 8 liters of carbon disulfide, in which 200 mg of phosphorus had been dissolved. After six days’ irradiation the phosphorus was driven off from the carbon disulfide; it showed considerable radioactivity, which apparently is due to the endothermic reaction

\[ \mathrm{S}^{32}_{16} + n = \mathrm{P}^{*32}_{15} + p, \]

occurring under the action of neutrons possessing energies of at least 0.9 MeV. In view of the low energy of the primary neutrons, we must come to the conclusion that the fast neutrons causing the transformation of sulfur into radioactive phosphorus appear upon the absorption of slowed-down primary neutrons in uranium, i.e. upon the fission of uranium. Halban, Joliot, and Kowarski^67, using an ionization chamber, detected the appearance, in fission events, of a certain relatively small number of very fast—up to 11 MeV—neutrons.

A series of French and American studies^62–64 was devoted to determining the number of neutrons emitted in fission by measuring the total number of neutrons present (quasi-stationarily) in a large vessel containing a solution of a uranium compound in water (or a mixture of a uranium compound and water), with a neutron source at the center.

Using a dysprosium detector, or another similar method, the density \(\rho\) of slow neutrons was determined at various distances \(a\) from the neutron source, and the integral \(\int \rho a^2\, da\) was calculated in the presence and in the absence of uranium, or when a uranium salt was replaced by another salt. Initially, Halban, Joliot, and Kowarski^62 found a certain increase in the integral when a 1.6-molar solution of ammonium nitrate was replaced by a uranyl-nitrate solution of the same concentration. Beginning at a distance of 13 cm from the source, the neutron density increases in the case of the uranyl-nitrate solution; at \(a = 25\) cm, \(\rho\) already increases by about a factor of five. Since the radon–beryllium photoneutrons used in this case cannot carry out reactions of the type \(n, 2n\), i.e. neutron knock-out, the authors believe that the additional number of neutrons is connected with the emission of more than one neutron as the result of a fission event caused by neutron capture.

In the following work\(^{62}\) a definite value had already been obtained for the number of neutrons \(\nu_f\) emitted as a result of the act of fission. The integral mentioned above, as is not difficult to see, must be proportional to the quantity \(Q\tau\), where \(Q\) is the number of neutrons formed per second (from the primary source and from uranium fission) and \(\tau\) is the mean lifetime of a neutron. Denoting the value of the integral by \(S\) and noting that \(\tau \sim \dfrac{1}{\sum c_i\sigma_i}\),\(^{1)}\) where \(c_i\) and \(\sigma_i\) are the concentrations and neutron-capture cross sections for the atoms present in the system under consideration, one may write

\[ S \sim Q\tau \sim Q\frac{1}{\sum c_i\sigma_i}, \]

\[ S' \sim Q'\tau' \sim Q'\frac{1}{\sum' c_i\sigma_i}, \]

where the unprimed and primed letters refer respectively to the absence and presence of uranium, or

\[ \frac{S'}{S}=\frac{Q}{Q'}\frac{\sum c_i\sigma_i}{\sum' c_i\sigma_i}. \]

Further, the number of additionally generated neutrons can, in first approximation, be expressed as follows:

\[ Q'-Q=\Delta Q=Q\frac{c_{\mathrm{U}}\sigma_f}{\sum c_i\sigma_i}\nu_f, \]

where \(\sigma_f\) is the capture cross section with fission. From these equations one obtains, in first approximation,

\[ \nu_f=\frac{S'-S}{S}\cdot \frac{\sum c_i\sigma_i}{c_{\mathrm{U}}\sigma_f} +\frac{\sum' c_i\sigma_i-\sum c_i\sigma_i}{c_{\mathrm{U}}\sigma_f}. \]

Halban, Joliot, and Kowarski\(^{62}\) obtained for \(\dfrac{S'-S}{S}\) the value \(0.05 \pm 0.01\). Taking the capture cross sections of thermal neutrons, expressed in \(10^{-24}\ \text{cm}^2\), to be: for hydrogen \(0.27 \pm 0.03\), for uranium \(1.3 \pm 0.45\), for uranium fission 2, for \(\nu_f\) the value \(3.5 \pm 0.7\) was obtained. Allowance for resonance absorption of neutrons in the slowing-down process is made by introducing a “resonance-absorption cross section,” which was determined by special experiments of Halban, Kowarski, and Savitch\(^{26}\) and was taken to be \(6.4 \pm 1.1\) (in these experiments the change in the activity of a gold detector was measured when two-centimeter layers of an ammonium nitrate solution and of uranyl nitrate of the same concentrations as in the experiments for determining neutron density were placed between it and the source of partially slowed neutrons).

Determinations of the distribution of neutron density and of their total number in a uranium–water system were also made by Anderson, Fermi, and Hanstein\(^{63}\) and by Anderson, Fermi, and Szilard\(^{64}\). In the latter, more accurate work, in 540 l of a 10% solution

\(^{1)}\) It is assumed that all capture cross sections vary inversely proportionally to the neutron velocity.

MnSO₄, 52 cylindrical jars were placed, which were either filled with uranium oxide U₃O₈ in a total amount of 200 kg, or left empty. A photoneutron source was placed at the center. The activity of the MnSO₄ solution, proportional to the total number of thermal neutrons in the volume, in the presence of uranium proved to be 10% greater than without uranium. Without going into the details of the additional experiments and the recalculation of the experimental data, we shall give the result. The authors, without indicating the value of the probable error, suppose that, for one thermal neutron absorbed in uranium, an average of 1.5 neutrons is produced.

To recalculate the neutron yield per fission event (and not per neutron-absorption event in uranium), one may use the data of Anderson and Fermi^65, according to which, for the total capture cross section of uranium for thermal neutrons, equal to \(3.2\cdot 10^{-24}\ \mathrm{cm}^2\), capture with fission accounts for \(2\cdot 10^{-24}\ \mathrm{cm}^2\) and simple capture (with \(\gamma\)-emission) for \(1.2\cdot 10^{-24}\ \mathrm{cm}^2\). Hence we obtain \(\nu_f = 1.5\,\frac{2+1.2}{2}=2.4\). This value lies between the values obtained by Zinn and Szilard (2) and by Halban, Joliot, and Kowarski (\(3.5\pm 0.7\)).

Similar results were also obtained by Hadzhivara^68, who, like the French authors^67, notes the presence of neutrons with energies up to 10 MeV.

6. CHAIN DECAY OF URANIUM

Chain decay by fast neutrons. The emission of more than one neutron upon the absorption of one neutron by uranium, in principle, makes it possible to carry out a nuclear chain reaction with branching chains. Halban, Joliot, and Kowarski^62 were the first to note that the discovery of a large neutron yield in fission is a step toward carrying out an exothermic nuclear chain reaction. A quantitative treatment of the question of the possibility of macroscopic decomposition of uranium was first proposed by Perrin^69. In this work Perrin considers the action only of fast neutrons. Therefore the effective cross sections are assumed to be constant. It is assumed that uranium, or some compound of it, is arranged in the form of a sphere of radius \(R\), at the center of which there is a neutron source giving \(Q_0\) neutrons per second. Denoting by \(F(r,t)\) the number of neutrons in a cubic centimeter as a function of the time \(t\) and of the distance \(r\) of the volume element from the center, Perrin writes the equation

\[ \frac{\partial F}{\partial t} = D\Delta F(r,t) + \left[c\nu(\nu_f-1)\sigma_f-\sum c_i\sigma_{ci}\right]\overline{v}F(r,t) \tag{1} \]

for the change of the neutron concentration with time. In this equation the first term on the right-hand side represents the change of concentration due to diffusion of the neutrons, while the second represents the change of concentration due to the appearance of new neutrons and due to absorption of neutrons. The notation here is as follows: \(D\) is the diffusion coefficient

neutrons, \(c_U\) is the concentration of uranium atoms, \(c_i\) of atoms of other substances, \(\nu_f\), as before, is the number of neutrons produced in fission, \(\sigma_f\) is the cross section for capture with fission, \(\sigma_{ci}\) is the capture cross section of an atom of the \(i\)-th substance, \(\bar v\) is the mean velocity of the neutrons.

If the mean free path of the neutrons is significantly smaller than the radius of the sphere, then one may write \(D=\frac{1}{3}\bar v\lambda\); here

\[ \lambda=\frac{1}{\sum c_i\sigma_{si}}, \]

where \(\sigma_{si}\) is the scattering cross section of atoms of the \(i\)-th substance. Taking this into account, Perrin rewrites equation (1) in the form:

\[ \frac{dF}{dt}=\frac{\lambda}{3}\Delta(\bar vF)+\left[c_U(\nu_f-1)\sigma_f-\sum c_i\sigma_{ci}\right]\bar vF . \tag{2} \]

In the limiting stationary regime we have \(\frac{\partial F}{\partial t}=0\) (for \(\frac{\partial F}{\partial t}>0\) the reaction rate increases with time); then instead of (2) one obtains:

\[ \Delta(\bar vF)+a^2(\bar vF)=0, \tag{3} \]

where \(a^2=\frac{3}{\lambda}\left[c_U(\nu_f-1)\sigma_f-\sum c_i\sigma_{ci}\right]\). Taking into account the boundary conditions (a source near the center) and spherical symmetry, Perrin obtains the solution of (3) in the following form:

\[ \bar vF=\frac{3Q_0}{4\pi\lambda}\frac{1}{\sin aR}\cdot\frac{\sin a(R-r)}{r}. \]

The neutron density becomes infinite when \(R_{cr}=\frac{\pi}{a}\). For \(R>R_{cr}\), according to Perrin, an explosive reaction of uranium fission will take place.

For the case of powdered \(U_3O_8\), Perrin, assuming its density to be \(4.2\ \mathrm{g/cm^3}\), taking \(\sigma_{sU}=6\cdot10^{-24}\ \mathrm{cm^2}\), \(\sigma_{sO}=2\cdot10^{-24}\ \mathrm{cm^2}\), \(\sigma_f=10^{-25}\ \mathrm{cm^2}\), \(\nu_f=3\), and neglecting absorption in oxygen, obtains \(R_{cr}=130\ \mathrm{cm}\) and, for the critical mass of \(U_3O_8\), obtains the value \(42\ \mathrm{t}\).

Perrin assumes that the critical mass can be reduced if the uranium-containing mass is surrounded by a certain “neutron insulation,” for example, lead or iron. With a layer of iron \(35\ \mathrm{cm}\) thick, the critical mass of uranium oxide, according to Perrin’s calculations, is reduced to \(12\ \mathrm{t}\).

Peierls\({}^{70}\) generalized Perrin’s calculations, showing that the critical conditions found by Perrin do not depend on the position of the neutron source. Along with this, Peierls also considered a system in which the probability of branching is very large, so that the critical dimensions of the system are smaller than the neutron path length and the use of the differential diffusion equation is inadmissible. This latter case has no relation to the decay of uranium.

A substantial shortcoming of Perrin’s work is the absence of allowance for the slowing down of neutrons, which occurs both in elastic and

and in inelastic collisions of neutrons with nuclei of uranium and other elements (oxygen). Zeldovich and Khariton\(^{71}\) showed that even in the case of an infinitely extended mass of \(\mathrm{U_3O_8}\) an explosion (infinite branching of the chain) is impossible because of the large value of \(\gamma\)—the probability that the neutron formed with energy \(E_0\) is slowed down, before having time to cause a new act of fission, to the energy \(E_{\mathrm{cr}}\), approximately equal to \(1.5\ \mathrm{MeV}\) (see p. 331), below which it can no longer cause fission.

For the quantity \(\gamma\), Zeldovich and Khariton, proceeding from the equations determining the change with time of the mean energy \(E\) of the neutrons and of the number of neutrons during scattering:

\[ \frac{dE}{dt}=-E\overline{v}\sum s_i c_i \lambda_i, \]

\[ \frac{dN}{dt}=-N\overline{v}\sum \sigma_i c_i, \]

where

\[ \lambda_i=\frac{2m_i}{(m_i+1)^2} \]

(\(m_i\) is the mass of the \(i\)-th nucleus, expressed in neutron masses), obtain the expression

\[ \gamma=\exp\left(\int_{E_0}^{E_{\mathrm{cr}}}\psi(E)\,d\ln E\right), \]

where

\[ \psi=\frac{\sum c_i\sigma_i}{\sum c_i\sigma_{s i}\lambda_i}; \]

for \(\psi\) independent of energy

\[ \gamma=\left(\frac{E_{\mathrm{cr}}}{E_0}\right)^\psi . \]

The possibility of explosion is determined by the inequality

\[ \nu_f(1-\gamma)>1, \tag{4} \]

which expresses the necessity that more than one neutron appear in place of one neutron absorbed or slowed below \(E_{\mathrm{cr}}\). Having calculated the quantity \(\nu_f(1-\gamma)\) for various possible values of \(\nu_f\) and \(E_0\), Zeldovich and Khariton obtained for \(\mathrm{U_3O_8}\) in an unlimited mass the following table of values of \(\nu_f(1-\gamma)\) (see Table 1).

Table 1

In the calculations for \(E_{\mathrm{cr}}\) the value \(1.5\ \mathrm{MeV}^{13}\) was taken, \(\sigma_{s\mathrm{O}}=2\cdot10^{-24}\ \mathrm{cm}^2\), \(\sigma_{s\mathrm{U}}=6\cdot10^{-24}\ \mathrm{cm}^{2\,1)}\), \(\sigma_{c\mathrm{O}}=0\), \(\sigma_{c\mathrm{U}}=\sigma_f=0.5\cdot10^{-24\,25}\).

As is seen from Table 1, oxygen greatly impedes the realization of a uranium chain fission. The criterion \(\nu_f(1-\gamma)\) becomes greater than unity only for the most favorable combination of \(\nu_f\) and \(E_0\).

One might have thought that the use of pure uranium would ensure the realization of a chain explosion on fast neutrons; however, the presence of inelastic scattering according to the calculations of Zeldovich and Khariton

\(^{1)}\) Judging from the data of recent works\(^{27,72}\), for \(\sigma_{s\mathrm{U}}\) one should take a somewhat larger value; however, this will only slightly affect the result of the calculation.

and in this case (a very favorable one in the sense of elastic collisions) leads to a powerful rupture of the chains and, apparently, to the impossibility of an explosion.

It should also be noted that the presence of losses of neutron energy in elastic collisions strongly limits the possibility of applying the “neutron insulation” proposed by Perrin, since neutrons returning from comparatively distant layers of the “insulator” will have an energy less than \(E_{\mathrm{cr}}\).

Enney and Rosenberg\(^{73}\) attempted experimentally to resolve the question of the possibility of realizing a chain reaction in uranium. They placed a neutron source inside a 14-kg block of uranium oxide \(U_3O_8\) and measured the increase, caused by uranium, in the number of fast neutrons emitted by an Rn—Be source surrounded by 4 cm of paraffin. In order that only fast neutrons be recorded, a hexane chamber\(^{74}\) was used as the detector. The authors obtained, when the source was surrounded by uranium, a 20% increase in the number of fast neutrons instead of the 5% decrease which, in their opinion, should have been connected with absorption in uranium, and they believed that this increase indicates the possibility, with a further increase in the layer of uranium surrounding the source, of an infinite “amplification” of the neutron source up to catastrophic values. These conclusions, however, are insufficiently substantiated. In view of the uncertainty of the neutron spectrum of the source used (Rn—Be + 4 cm of paraffin) and the lack of clarity on the question of whether the hexane chamber counts precisely those neutrons which are capable of causing further fission, extreme caution must be observed in interpreting the observed 20% amplification, without which it is easy to arrive at erroneous conclusions.

Perrin also considered\(^{75}\) the behavior of a system of uranium (uranium oxide) with the addition of a certain amount of water and cadmium. The presence of hydrogen atoms causes a comparatively rapid conversion of part of the fast neutrons into slow and thermal ones. If there is now a system with a mass exceeding the critical mass under the simultaneous action of fast and thermal neutrons, and the whole system begins to heat up owing to the release of energy in fission, then the rise in temperature will cause a decrease in the capture cross section of uranium for thermal neutrons (the cross section is inversely proportional to the velocity of the neutrons). The capture of thermal neutrons, however, occurring chiefly on account of the cadmium impurity, will remain practically unchanged. As a result, the rise in temperature will have the consequence that the system passes from a supercritical to a subcritical state, since the critical size must grow with increasing temperature. Consequently, a self-regulating “explosion-safe” system is obtained. Perrin\(^{75}\) gives the following example: for \(U_3O_8\) containing 3% water and 0.01% cadmium, \(R_{\mathrm{cr}} = 65\) cm at room temperature and 80 cm at \(900^\circ\).

Perrin’s calculation\(^{75}\) contains, in addition to neglecting elastic and inelastic slowing down of neutrons, one more substantial omission. Perrin assumes that the conversion of fast neutrons into slow ones in the рас-

considered by him, occurs with the same yield (about 85%), which Gal'ban, Kovarskii, and Savich^26 obtained for a 1.6 molar solution of uranyl nitrate in water. In reality, however, at low (3%) concentrations of water by weight in uranium, the resonance capture of neutrons by uranium will, as is shown below (see p. 349), be very large and will lead to the production of thermal neutrons from fast ones with a yield of about 15%. At the same time, such an amount of water practically eliminates, because of energy loss in elastic collisions with protons, fission by fast neutrons. We therefore come to the conclusion that the figures given by Perrin are completely unrealistic, since even in pure uranium the occurrence of an explosion is unlikely; the addition of small amounts of hydrogen only worsens the situation.

Adler and Gal'ban^76, simultaneously with Perrin, arrived in practice at the same conclusions as Perrin.

Chain decay with slow neutrons. The second variant for carrying out a chain explosion of uranium—a detonation decay on slow neutrons—may be envisaged as follows. Let there be a system consisting of uranium and a moderator, whose purpose is to slow neutrons rapidly from their initial energies down to thermal energies, at which the fission cross section again becomes sufficiently large. Rapid slowing-down is necessary so that the neutrons “slip through” the resonance level of uranium-238 with minimal losses. To achieve effective slowing-down it is necessary to take a large amount of moderator (for example, water). However, with a large amount of moderator one must face the fact of capture of neutrons by the nuclei of the moderator, which, like resonance capture, leads to the breaking of chains. This dual role of the moderator was pointed out by Anderson, Fermi, and Szilard^64; they note the impossibility, at the present time, of answering the question whether a chain explosion can in general be realized in a mixture of uranium with water.

A detailed quantitative analysis of chain fission of uranium by slow neutrons was carried out by Zel'dovich and Khariton^77. They formulate the condition for the occurrence of an explosion, i.e., the condition for the occurrence of infinitely branching chains^78, in the following way. The consideration, just as in ^71, is conducted for the case of an infinitely large system. Let, per unit time, \(N\) fast neutrons arise in the system (as a result of fission events caused by neutrons, and also from external neutron sources). Of these, \(\varphi N\) will “slip through,” upon slowing down, the region of resonance capture and will become slow, thermal neutrons (\(\varphi\) is the probability that a fast neutron slows down without being captured resonantly by a uranium-238 nucleus). Of the \(\varphi N\) neutrons that have “slipped through,” \(\theta\) will be captured by uranium nuclei [the remaining \((1-\theta)\varphi N\) neutrons will be captured by nuclei of the moderating impurity, for example, hydrogen]. If for each slow neutron captured by uranium \(\nu\) new fast neutrons are formed, then in all \(\nu\theta\varphi N\) additional neutrons are formed. Let \(N_0\) be the number of neutrons arising in the system from external sources.

Then, by definition,

\[ N=N_0+\nu\theta\varphi N, \tag{5} \]

or

\[ N=\frac{N_0}{1-\nu\theta\varphi}. \tag{6} \]

Hence the critical condition for the occurrence of an explosion is obtained:

\[ \nu\theta\varphi>1. \tag{7} \]

Let us note that among the \(\theta\varphi N\) there are also slow neutrons captured by uranium 238 with the formation of uranium 239 and subsequent \(\beta\)-emission [this type of capture, according to the Breit–Wigner formula, is practically absent\(^1\) in the energy interval from somewhat below the resonance energy to energies close to thermal, when the effective capture cross section begins to increase proportionally to \(E^{-1/2}\)], and neutrons captured by uranium 235, which then undergoes fission. Since \(\nu_f\), introduced by us earlier, refers to the act of fission, then

\[ \nu=\nu_f\frac{\sigma_f}{\sigma_f+\sigma'_{cU}} =\nu_f\frac{\sigma_f}{\sigma_{cU}}, \tag{8} \]

where \(\sigma_f\) is the cross section for capture of a neutron by uranium with fission, \(\sigma'_{cU}\) is the cross section for simple (radiative) capture of a neutron by uranium, and \(\sigma_{cU}\) is the total capture cross section.

The quantity \(\theta\) is expressed as follows:

\[ \theta=\frac{c_U\sigma_{cU}}{c_U\sigma_{cU}+c_H\sigma_{cH}}. \tag{9} \]

The main task of the calculation is the determination of the quantity \(\varphi\) as a function of the composition of the system. Using, for the case of dilution with hydrogen, the circumstance that at each collision with a hydrogen nucleus the neutron is scattered in energy with uniform density over the entire interval from zero to the energy before the collision,

\(^1\) The Breit–Wigner formula for the cross section for capture of a neutron of energy \(E\) by a nucleus, in the presence of one resonance level, has the following form:

\[ \sigma_E=\sigma_r\sqrt{\frac{E_r}{E}}\, \frac{\left(\dfrac{\Gamma}{2}\right)^2}{(E-E_r)^2+\left(\dfrac{\Gamma}{2}\right)^2}; \]

here \(\sigma_r\), as is easily seen, is the value of \(\sigma_E\) at \(E=E_r\), i.e. at resonance, \(\Gamma\) is the width of the resonance level. The formula gives a maximum at \(E=E_r\); then, as the neutron energy decreases, the quantity \(\sigma_E\) rapidly decreases (the faster, the smaller \(\Gamma\) is), remaining very small until \(E\) decreases to such an extent that \(\sqrt{E_r/E}\) becomes sufficiently large.

and introducing \(w\)—the probability of being captured in a given collision, Zeldovich and Khariton obtain the integral equation

\[ \varphi(E)=[1-w(E)]\frac{1}{E}\int_0^E \varphi(\varepsilon)\,d\varepsilon, \]

whose integration, taking into account the fact that for \(E\)’s somewhat significantly exceeding \(E_r\), \(\varphi\) approaches a certain asymptotic value, leads to the expression

\[ \varphi=\exp\left(-\int_0^\infty w\,d\ln E\right). \tag{10} \]

The probability of being captured at the first collision, when the neutron energy is equal to \(E\), is expressed, obviously, as follows:

\[ w=w(E)=\frac{c_{\mathrm U}\sigma_{\mathrm{CU}}(E)} {c_{\mathrm U}\sigma_{\mathrm{CU}}(E)+c_{\mathrm H}\sigma_{\mathrm{SH}}(E)}. \tag{11} \]

If we had exact data on the dependence of \(\sigma_{\mathrm{CU}}\) on energy, then the calculation of \(\varphi\) could be carried out by numerical integration of (10). Calculating \(\varphi\) by means of the Breit-Wigner formula with the values \(\sigma_r=3000\cdot10^{-24}\) and \(\Gamma=0.2\) (these values more or less correspond to the available data on the absorption of slow neutrons in uranium) and taking \(\sigma_{\mathrm{SH}}=20\cdot10^{-24}\ \mathrm{cm}^2\), Zeldovich and Khariton obtained for the case of equal atomic concentrations of hydrogen and uranium (\(\eta=1\)) the value \(\varphi=0.84\). However, such a calculation is not very reliable in view of the fact that the formula corresponding to a single resonance level is apparently inapplicable to the case under consideration\(^ {65}\). A direct experiment by Halban, Kowarski, and Savitch\(^ {26}\) gives \(\varphi=0.86\) for \(\eta=62=\dfrac{c_{\mathrm H}}{c_{\mathrm U}}\), which corresponds to a considerably greater capture under equal conditions.

In view of the unreliability of applying the Breit-Wigner formula, Zeldovich and Khariton use the circumstance that \(\int w\,d\ln E\) is inversely proportional to the square root of the ratio \(\dfrac{c_{\mathrm H}}{c_{\mathrm U}}\), denoted earlier by \(\eta\), i.e.

\[ \varphi=\exp\left(-a\sqrt{\frac{c_{\mathrm U}}{c_{\mathrm H}}}\right) =\exp\left(-a\eta^{-\frac12}\right). \]

The constant \(a\) can be determined directly from the experiments of Halban, Kowarski, and Savitch\(^ {26}\), in which \(c_{\mathrm H}\) and \(c_{\mathrm U}\) are known and the value of \(\varphi\) is determined. Having determined \(a\), one can then calculate the value of \(\varphi\) for any composition, and the result will not depend on the number and distribution of the resonance levels in the uranium nucleus. In this way one obtains \(a=1.36\), and then

By means of elementary calculations one obtains the values of \(\theta\) and \(\theta\varphi\) for various ratios of the hydrogen and uranium concentrations. These values are given in Table 2.

Table 2

The maximum value of \(\theta\varphi\) corresponds to \(\eta=\dfrac{c_{\mathrm H}}{c_{\mathrm U}}\simeq 4\) and is equal to \(\sim 0.375\). Consequently, the critical conditions for the occurrence of an explosion (7) will be satisfied if \(\nu\) is greater than \(\dfrac{1}{0.375}\), i.e., greater than 2.75. Analyzing by means of the method set out above the results of Joliot et al.\(^{62}\), Zeldovich and Khariton\(^{77}\) obtain for \(\nu\) the value 1.95; consequently, the maximum possible value of the criterion \(\nu\theta\varphi\) is \(0.375\cdot 1.95=0.73\). Thus, for no composition of a mixture of uranium with water are the infinite development of chains and an explosion of uranium possible. The greatest observed effect may be an increase in the intensity of the neutron source due to neutrons produced by fission.

According to (6), this increase will be

\[ \frac{N}{N_0}=\frac{1}{1-\nu\theta\varphi}\simeq 4. \]

An effect of just this order was observed by Halban, Joliot, Kowarski, and Perrin\(^{79}\) in their study of the distribution of neutrons in a large mass (300 kg) of uranium mixed with water in various proportions.

It is interesting to note that the analysis of the data of Joliot et al.\(^{62}\), carried out “theoretically,” i.e., on the basis of the Breit–Wigner formula with a single level and, correspondingly, with the value \(\varphi=0.84\) at \(\eta=1\), which gives \(a=0.168\) (instead of \(a=1.36\) in the “empirical” determination using the data of the work of Halban, Kowarski, and Savitch\(^{26}\)), gives for \(\nu\theta\varphi\) the value 0.68, i.e., very close to the value 0.73 already given. The reason for such insensitivity of the magnitude of the criterion \(\nu\theta\varphi\) to the method of calculation, i.e., to the value of \(\varphi\) used in the calculation, is easy to understand. The smaller the value of \(\varphi\) we use in the calculation, the larger the value of \(\nu\) we shall obtain (since otherwise the experimentally observed neutron-density distribution would not be ensured). The product of the two quantities \(\nu\varphi\), however, will change very little. This circumstance contributes to a significant degree to the reliability of the value obtained for \(\nu\theta\varphi\).

\(^{1)}\) The values \(\eta\) equal to 17 and 62 correspond to the experiments of Anderson, Fermi, and Szilard\(^{64}\) and of Halban, Joliot, and Kowarski\(^{62}\).

7. PATHS FOR ACHIEVING A CHAIN EXPLOSION OF URANIUM WITH THERMAL NEUTRONS

We have come to the conclusion that a thermal explosion of a mixture of uranium with water is impossible for any ratio of the amounts of uranium and water. To achieve an explosion, i.e., to increase the quantity $\psi_0$ to a value exceeding unity, one may try two paths: 1) replacing hydrogen by another diluent, 2) enriching uranium with a light isotope of atomic weight 235. Let us consider each of these paths.

Suppose that we replace hydrogen, which serves to slow down neutrons, by some other element with atomic weight $m$, capture cross section $\sigma_c$, and scattering cross section $\sigma_s$. At each collision of a neutron with a “moderator” nucleus the neutron energy will change on the average by

$$ \frac{2m}{(m+1)^2} $$

of the magnitude of the energy it had before the collision (assuming that the collisions occur as in the case of elastic spheres). In the case of hydrogen this relative change in energy is equal to 0.5, in the case of deuterium 0.45, in the case of helium 0.32, in the case of carbon 0.142, in the case of nitrogen 0.125, etc. If one also takes into account that for hydrogen, in the energy interval of interest to us, the scattering cross section is approximately $20 \cdot 10^{-24}\ \mathrm{cm}^2$, while for elements from deuterium to nitrogen it is approximately $2 \cdot 10^{-24}\ \mathrm{cm}^2$, then in a first approximation one may say that deuterium slows down 10 times “worse” than hydrogen, helium 17 times, carbon 35 times, nitrogen 40 times, etc.

Let us now note that hydrogen, other conditions being equal, could ensure the explosion condition if its capture cross section for thermal neutrons were not $0.27 \cdot 10^{-24}\ \mathrm{cm}^2$, but about 5 times smaller (this result is obtained if one adds to Table 2 a number of rows with values of $\theta$, calculated under the assumption of various gradually decreasing values of $\sigma_{\mathrm{cH}}$, and looks at what value of $\sigma_{\mathrm{cH}}$ first satisfies the condition $\psi_0 = 1$). Further, we may assert that in order to ensure the possibility of an explosion of a mixture of uranium with one or another diluent, the capture cross sections of the latter must be approximately as many times smaller than the “explosive cross section” of hydrogen, equal to $\sim 0.054 \cdot 10^{-24}\ \mathrm{cm}^2$, as the given diluent slows neutrons “worse” than hydrogen. As a result we obtain the following “maximum explosive capture cross sections,” expressed in $10^{-24}\ \mathrm{cm}^2$, for various elements that may be used as diluents (see Table 3).

Table 3

For comparison, in the third row of Table 3 we give the data of Frisch, Halban, and Koch\({}^{80}\) on the capture cross sections of certain light elements. It is evident that the data on capture cross sections require further refinement.

Let us now consider what degree of enrichment \(n\) of uranium with the isotope of atomic weight 235 is necessary in order that the condition \(v\varphi = 1\) be satisfied upon dilution with hydrogen.

In contrast to the cases just considered, where the calculation had to be carried out only very approximately, for different contents of uranium-235 the calculation can be performed rigorously within the framework of the method set forth above. It is only necessary, in all formulas in which the quantity \(\sigma_f\) enters, to replace it by the quantity \(n\sigma_f\).

A calculation carried out in this way showed that the quantity \(v\varphi\) reaches the value 1 at \(n \simeq 1.85\). Let us recall that this figure refers to an infinite volume. In the case of a finite volume, a somewhat greater enrichment will be necessary: the smaller the amount of mixture taken, the greater it must be.

It should be noted that approximately a twofold enrichment of the fairly considerable quantities of uranium that are necessary to produce a chain explosion (as will be shown in the next section) is an extremely cumbersome task, close to being practically impossible.

8. CRITICAL MASS

In a finite mass of uranium with a moderator it is necessary, as Peierls\({}^{69}\) pointed out, to take into account jointly the time variation of the neutron concentration, connected both with diffusion and with various nuclear processes (fission and capture). Let us write the corresponding equation for the balance of the density of thermal neutrons \(\rho\) in a system not supplied with an external neutron source:

\[ \frac{\partial \rho}{\partial t}=D\Delta\rho+f\rho. \]

Here \(D\) is the diffusion coefficient of thermal neutrons, while the quantity \(f\) can be expressed in the following way:

\[ f=u\left[c_U\sigma_{cU}v\varphi-c_U\sigma_{rU}-\sum c_i\sigma_{ci}\right], \]

where the first term corresponds to the number of slow neutrons appearing per unit time as a result of fission events, taking into account the circumstance that only a fraction \(\varphi\) is slowed without capture to the resonance level of uranium-238. The last term corresponds to the capture of neutrons by the nuclei of atoms of the moderating substances.

The solution of this equation for a spherical mass may be represented in the form

\[ \rho=\sum \psi_k(r)e^{t\left(f-\varkappa_k\frac{D}{r^2}\right)}. \]

It is easy to see that one may restrict oneself to considering the first eigenfunction and the first characteristic number, since the subsequent terms of the sum, with increasing \(t\), will have rela-

relatively ever smaller value. Therefore one may take a solution of the form

\[ \rho=c_0\psi_0 e^{pt},\quad \text{where}\quad p=-f-\varkappa_0\frac{D}{r^2}, \]

from which we find the critical size of the sphere

\[ r_{\mathrm{cr}}=\sqrt{\frac{\varkappa_0 D}{f}} =\pi\sqrt{\frac{D}{f}} =\frac{\pi}{\sqrt{3}}\sqrt{\frac{\lambda_s\lambda_c}{(\nu\varphi-1)}}, \]

where \(\lambda_s\) and \(\lambda_c\) are the neutron mean free paths for scattering and capture, respectively.

Let us consider a concrete example. Let the system consist of a mixture of \(\mathrm{U_3O_8}\) with \(99.5\%\) heavy water, with the amount of \(\mathrm{U_3O_8}\) equal to \(17.5\%\) by weight, which corresponds to \(c_U:c_D=1:100\). We shall take the capture cross sections of deuterium and oxygen to be zero. We shall assume that the uranium oxide is uniformly distributed in the water. Then, taking

\[ \begin{aligned} \sigma_{sU}&=6\cdot 10^{-24}\ \mathrm{cm}^2, & \sigma_{sD}&=2.5\cdot 10^{-24}\ \mathrm{cm}^2,\\ \sigma_{sH}&=35\cdot 10^{-24}\ \mathrm{cm}^2 & &\text{(for slow neutrons)},\\ \sigma_{sO}&=2.5\cdot 10^{-24}\ \mathrm{cm}^2, & \sigma_{cU}&=3.2\cdot 10^{-24}\ \mathrm{cm}^2,\\ \sigma_{cH}&=0.27\cdot 10^{-24}\ \mathrm{cm}^2, & \nu&=1.95, \end{aligned} \]

finding for \(\varphi\) from Table 2, with the aid of the considerations given on p. 351\({}^{1)}\), the value \(0.7\), and calculating from (9) \(\theta=0.959\), we obtain \(\nu\theta\varphi\simeq 1.3\) and further:

\[ R_{\mathrm{cr}}\simeq \frac{\pi}{\sqrt{3}}\sqrt{\frac{4.6\cdot 450}{0.3}}\simeq 150\ \mathrm{cm}, \]

or, for the critical mass of uranium oxide and water:

\[ M_{\mathrm{cr}}^{\mathrm{U_3O_8}}\simeq 2.5\ \mathrm{t},\qquad M_{\mathrm{cr}}^{\mathrm{D_2O}}\simeq 15\ \mathrm{t}. \]

Finally, let us dwell briefly on the question of the character of the course of the process in time in a system in which the critical conditions for branching of the chains (4) and (7) can be reached, confining ourselves to the premises and conclusions of the theory. As we have seen (see above), under given supercritical conditions, the intensity of the reaction and the concentration of neutrons grow exponentially. At the same time, however, for any appreciable probability of chain branching, the time for the rate of reaction to increase by a factor of \(e\) proves to be of the order of \(10^{-7}\) sec. (for fast neutrons)\({}^{2)}\). During \(10^{-4}\)—

\({}^{1)}\) Oxygen and deuterium were assumed equivalent to an additional amount of hydrogen, and the effective value of \(\eta\) was found. Then, from Table 2, by interpolation, the value of \(\varphi\) corresponding to the obtained value of \(\eta\) was found.

\({}^{2)}\) Adler considers in detail the kinetics of the process inside the above-mentioned time interval in the special case of a certain number of neutrons concentrated at the initial moment at the center of the sphere. These calculations, which concern the course of the process over a time less than the diffusion time, have no relation to the course of the real process considered by us below.

—\(10^{-5}\) sec. the released energy will prove sufficient to evaporate the entire mixture; moreover, we have assumed that the reaction is caused by cosmic neutrons. With such a rapid development of the reaction one can no longer neglect consideration of the very process by which supercritical conditions are created, as, for example, Flugge does\(^{82}\). A detailed analysis of the transition through the threshold is necessary, i.e., of the course of the reaction near \(p = 0\), where the behavior of the system depends sensitively on a number of factors that may be neglected far from the threshold. Thus, the consumption of uranium and the appearance of new nuclei capable of capturing neutrons hinder the branching of chains. Calculations show that the effect of thermal expansion, caused by the energy release of the nuclear reaction, is still stronger (by \(\sim 10^8\) times). The significance of thermal expansion is connected with the fact that, for a mixture of constant composition, Perrin’s formulas imply

\[ (R\delta)_{cr}=\mathrm{const} \]

(\(\delta\) is the density of uranium or of a uranium-containing substance), or

\[ (R^3\delta^3)_{cr}\sim (M\delta^2)_{cr}=\mathrm{const}. \]

(\(M\) is the mass), so that the critical mass increases as the density decreases, and in a system of given mass a decrease in density worsens the conditions for chain branching.

The very short relaxation time for the development of neutron chains leads to the fact that, for any method of passing through critical conditions (addition of uranium, bringing two parts of the system closer together), the nuclear reaction proceeds with such intensity that, as a result of uranium consumption and thermal expansion, on the average \(p=0\) is maintained the whole time, and the reaction ceases practically simultaneously with the cessation of the supply of uranium or the bringing together of parts of the system\(^{83}\). In this case the chain fission that has begun ceases without affecting the critical mass of uranium. In this respect the system differs essentially from explosives and, because of its self-regulation, would, on the contrary, be extremely convenient for power applications; special devices (for example, the addition of cadmium, see \(^{71,72}\)) are useless.

It is curious to note that the presence of even a small quantity (1%) of delayed neutrons, emitted with a half-period of \(\sim 10\) sec. after fission, appreciably slows the development of the reaction near critical conditions; however, the relaxation time in this case too remains sufficiently small for the conclusions drawn above to be valid.

9. ENERGY PROSPECTS

The material set forth in the preceding sections shows that at present it is still impossible to draw final conclusions about the possibility or impossibility of realizing in uranium a nuclear fission reaction with infinitely branching chains. If such a reaction is realizable, then, as was indicated in the preceding

in the branch, regulation of the reaction rate is carried out automatically, ensuring its calm course despite the enormous amount of energy at the experimenter’s disposal. This circumstance is exceptionally favorable for the energetic use of the reaction. We shall therefore give—although this is a case of counting one’s chickens before they are hatched—some figures characterizing the possibilities of the energetic use of uranium.

If the fission process proceeds on fast neutrons, and consequently the reaction captures the principal isotope of uranium (\(U^{238}\)), then the calorific value of uranium is

\[ Q_U = 2 \cdot 10^8 \mathrm{eV} = 4.6 \cdot 10^9 \, \text{kg cal/mol} = 1.8 \cdot 10^{13} \, \text{kg cal/t}; \]

the corresponding figure for coal will be

\[ Q_C = 8 \cdot 10^6 \, \text{kg cal/t}. \]

With the ratio

\[ \frac{Q_U}{Q_C} \approx 2 \cdot 10^6 \]

and a ratio\(^{1)}\) of the prices of uranium and coal on the world market of \(\sim 500\), the cost of a calorie from the principal isotope of uranium proves to be approximately 4,000 times cheaper than from coal (if, of course, the processes of “combustion” and heat removal do not turn out, in the case of uranium, to be considerably more expensive than in the case of coal). In the case of slow neutrons, the cost of a “uranium” calorie (if one proceeds from the figures cited above) will be, taking into account that the abundance of the isotope \(U^{235}\) is 0.007, only 30 times cheaper than a “coal” calorie, all other conditions being equal.

World production of uranium ores and compounds in 1934\(^{84}\) amounted to approximately 700 t (not counting the USA). Converted into uranium this gives \(\sim 300\) t, which is equivalent to \(6 \cdot 10^8\) t of coal, i.e., more than half of the world’s annual coal production if the process is carried out on fast neutrons, and only \(5 \cdot 10^6\) t in the case of slow ones. The comparatively great abundance\(^{85}\) of uranium (some authors believe that the abundance of uranium is the same as that of copper) will probably make it possible, if necessary, to increase production considerably.

It should be expected that the question of the possibility or impossibility of carrying out chain “burning” of uranium on slow or on fast neutrons will be resolved in the near future. Until this question is positively resolved, a more detailed analysis of the energy prospects associated with uranium is hardly expedient.

Addendum

At the May session of the Academy of Sciences of the USSR, K. A. Petrzhak and G. N. Flerov reported that they had discovered the appearance of uranium fragments in the absence of a neutron source. The number of fission events they observed was very small. Petrzhak and Flerov indicate that if the fragments are connected with the spontaneous decay of uranium, then the corresponding half-life is \(10^{16}\) years if \(U_{238}\) decays, or \(10^{14}\) and \(10^{12}\) years for \(U_{235}\) and \(U_{234}\), respectively.

For thorium, an analogous effect was not discovered.

\(^{1)}\) The price ratio is taken for uranium oxide. Metallic uranium is at present still considerably more expensive, and it is precisely it that would be needed for using the principal isotope (see p. 345).

References

1. O. Hahn and F. Strassmann, Naturwiss., 26, 756, 1939; 27, 11, 1939.
2. I. Curie et P. Savitch, C. R., 206, 906, 1643, 1938; J. Phys. et Rad., 9, 355, 1938.
3. E. Fermi, F. Amaldi, O. Agostino, F. Rasetti and E. Segrè, Proc. Roy. Soc., 146, 483, 1934.
4. L. Meitner and O. Frisch, Nature, 143, 239, 1939.
5. N. Bohr, Nature, 137, 344, 351, 1936.
6. N. Bohr and F. Kalkar, Kgl. Danske Vid. Selskab. Math., Phys. Med., 14, N. 10, 1937.
7. O. Frisch, Nature, 143, 276, 1939.
8. F. Joliot, C. R., 208, 341, 1939.
9. W. Jentschke u. F. Prankl, Naturwiss., 27, 134, 1939.
10. G. Droste, Naturwiss., 27, 198, 1939.
11. J. Thibaud et A. Moussa, C. R., 208, 652, 1939.
12. I. Noddak, Ang. Chemie, 47, 653, 1934.
13. R. Roberts, R. Meyer and L. Hafstad, Phys. Rev., 55, 416, 1939.
14. R. Fowler and R. Dodson, Phys. Rev., 55, 417, 1939.
15. G. Green and L. Alvarez, Phys. Rev., 55, 417, 1939.
16. P. Abelson, Phys. Rev., 55, 418, 1939.
17. N. Feather, Nature, 143, 597, 1939.
18. D. Corson and R. Thornton, Phys. Rev., 55, 509, 1939.
19. N. Perfilov, DAN, 23, 893, 1939.
20. A. Zhdanov and L. Mysovsky, DAN, 23, 136, 1939; A. Zhdanov, L. Mysovsky and M. Mysovskaya, DAN, 23, 341, 1939; A. Zhdanov and L. Mysovsky, DAN, 25, 9, 1939.
21. E. McMillan, Phys. Rev., 55, 510, 1939.
22. L. Meitner, O. Hahn u. F. Strassmann, Z. Physik, 106, 249, 1937.
23. A. Grosse, E. Booth and I. Dunning, Phys. Rev., 56, 382, 1939.
24. H. Anderson, E. Booth, J. Dunning, E. Fermi, G. Glasoe and F. Slack, Phys. Rev., 55, 511, 1939.
25. R. Ladenburg, M. Kanner, H. Barshall and C. Van Vooris, Phys. Rev., 56, 168, 1939.
26. H. Halban, L. Kowarski et P. Savitch, C. R., 208, 1396, 1939.
27. L. Goldstein, A. Rogozinski et R. Walen, J. Phys. et Rad., 10, 477, 1939.
28. N. Bohr, Phys. Rev., 55, 418, 1939; Nature, 143, 330, 1930.
29. N. Bohr and K. Wheeler, Phys. Rev., 56, 426, 1939.
30. Ya. Frenkel, ZhETF, 9, 641, 1939.
31. S. Flügge u. G. Droste, Z. physik. Chem., 42, 274, 1939.
32. L. Meitner and O. Frisch, Nature, 143, 471, 1939.
33. V. Khlopin, M. Passvik-Khlopina and N. Volkov, DAN, 24, 117, 1939.
34. P. Abelson, Phys. Rev., 55, 418, 670, 876, 1939; 55, 1, 1939.
35. N. Feather and E. Bretcher, Nature, 143, 516, 1939.
36. V. Khlopin, M. Passvik-Khlopina and N. Volkov, DAN, 24, 847, 1939.
37. V. Khlopin, M. Passvik-Khlopina and N. Volkov, DAN, 24, 851, 1939.
38. O. Hahn u. F. Strassmann, Naturwiss., 27, 451, 1939.
39. G. Seaborg and Segrè, Phys. Rev., 55, 808, 1939.
40. O. Hahn u. F. Strassmann, Naturwiss., 27, 89, 1939.
41. F. Heyn, A. Aten and C. Bakker, Nature, 143, 516, 1939.
42. A. Langsdorf, Phys. Rev., 56, 205, 1939.
43. A. Snell, Phys. Rev., 52, 1007, 1937.
44. O. Hahn u. F. Strassmann, Naturwiss., 27, 529, 1939.
45. O. Hahn u. F. Strassmann, Physik. Z., 40, 673, 1939; Naturwiss., 28, 54, 1940.
46. J. Thibaud et A. Moussa, C. R., 208, 744, 1939.
47. R. Dodson and R. Fowler, Phys. Rev., 55, 880, 1939.

1. E. Bretcher and L. Cook, Nature, 143, 559, 1939.
2. O. Hahn, F. Strassmann u. S. Flügge, Naturwiss., 27, 544, 1939.
3. F. Heyn, A. Aten and C. Bakker, Nature, 143, 679, 1939.
4. I. Nishina, T. Yasaki, H. Esoe, K. Kimura and M. Ikawa, Nature, 144, 547, 1939.
5. L. Meitner, Nature, 143, 637, 1939.
6. F. Joliot, J. de Phys. et Rad., 10, 159, 1939.
7. T. Bjerge, K. Brostrom and J. Koch, Nature, 143, 794, 1939.
8. R. Roberts, R. Meyer and P. Wang, Phys. Rev., 55, 510, 1939.
9. R. Roberts, L. Hafstad, R. Meyer and P. Wang, Phys. Rev., 55, 664, 1939.
10. D. Gibbs and G. Thomson, Nature, 144, 202, 1939.
11. G. Fertel, P. Moon, G. Thomson and C. Winn-Williams, Nature, 142, 829, 1938.
12. J. Mouzon, R. Park and J. Richards, Phys. Rev., 55, 668, 1939.
13. J. Mouzon and R. Park, Phys. Rev., 56, 238, 1939.
14. W. Zinn and L. Szilard, Phys. Rev., 55, 799, 1939; 56, 619, 1939.
15. H. Halban, F. Joliot et L. Kowarski, Nature, 143, 470, 680, 1939.
16. H. Anderson, E. Fermi and H. Hanstein, Phys. Rev., 55, 797, 1939.
17. H. Anderson, E. Fermi and L. Szilard, Phys. Rev., 56, 284, 1939.
18. H. Anderson and E. Fermi, Phys. Rev., 55, 1106, 1939.
19. M. Dode, H. Halban, F. Joliot et L. Kowarski, C. R., 208, 995, 1939.
20. H. Halban, F. Joliot and K. Kowarski, Nature, 143, 939, 1939.
21. T. Hagiwara, The Rev. of Phys. Chem. of Japan, 13, 145, 1939.
22. F. Perrin, C. R., 208, 1394, 1939.
23. R. Peirls, Proc. Camb. Phil. Soc., 35, 610, 1939.
24. Ya. Zeldovich and Yu. Khariton, ZhETF, 9, 1425, 1939.
25. M. Whittaker, C. Barton, W. Bright and E. Murphy, Phys. Rev., 55, 793, 1939.
26. C. Haenny et A. Rosenberg, C. R., 208, 898, 1939.
27. L. Goldstein et A. Rogozinski, C. R., 206, 1835, 1939.
28. F. Perrin, C. R., 208, 1573, 1939.
29. F. Adler and H. Halban, Nature, 143, 793, 1939.
30. Ya. Zeldovich and Yu. Khariton, ZhETF, 10, 196, 1940.
31. N. N. Semenov, Chain Reactions, Leningrad, 1934.
32. H. Halban, F. Joliot, L. Kowarski et F. Perrin, J. Phys. et Rad., 10, 428, 1939.
33. O. Frisch, H. Halban and J. Koch, Nature, 140, 895, 1937.
34. F. Adler, C. R., 209, 301, 1939.
35. S. Flügge, Naturwiss., 27, 402, 1939.
36. Ya. Zeldovich and Yu. Khariton, ZhETF, 10, 477, 1940.
37. Kruṣch, Die metallische Rohstoffe, I. Heft, Stuttgart, 1937.
38. J. Mellor, A Comprehensive Treatise of Anorg. and Phys. Chemistry, 12, 3, London, 1932.