Determination of the Absolute Yield of Neutron Sources

M. A. Bak, K. A. Petrzhak, Yu. F. Romanov

The most widespread neutron standards are sources in which beryllium is irradiated by $\alpha$-particles or $\gamma$-quanta from natural emitters. Such sources possess comparatively good stability, continuous operation, compactness, and reproducibility.

The principal characteristics of such a source are its yield and its neutron energy spectrum. By the yield of a source is understood the total number of neutrons emitted per second per one millicurie of active substance.

Determination of the absolute number of neutrons is of great scientific and practical interest, which has not diminished from the time of the discovery of neutrons to the present day. The principles of existing methods for measuring the number of neutrons consist in recording secondary processes caused by neutrons, and also in recording charged particles or $\gamma$-quanta accompanying the emission of neutrons $^{1,2,3}$.

Some attempts to estimate the neutron yield of a radon–beryllium source first appeared as early as 1934 in the works of Dunning $^{4}$ and Fermi $^{5}$.

Dunning, studying the energy spectrum of neutrons from the ranges of recoil protons knocked out of a thin layer of paraffin, roughly estimated the yield as $1.5 \cdot 10^{3}$ neutrons per second. In a similar manner, Fermi and collaborators, studying the radioactivity induced by neutrons in various elements, concluded that the yield was approximately equal to $10^{3}$ neutrons per second. In the same year, Dee $^{6}$ determined the average number of neutrons produced by one $\alpha$-particle interacting with aluminum and beryllium. The neutrons were recorded in a Wilson chamber by recoil protons. He found that, on average, for one $\alpha$-particle of radon and its decay products bombarding aluminum, there are $1.3 \cdot 10^{-6}$ neutrons.

For beryllium this number increases by a factor of 70. On the basis of these data one may calculate the yield of a radon–beryllium source, which is found to be close to \(10^4\) neutrons per second, which considerably exceeds the data of preceding works. From similar measurements carried out in work 7, it follows that in a radon–beryllium source only \(10^3\) neutrons per second would be obtained per millicurie of radon.

As a result of studying neutron absorption in paraffin spheres of various radii and in various cylindrical layers of water surrounded by cadmium screens, Fink\({}^{8}\) roughly estimated the value of the yield of a radon–beryllium source at \(1.4\cdot 10^4\) neutrons per second.

If in the works listed the neutron yield was determined approximately and incidentally, then in subsequent investigations special attention was devoted to this question.

One of the first methods, which has not lost its importance up to the present time, is the method of slowing down neutrons with subsequent counting of slow neutrons. If a source of fast neutrons is placed in a hydrogen-containing medium, then the neutrons emitted, as a result of interaction with hydrogen nuclei, will be slowed down and absorbed. In connection with this, a stationary distribution of slow neutrons is established in the moderator. The form of the function of the spatial distribution of slow neutrons in the moderator is determined by the energy spectrum of the initial neutrons. The total number of neutrons \((Q)\) emitted per second by the source is equal to the number of neutrons absorbed per second in the entire volume of the moderator, i.e.,

\[ Q=\int_V \rho(r,\theta,\varphi)\, v n_H \sigma_H r^2 \sin\theta\, dr\, d\theta\, d\varphi, \tag{1} \]

where \(\rho(r,\theta,\varphi)\) is the density of slow neutrons as a function of the coordinates \(r,\theta,\varphi\); \(\sigma_H\) is the effective capture cross section by hydrogen of slow neutrons of velocity \(v\), calculated per one nucleus; \(n_H\) is the concentration of hydrogen in the moderator.

Absorption of neutrons by other nuclei included in the composition of the moderator is neglected. (Taking into account neutron absorption by other nuclei leads to the fact that instead of \(n_H\sigma_H\) there appears \(\sum_i n_i\sigma_i\).) For a point or spherical source whose neutron emission is isotropic, this expression takes the form

\[ Q=4\pi \int_0^\infty \rho(r)\, v n_H\sigma_H r^2 dr. \tag{2} \]

If we assume that the effective cross section for the capture of slow neutrons by hydrogen obeys the law \(\sigma_{\mathrm H}=\sigma_{0\mathrm H}\frac{1}{v}\), then the subintegral function will not depend on \(v\). Then

\[ Q=4\pi n_{\mathrm H}\sigma_{0\mathrm H}\int_{0}^{\infty}\rho(r)r^{2}dr . \tag{3} \]

By registering neutrons with some detector and measuring the intensity of secondary processes, one can construct the dependence of the number of registrations \(N(r)\) on distance. \(N(r)\) will be proportional to the density \(\rho(r)\), if the detector does not distort the neutron distribution.

\[ Q=4\pi n_{\mathrm H}\sigma_{0\mathrm H}\int_{0}^{\infty}\frac{N(r)r^{2}}{\sigma_{\mathrm d}vB}\,dr =4\pi\frac{n_{\mathrm H}\sigma_{0\mathrm H}}{B\sigma_{0\mathrm d}}\int_{0}^{\infty}N(r)r^{2}dr, \tag{4} \]

if the cross section for neutron capture by the detector \(\sigma_{\mathrm d}\) also obeys the law \(\frac{1}{v}\). The constant \(B\) is proportional to the amount of detector material and depends on the particular features of counting the secondary processes caused by neutrons.

Thus, the method requires determining the absolute efficiency of the detector and knowing the ratio of the effective cross sections for the capture of slow neutrons by the moderator and by the detector. The value of the integral is determined by measuring \(N(r)\) at different distances from the source. In practice, the integration is performed graphically, since the analytic form of the distribution function \(N(r)r^{2}\) is not known.

The principle of this method was proposed in 1936 by Amaldi and Fermi\(^{9}\). Placing a radon–beryllium source in a large vessel with water, they determined the spatial distribution of thermal neutrons. The detector was rhodium foil, coated on one side with cadmium. Their method for calculating the neutron yield did not fully correspond to the description given above, but assumed knowledge of many constants connected with the processes of neutron slowing down and capture and with \(\beta\)-counting of radioactive rhodium. They found that the yield of the radon–beryllium source was equal to \(2.7\cdot10^{4}\) neutrons per second. Amaldi, Hafstad, and Tuve\(^{10}\) in 1936 repeated this experiment, somewhat improving the \(\beta\)-counting technique. They concluded that the yield was \(2.5\cdot10^{4}\) neutrons per second.

Becker\(^{11}\) was the first to use radium as a neutron source and measured the number of neutrons from a radium–beryllium source by the same method. The source contained \(94.33\) mg of radium and \(2\) g of beryllium.

The moderator was water, and the detector used was silver and rhodium. Assuming similarity of the $\beta$-spectrum of the UX$_2$ preparation to the $\beta$-spectra of silver and rhodium, Becker found that one milligram of radium corresponds to $2.1 \cdot 10^4$ neutrons per second.

Walker$^{12}$ reported in 1946 that in October 1944 he had determined the total number of neutrons emitted by a source containing 500 mg of radium. Yü$^{13}$ describes this work in detail in his book. All neutrons from the source were slowed down and absorbed in a large tank filled with a boric-acid solution. The spatial distribution of slow neutrons in the bulk of the solution was measured by means of thin manganese foil. Calibration of the foil was carried out by successively placing it and a proportional counter filled with boron trifluoride in the same field of thermal neutrons, produced by another arbitrary source in paraffin. In this way the neutron density corresponding to a definite activity of the foil was found. It was assumed that the counter registered all $\alpha$-disintegrations of boron, the number of which is exactly known. Walker obtained that the source emits $(5.9 \pm 0.3)\cdot 10^5$ neutrons per second.

In work$^{14}$ the number of neutrons was determined by measuring the spatial distribution of slow neutrons in water with indium foil. By placing the foil and a chamber, whose electrodes were coated with a known layer of lithium, in the same neutron flux, the authors calibrated the foil. The activity of the indium foil was measured with a $\beta$-counter filled with argon. The ratio of the cross sections for capture of slow neutrons by lithium and hydrogen needed for the calculation was taken from the literature. As a result it was found that a source consisting of 501.87 mg of radium in the form of bromide salt and 2.5 g of beryllium gives $(3.01 \pm 0.15)\cdot 10^6$ neutrons per second.

Larson$^{15}$ in 1954 determined the neutron yield of a radium-beryllium source, using the above-described method. Neutrons were detected in two ways: by a chamber filled with boron trifluoride, by the method of counting $\alpha$-disintegrations of boron, and by gold foil, whose activity was measured by the $\beta-\gamma$ coincidence method. In the first case the moderator was an aqueous solution of boric acid at three different concentrations; in the second case, pure water. Larson carefully investigated the sources of possible errors. Corrections were introduced for absorption of neutrons by the chamber walls, for perturbation of the neutron field near the detector, and for absorption of slow neutrons by the source itself. Larson found that a source containing 250 mg of radium emits $(2.57 \pm 0.12)\cdot 10^6$ neutrons per second (detector—a boron chamber) and $(2.62 \pm 0.08)\cdot 10^6$ neutrons per second (detector—gold). The final result proves to be equal to $(2.60 \pm 0.08)\cdot 10^6$ neutrons per second.

In paper ^16 measurements were also made with a radium–beryllium source. The moderator was water, and detection was carried out with gold, similarly to the way it was done in Larson’s paper ^15. As a result it was found that one gram of radium corresponds to \(15.53\cdot 10^6\) neutrons per second.

At the end of 1954 a note by Gelloud and Henny ^17 was published. Detecting neutrons, slowed down in a solution of boric acid, by means of an emulsion containing boron nuclei, they determined that \(1\ \text{g}\) of radium gives \((1.5\pm 0.07)\cdot 10^7\) neutrons per second. Their source contained \(47.29\ \text{mg}\) of radium.

Paneth, Glückauf, and Loleit ^18 in 1936 developed the so-called “helium” method. The experimental conditions of the experiment were as follows. A copper vessel of radius \(10\ \text{cm}\), at the center of which was a radon–beryllium source, was filled with methyl ester of boric acid \(B(OCH_3)_3\) and immersed in a reservoir with water. The helium accumulated as a result of many days’ irradiation of boron by neutrons, according to the reaction \(B^{10}(n,\alpha)Li^7\), was separated and quantitatively determined with the aid of specially developed techniques. The presence of helium was first detected qualitatively—spectroscopically. The method of their microchemical analysis made it possible to determine a quantity of helium of the order of \(10^{-7}\ \text{cm}^3\) (under normal conditions). Knowing the duration of irradiation, one can calculate the neutron yield. It turns out to be \(6.7\cdot 10^3\) neutrons per second. However, in the experiment no allowance was made for the fraction of neutrons escaping beyond the limits of the vessel and not absorbed by boron. Therefore the true yield is greater than the value obtained. It is interesting to note that in an earlier paper ^19, based on this same method, Paneth and Loleit found that the yield exceeds 3000 neutrons per second.

Glückauf and Paneth ^20, irradiating with \(\gamma\)-rays of radon and its products a beryllium sphere of radius \(0.84\ \text{cm}\), found that the amount of helium accumulated in the beryllium is approximately twice as large as in methyl ester of boric acid, i.e., the reaction

\[ Be^9 + h\nu \to 2He^4 + n_0^1 \]

takes place. However, the neutron yield by means of separating helium from beryllium was not determined.

Sayd and Harris ^21 in 1947 developed a method for determining the number of neutrons from the production of helium as a result of the reaction \(B^{10}(n,\alpha)Li^7\), with subsequent comparison of the effects caused by small and large neutron fluxes. In an aqueous solution of \(H_3BO_3\) and \(MnSO_4\), upon irradiation by neutrons from a radium–beryllium source placed at the center of the vessel, helium and a \(\beta\)-active isotope of manganese accumulate. Since the amount of helium is too small for detection, a relative method was applied. A small part of this same solution, sealed in an ampoule, was irradiated in a reactor by a large flux of slow neutrons for the same length of time. The amount

helium (about \(10^{-4}\ \mathrm{cm}^3\) under normal conditions), accumulated in the ampoule, was measured by Paneth’s method\(^{18}\), and the \(\gamma\)-activity of the solution contained in the ampoule was compared with the \(\gamma\)-activity of a solution irradiated with a radium–beryllium source. It is obvious that the ratio of the activities is equal to the ratio of the volumes of helium accumulated in the ampoule and in the vessel. Introducing a correction allowing for the fraction of neutrons not absorbed by boron, the authors obtained that source No. 38 of the Argonne Laboratory, containing 504 mg of radium mixed with 3 g of beryllium, gives \((5.5 \pm 0.4)\cdot 10^6\) neutrons per second.

This helium method is, in essence, a certain modification of the above-described method of determining the number of neutrons by finding the spatial distribution of slow neutrons in a moderator. Here the integration is contained in the very fact of helium accumulation, while the determination of the absolute efficiency of the detector is reduced to the measurement of a small quantity of helium.

A somewhat different modification of this method was used in the work of Nield and Sharff-Goldhaber\(^{22}\), who in 1946 determined the number of neutrons emitted by a photoneutron source consisting of 100 mg of radium and 85 g of beryllium. The source was placed at the center of a large vessel with an aqueous solution of manganese sulfate, in which there was an additional absorber—manganese powder. After irradiation the solution was thoroughly mixed, which was essentially a kind of integration. First the fraction of neutrons not captured by the absorber, \(R\), was found. For this purpose, with the aid of a large thin-walled \(\beta\)-counter, the activity of the solution irradiated in the presence of the absorber and without it was measured. Then the absolute number of neutrons \(N_a\) captured by the absorber per unit time was determined from its \(\beta\)-activity, which was found by comparison with the activity of a \(UX_2\) preparation. Whereas in work\(^{1}\) it was assumed that the \(\beta\)-spectrum of \(UX_2\) is similar to the spectra of silver and rhodium, in this work it was assumed to be similar to the spectrum of manganese. The total number of emitted neutrons is equal to

\[ Q=\frac{N_a}{1-R}. \]

The authors found that the source gives \((8.6 \pm 0.8)\cdot 10^4\) neutrons per second. This corresponds to a photoneutron yield of 860 neutrons per second.

Hammermeshfelder and M. Goldhaber\(^{23}\) compared this source with a radium–beryllium source by the following method\(^{24}\). If the investigated source \(Q_x\) and a source emitting a known number of neutrons \(Q_0\) are successively surrounded by a sufficiently large layer of hydrogen-containing moderator and the thermal neutrons are detected at different distances from the source, then according to expression (3) the sought-

DETERMINATION OF THE ABSOLUTE YIELD OF NEUTRON SOURCES

the number \(Q_x\) will be equal to

\[ Q_x = Q_0 \frac{\displaystyle\int_0^\infty N_x(r) r^2 dr} {\displaystyle\int_0^\infty N_0(r) r^2 dr}, \tag{5} \]

where \(N_x(r)\) is the activity of a thermal-neutron detector successively placed at different distances \(r\) from the fast-neutron source under study, and \(N_0(r)\) is the activity of the same thermal-neutron detector corresponding to a fast-neutron source with \(Q_0\).

Expression (5) is valid for point sources of fast neutrons of any energy spectrum, if thermal neutrons are being detected. In this way Hammersfelder and M. Goldhaber found that the yield of a radium-beryllium source is \(6.8 \cdot 10^3\) neutrons per second.

By the same method of an additional absorber, the absolute number of neutrons from a radium-beryllium source was determined in the work of Sachs and Ranganad\({}^{25}\). A neutron source placed in a solution of manganese sulfate was surrounded by a uniform layer of metallic manganese powder. The activity of the powder after irradiation was measured with an end-window \(\beta\)-counter, with corrections introduced for geometry, backscattering, and self-absorption. The activity of the solution, thoroughly mixed after irradiation, was measured with a long counter. The authors determined that a source containing 95 milligrams of radium emits \(1.25 \cdot 10^6\) neutrons per second.

Alder and Huber\({}^{26}\), measuring the yield of a radium-beryllium source, also used the principle of an additional absorber, applied in work\({}^{22}\). An aqueous solution of manganese sulfate was placed in a spherical vessel 50 cm in diameter, surrounded by water. The source was located at the center of the vessel. In this work, instead of an additional absorber—manganese powder—the authors used a solution of manganese sulfate at two different concentrations. The solution was thoroughly mixed, and its activity was determined by means of a special counter, which was calibrated in the following manner. A definite quantity of solution of the given concentration was irradiated with neutrons produced as a result of the reaction \(\mathrm{D}(d,n)\mathrm{He}^3\). After irradiation, the activity of part of the solution was measured with this counter, and from another part manganese was precipitated in the form of \(\mathrm{MnCO}_3\). A thin layer of this precipitate was placed inside a \(2\pi\)-counter intended for the absolute measurement of \(\beta\)-activity. Having determined the fraction of neutrons escaping from the solution into the water, and taking into account the correction for the presence of sulfur, the authors found that the investigated source, containing 96.49 mg of radium, emits \((6.10 \pm 0.45)\cdot 10^5\) neutrons per second,

For determining the neutron yield, one can use a neutron generator of the type D(d, n)He³. The energy of the neutrons produced in this reaction is practically independent of their angle of emission, if the deuteron energy is close to 100 keV. In connection with this, it becomes possible, by determining the scattering cross section of neutrons on certain light nuclei, to find the number of neutrons emitted by this generator by the method of counting recoil nuclei.

Ladenburg and Kanner²⁷ in 1937 compared the yield of a radium–beryllium source and a source in which neutrons are obtained as a result of the bombardment of heavy ice by deuterons. Fast neutrons were registered with the aid of recoil nuclei in an ionization chamber filled either with nitrogen or with oxygen. Having determined the effective scattering cross section of these neutrons by the nuclei of liquefied nitrogen and oxygen, they found that per microampere of deuteron beam of energy 100 keV there are \(2.3 \cdot 10^5\) neutrons per second. This result was obtained on the assumption of an isotropic distribution of the neutrons produced by the reaction D(d, n)He³ at the given deuteron energy. Comparing the obtained number of neutrons with that emitted by a radium–beryllium source by the method of detecting slow neutrons, they found that the yield is \(6 \cdot 10^3\) neutrons per second.

It is known that introducing a neutron source into an operating reactor increases the reactor power, while, on the other hand, introducing an absorber decreases its power, so that, by placing a calibrated source and absorber inside the reactor, one can obtain the initial power. As a result of such balancing of powers, one can find the number of neutrons emitted by the source by measuring the absolute activity of the absorber. In this method there is no particular need to carry out an absolute balancing of two oppositely acting effects, since they are relatively small and linear. In order to increase the accuracy of the method, the source is moved in the reactor from the center to the surface and back. In Littler’s work²⁸ this method was applied. The absorbers were sodium and phosphorus, whose absolute activity was measured by the coincidence method. According to the author’s measurements, a source containing 1290 mg of radium in the form of sulfate and 12 g of beryllium emits \(9.3 \cdot 10^6\) neutrons per second. The method permits measurements with an accuracy of 4.5%; however, the absolute number of emitted neutrons must be of the order of \(10^7\) neutrons per second, i.e., the source must contain not less than one gram of radium.

In a number of works there are individual indications of yield values obtained by some authors without a description of the research procedure. Thus, Gaigerl and Broda²⁹ confine themselves to indicating that the source they used, containing 300 mg of radium in the form of chloride mixed with 2–3 g of beryllium, gave about \(3 \cdot 10^6\) neutrons per sec—

du. In this same work there is a reference to the work of Bower et al.,\(^{30}\) where it was found that one millicurie of radon–beryllium produces \(1.5 \cdot 10^4\) neutrons per second. In the work of Jonker and Blok\(^{31}\) there is a reference to a number of studies\(^{32,33,34}\) in which it was determined that 100 milligrams of radium mixed with beryllium emit \((0.9—1.0)\cdot 10^6\) neutrons per second. Littler\(^{28}\) refers to works\(^{35,36,37}\) in which the yield from a radium–beryllium source was found to be \((1.1—1.6)\cdot 10^4\) neutrons per second. In work\(^{38}\) it was found that a radium–beryllium source containing 500 mg of radium and 5 g of beryllium emits \((5.85 \pm 0.76)\cdot 10^6\) neutrons per second.

In recent years, works have appeared in which sources of other types have been investigated.

In the work of Bretscher, Cook, et al.,\(^{39}\) published in 1949, a method is described for preparing a source in which radium is chemically introduced into the composition of the crystalline compound \(\mathrm{RaBeF}_4\). Neutron formation here occurs not only through the reaction \(\mathrm{Be}^9(\alpha,n)\mathrm{C}^{12}\), but also through the reaction \(\mathrm{F}^{19}(\alpha,n)\mathrm{Na}^{22}\). The presence of four fluorine atoms in the molecule makes the effect of the second reaction appreciable. According to relative measurements, 1 g of \(\mathrm{RaBeF}_4\) gives on average \(1.84\cdot 10^6\) neutrons per second. It should be noted that the ratio of the number of beryllium atoms to the number of radium atoms in a “mixed” radium–beryllium source is of the order of \(200:1\), whereas in this source it is equal to \(1:1\), yet the yield is only 4–6 times smaller. This is apparently explained by an increase in the probability of encounter of the \(\alpha\)-particle with the beryllium nucleus.

Andersen and Feld\(^{40}\) investigated the relative yields of pressed sources consisting of a mixture of radium bromide with metallic beryllium powder. They give a formula for determining the yield of pressed sources, according to which the source gives

\[ 1.7\cdot 10^4 \frac{M_{\mathrm{Be}}}{M_{\mathrm{Be}} + M_{\mathrm{RaBr}_2}} \]

neutrons per second per 1 mg of radium, where \(M\) denotes the masses of the corresponding components of the mixture.

In the work of Spinks and Graham\(^{41}\), by comparison with a standard source, a polonium–beryllium source containing 2.1 curies of polonium was calibrated. It was found that it emits \(2\cdot 10^6\) neutrons per second.

Crouch and Diller\(^{42}\) in 1953 proposed a new method for measuring the yield of polonium–beryllium neutron sources. In view of the fact that polonium practically does not emit hard \(\gamma\)-rays, these authors propose to register, by the coincidence method, neutrons and \(\gamma\)-rays accompanying neutron emission. It is proposed to register the \(\gamma\)-rays by means of a NaI crystal activated with thallium. The authors propose to detect the neutrons, after moderation in a hydrogen-containing medium, with boron;

using the time delay necessary for slowing down. If a known number of γ-quanta falls on one neutron, then, by counting the number of coincidences \(n-\gamma\) and independently determining the probability of coincidence under the conditions of the experiment, one can find the yield of the source. The method is under development; here it is necessary first of all to determine the average number of γ-quanta accompanying the formation of one neutron.

Stuart\(^{43}\) measured the number of neutrons emitted by a source consisting of 13 g of plutonium and 7 g of beryllium. This source has γ-radiation of low intensity, a long lifetime (\(T\sim 24000\) years), and a comparatively high yield. In addition, the \(U^{235}\) α-emitter following plutonium has a half-life of \(\sim 10^7\) years. This makes the source a good standard. Stuart measured the neutron spectrum and the intensity of the source by recoil protons in an emulsion. He found that the source gives \(1.2\cdot 10^6\) neutrons per second whose energy exceeds \(0.5\) MeV, i.e., about 100 neutrons per 1 mg of plutonium.

Whereas in works\(^{22,23}\) an absolute determination of the yield of a photoneutron source was made and a subsequent comparison of a radium–beryllium source with it, in the works cited below the yield of photoneutron sources was found by comparison with the already known yield of radium–beryllium sources.

Curtiss and Carson\(^{45}\) in 1949 prepared two photoneutron sources, each consisting of a beryllium sphere 4 cm in diameter, at the center of which 1 g of radium was placed. The careful manufacture of these sources ensured good reproducibility. The sources were found to differ by 0.1%. The neutron yield, found by the method of comparison with another known source by means of a long counter filled with \(BF_3\) gas enriched with the isotope \(B^{10}\), proved equal to \(1.1\cdot 10^3\) neutrons per second per 1 mg of radium.

In work\(^{46}\) a photoneutron source containing 1935 mg of radium was used. The source emitted \(4.17\cdot 10^6\) neutrons per second, which was established by comparison with existing radium–beryllium sources, namely with source No. 44 of the Los Alamos Laboratory, emitting \(5.9\cdot 10^6\) neutrons per second, with source No. 37, emitting \(4.28\cdot 10^6\) neutrons per second, and with source II of the Metallurgical Laboratory, which gives \(12.8\cdot 10^6\) neutrons per second.

In the present review, works are cited that were published in print up to 1955 and devoted to the question of determining the absolute number of neutrons emitted every second by neutron sources. Most investigators used, in essence, one and the same method, namely the method of slowing down neutrons in hydrogen-containing media with subsequent detection

slow neutrons either by a \(\frac{1}{v}\) detector or by a resonance detector.

The method presupposes spatial integration of the distribution of slow neutrons in the moderator and determination of the absolute efficiency of the detector. The helium method\(^{18,21}\) and the method of the additional absorber\(^{22,25,26}\) are certain modifications of this method. The accuracy of the measurement lies within 5–10 percent.

Detection of monochromatic neutrons from the reaction \(\mathrm{D}(d,n)\mathrm{He}^3\) makes it possible to determine the number of neutrons emitted by this generator\(^{27}\). Subsequent comparison with a radium–beryllium source by the method of detecting neutrons in a moderator makes it possible to estimate the yield. The accuracy of this method is about \(10\%\).

An original method is one based on the influence of the source and neutron absorber on the power of a nuclear reactor\(^{28}\). Here an accuracy of \(4.5\%\) is achieved.

A promising method is the registration of charged particles produced as a result of nuclear reactions with the formation of neutrons\(^{2}\). Unfortunately, the published literature contains no results of application of this method. Such reactions, for example, may be the following:

\[ \begin{aligned} \mathrm{D}^2 + \mathrm{D}^2 &\to \mathrm{He}^3 + n_0^1,\\ \mathrm{D}^2 + \mathrm{H}^3 &\to \mathrm{He}^4 + n_0^1,\\ \mathrm{H}^1 + \mathrm{H}^3 &\to \mathrm{He}^3 + n_0^1,\\ \mathrm{D}^2 + h\nu &\to \mathrm{H}^1 + n_0^1 \end{aligned} \]

(in the first case the formation of tritium and a proton is possible). After determining the number of charged particles and, correspondingly, the number of neutrons, a comparison should be made with a continuously operating source, thereby completing the calibration. It may be assumed that the accuracy of this method will be sufficiently good, especially in the photodisintegration of the deuteron\(^{2,47}\).

Below is a table in which the results of all the cited works are compared. The first and second columns include the authors’ names and the numbers of the literature references; the third column gives the year of publication of the work; the following columns show the type of source, the quantities of radium or radon and beryllium present in it, the type of moderator, and the type of detector. Finally, the total number of neutrons emitted by the source is given. The last part of the table shows the neutron yield for \(\mathrm{Rn}+\mathrm{Be}\) and \(\mathrm{Ra}+\mathrm{Be}\) sources. Some entries in the table have remained unfilled because no definite answer was given for them in the corresponding original works.

DETERMINATION OF THE ABSOLUTE YIELD OF NEUTRON SOURCES

It is evident from the table that over the course of twenty years researchers showed an unfailing interest in this question. Whereas in the first years of the investigations the work was carried out with sources of the Rn + Be type, in recent times work has been done mainly with sources of the Ra + Be type. This fact of the “displacement” of radon by radium indicates the desire of investigators to work with sources that are sufficiently stable in time. The table shows that the yield values of sources within one and the same type differ considerably from one another. This is explained by a number of reasons,

Values of the intensity of one and the same source, obtained as a result of measurements in different laboratories and expressed in fractions of the value found at the Argonne laboratory.

the chief of which are the nonstandard technology of source manufacture and the degree of purity of the initial products. In this connection the neutron yield cannot be the same for different sources and cannot serve as a criterion of the correctness of the measured number of neutrons emitted by the source.

In recent years, comparative measurements of the same sources have been carried out in a number of countries in order to check the reliability of various methods of quantitative determination of neutron yields. On the basis of these relative measurements, Hughes \(^{13,47}\) constructed a diagram (see figure) showing the values of the total

intensities of one and the same source, obtained as a result of measurements in different laboratories and reduced to the value obtained by the Argonne Laboratory and adopted as unity. For comparison the following neutron standards were used: Harwell[^28], Argonne[^21], Los Alamos[^12], Italian[^14], Swiss[^26], Swedish[^15], and Belgian[^16]. Data on the French and one of the American (National Bureau of Standards) sources have not been published. The diagram shows that repeated comparison of sources led to better agreement of the results, which confirms the reliability of the various methods.

It is quite obvious that in the coming years more detailed work will continue on bringing the results of the corresponding laboratories into mutual agreement.

CITED LITERATURE

1. I. A. Vlasov, UFN 42, issue 2, 169 (1951).
2. A. Wattenberg, Ann. Rev. Nuclear Sci. 3, 119 (1953).
3. H. H. Barschall, L. Rosen, R. F. Taschek, J. H. Williams, Rev. Mod. Phys. 24, No. 1, 1 (1952).
4. J. R. Dunning, Phys. Rev. 45, 586 (1934).
5. E. Fermi, E. Amaldi, O. D’Agostino, F. Rasetti, E. Segre, Proc. Roy. Soc. 146, 483 (1934).
6. R. Jaeckel, Zeits. f. Physik 91, 493 (1934).
7. C. D. Ellis, W. J. Henderson, Nature 133, 530 (1934).
8. G. A. Fink, Phys. Rev. 50, 738 (1936).
9. E. Amaldi and E. Fermi, UFN 17, issue 3, 5 (1937).
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