Full Text
From Current Literature
Detailed Analysis of the Disintegration of Light Nuclei by High-Energy Nucleons
Although at present the cross sections of inelastic collisions of high-energy nucleons are well known, there is still fairly little information about exactly which reactions make up the overall picture of such collisions. This year three papers appeared in which a detailed analysis is made of all reactions of interaction of neutrons of mean energy 90 MeV with helium and carbon nuclei¹ ² and of most products of the disintegration, by protons of energy 330 MeV, of beryllium and carbon nuclei.³
The study of the interaction of neutrons with helium and carbon nuclei was carried out using a Wilson chamber, 56 cm in diameter, placed in a pulsed magnetic field with an induction of up to 22,000 gauss.
In paper 1 the chamber was filled with 99% helium to a pressure of 815 mm Hg and with water vapor, so that the ratio of the number of helium and oxygen nuclei immediately after expansion was 51.8. In paper 2, to fill the chamber a mixture of methane with hydrogen was used, and the composition of the mixture after expansion was: 474.5 mm Hg methane, 348.5 mm Hg hydrogen, and 17.5 mm Hg water vapor. In processing the measurement results the necessary corrections for the small admixture of oxygen were introduced.
Neutrons with a mean energy of 90 MeV were obtained by bombarding beryllium targets with deuterons of energy 190 MeV; they were collimated by apertures in thick layers of concrete and lead or copper and entered the chamber through an aluminum window 25 microns thick.
Light particles—protons, deuterons, tritons, He³, and α-particles—were identified by the radius of curvature of the trajectories and by the length and density of the track. In some cases the identification problem was simplified by the possibility of observing the gradual change in the radius of curvature near the end of the trajectory. The Wilson chamber did not, however, make it possible to determine exactly the masses of “heavy” fragments (Li, Be, B, and C nuclei) formed in the disintegration of carbon nuclei. Therefore in paper 2, in order to clarify the nature of the products of the interaction of neutrons with carbon nuclei, the rotating-disk method was also used; it will be discussed below.
In studying the disintegration of helium nuclei by neutrons, on each photograph there were observed, on the average, three two-prong stars and the same number of strongly ionizing single tracks. Stars with three or more rays from the disintegration of oxygen nuclei were rarely encountered.
The following lists all possible reactions of helium disintegration:
1) \(n + \mathrm{He}^4 \to d + t\) (abbreviated as \(dt\)),
2) \(n + \mathrm{He}^4 \to p + t + n\) \((pt)\),
3) \(n + \mathrm{He}^4 \to d + d + n\) \((dd)\),
4) \(n + \mathrm{He}^4 \to p + d + 2n\) \((pd)\),
5) \(n + \mathrm{He}^4 \to p + p + 3n\) \((pp)\),
6) \(n + \mathrm{He}^4 \to \mathrm{He}^3 + 2n\) \((\mathrm{He}^3)\),
7) \(n + \mathrm{He}^4 \to \mathrm{He}^4 + n\) \((\mathrm{He}^4)\) (elastic scattering).
The first five reactions lead to the formation of two-prong stars; the last two, to the appearance of strongly ionizing single particles.
Since in two-prong stars from the disintegration of helium nuclei there can be only particles with unit charge \((p, d, t)\), the specific ionization and curvature of the trajectory in the magnetic field unambiguously determined the type and energy of the particles. The non-coplanarity of the two tracks with the direction of the primary neutrons distinguished cases 2–5 from the \(dt\) process, which served as an additional identification factor. Of the 179 two-prong stars, only in eight cases was it not possible to establish precisely which reaction the observed stars corresponded to.
For the \(dt\), \(pt\), and \(dd\) reactions, from the magnitude of the energy and momenta of the secondary charged particles it was possible to determine what the energy of the primary neutrons had been. For the \(pd\) reaction it was possible to estimate the lower limit of this energy, on the assumption that the two undetected neutrons share the residual momentum between them. Only in the case of \(pp\) could the energy of the primary neutrons not be estimated with any reliability. In the study of two-prong stars, only those were taken into account in which both prongs lay at angles not exceeding \(\pm 30^\circ\) to the horizontal direction. To determine the total cross sections of the various reactions, the authors introduced a geometrical correction taking into account the fraction, out of the total number of various stars, falling within angles \(\pm 30^\circ\). The correctness of this correction was confirmed by a direct count of the total number of stars at all angles (without detailed analysis of these stars).
Two-prong stars do not exhaust all variants of the inelastic interaction of neutrons with helium nuclei. Such interactions also include one-prong stars with the formation of \(\mathrm{He}^3\). Meanwhile, the accuracy of the method in the overwhelming majority of cases did not permit one to distinguish the tracks of \(\mathrm{He}^3\) and \(\mathrm{He}^4\). In order to estimate the yield of \(\mathrm{He}^3\), author 1 assumed that the ratio of the cross sections of the \(\mathrm{He}^3\) and \(pt\) reactions is equal to the ratio of the cross sections of the \(nn\)- and \(np\)-scattering, i.e. for \(90\ \mathrm{MeV}\) it is equal to \(1/3\), if one takes \(\sigma_{nn} = \sigma_{pp}\). In doing so, to calculate the \(\mathrm{He}^3\) yield the author took into account not only the pure \(pt\) case, but also the \(dt\) case with deuterons emitted forward, since in such a process of capture of a proton from the \(\mathrm{He}^4\) nucleus by the bombarding neutron (“pick-up”) the deuteron is not formed at the very instant of collision, so that the first stage of the collision here may be regarded as the formation of \(n + p + t\).
Thus, for the \(\mathrm{He}^3\) yield it was adopted:
\[ \sigma_{\mathrm{He}^3} = \frac{1}{3}\left[\sigma_{pt} + \sigma_{dt\ d-\mathrm{forward}}\right]. \]
The sum of the data on the inelastic interaction of neutrons with helium nuclei is given in Table I. The appearance of noninteger values in the second row of this table is connected with the fact that the eight unidentified stars were distributed among the various cases in the same ratio as the identified ones (four stars between \(pt\) and \(pd\), four between the first five cases).
The corrected values include the above-mentioned geometrical correction. The absolute values of the cross sections were obtained on the assumption that
FROM CURRENT LITERATURE
Table 1
| pt | dt | pd | dd | pp | He³ | Total | |
|---|---|---|---|---|---|---|---|
| Identified . . | 88.0 | 33.0 | 31.0 | 17.0 | 2.0 | — | 171.0 |
| Not identified . . | 5.1 | 0.8 | 1.7 | 0.4 | — | — | 8.0 |
| Sum . . . | 93.1 | 33.8 | 32.7 | 17.4 | 2.0 | — | 179.0 |
| Corrected sum | 212.6 | 75.5 | 76.3 | 37.0 | 3.8 | [83.5] | 488.7 |
| Sum for neutrons with energy \(>40\) MeV | 209.1 | 66.5 | 76.3 | 35.2 | 3.8 | [80.8] | 471.7 |
| Possible error, % . . . | 7.3 | 12.3 | 12.1 | 16.8 | 48.0 | — | 5.2 |
| Cross section \((\times 10^{27}\ \text{cm}^2)\) | 42 | 13 | 15 | 17 | 0.8 | [16] | 94 |
| Possible error \((\times 10^{27}\ \text{cm}^2)\) . . . | 6 | 2.5 | 2.5 | 1.5 | 0.4 | — | — |
In all, 472 cases of inelastic collisions and 484 acts of elastic scattering were observed; and the total cross section for the interaction of neutrons with mean energy 90 MeV with helium nuclei, on the basis of interpolation of the data for H, D, Li, and Be, was taken to be \(1.9\cdot 10^{-25}\ \text{cm}^2\).
Elastic scattering was studied by counting the endings of He⁴ tracks in the chamber and single unfinished tracks, with the introduction of the corresponding geometrical corrections. The cross section for elastic scattering \(n+\mathrm{He}^4\), determined in ¹ as \(96\pm17\cdot 10^{-27}\ \text{cm}^2\), was close to the cross sections for inelastic interaction, and elastic scattering proved, as for other nuclei in this neutron-energy region, to be very close.
In ¹ the obtained cross sections for various reactions \(n+\mathrm{He}^4\) are compared with the predictions of theoretical work ⁴. When the total cross section is normalized to the value \(1.9\cdot 10^{-25}\ \text{cm}^2\), the theory gives the following cross sections (in \(10^{-27}\ \text{cm}^2\)): elastic scattering — 125, pt — 46, dt — 12.5, pd — 1.5, dd — 0, pp — 0, He³ — 5. Thus, for the first three cases, good agreement of experiment and theory is observed. The theory also correctly predicted the small probability of the pp case. The ratio of the yields of He³ and pt in theory ⁴ was estimated as
\[ \frac{\frac{1}{4}}{\frac{1}{4}+\frac{3}{4}} \left(\frac{V_{\text{singlet}}}{V_{\text{triplet}}}\right)^2 \simeq \frac{1}{12}, \]
whereas in ¹ it is taken to be equal to
\[ \frac{\sigma_{np}}{\sigma_{np}} \simeq \frac{1}{3}. \]
In support of his estimate, the author of ¹ cites unpublished experiments of V. Powell on \(nd\)-interaction at 90 MeV. In this interaction the cross section for the production of protons of small energy \((<10\ \text{MeV})\), corresponding to quasifree \(nn\)-scattering, was \(14.6\cdot10^{-27}\ \text{cm}^2\), while the cross section for the production of protons of higher energy, corresponding to quasifree \(np\)-scattering, was \(51.1\cdot10^{-27}\ \text{cm}^2\).
For some helium-splitting reactions in ¹, data are given on the spectra and angular distribution of the products. These results are presented in Figs. 1–4. It should be noted that although the total cross section of the dt process, found in ¹, agrees satisfactorily with theory ⁴,
the angular distribution of the deuterons in this reaction (Fig. 1) strikingly contradicts the theory. Thus, the ratio of the number of deuterons emitted into the forward and backward hemispheres proved to be about 1:1, whereas in the predictions it was
Fig. 1. Angular distribution of deuterons in the reaction
\(n + \mathrm{He}^4 \to d + t\).
Fig. 2. Spectrum of deuterons produced in the reaction
\(n + \mathrm{He}^4 \to d + t\).
Fig. 3. Spectra of protons produced in the reactions \(n + \mathrm{He}^4 \to p + t + n\) and \(n + \mathrm{He}^4 \to p + d + 2n\), and spectrum of tritons produced in the reaction
\(n + \mathrm{He}^4 \to p + t + n\).
Inside the figure:
- \(p(pt)\)
- \(p(pd)\)
- \(t(pt)\)
intervals of 20 MeV
of 5 MeV
predicted as 1000:1. The appreciable yield of deuterons backward is evidently associated with the capture of the incident neutron by a neutron in the \(\mathrm{He}^4\) nucleus, with the triton flying forward and the second deuteron receiving a small momentum backward.
FROM CURRENT LITERATURE
The existence of such a process is also supported by the presence of high-energy tritons (Fig. 3) and by the forward direction of the tritons (Fig. 4) in the \(pt\) process. Reproduction of the spectrum of primary neutrons up to the energies of the secondary particles in the cases \(pt\) and \(pd\) gave a spectrum close to the true one, which indicates a weak dependence of the cross sections of these reactions on the neutron energy. In the same case, the reproduced spectrum proved to be shifted toward lower energies, which indicates a noticeable decrease in the cross section of this reaction with increasing neutron energy. From a detailed balance of the reaction
\[ d+t \rightleftarrows n+\mathrm{He}^{4} \]
one can determine, on the basis of the data of [1], that at a neutron energy of \(90\ \mathrm{Mev}\)
\[ \sigma\bigl(d+t\to n+\mathrm{He}^{4}\bigr)=(3.85\pm0.75)\cdot 10^{-27}\ \mathrm{cm}^{2}. \]
In connection with the question of the applicability of the \(\alpha\)-particle model of light nuclei, it is of interest to compare the data presented with the results of bombarding carbon nuclei \(C^{12}\) with neutrons of energy \(90\ \mathrm{Mev}\). Part of the investigation of the nuclear reactions \(n+C^{12}\) was carried out with a Wilson chamber. Absolute cross-section measurements were made by comparing the yield of various reactions with the yield of \(np\)-scattering. However, as has already been mentioned, the Wilson chamber cannot distinguish the masses of heavy fragments. Therefore the “rotating-disk method” was additionally used. A polyethylene disk of diameter \(53.5\ \mathrm{cm}\) rotated at a definite speed in front of a collimated neutron beam (diameter \(8.4\ \mathrm{cm}\)) incident on the periphery of the disk. In neutron bombardment of carbon the following radioactive isotopes were formed: \(\mathrm{He}^{6}\) \((\beta^{-};\ T_{1/2}=0.87\ \mathrm{sec};\ E^{\beta}_{\max}=3.7\ \mathrm{Mev})\); \(\mathrm{Li}^{8}\) \((\beta^{-};\ 0.89\ \mathrm{sec};\ 12.7\ \mathrm{Mev})\); \(\mathrm{Li}^{9}\) \((\beta^{-};\ 0.168\ \mathrm{sec};\ 11\ \mathrm{Mev})\); \(\mathrm{Be}^{7}\) \((K;\ 52.93\ \mathrm{days};\ 0.48\ \mathrm{Mev},\ \gamma)\); \(\mathrm{Be}^{10}\) \((\beta^{-};\ 2.5\cdot10^{6}\ \mathrm{years};\ 0.56\ \mathrm{Mev})\); \(\mathrm{B}^{8}\) \((\beta^{+};\ 0.65\ \mathrm{sec};\ 13.7\ \mathrm{Mev})\); \(\mathrm{B}^{12}\) \((\beta^{-};\ 0.025\ \mathrm{sec};\ 13.46\ \mathrm{Mev})\); \(\mathrm{C}^{10}\) \((\beta^{+};\ 19.1\ \mathrm{sec};\ 2.2\ \mathrm{Mev})\) and \(\mathrm{C}^{11}\) \((\beta^{+};\ 20.5\ \mathrm{min};\ 0.98\ \mathrm{Mev})\).
Fig. 4. Angular distribution of protons formed in the reactions \(n+\mathrm{He}^{4}\to p+t+n\) and \(n+\mathrm{He}^{4}\to p+d+2n\), and of tritons formed in the reaction \(n+\mathrm{He}^{4}\to p+t+n\).
Simultaneously with the activation, the rate of radioactive decay of the isotopes formed was measured. For this purpose, opposite the disk, at different angles to the point of exit of the neutron beam and at an angle of \(180^\circ\) to one another, two pairs of end-window counters were placed, directed toward the disk from both sides. When the disk rotates with angular velocity \(\omega\ \mathrm{radians/sec}\), the interval of angles where irradiation takes place is \(\alpha\) radians, and the counters are located at an angle \(\theta\) radians relative to the place of irradiation (counting the angle in the direction of motion of the disk); the activity of an isotope with decay constant \(\lambda\), after the disk has made \(n\) revolutions, is evidently equal to
\[ A = k\, \frac{\left(1-e^{-\alpha\lambda/\omega}\right)\left(1-e^{-n\cdot 2\pi\lambda/\omega}\right)} {1-e^{-2\pi\lambda/\omega}} \cdot e^{-\lambda\theta/\omega}, \]
where \(k=\Pi N\sigma\varepsilon\) \((\Pi\) in \(\mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\) is the neutron flux, \(N\) is the number of carbon nuclei over the entire area of the beam, \(\sigma\) in \(\mathrm{cm}^{2}\) is the cross section of the corresponding reaction, \(\varepsilon\) is the efficiency of registration of the decay by the end-window counter).
All isotope yields were compared with the yield of \(C^{11}\), since the cross section of the reaction \(C^{12}(n,2n)C^{11}\) at a neutron energy of \(90\) MeV is known:
\[ \sigma = 22 \pm 4 \cdot 10^{-27}\ \text{cm}^2. \]
For short-lived isotopes of the \(B^{12}\) type, in the expression given
\[ \frac{\omega \lambda}{\omega} \ll 1 \quad\text{and}\quad \frac{2\pi \lambda n}{\omega}=\lambda t \gg 1 \]
(\(t\) is the time from the beginning of irradiation); for the isotope \(C^{11}\):
\[ \frac{\omega \lambda}{\omega} \ll 1 \quad\text{and}\quad \frac{2\pi \lambda}{\omega} \ll 1. \]
Therefore
\[ \frac{A_{B^{12}}(\theta)}{A_{C^{11}}} = \frac{\sigma_B \varepsilon_B}{\sigma_C \varepsilon_C} \cdot \frac{\dfrac{\lambda_B}{2\pi \omega}\cdot e^{-\lambda_B \theta/\omega}} {\left(1-e^{-2\pi\lambda_B/\omega}\right)\left(1-e^{-\lambda_C t}\right)} \tag{*} \]
By varying the thickness of the disk, the speed of its rotation (from zero to 6000 revolutions/min), and the thickness of the absorbers placed between the disk and the counters, the author\(^2\) determined the production cross sections of all the isotopes listed above. The main results of work\(^2\) are presented in Tables II and III.
The author\(^2\) attempted to use the data obtained with a Wilson chamber to estimate the yield of individual concrete isotopes—including stable ones. For such estimates he used, in particular, the conclusion he had drawn on the basis of comparing the production cross sections of \(B^{12}\) (without neutron emission) and other boron isotopes (with neutron emission), and also certain other data, that in reactions with emission of charged particles no more than 10% of the events are not accompanied by simultaneous neutron emission. However, these estimates are extremely crude and in a number of cases contradict other figures cited in\(^2\); we shall not dwell on them. The data of work\(^2\) satisfactorily agree with the results of other studies of the interaction of \(90\)-MeV neutrons with carbon nuclei. The elastic-scattering cross sections and the integral cross sections of inelastic collisions obtained in different works are close, as are also the production cross sections in various reactions of protons with energies above \(20\) MeV, deuterons above \(27\) MeV, and tritons above \(33\) MeV (equal\(^2\), respectively, to \(85.3 \pm 9.2\), \(26.1 \pm 3.4\), and \(3.9 \pm 0.93 \cdot 10^{-27}\ \text{cm}^2\)).
Comparison of the results of the interaction of neutrons with helium and carbon nuclei indicates the impossibility of a simple interpretation based on the \(\alpha\)-particle model. In Table IV the relative fractions of different processes (in the notation of Table I) are compared for the interactions \(n + He^4\) and \(n + C^{12}\), with formation, in addition to other products, of two \(\alpha\)-particles (i.e., as if by interaction of the neutron with an \(\alpha\)-particle inside the \(C^{12}\) nucleus). Table V gives the relative fractions of the yields of \(p\), \(d\), \(t\), and \(He^3\) for all reactions of neutrons with \(He^4\) and \(C^{12}\).
The difference in the interaction of neutrons with helium and carbon nuclei is evidently connected with the fact that, unlike protons and neutrons, the composite particles (\(He^3\), \(t\), and \(\alpha\)) formed in a carbon nucleus are, with greater probability, broken up as a result of new collisions in the same nucleus. Therefore the yields of \(p\), \(n\), and \(d\) from the \(C^{12}\) nucleus are higher than from \(He^4\), while the yields of \(t\) and \(He^3\) are much lower. Similar considerations are applicable also to quasifree scattering \(n + He^4\). Whereas, for example, the cross section for quasifree scattering \(pp\) in lithium nuclei is higher than the cross section for free scattering, the total cross section of reactions with emission of \(\alpha\)-particles from \(C^{12}\) nuclei is only \(73.4 \cdot 10^{-27}\ \text{cm}^2\), i.e., smaller than the cross section for elastic scattering \(n + He^4\) (\(96 \cdot 10^{-27}\ \text{cm}^2\)).
*) In the text of\(^2\), in this formula the factor \(\left(1-e^{-\lambda_C t}\right)\) is erroneously placed in the numerator.
FROM CURRENT LITERATURE
Table II
Summary of data on the interaction of 90 MeV neutrons with C\(^{12}\) nuclei
| Number of stars | Cross section \((\times 10^{-27}\ \text{cm}^2)\) | Number of detected fast particles: p \(>20\) MeV | Number of detected fast particles: d \(>27\) MeV | Number of detected fast particles: t \(>33\) MeV | |
|---|---|---|---|---|---|
| Two-prong: | 557 | \(125 \pm 10\) | 278 | 66 | 7 |
| pB | 422 | \(95 \pm 9\) | 278 | — | — |
| dB | 104 | \(24 \pm 4\) | — | 66 | — |
| tB | 16 | \(3.6 \pm 1.0\) | — | — | 7 |
| \(\alpha\)Be | \(11 \pm 2\) | \(2.5 \pm 1.1\) | — | — | — |
| LiLi | \(4 \pm 2\) | \(0.9 \pm 0.6\) | — | — | — |
| unidentified | 4 | — | — | — | — |
| Three-prong: | 318 | \(71 \pm 9\) | 68 | 25 | 3 |
| \(\alpha\alpha\alpha\) | 43 | \(9.8 \pm 2.0\) | — | — | — |
| He\(^3\alpha\alpha\) | 5 | \(1.1 \pm 0.4\) | — | — | — |
| p\(\alpha\)Li | 78 | \(17.7 \pm 2.5\) | 30 | — | — |
| pHe\(^3\)Li | 7 | \(1.6 \pm 0.6\) | 1 | — | — |
| d\(\alpha\)Li | 46 | \(10.5 \pm 2.0\) | — | 10 | — |
| dHe\(^3\)Li | 2 | \(0.4 \pm 0.2\) | — | — | — |
| t\(\alpha\)Li | 6 | \(1.4 \pm 0.5\) | — | — | — |
| tHe\(^3\)Li | 4 | \(0.9 \pm 0.4\) | — | — | — |
| p\(\beta\)Be | 28 | \(6.3 \pm 1.5\) | 19 | — | — |
| pdBe | 43 | \(9.8 \pm 2.0\) | 12 | 11 | — |
| ptBe | 13 | \(2.9 \pm 0.9\) | 6 | — | 1 |
| ddBe | 25 | \(5.7 \pm 1.3\) | — | 3 | — |
| dtBe | 18 | \(4.1 \pm 1.0\) | — | 1 | 2 |
| Four-prong: | 151 | \(34 \pm 7\) | 32 | 17 | 3 |
| pp\(\alpha\alpha\) | 29 | \(6.6 \pm 1.5\) | 11 | — | — |
| ppHe\(^3\alpha\) | 2 | \(0.4 \pm 0.2\) | — | — | — |
| pd\(\alpha\) | 41 | \(9.3 \pm 2.0\) | 10 | — | — |
| pdHe\(^3\alpha\) | 1 | \(0.2 \pm 0.2\) | 1 | — | — |
| dd\(\alpha\alpha\) | 25 | \(5.7 \pm 1.3\) | — | 11 | — |
| dt\(\alpha\alpha\) | 8 | \(1.8 \pm 0.6\) | — | 2 | 1 |
| dtHe\(^3\alpha\) | 5 | \(1.1 \pm 0.4\) | — | 1 | — |
| pt\(\alpha\) | 15 | \(3.4 \pm 1.0\) | 4 | — | 1 |
| ptHe\(^3\alpha\) | 2 | \(0.4 \pm 0.2\) | 1 | — | — |
| pppLi | 1 | \(0.2 \pm 0.2\) | 2 | — | — |
| ppdLi | 7 | \(1.6 \pm 0.6\) | 2 | — | — |
| pddLi | 5 | \(1.1 \pm 0.4\) | — | 2 | — |
| dddLi | 1 | \(0.2 \pm 0.2\) | — | — | — |
| pdtLi | 7 | \(1.6 \pm 0.6\) | 1 | 1 | 1 |
| ddtLi | 2 | \(0.4 \pm 0.2\) | — | — | — |
| Five-prong: | 7 | \(1.6 \pm 0.6\) | — | — | — |
| pppd\(\alpha\) | 2 | \(0.4 \pm 0.2\) | — | — | — |
| ppdd\(\alpha\) | 1 | \(0.2 \pm 0.2\) | — | — | — |
| pddd\(\alpha\) | 1 | \(0.2 \pm 0.2\) | — | — | — |
| pddt\(\alpha\) | 3 | \(0.7 \pm 0.3\) | — | — | — |
| Total stars | 1033 | \(232 \pm 17\) | 378 | 115 | 13 |
Table III
Cross sections for the formation of various products in the bombardment of carbon nuclei by neutrons with an energy of 90 MeV
| H$^1$ | H$^2$ | H$^3$ | He$^3$ | |
|---|---|---|---|---|
| $\Sigma\sigma$ | $160 \pm 24$ | $79 \pm 18$ | $22.3 \pm 7.1$ | $6.1 \pm 2.6$ |
| $\Sigma\nu\sigma$ | $176 \pm 29$ | $93.6 \pm 22.4$ | $22.3 \pm 7.1$ | $6.1 \pm 2.6$ |
| He$^4$ | Li | Be *) | B | C | |
|---|---|---|---|---|---|
| $\Sigma\sigma$ | $73.4 \pm 16.8$ | $38.5 \pm 9.0$ | $31.3 \pm 7.8$ | $123 \pm 14$ | Elastic scattering — $275 \pm 50$; C$^{12}$(n, 2n) C$^{11}$ — $22 \pm 4$ |
| $\Sigma\nu\sigma$ | $121 \pm 28$ | $39.4 \pm 9.9$ | $31.3 \pm 7.8$ | $123 \pm 14$ | Elastic scattering — $275 \pm 50$; C$^{12}$(n, 2n) C$^{11}$ — $22 \pm 4$ |
| Data from the rotating-disk method | He$^6$ | Li$^9$ | Be$^7$ | B$^{12}$ | C$^{10}$ |
|---|---|---|---|---|---|
| Data from the rotating-disk method | $2.54 \pm 0.98$ | $<1.0$ | $8.8 \pm 4.6$ | $4.93 \pm 1.0$ | $0.67 \pm 0.50$ |
| Data from the rotating-disk method | Li$^8$ $0.82 \pm 0.42$ |
B$^8$ $<1.0$ |
The cross sections are given in units of $10^{-27}\ \text{cm}^2$. The value $\Sigma\sigma$ determines the sum of the cross sections of all reactions in which the given product is formed, irrespective of the multiplicity of formation. The value $\Sigma\nu\sigma$ determines the total cross section for the formation of the given product with account of the yield multiplicity.
*) Without taking into account the yield of Be$^8$, which gives two $\alpha$-particles.
From the data presented in Tables II and III one can estimate the mean number of secondary neutrons emitted in one inelastic collision of a neutron of energy 90 MeV with a carbon nucleus: \(\bar{\nu} \simeq 1.5 \pm 0.3\). Relatively detailed results of work \(^{2}\) were obtained owing to the combination of two methods, which made it possible to register both the outgoing particles and the final nuclei. Considerably less definite results were given by work \(^{3}\), in which the charged fission products of carbon and beryllium nuclei by protons of energy 330 MeV were investigated.
In this work targets in the form of beryllium strips (\(8.7\ \mathrm{mg/cm^2}\)) and polystyrene (\(2.9\ \mathrm{mg/cm^2}\)) of width 2 mm were introduced into the proton beam inside the synchrocyclotron chamber. The fission products were bent by the magnetic field of the accelerator, descending somewhat as they did so, and struck Ilford C-2 photographic plates placed, as shown in Fig. 5, in a copper protective wall; channels cut in the latter determined the direction of the particles being recorded. The plates were arranged along the continuation of the radial line center of the chamber—target, so that the recorded particles described an arc of \(180^\circ\) in the magnetic field. The distances of the plates from the target were about 46, 61, and 88 cm, which corresponded to \(H\rho = 14300\) gauss-cm for protons emerging from the target in the forward direction.
Fig. 5. Diagram of the apparatus for observing products of the fission of Be\(^9\) and C\(^ {12}\) nuclei by protons of energy 330 MeV.
Table IV
| pt | dt | pd | dd | pp | He\(^3\) | |
|---|---|---|---|---|---|---|
| n + He\(^4\) | 44.7 | 13.8 | 16.1 | 7.5 | 0.8 | 17.1 |
| n + C\(^ {12}\) | 12.2 | 6.5 | 33.3 | 20.4 | 23.6 | 4.0 |
Table V
| p | d | t | He³ | |
|---|---|---|---|---|
| n + He⁴ | 34.2 | 24.3 | 32.2 | 9.3 |
| n + C¹² | 59.0 | 31.6 | 7.4 | 2.0 |
\(E_p\) about 5, 10 and 20 MeV, and the energies of the other particles
\[ E = E_p \frac{z^2}{A}. \]
With this interval of recorded energies, protons from free pp scattering in polystyrene could not act as a hindrance. In analyzing the data, only tracks entering the emulsion at angles \(180 \pm 10^\circ\) to the initial beam were selected. Particle identification was carried out according to the plots constructed for all expected products: trajectory curvature—range in the emulsion. These plots were checked for multiply charged ions using the characteristic gamma tracks of Li³ and B⁸ \((\mathrm{Li}^8 \to \mathrm{Be}^8 \to 2\alpha;\ \mathrm{B}^8 \to \mathrm{Be}^8 \to 2\alpha)\).
Thus, the effect of electron capture on the curvature of tracks of multiply charged ions at the end of their range was established empirically. In individual cases (for example, to distinguish H² and He³), the grain density was determined. A geometrical correction was introduced for ne-
Table VI
| \(\rho\) (cm) | Be⁹ fission products, %: 22–24 | Be⁹ fission products, %: 29.5–31.5 | Be⁹ fission products, %: 43–45 | Be⁹ fission products, %: total | C¹² fission products, %: 22–24 | C¹² fission products, %: 29.5–31.5 | C¹² fission products, %: 43–45 | C¹² fission products, %: total |
|---|---|---|---|---|---|---|---|---|
| H¹ | 11.6 | 10.0 | 5.9 | 27.5 | 13.1 | 8.8 | 6.7 | 28.6 |
| H² | 4.3 | 3.7 | 3.7 | 11.7 | 2.5 | 2.9 | 3.5 | 8.9 |
| H³ | 4.5 | 4.0 | 3.3 | 11.8 | 1.7 | 1.6 | 1.8 | 5.1 |
| He³ | 4.6 | 4.5 | 1.6 | 10.7 | 3.5 | 3.4 | 2.2 | 9.1 |
| He⁴ | 14.0 | 15.4 | 4.1 | 33.5 | 17.1 | 16.9 | 6.2 | 40.2 |
| Li⁶, Be⁷ | 0.8 | 1.2 | 0.2 | 2.2 | 0.9 | 0.9 | 0.1 | 1.9 |
| Li⁷ | 0.3 | 0.3 | 0.3 | 0.9 | 0.8 | 0.1 | 0.8 | 1.7 |
| Li⁸ | — | — | — | — | — | 0.1 | — | 0.1 |
| B⁸ | — | — | — | — | — | — | 0.1 | 0.1 |
| Unclassified products and background | — | — | — | 1.7 | — | — | — | 4.3 |
| Total number of events | — | — | — | 1082 | — | — | — | 812 |
transition from the observed number of tracks per unit area and unit azimuthal angle to the number of tracks per unit radius of curvature and unit solid angle. The measurement results are given in Table VI.
As has already been said, the results of work 3 are considerably less definite than the results of the work described above 2. Quite apart from the fact that the yields of individual products are given only in relative units, we point out that even from the absolute yields of various products one cannot draw a conclusion about the share of various reactions in the inelastic interaction of high-energy protons with Be⁹ and C¹² nuclei.
For example, in the formation of He⁴ in the reaction p + Be⁹, 3p, 3d, t + He³, d + He⁴, etc. may appear. The choice of one possibility or another on the basis of the law of conservation of charge is determined by the variants in which neutrons are formed. As a result it becomes practically impossible to derive, from the known fraction of various products, the fraction of various reactions. A noticeable error is evidently also connected with the energy limitation of the recorded particles.
In Table VII the relative yields of various products are compared for the bombardment of carbon by neutrons of energy 90 MeV 2 and by protons of energy 330 MeV 3.
Table VII
| Relative yield (in %) | p | d | t | He³ | He⁴ | He⁶ | Li | Be | B | C |
|---|---|---|---|---|---|---|---|---|---|---|
| Neutrons 90 MeV | 27.8 | 14.8 | 3.5 | 0.9 | 19.0 | 0.4 | 6.0 | 4.8 | 19.3 | 3.4 |
| Protons 330 MeV | 28.6 | 8.9 | 5.1 | 9.1 | 40.2 | — | 3.8 | 3.8 | 3.8 | — |
The main difference in the results consists in the sharp decrease in the second case of the yield of heavy fragments and in the increase of the yield of α-particles. This discrepancy is strongly connected precisely with the energy limitation of the particles recorded in the second case. Whereas almost all α-particles fell within the interval of their registration, 5–20 MeV, a large part of the light particles had higher energy (for example, as shown in 2, the fraction of protons with energy above 20 MeV amounts to about 50% of all protons, whereas the number corresponding to deuterons with energy above 10 MeV), and a large part of the heavy fragments had energy below the threshold (equal, for example, to 12.5 MeV for B¹⁰). Therefore the results of work 3 are not indicative for a quantitative determination of the relative yields of different products and of the cross sections of various reactions.
G. I.
CITED LITERATURE
- P. Tannenwald, Phys. Rev. 89, 508 (1953).
- D. Kellogg, Phys. Rev. 90, 224 (1953).
- W. Barkas and H. Tyren, Phys. Rev. 89, 1 (1953).
- J. Heidmann, Phil. Mag. 41, 444 (1950).