From Current Literature

Study of Reactions of the Type (d, p) on Magnesium, Aluminum, Silicon, and Oxygen

The energy levels of atomic nuclei have at present been studied very inadequately. Meanwhile, knowledge of them is of very great importance for all nuclear physics, since it is the experimental foundation of nuclear theory. Therefore, the study of energy levels belongs among the most important tasks in this branch of physics.

Recently three works have been published, carried out by O. A. Nemilov, L. I. Gedeonov, and B. L. Funshtein, on the study of protons arising when several substances—magnesium, aluminum, silicon, and oxygen—are bombarded with deuterons \(^{1-3}\). The aim of these works was to determine the energy levels belonging to the nuclei formed as a result of transformations of the type \((d, p)\), and to study the angular distribution of the protons, knowledge of which is extremely important for establishing the mechanism of a reaction of this type.

The distribution of protons by energy was studied in the following way. Near the target made of the substance under investigation and bombarded by deuterons, an ordinary photographic plate was placed, and between the plate and the target there was a wedge-shaped stepped filter consisting of sheets of aluminum foil. Thus, the differently spaced portions of the photographic plate were separated from the target by an aluminum layer of varying thickness. Suppose that all the protons formed in the given reaction have the same kinetic energy. Then the pattern of blackening of the photographic plate under the action of the protons will be as follows: at the place where the thickness of the wedge-shaped filter is so great that, for the given energy, protons cannot overcome it, the plate will remain unblackened; this unblackened region extends up to that place on the photographic plate in front of which there is a layer of filter of such thickness that, in passing through it, the protons lose almost all their energy and become stopped in the emulsion of the photographic plate. Since the ionizing ability of particles is greatest at the end of their range, the protons stopping in the emulsion will cause a sharp blackening of the photographic plate. In regions of the photographic plate protected by still thinner layers of the filter, the blackening will be somewhat weaker, since the particles pass through the photoemulsion with greater energy and, consequently, with lower ionizing ability. Therefore, if all the protons have the same kinetic energy, then on the plate after development there will be a sharp dark band, the degree of blackening of which gradually decreases in the direction of decreasing wedge thickness. Having determined the thickness of the filter (the number of layers of aluminum foil) in the region adjoining the boundary of the dark band, and taking into account the geometrical conditions of the experiment, one can find the range of the protons

of a given energy in aluminum. Since the range is uniquely related to the energy of the particle, the energy of the protons is thereby also determined.

In reality, several bands with different degrees of blackening appeared on the photographic plates, indicating the occurrence in each of the reactions studied of several groups of protons with different kinetic energies and intensities. The energy of each group was determined from the thickness of the filter near the boundary of the band it produced, while the difference in the intensities of blackening made it possible to determine the relative number of protons belonging to the given group.

The measurements were made with protons that emerged at an angle of \(130\text{–}150^\circ\) with respect to the beam of primary deuterons. The energy of the bombarding deuterons was \(3.9\ \mathrm{MeV}\). For a more accurate determination of the blackening boundary (i.e., of the energy of the various groups of particles), the plates were photometered. From the photometry results, graphs were constructed; one of them, obtained in the investigation of magnesium, is shown as an example in Fig. 1. On this graph, the horizontal axis gives the distance measured from the edge of the wedge-shaped filter (for clarity, the filter is shown in the lower part of the graph); the vertical axis gives the coefficient of blackening (degree of opacity) of the plate, i.e., the ratio of the intensity of the light passing through the unexposed part of the plate to the intensity of the light passing through the given point.

Fig. 1. Blackening of a photographic plate irradiated by reaction products during the bombardment of magnesium by deuterons.

The blackening curves obtained in this way have a step-like form: each step is associated with a group of particles having one and the same energy. Usually, for each substance several filters of different initial and final thickness were used. From these measurements the reaction energy corresponding to each group of protons was determined, and then, from the reaction energy and the masses of the isotopes participating in the reaction, the energy levels of the nuclei formed as a result of the reaction were calculated (for more detail on this method of determining energy levels, see the article by V. N. Kondrat’ev, “Energy Levels of Atomic Nuclei”).

The photometric data also served to determine the relative intensity of each group. It was assumed here that

the darkening of the plate is directly proportional to the number of particles acting upon it. It is known that, within certain limits, this is the case for light quanta. The applicability of this assumption to heavy particles was checked by control experiments. In these experiments, various parts of the photographic plate were irradiated with α-particles from a polonium preparation for different intervals of time, chosen so as to cover the entire range of degrees of darkening encountered in the experiments with proton registration. However, the difficulties in taking into account the dependence of the degree of darkening on the particle energy, the background from γ-rays, and also the nonidentity of the exposure and development conditions of the plates make the estimate of the intensities approximate.

Fig. 2. Excited nuclear levels of Mg²⁵, Al²⁸, Si²⁹, and O¹⁷ (in MeV).

Since in these experiments no preliminary separation of isotopes was performed, it is in principle possible that the groups of protons observed when deuterons act on a given substance belong to different isotopes of that substance. Therefore, in order to assign each group to a definite isotope, it is necessary (with the exception of aluminum, which has only one stable isotope, Al²⁷) to make use of additional considerations. The energies of reactions of the type \((d,p)\), obtained in experiments with magnesium, aluminum, silicon, and oxygen, together with the relative intensities (where they could be measured), are given in the table. In estimating the intensities, the intensity of the particles with the maximum range was taken as unity. The energy levels of the product nuclei of the reactions are shown in Fig. 2. A brief description of the experiments and a discussion of the results for each of the substances studied are given below.

Magnesium. A magnesium target 2–3 μ thick was obtained by evaporation in vacuum. The measurements were made with four photographic plates irradiated with different filters. The mean error in determining the position of the edge of a band was \(\sim 0.2\) mm; the resulting errors in the energies are given in the table. As can be seen from the table,

In experiments with magnesium, four groups of protons were found. Magnesium has three stable isotopes, \( \mathrm{Mg}^{24} \), \( \mathrm{Mg}^{25} \), and \( \mathrm{Mg}^{26} \), whose percentage abundances are, respectively, 78.6%, 10.11%, and 11.29%. Since all four groups of protons have similar intensities, it is natural to suppose that they arise from the action of deuterons on the principal isotope of magnesium, i.e., in the reaction \( \mathrm{Mg}^{24}(d,p)\mathrm{Mg}^{25} \); for, if any group arose in a reaction on another isotope of magnesium, then this reaction would have to occur with a probability roughly an order of magnitude greater than on the principal isotope. Therefore all the excitation levels determined by these groups of protons refer to the nucleus \( \mathrm{Mg}^{25} \) and give its ground state (with an accuracy of up to \( \pm 0.30 \) MeV) and three excited states with energies \( (0.70 \pm 0.27) \) MeV, \( (1.71 \pm 0.26) \) MeV, and \( (2.25 \pm 0.25) \) MeV, shown in Fig. 2. This picture of levels is partly confirmed by the data of other authors. The excitation levels of the nucleus \( \mathrm{Mg}^{25} \) were studied by MacMillan and Lauritsen\(^5\) and by Pollard, Sailor, and Wyly\(^6\) by means of the reaction \( \mathrm{Al}^{27}(d,\alpha)\mathrm{Mg}^{25} \). In the first work, two energy values were found that determine an excited level at 0.7 MeV; in the second, two excited levels at 0.68 and 2.35 MeV. Thus, for the first three groups of protons there is complete agreement with the excited levels of \( \mathrm{Mg}^{25} \) obtained from another reaction.

In Fig. 1, showing the photometric curve for magnesium, there is no first group of protons, which has the greatest energy (it was obtained with a thicker filter than that shown in Fig. 1); but besides the other three groups (2, 3, and 4), there are groups 5 and 6. The energy of the protons belonging to group 5 agrees, to within 0.2 MeV, with the energy of formation of the isotope \( \mathrm{O}^{17} \) in the ground state by the reaction \( \mathrm{O}^{16}(d,p)\mathrm{O}^{17} \). Since this group was observed also in experiments with oxygen, it is natural to suppose that the magnesium target was partially oxidized. Group 6 is formed by deuterons elastically scattered by the material of the target backing (silver, platinum) onto which the magnesium was deposited. Control experiments on the bombardment of pure silver or platinum, carried out in order to determine the energy of the primary deuterons, gave only this group. The same group also arises in experiments with other substances.

Aluminum. The target was aluminum foil of thickness equivalent to 1.1 cm of air. Twelve photographic plates were irradiated, and the four most successful of them were photometered; moreover, all of them were irradiated with different filters. On all plates five groups of protons were found; the corresponding reaction energies are given in the table. Aluminum has only one stable isotope, \( \mathrm{Al}^{27} \), and therefore all protons must belong to the reaction \( \mathrm{Al}^{27}(d,p)\mathrm{Al}^{28} \). The level system of the nucleus \( \mathrm{Al}^{28} \) is shown in Fig. 2. It is not impossible that between the levels with energies 1.10 and 2.42 MeV there is yet another level that under the given conditions cannot be resolved. The reaction \( \mathrm{Al}^{27}(d,p)\mathrm{Al}^{28} \) has already been studied in three papers\(^5\)–\(^8\). However, the results of these works differ. The levels obtained in the papers cited\(^2,3\) are closest to the data of MacMillan and Lauritsen\(^5\), who obtained levels at 0.8, 2.3, 3.5, and 4.7 MeV.

Silicon. The target was prepared by depositing onto platinum foil particles of silicon several microns in size, suspended in a mixture of ether and acetone. The thickness of the silicon layer was \( \sim 1 \,\mathrm{mg/cm^2} \). In several experiments, quartz films about \( 5 \,\mu \) thick served as the target. Five plates were studied, three of them exposed with quartz targets. The large difference in the intensity of the proton groups did not make it possible to obtain all groups on one and the same plate and to measure the relative intensities of the groups. In order to exclude the influence of the comparatively slow protons from oxygen, co-

...contained in quartz; when working with quartz targets it was necessary to limit the observations to only the groups of the most energetic protons. Five groups of protons were found (see the table). Silicon has three stable isotopes, \(Si^{28}\), \(Si^{29}\), and \(Si^{30}\), whose relative contents are, respectively, \(92.2\%\), \(4.67\%\), and \(3.05\%\). The maximum value of the reaction energy agrees well with the reaction \(Si^{28}(d,p)Si^{29}\), if it is assumed that the \(Si^{29}\) nuclei are in the ground state. Apparently all the remaining groups also belong to this reaction, since, in order to give the observed pattern of intensities, the other isotopes would have to have effective cross sections for the \((d,p)\)-process several tens of times larger than that of the principal isotope, which is unlikely. The scheme of the energy levels of the \(Si^{29}\) nucleus is given in Fig. 2. This reaction was studied by Allen and Wilkinson\(^8\), who obtained the following values for the reaction energy: \(6.16\), \(4.48\), \(4.16\), and \(3.16\) MeV. It is evident from the table that the first three values are in good agreement with the results obtained in work\(^2\).

Oxygen. The target was a layer of tungsten oxide deposited on gold foil. The thickness of the layer was \(\sim 1\ \mathrm{mg}/\mathrm{cm}^2\). Two groups of protons were found, corresponding to reaction energies of \(1.9\) and \(1.0\) MeV. Oxygen has three stable isotopes, \(O^{16}\), \(O^{17}\), and \(O^{18}\), but the percentage content of the last two is very small (\(0.039\) and \(0.204\%\)), so in the present case both groups of protons arise in the reaction \(O^{16}(d,p)O^{17}\). They correspond to an excited level with energy \(0.9\) MeV, in good agreement with the results of earlier works \((0.93 \pm 0.9)\) MeV\(^{9-12}\).

In addition to determining the energy levels of nuclei, in work\(^3\) the angular distribution of protons formed in reactions with oxygen and aluminum was investigated. The investigation was carried out by means of a wedge-shaped filter bent along a circumference, at the center of which the target was placed. On the side opposite the filter, a photographic plate registering protons was pressed tightly against it. After irradiation the plate was photometered along lines corresponding to several definite angles of proton emission. For each angle its own photometric curve was constructed. By comparing the heights of the steps formed by the same proton groups at different angles of emission, the authors determined the dependence of the relative intensity of these groups on the direction of motion of the protons. The proportionality between the intensity of the particles and the blackening of the photographic plate was checked by means of polonium \(\alpha\)-particles, and the necessary corrections were taken into account.

Experiments with oxygen were carried out at two deuteron energies: \(2.6\) and \(3.9\) MeV. In both cases the angular distribution of protons in the reaction \(O^{16}(d,p)O^{17}\) was sharply asymmetric: the majority of particles moved in a direction close to the direction of the beam of bombarding deuterons; this asymmetry is the more pronounced the lower the proton energy. The angular distributions of protons found in work\(^3\) differ substantially from the distribution recently obtained by Heydenburg and Inglis\(^ {11}\) by means of counters placed at different angles relative to the target.

Experiments with aluminum were carried out under analogous conditions at a deuteron energy of \(3.9\) MeV. The angular distribution of protons belonging to the last three (slow) groups is shown in Fig. 3, a, and to the first two (fast) groups in Fig. 3, b (on the horizontal axis are plotted the angles of proton emission, and on the vertical axis the ratio of the intensity of protons emitted at angle \(\theta\) to the intensity of protons emitted at an angle of \(90^\circ\), in a coordinate system connected with the center of mass of both particles). From Fig. 3 it is seen that with increasing proton energy the degree of directionality of the angular distribution decreases. For the three slow groups shown in Fig. 3, a, it is clearly visible, whereas for the two groups bo...

...of fast protons (Fig. 3, b), no directionality is observed.

The circumstance that in both reactions the majority of protons move forward, i.e., in the direction of motion of the deuterons, and that this directionality increases as the energy acquired by the protons at the moment of reaction decreases, is extremely important, since it indicates that the proton retains some fraction of the deuteron’s initial momentum. Such retention is possible only if the protons formed in the reaction do not enter into the composition of an intermediate nucleus, but are fragments of deuterons. Recently Serber[^18] and Peaslee[^14] showed theoretically that a reaction of the type \((d, p)\) can proceed without the formation of an intermediate nucleus into which the deuteron would enter as a whole, and is carried out by pulling out and capturing the neutron by the nuclear field from the deuteron flying past (see also the addition in the book[^15]). With such a reaction mechanism the proton retains part of the momentum that it possessed while part of the deuteron, and the influence of this part will manifest itself in it the more strongly, the smaller the energy acquired by it at the moment of the reaction. The results of the study of the angular distribution of protons obtained in the paper under review[^8] confirm the described mechanism of reactions of the \((d, p)\) type.

Fig. 3. Angular distributions of groups of protons formed in the reaction \(\mathrm{Al}^{27}(d,p)\mathrm{Al}^{28}\) at a deuteron energy of \(3.9\ \mathrm{MeV}\). \(a\)—for three groups of slow protons; \(b\)—for two groups of fast protons.

V. A. Leshkovtsev

CITED LITERATURE

1. Yu. A. Nemilov and L. I. Gedeonov, DAN SSSR, LXIII, No. 2 (1948).
2. Yu. A. Nemilov, DAN SSSR, LXIV, No. 3 (1949).
3. Yu. A. Nemilov and B. L. Funshtein, DAN SSSR, LXIV, No. 4 (1949).
4. V. N. Kondrat’ev, UFN, vol. XXXVIII, issue 2 (1949).
5. E. McMillan and E. O. Lawrence, Phys. Rev., 47, 343 (1935).
6. E. Pollard, V. S. Saylor and L. D. Wyly, Bull. Am. Phys. Soc. 29, No. 3 (1948); Phys. Rev. 74, 1233 (1948).

1. H. L. Schultz, W. L. Davidson and L. H. Ott, Phys. Rev. 58, 1043 (1940).
2. H. R. Allan and C. A. Wilkinson, Proc. Roy. Soc. 194, 131 (1948).
3. Burcham and Smith, Proc. Roy. Soc. 168, 176 (1938).
4. E. Pollard and W. L. Davidson, Phys. Rev. 72, 162, 736 (1947).
5. Heydenburg and Inglis, Phys. Rev. 73, 230 (1948).
6. Alburger, Phys. Rev. 74, 1240 (1948).
7. R. Serber, Phys. Rev. 72, 1008 (1947).
8. D. C. Peaslee, Phys. Rev. 74, 1001 (1948).
9. A. Akhiezer and I. Pomeranchuk, Some Problems in Nuclear Theory, Gostekhizdat (1948).