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PHOTODISINTEGRATION OF THE DEUTERON BY HIGH-ENERGY $\gamma$-RAYS
In the case of photons of low energies, comparable in order of magnitude with the binding energy of the deuteron, the phenomenological theory of the photodisintegration of the deuteron by $\gamma$-rays gives fairly good agreement with experiment. With increasing $\gamma$-ray energy this agreement deteriorates, and in the region of energies exceeding 150 MeV, when the interaction of $\gamma$-rays with virtual mesons apparently begins to play a decisive role in the process of photodisintegration (the meson cloud around the nucleons), there is in general no satisfactory theory of this phenomenon. In this connection, deserving-
Of interest is the work *), in which the cross section for photodisintegration of the deuteron by the bremsstrahlung spectrum of γ-rays with an upper energy limit of 320 MeV was measured. A beam of γ-rays struck a chamber filled with gaseous deuterium under high pressure. The protons produced as a result of deuteron disintegration by a photon were recorded by means of photographic plates. The secondary particles were collimated by a system of slits in such a way that measurements could be made at angles of 45, 90, and 135°.
The minimum energy required for the proton to penetrate the chamber walls and reach the plate was 70 MeV for 45° and 135° and 60 MeV for 90°. This circumstance excluded the possibility that the photographic plate could be reached by recoil protons from meson photoproduction. The energy of the protons was calculated from the thickness of the absorbing material between the end of the proton track and the target. In the case of photodisintegration of the deuteron into a proton and a neutron, the relation
\[ k = 2T\left[1-\left(\frac{T}{M}\right)\left(p\cos\frac{\theta}{M}\right)\right]^{-1} \]
holds between the energy \(T\) and momentum \(p\) of the proton of mass \(M\), the angle \(\theta\) between the direction of proton emission and the original beam, and the energy \(k\) of the photon that caused the photodisintegration.
Taking in this relation \(k = 320\) MeV, we obtain 93, 136, and 200 MeV for the maximum energies of protons emitted at angles of 45°, 90°, and 135°, respectively.
The energy spectrum of protons obtained in the work is shown in the figure.
From the figure it is seen that the energy spectrum is formed at proton energies of 95, 135, and 200 MeV, which agrees well with the expected theoretical values.
Hence one may, in all probability, conclude that these protons are indeed photoprotons produced by the disintegration of the deuteron by a photon into a proton and a neutron.
*) S. Kikuchi, Phys. Rev. 85, 1062 (1952).
Assuming that the bremsstrahlung photon spectrum is proportional to $\frac{1}{E}$, the differential cross section per photon for photodisintegration as a function of photon energy was calculated from the results presented in the figure.
These data are collected in Table I.
Table I
Differential cross section as a function of photon energy in the laboratory system
| Angle | Photon energy in MeV | Diff. cross section in $10^{-30}\ \mathrm{cm}^2$ | Angle | Photon energy in MeV | Diff. cross section in $10^{-30}\ \mathrm{cm}^2$ |
|---|---|---|---|---|---|
| $45^\circ$ | 133 | 14,4±1,8 | $90^\circ$ | 158 | 2,7±0,6 |
| $45^\circ$ | 144 | 12,8±1,9 | $90^\circ$ | 178 | 2,4±0,7 |
| $45^\circ$ | 152 | 6,6±1,8 | $90^\circ$ | 194 | 2,4±0,7 |
| $45^\circ$ | 162 | 10,7±3,0 | $90^\circ$ | 211 | 3,4±1,0 |
| $45^\circ$ | 170 | 6,9±2,2 | $90^\circ$ | 226 | 5,1±1,3 |
| $45^\circ$ | 189 | 5,4±2,1 | $90^\circ$ | 248 | 5,2±1,7 |
| $45^\circ$ | 205 | 6,5±2,3 | $90^\circ$ | 272 | 5,5±1,3 |
| $45^\circ$ | 228 | 5,0±2,6 | — | — | — |
| $45^\circ$ | 285 | 8,0±3,8 | $135^\circ$ | 250 | 0,99±0,27 |
| $45^\circ$ | 304 | 12,3±4,0 | $135^\circ$ | 272 | 0,99±0,35 |
In the case of $45^\circ$ one can trace the dependence of the cross section on the photon energy in a very broad region. Below $150$ MeV it falls very steeply with increasing energy; around $150$ MeV it begins to level off and then rises again with increasing energy. The angular distribution in the laboratory system shows a very strong forward asymmetry.
Table II
Total cross section as a function of photon energy
| Photon energy in the laboratory system in MeV | Photon energy in the center-of-mass system in MeV | Total cross section in $10^{-29}\ \mathrm{cm}^2$ |
|---|---|---|
| 133 | 125 | 6,2±0,5 |
| 158 | 146 | 3,4±0,8 |
| 178 | 163 | 3,0±0,8 |
| 194 | 176 | 3,0±0,9 |
| 211 | 191 | 4,3±1,2 |
| 226 | 202 | 6,4±1,7 |
| 248 | 220 | 6,6±2,2 |
| 272 | 239 | 6,9±1,7 |
The total cross section was roughly estimated by multiplying the differential cross section at \(90^\circ\) by \(4\pi\). Below \(150\ \mathrm{MeV}\), where there are no corresponding data for \(90^\circ\), it was assumed that the total cross section is proportional to the differential cross section at \(45^\circ\). The results are shown in Table II. The indicated errors refer to relative values. As for the absolute values, the error may reach \(\sim 300\%\).
In conclusion, it is noted that the increase in the photodisintegration cross section above \(150\ \mathrm{MeV}\) may be explained by the increasing role of the process of virtual-meson emission upon absorption of a photon in the energy region lying above the meson threshold. Therefore, comparison of experiment with various versions of meson theory in this energy region is far more promising than in the region of low energies.
V. F.