DOPPLER EFFECT FOR $\gamma$ RAYS WITH ENERGIES OF 4.5 AND 4.8 MeV

The existence of the Doppler effect for $\gamma$ rays, of course, is beyond doubt. In its most striking form this effect was investigated for $\gamma$ rays with energies of about $65$ MeV, arising in the decay of $\pi^0$ mesons in flight[^1]. As is known, the presence of the Doppler effect in this case served as one of the first and most serious arguments in favor of the supposition that, when a target is irradiated with fast protons, $\pi^0$ mesons arise which decay in the immediate vicinity of the target into two $\gamma$ quanta. During 1949–1951 several investigations were carried out[^2] in which Doppler broadening, and even shifts of the $\gamma$ lines of certain radioactive substances, or of $\gamma$ lines arising in positron annihilation, were observed. However, in none of these experiments was the velocity of motion of the particle emitting the $\gamma$ ray determined from experience with sufficiently high accuracy. A corresponding experiment was performed in the paper under review[^3], from which it follows that the usual first-order Doppler-effect formula is valid for $\gamma$ rays with energies of 4.8 and 4.5 MeV emitted by a particle moving with a velocity of $0.008c$. At the authors’ disposal was an accelerator from which singly charged particles with a maximum energy of 1 MeV (or $\alpha$ particles with correspondingly higher energy) could be obtained, and the first task consisted in choosing the most suitable nuclear reaction giving $\gamma$ radiation. It is obvious that in order to know the velocity of motion of the emitter it is most convenient to make use of a reaction of radiative capture of a proton or an $\alpha$ particle: in this case the momentum of these particles is transferred to the nucleus, which moves at its acquired velocity up to the moment of emission of the $\gamma$ quantum. The authors point out that the largest Doppler shift could be obtained in the reaction $^2\mathrm{H}(p,\gamma)^3\mathrm{He}$, but, unfortunately, this reaction is not resonant, and therefore, to observe the Doppler effect, the energy of the protons would have to be maintained with high accuracy constant. For this reason the authors used the reaction $^7\mathrm{Li}(\alpha,\gamma)^{11}\mathrm{B}$, for which resonance occurs at energies of 401, 819, and 985 keV. When the $^7\mathrm{Li}$ nucleus absorbs a particle with an energy of about 958 keV, it acquires a velocity equal to $0.00825c$, whose direction coincides with the direction of the $\alpha$-particle beam. As a result of the reaction $^7\mathrm{Li}(\alpha,\gamma)^{11}\mathrm{B}$, an excited level of $^{11}\mathrm{B}$ is formed with an energy of 9.27 MeV, which “de-excites” by emitting two $\gamma$ quanta with energies of 4.81 and 4.46 MeV. Measurements of the resonance width show that the emission of the first $\gamma$ quantum occurs in a time of order $10^{-19}$ sec, and of the second in a time $\sim 10^{-16}$ sec. In both cases these times are considerably less than the slowing-down time of the moving $^{11}\mathrm{B}$ nucleus, which can be calculated and is equal to $\sim 10^{-13}$ sec. It may therefore be assumed that the source of the $\gamma$ radiation is indeed moving with a constant velocity equal to $0.008c$. The $\gamma$ radiation was observed with the aid of two crystalline-

…scintillation counters NaI(Tl), placed at angles of 48° and 132° to the $\alpha$-particle beam, respectively. For such angles the Doppler shift of the energies of the $\gamma$ quanta registered by the two counters should be equal to 1.1%. From the standpoint of experimental technique, the greatest difficulties in this experiment are connected with the need to ensure sufficiently stable operation of the apparatus—consisting of the counters, power supplies, and amplifier—required in order to observe such a shift of the line. To bypass this difficulty, the authors made relative measurements, using as a standard for comparison the $\gamma$ radiation of $^{137}\mathrm{Cs}$: for two minutes they measured the radiation of $^{11}\mathrm{B}$, then measured the radiation of $^{137}\mathrm{Cs}$ for the same interval of time, accumulating approximately the same number of counts as in the first experiment. Such series of measurements were carried out many times. The influence of instability of the apparatus was eliminated by reducing the different series of measurements to the same position of the maximum for the radiation of $^{137}\mathrm{Cs}$ when constructing the overall distribution of pulses by amplitude. The spectra obtained are shown in the figure on a double logarithmic scale. Along the ordinate axis is plotted the number of counts, and along the abscissa axis the pulse amplitude, measured by the pulse analyzer. Region $A$ of the graph corresponds to the $\gamma$ radiation of $^{137}\mathrm{Cs}$, and region $B$ to the radiation of $^{11}\mathrm{B}$. The white and black circles indicate, respectively, the number of counts in the counters placed at angles of 132° and 48° to the $\alpha$-particle beam. We see that the two contours, marked by white and black circles for the radiation of $^{137}\mathrm{Cs}$, show no displacement, whereas contours $I$ and $II$ (these contours correspond to $\gamma$ quanta from $^{11}\mathrm{B}$ with energies of 4.46 and 4.81 MeV, respectively) are noticeably shifted. The direction of this shift and its magnitude, estimated by the authors, coincide with the expected value of the shift for the Doppler effect under these conditions.

In addition to the confirmation obtained of the Doppler effect for $\gamma$ radiation, the work under discussion is also of interest from another point of view: it provides a new method for measuring the lifetimes of excited nuclear states lasting less than $10^{-14}$ sec. Indeed, the absence of a Doppler shift in the case considered, or in analogous cases, would indicate that the lifetime in the excited state is greater than the slowing-down time of the nucleus, which can readily be calculated.

A. V.

CITED LITERATURE

1. Bjorklund et al., Phys. Rev., 82, 20 (1951).
2. Eliot and Bell, Phys. Rev., 73, 168 (1949); Du Mond, Lind, Watson, Phys. Rev., 75, 1226 (1949); Hutchinson, Scarrot, Phil. Mag., 42, 792 (1951).
3. Jones, Wilkinson, Phil. Mag., 43, 959 (1952).