Precision Measurement of the Wave-Length and Spectral Profile of the Annihilation Radiation fromCu64with the Two-Meter Focusing Curved Crystal Spectrometer

Abstract

The two-meter focusing curved crystal spectrometer has been used to make a direct precision wave-length measurement of the annihilation radiation from ${\mathrm{Cu}}^{64}$ by first-order reflection from both sides of the (310) planes of the curved quartz lamina. The instrument constant has been calibrated (by measurements of the $K$ spectrum from a tungsten target x-ray tube) so as to give gamma-ray wave-lengths correct to \ifmmode\pm\else\textpm\fi{}0.01 x.u. Using a source of 2.5 curies of neutron-activated ${\mathrm{Cu}}^{64}$, a sharp annihilation radiation line substantially symmetrical to within the precision of our observations was obtained. The measured wave-length at the peak of this line after conversion (by the multiplying factor $\frac{{\ensuremath{\lambda}}_{s}}{{\ensuremath{\lambda}}_{g}}=1.00203$) from the conventional Siegbahn scale of x.u. to angstroms was 0.024271\ifmmode\pm\else\textpm\fi{}0.000010A which is in satisfactory agreement with the value 0.0242650\ifmmode\pm\else\textpm\fi{}0.0000025A obtained by DuMond and Cohen for the Compton wave-length in their 1947 least squares evaluation of the atomic constants $F$, ${N}_{0}$, ${m}_{0}$, and $h$ from a wide variety of sources of information. The present measurement therefore adds another important confirming datum to the above-mentioned 1947 set of least squares adjusted values. It also adds further independent evidence favorable to the higher iodine value of the Faraday and unfavorable to the silver value.The profile of the observed annihilation "line" is slightly broader than a careful analysis of all instrumental causes seems capable of accounting for. The residual "natural" profile, after abstraction of the instrumental broadening, is roughly estimated to have a half-width of 0.096 x.u. If this were ascribed to a Doppler effect of the motions of recombining pairs of moving negative and essentially stationary positive electrons the velocities would correspond to electrons of only 16 ev, an order of energy which can hardly be associated with anything but the conduction electrons in copper. The 0.66-Mev positrons emitted by the ${\mathrm{Cu}}^{64}$ nuclei are so rapidly retarded by large parameter inelastic "collisions" with electrons as Heitler has shown, that less than two percent of them undergo annihilation before reaching thermal velocities. They then become virtually stationary targets for annihilation chiefly by conduction electrons and possibly $M$ electrons. The repulsion of the nuclear fields probably explains why annihilation by $K$ and $L$ electrons is improbable.