Formation of Sodium and Potassium Nuclides in the Bombardment of Light Elements with 29-GeV Protons

Cross sections for the formation of ${\mathrm{Na}}^{22}$, ${\mathrm{Na}}^{24}$, ${\mathrm{K}}^{42}$, and ${\mathrm{K}}^{43}$ from Ti, Fe, and Cu targets at 29 GeV have been measured. The recoil properties of ${\mathrm{Na}}^{24}$ and ${\mathrm{K}}^{42}$ have been investigated by means of thick-target integral-range measurements. The formation cross sections decrease slightly with increasing mass difference between target and product, the values for ${\mathrm{Na}}^{24}$ ranging from 4.2±0.3 mb for Ti to 3.5±0.3 mb for Cu. The effective ranges, $\mathrm{FW}$ and $\mathrm{BW}$ (the fraction of fragments recoiling into the forward and backward catchers times the target thickness, respectively), vary with mass difference in the opposite way. The values of FW for ${\mathrm{Na}}^{24}$ in Ti, Fe, and Cu thus are 0.49, 0.66, and 1.00 mg/${\mathrm{cm}}^2$. The results of both types of measurements are compared with Monte Carlo cascade-evaporation calculations. While the cross sections are in good agreement with calculation the effective ranges are not, and the discrepancy indicates that the cascade calculation probably overestimates the forward component of velocity of the residual nuclei. The average effective ranges, $\frac{1}{2}\mathrm{}(FW+BW)\mathrm{}$, are in good agreement with evaporation calculations. This agreement, as well as that of the cross-section data, indicates that the spallation process can account for these experimental results.