The Disintegration of Lithium by Protons of High Energy

Abstract

The results obtained by Lawrence, Livingston and White have been extended to protons having an energy up to 1,125,000 electron-volts. After the rapid increase found by Cockroft and Walton at lower voltages the number of disintegrations per proton increases above 400,000 electron-volts proportionally to the $\frac{3}{2}$ power of the energy. The range of the proton is known to be proportional to the same power of the energy. These facts indicate that the probability of disintegration of the individual lithium nucleus is independent of the energy of the proton above 400,000 volts. The relative number of disintegrations over the whole range from zero to 1,125,000 electron-volts is given quite exactly by $N=k^{\prime }V{e}^{-\frac{a}{V^{\frac{1}{2}}}}$ where $V$ is the energy of the protons and $k^{\prime }$ and $a$ are constants. From 400,000 to the upper limit reached this formula is practically indistinguishable from $N=k(V^{\frac{3}{2}}-{V_0}^{\frac{3}{2}})$ when the experimentally determined values of the constants are used. The more complex formula has theoretical justification and the radius of the lithium nucleus as calculated from the experimental value of $a$ is about 4×${10}^{-13\mathrm{}}$ cm. The cross section effective for disintegration seems to be much smaller, with a radius of 1.4×${10}^{-14\mathrm{}}$ cm. The actual number of disintegrations is half the number of alpha-particles emitted and is equal to 2.0 disintegrations per ${10}^9$ protons at 250,000 electron-volts; 10.2 disintegrations per ${10}^9$ protons at 500,000 electron-volts; 40 disintegrations per ${10}^9$ protons at 1,000,000 electron-volts. The results at 500,000 volts are in excellent agreement with those of Cockroft and Walton. The form of the curve differs slightly and the probable causes of this difference are discussed.