330 



CORNELIUS A. TOBIAS 



0.1 



Al, g/cm^ 

 1 10 



100 



1000 



10' 



10- 



c 

 o 

 _2 



w 



3 

 C 



> 

 0) 



o> 

 a> 



® 10 



0) 



o 



ARGON 



NEON 



CARBON 



PROTON & ALPHA 



DEUTERON 



.^^J 



PROTONS, BERKELEY 



900mev ALPHA 

 •^ -''^450mev 



DEUTERONS 



BERKELEY 



HILAC 

 BERKELEY 



0.01 



100 



1000 



Grams/cm' 



Range in water or soft tissue 



Fig. 1. Range energy relationship for protons, alpha particles, carbon, neon, and 

 argon nuclei. Black dots indicate ranges of the cyclotron beams available in Berkeley. 

 Black triangle signifies the protons of the Uppsala cyclotron. Black square is the 

 proton beam of the Harvard and French Atomic Energy Commission cyclotrons. Open 

 circles indicate beams of the Yale and Berkeley heavy ion accelerators. 



which have been utilized at various laboratories in biological and medical 

 studies. Since biological experimentation has usually been secondary to the 

 use of machines in physics research, we may note that certain interesting and 

 desirable energy ranges have not as yet been explored with biological speci- 

 mens. For example, one does not have ions heavier than alpha particles with 

 kinetic energy greater than 10 Mev per nucleon. Unlike x-rays or electrons, 

 nuclear particles of equal energy travel almost to the same depth in an ab- 

 sorber. Some particles are, however, lost because of inelastic collisions. Others 

 show slight differences in their respective ranges owing to straggling and 

 multiple elastic scattering. The root mean square fluctuation ^/AR' of the 

 range R increases as the particle energy and penetration increases. 



V ^ (observed) — - ^R (initial energy spread) r Ar~ (straggling) r ^B (scattering) 



The exact relationships are complicated. However, the fractional straggling 



>/Aij^ for particles of the same velocity is independent of charge and varies 

 with the square root of the mass of the particle. 



VAi 



R. 



Ri 



M, 



Va/ V M, 



2 



Thus, a proton has more than 40 times less straggling than an electron; 



