26 May 1951
Note on range of charged particles:
Assumptions: Rest Mass (M sub 0), kinetic energy E, charge Z, velocity v, range R gm/(cm exponent 2), x amount of material displaced
(a) Rest Mass (M sub 0) > > (m sub e), mass of electron
(b) No other types of energy loss except ionization
(c) Z is constant
From simple physical (as well as more erudite quantum mechanical) arguments
(dE)/(dx) [or: (dE)/(d sub x)?]= ((Z exponent 2) f(v)) (<--------1*)
in which f(v) is some unspecified function of velocity.
E = (((M sub 0)(c exponent 2))
/(square root of (1-((v/c) exponent 2)))) - ((M sub 0)(c exponent 2))
or v=g(E/(M sub 0))
therefore (<--------1*) becomes
((dE)/(dx)) [or: (dE)/(d sub x)?]= ((Z exponent 2) (h(E/(M sub 0))))
where h is the function of (E/(M sub 0)) obtained by

26 May 1951
Note on range of charged particles:
Assumptions: Rest Mass (M sub 0), kinetic energy E, charge Z, velocity v, range R gm/(cm exponent 2), x amount of material displaced
(a) Rest Mass (M sub 0) > > (m sub e), mass of electron
(b) No other types of energy loss except ionization
(c) Z is constant
From simple physical (as well as more erudite quantum mechanical) arguments
(dE)/(dx) [or: (dE)/(d sub x)?]= ((Z exponent 2) f(v)) (<--------1*)
in which f(v) is some unspecified function of velocity.
E = (((M sub 0)(c exponent 2))
/(square root of (1-((v/c) exponent 2)))) - ((M sub 0)(c exponent 2))
or v=g(E/(M sub 0))
therefore (<--------1*) becomes
((dE)/(dx)) [or: (dE)/(d sub x)?]= ((Z exponent 2) (h(E/(M sub 0))))
where h is the function of (E/(M sub 0)) obtained by