Bethe-Bloch formula

Example Problem Evaluate the stopping power of beryllium metal for 1808+ ions with a kinetic energy of 540 MeV (E/A = 30MeV) using the Bethe-Bloch formula. 

The stopping powers of polystyrene for ions were calculated from those of C and H [32a] based on the additivity rule. For 20 KeV electrons, the stopping power was calculated from that for lOkeV electrons [32b] based on the Bethe-Bloch formula. 

The Bethe-Bloch equation has to be modified for this case, and it will be valid both for electrons and positrons. The maximal energy transfer will become Tnax = TJ2 and the Bethe-Bloch formula becomes (Leo 1987)... 

Besides these distinct microscopic features, particle radiation also differs considerably from photon radiation with respect to the macroscopic distribution, i.e., the depth dose distribution. The typical shape is caused by the velocity-dependent stopping power, as described by the Bethe-Bloch-formula [63, 64] ... 

Abstract The effects of interactions of the various kinds of nuclear radiation with matter are summarized with special emphasis on relations to nuclear chemistry and possible applications. The Bethe-Bloch theory describes the slowing down process of heavy charged particles via ionization, and it is modified for electrons and photons to include radiation effects like bremsstrahlung and pair production. Special emphasis is given to processes involved in particle detection, the Cherenkov effect and transition radiation. Useful formulae, numerical constants, and graphs are provided to help calculations of the stopping power of particles in simple and composite materials. 

As it stands, ALbiocB. equation (16), when added to the Bethe formula, extends its range of validity into the classical regime. Alternatively one may introduee an inverse-Bloch correetion [10,11]... 

Despite the apparent similarity of the Bohr and the Bethe stopping power formulae, the conditions of their validity are rather complimentary than the same. Bloch [23] pointed out that Born approximation requires the incident particle velocity v ze jh, the speed of a Is electron around the incident electron while the requirement of Bohr s classical theory is exactly the opposite. For heavy, slow particles, for example, fission fragments penetrating light media, Bohr s formula has an inherent advantage, although the typical transition energy has to be taken as an adjustable parameter. 

When both kinds of particles are taken into account and when d is evaluated, their formula reduced to Bethe s (57.2). A level density formula of the same form as Bethe s was obtained by Sneddon and Touschek using a quite different method of calculation. The numerical coefficients, however, are not the same and this formula leads to rather lower spacings. None of these calculations take into account factors other than energy and spin. Recently, however, a more elaborate calculation has been made by Bloch... 

Bloch [8.1] derived a formula for the stopping power which is valid for all values of X, and which is therefore a synthesis of the quantal result of Bethe [2.8] and the classical stopping power deduced by Bohr [6.21]. Bloch [8.1] found that the transition between the classical and the quantal results can be accounted for by setting... 

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