Bethe-Bloch stopping power

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. 

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. 

Fig. 2. Stopping power calculations for bare ions, H and according to the linear (DF) and non-linear (NL) formulations described in the text, for a medium with Tg = 1.6. The asymptotic Bethe and Bloch limits are also indicated.

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. 

The mean rate of energy loss, i.e., the stopping power is given by the Bethe-Bloch equation... 

Stopping power vs. relative momentum, py = p/Mc, for muons in copper. The solid curve indicates the total stopping power, the dash-dotted and dashed lines the Bethe-Bloch equation with and without density effect correction. The vertical bands separate the validity regions of various approximations indicated in the figure. The dotted line denoted with p. indicates the Barkas effect. In the Bethe-Bloch region the stopping power scales with the particle mass and Z/A of the medium... 

One can deduce via integration of the Bethe-Bloch equation the R range of particles losing energy in matter via ionization only. As the stopping power scales with momentum, R/M will... 

Stopping power due to ionization according to the Bethe-Bloch equation vs. relative momentum py = pIMc of heavy charged particles in liquid hydrogen, gaseous helium, carbon, aluminum, iron, tin and lead. Momentum scales are shown below the plot for muons, pions and protons and an energy scale for protons above... 

Stopping power due to ionization, according to the Bethe-Bloch equation, vs. kinetic energy of heavy charged particles in copper... 

Stopping power data for protons and alpha particles have been tabulated in the ICRU Report 49 (ICRU 1993a). While at high energies the Bethe-Bloch theory is accurate to a few percent, at low energies sufficiently accurate values are obtained by fitting experimental data, and in the... 

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... 

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] ... 

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