# Transition from Classical into Quantum Theory for Calculating the Stopping Power of Charged Particles

## Abstract

In this search, we described the most important corrections to standard energy loss formula of charged particles and discussed this formalism with a few remarks by the implication of the inverse – Bloch correction to the stopping power calculations. The inverse Bloch correction extends the range of validity of classical Bohr and quantum Bethe regime. Bohr model operates with a charged particles penetrating in matter as a number of interactions with a harmonically bound classical target electrons but in Bethe theory, all the calculations of energy loss of fast charged particles are based on the first Born approximation which the entire physical system is considered quantized. All the results are got by programming the equations in matlab program.## References

- N. R. Arista and A. F. Lifschitz, Non – linear calculation of antiproton stopping powers at finite velocities using the extended Friedel sum rule, Nucl. Inst. And Meth. In physics Research, B, Vol.193, pp.8–14(2002).

- B. A. Weaver and A. J. Westphal, Energy loss of relativistic heavy ions in matter, Nucl. Inst. And Meth. In physics Research, B, Vol.187, pp.285–301(2002).

- S. T. Lai, E. Murad, and W. J. McNeil, J, Spacecraft and Rockets, Vol.39, no.1, pp.106 – 114 (2002).

- N. R. Arista and P.Sigmund, Stopping of ions based on semiclassical phase shifts, phys. Rev., A, Vol.76, no.6 (2007).

- J. F. Ziegler, The Stopping of Energetic Light Ions in Elemental Matter, J. Appl. Phys. Rev. Appl. Phys., Vol.85, pp.1249 – 1272 (1999).

- John R. Sabin and Jens Oddershede, Shell corrections to electronic stopping powers from orbital mean excitation energies, phys. Rev., A, Vol.26, no.6, pp.3209 –3219 (1982).

- P. Sigmund and A. Schinner, Electron ejection in collisions between swift heavy ions and atoms, Elsevier 2006).

- P. Sigmund and A. Schinner, Binary stopping theory for swift heavy ions, Europ. Phys. J. D., Vol.12, pp.425 – 434 (2000).

- P. Sigmund, Low – speed limit of Bohr's stopping power formula, phys. Rev., A, Vol.54, no.4, pp.3113–3117(1996).

- P. Sigmund , Charge – dependent electronic stopping of swift nonrelativistic heavy ions, phys. Rev., A, V.56, no.5, pp.3781–3793(1997).

- P. Sigmund and A. Schinner, Shell correction in stopping theory, Nucl. Inst. And Meth., B, Vol.243, no.2, pp.457 – 460 (2006).

- F. Bloch, Bremsvermogen von Atomen mit mehreren Elektronen, Z. phys. Vol.81, pp.363(1933).

- J. Lindhard and M. Scharff, Energy loss in matter by fast particles of low charge, Mat. Fys. Medd. Dan. Vid. Selsk., Vol.27, no.15(1953).

- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of standards, Applied Mathematics Searies, Vol.55, pp.259(1964).

- P. Sigmund and A. Schinner, Binary theory of antiproton stopping, Europ. Phys. J. D Vol.15, pp.165(2001).

- P. Sigmund and A. Schinner, Effective charge and related/ unrelated quantities in heavy ion stopping, Nucl. Inst. And Meth., B, Vol.174, pp.535(2001).

- P. Sigmund and Andreas Schinner, Binary theory of light ion stopping, Nucl. Inst. And Meth., B, Vol.193, pp.49(2002).

- J. Lindhard, A. H. Sorensen, On the relativistic theory of stopping of heavy ions, phys. Rev., A, Vol.53, pp.2443(1996).