Bhabha, H. J.
(1935)
*On the calculation of pair creation by fast charged particles and the effect of screening*
Mathematical Proceedings of the Cambridge Philosophical Society, 31
(3).
pp. 394-406.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S030500410007746X

## Abstract

In a recent paper I developed a method for calculating the probability of the creation of an electron pair in the collision of two charged particles moving with a relative velocity very near that of light. I showed there that under certain conditions it is legitimate to treat one of the colliding particles, say the heavier one of charge Z_{2} and rest mass M_{2}, which we shall call the particle 2, as fixed at the origin of coordinates, and the other, of charge Z_{1} and rest mass M_{1}, which we shall call the particle 1, as moving classically along a straight line with uniform velocity V in the direction of the z-axis, passing the other particle 2 at a minimum distance of approach (impact parameter) b. I developed expressions (given by (18) to (22) of A) giving the probability of the transition of an electron from an initial state of negative energy E_{0} and momentum p_{0} lying in an element of momentum space dp_{0} to a final state of energy E and momentum p lying in an element of momentum space dp, under the combined perturbing influence of the two colliding particles when they pass at a minimum distance b. The initial state of the electron, left vacant after the transition, appears as a positron of momentum p_{+} = - p_{0}. To get the differential effective cross-section for the creation of the above pair, we must integrate this probability over all values of the impact parameter b, and this integration can be performed easily as shown in A. The final result can be written as a sum of a finite number of doubly infinite integrals (A, (24)). The purpose of this paper is to carry through the evaluation of these integrals for certain special cases, and to consider the effects of screening. The results have already been communicated in A.

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ID Code: | 2359 |

Deposited On: | 07 Oct 2010 09:10 |

Last Modified: | 17 May 2011 03:49 |

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