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From the diffusion equation to escape and survival probabilities

2 FROM THE DIFFUSION EQUATION TO ESCAPE AND SURVIVAL PROBABILITIES [Pg.121]

As previously remarked, the motion of an isolated pair of reactant radicals can be described by the diffusion equation. An isolated pair is formed at a time t0 and with a separation r0. The probability that these radicals are separated by r at a time t is p(r, t r0, f0) and this is a conditional probability (conditional upon the formation time and distance of separation). The exact location of the radical pair is unimportant only the [Pg.121]

The delta functions are zero unless r = r0 and t = t0, and the rate of radical pair creation is, in effect, infinitely fast. Consequently, eqn. (10) becomes [Pg.122]

Comparison with eqn. (A.10) of Appendix A, shows that p is the fundamental or Green s function solution of the diffusion equation, eqn. (10). [Pg.122]

To connect the experimental results of Chuang et al. [266] and Khudyakov et al. [267] and others with the diffusion equation (122), it is necessary to define the probability that the radical pair is extant at a time t, given that it was formed at t0 with separation r0 i.e. the survival probability, p(t r0, f0) is given by [Pg.122]




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And probability

Diffusion equations

ESCAP

Escape probability

Survival

Survival probability

Survive

Surviving

The Diffusion

The diffusion equation

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