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20. S e l e c t a Random Number RN f r o m ( 0 , 1 ) cosG = 1 . 0*RN ο s i n o = ( 1 . 0 - cos Θ) Fig. 21. F(s) = A(s)/A(smax) = 2 2 s /s max. H e r e A(s) is t h e area of a circle with radius s (see fig. 20). A particular value of s is obtained by calling for r a n d o m n u m b e r R N from (0,1) and solving F(s) = R N . 8 Isotropic direction distribution For an isotropic direction distribution, t h e cosine of t h e polar angle θ is a n uniformly distributed o n (—1,1) d t h e azimuthal angle φ is uniformly distributed on (0,2JT).

Box (18): when an annihilation event occurs, the encounter counter, N E N , is increased by o n e . T h e j u m p event index J at which the annihilation event occurred is recorded as J M P ( N E N ) = J. Box (19): after an annihilation event, the j u m p counter is set to zero and a neyv history is started. Box (20): the probability for an encounter event is given by the n u m b e r of encounters which occurred, N E N , divided by the n u m b e r of histories run, N H I S . T h e average n u m b e r of j u m p events to an encounter event is given by the S U M of the n u m b e r of j u m p events to an encounter event over all histories ending in an encounter, divided by the n u m b e r of histories ending in an encounter.

RESTI = . F A L S E . TRUE. TRUE. TRUE. TRUE. Test S e l e c t I n t e r s t i t i a l Jump D i r e c t i o n Index LDIR (16) Go Go t o Box 2 (19) PROBE = FL0AT(NEN)/FL0AT(NHIS) JSUM = SUM(JMP(J)) AVJE = FL0AT(JSUM)/FL0AT(NEN) (20) Write Output Data (21) Fig. 2 . 1 1 . Flow diagram for a Monte Carlo defect encounter program. Box (5): the j u m p step index J is increased by one at the beginning of each e n c o u n t e r event cycle. Box (6): the condition J = J M A X + 1 signals the end of the current history.

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Physics Reports vol.285


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