A beam of monoenergetic neutrons impinges perpendicularly on an infinite slab of

Question

A beam of monoenergetic neutrons impinges perpendicularly on an infinite slab of pure absorber. The slab cross section is sigma(sigma_s = sigma_f = 0), and the thickness is d. For this particular problem the average flux in the slab is to be calculated with Monte Carlo using (1) the collision estimator and (2) the path length estimator. The 68% confidence level of the result is given by sigma(x)/(x- squareroot N) where N Much greater than 1 and x is^the estimator. Show that for the collision estimator sigma(c)/c- = {e^-sigma d/(1 - e^-sigma d)}^1/2. Show that for the path length estimator sigma(l)/l- = (1 - 2 sigma de^-sigma d - e^-2sigma d)^1/2/1 - e^-sigma d Plot the results from a and b for 0 lessthanorequalto sigma d lessthanorequalto 4 and discuss the relative precision of the two estimators.

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Please submit this question again because it is getting blurred (not clearly visible ) at some places (specially the powers) that's why creating confusion and doubt.

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