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## Homework Statement

The behavior of a neutron losing energy by colliding elastically with nuclei of mass A is described by a parameter ξ1,

ξ1 = 1 + [itex]\frac{(A-1)^2}{2A}[/itex]*ln[itex]\frac{A-1}{A+1}[/itex]

An approximation, good for large A, is

ξ2= [itex]\frac{2}{￼A+2/3}[/itex]

Expand ξ1 and ξ2 in powers of A

^{−1}. Show that ξ2 agrees with ξ1 through (A−1)

^{2}. Find the difference in the coefficients of the (A−1)

^{3}term.

## Homework Equations

Taylor Expansion, see wiki page

ln(1-x)= x+ [itex]\frac{x^2}{2}[/itex]+ [itex]\frac{x^3}{3}[/itex]+...+[itex]\frac{x^n}{n}[/itex]

ln(1+x)= x- [itex]\frac{x^2}{2}[/itex]+ [itex]\frac{x^3}{3}[/itex]+...+(-1)^(n+1)[itex]\frac{(x^n)}{n}[/itex]

## The Attempt at a Solution

Alright so since it is in powers of A

^{−1}I decided to substitute x=A

^{−1}. I get:

ξ1= 1+ [itex]\frac{x((1/x)-1)^2}{2}[/itex]* ln(1-x)-ln(1+x)

I use the expansions from above and substitute.

Now I do not know how to expand the entire thing from here.

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