Integral Calculation for Yukawa Potential Differential Cross Section

[BREAD]

Homework Statement

Homework Equations

This is a calculation about differential cross section of Yukawa potential.

The Attempt at a Solution

I can't understand how that highlighted part can be -1 ,
we don't know if the parenthesis term (iq-1/a) is negative or positive tho.

 

[FactChecker]

Subtracting the value at r=0 would give you -1. For the value at r=∞ to disappear, we must have | e^{(iq - 1/a)} | < 1. So if q and a are real, that means | e^1/a | > 1, so a>0.

 

[BREAD]

Subtracting the value at r=0 would give you -1. For the value at r=∞ to disappear, we must have | e^{(iq - 1/a)} | < 1.

==========================================
I don't know why | iq - 1/a | should be smaller than 1 ?

 

[FactChecker]

==========================================
I don't know why | iq - 1/a | should be smaller than 1 ?

Sorry. You may have looked at my post as I was correcting it. | e^(iq-1/a)r | = | (e^(iq-1/a))^r | = | (e^(iq-1/a)) |^r = | (e^(-1/a)) |^r= 1/| (e^(1/a)) |^r

 

[BREAD]

Sorry. You may have looked at my post as I was correcting it. | e^(iq-1/a)r | = | (e^(iq-1/a))^r | = | (e^(iq-1/a)) |^r = | (e^(-1/a)) |^r= 1/| (e^(1/a)) |^r

===================

I appreciate for your quick reply