content_image/397509.jpg content_image/397515.jpg content_image/397516.jpg content_image/397508.jpg content_image/397514.jpg content_image/397522.jpg content_image/397523.jpg content_image/397521.jpg
<img src='content_image/397509.jpg'>

<img src='content_image/397515.jpg'>

<img src='content_image/397516.jpg'>

<img src='content_image/397508.jpg'>

<img src='content_image/397514.jpg'>

We can proceed exactly as in Sec. III E and obtain 

up to unimportant constants. However, we can also obtain a simpler expression. Substituting ρ = ρ$_{0}$e − βm (Φ − Φ 0 ) in Eq. (81), we obtain 

<img src='content_image/397522.jpg'>

This can be rewritten 

<img src='content_image/397523.jpg'>

up to unimportant constants. Finally, using Eqs. (79), (51), (57) and the relations κ = µ/α and α = 

<img src='content_image/397521.jpg'>

