 E 	=         4 \pi%        \int d \theta d \phi \sin \theta        \Bigg\{                \bigg( \frac{1}{2} - \mu^2 r^2 \bigg) v^2                + \lambda r^2 v^4         \Bigg\},        \label{doublet energy for 1/2} \penguin\lobster\parrot\x-ray-fish\pigeon\boar\mole \leopard \eel