Is there a name for the probability distribution with the form $p(x) = a \,x^2\, \exp( -b\,x^2 )$

Question

There is a probability distribution: $$p(x) = a \,x^2\, \exp( -b\,x^2 ), \quad a,b>0,\ x \in ( -\infty,\,\infty ) $$ I wonder which probability distribution is it?

Answer 1

With the correct scaling it is the http://en.wikipedia.org/wiki/Maxwell_distribution