Semi transparant volumetric white glass

I’m trying to create a semi transparant white tinted glass vase.

The problem is when i stick in volume scatter, the glass gets darker.
So how would one make glass that has a slightly white collor in it, without making it dark.
I like it to be volumetric (and cant to emission to lighten it up). ?

I know such glass exists, its a kind of milk-glass in the industry and sometimes glass artists mix it with transparant glass to get all kind of effects, i just want the milk alike glass with respect to where the vaze is thin (less white) and thick (more white)

Turn the number of volume bounces up. The default I think is 1 which is too low for your application.

Also make sure anisotropy on the scatter node is zero.