Heat the juice and the caster sugar together gently until the sugar has completely dissolved. Test for sweetness and if necessary add a little more sugar. Pour the mixture into a plastic container and put in the freezer. After three to 4 hours, when the mixture is pretty well frozen, spoon it into a food processor and whiz it until it is a mush. Beat the egg whites in a separate bowl until they're firm and stir into the mush.
Put it all back into the container and freeze for another 3 or 4 hours. The sorbet should be solid but have quite a soft texture.
To serve allow to stand in the fridge for 20 minutes or so before scooping into individual glasses or bowls.