Do neutron bombs have a beryllium cladding?

Main Question or Discussion Point

Neutron bombs (not that we hear much of them now) are said to produce intense neutron radiation but little blast. I long wondered how this could be done.

It then occured to me that fast neutrons from the DT reaction in a thermonuclear bomb could drive the energy-absorbing reaction Be-9 + n ---> 2He-4 + 2n; (absorbs 1.56 Mev)

and that these two neutrons may still have enough energy to split further beryllium, leading in total 6 slower neutrons for every fast one. This would both greatly increase the neutron flux and absorb much of the energy of the original thermonuclear reaction.

Is this how it's done? And if it is, can I expect a knock on the door at 3 am?
 

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