| It's not hypothetical. The Enhanced Radiation Weapon (the Neutron Bomb because it was designed to emit a great deal more high energy neutrons and gamma rays - ionizing radiation - than a 'normal' nuclear bomb) is still an atomic bomb. It still makes a big mushroom cloud. However, the radiation output of the detonation is enhanced so that an ERW with an explosive yield of between 1 and 5 kilotons, say, emits at the prompt radiation level of a 10 to 20 kiloton explosion.
It achieves this by using a fusion booster in a fission weapon and by the purposeful elimination of a neutron reflector or tamper. This allows the short, extremely high-energy (14.7 MeV neutrons) burst of ionizing radiation produced by the fusion package to escape the casing and irradiate nearby targets. Thus, it concentrates a large dose of prompt radiation on the target area in relation to the size of the blast.
Why would you want to do this? The U.S. (which is, I believe, the only nation to ever field the neutron bomb) had a couple of ideas. The primary use envisioned for such a weapon was to defend Western Europe against a massive Soviet conventional onslaught, by incapacitating Soviet tank crews and troops with radiation. The hope was that by using the (relatively) small yields of the enhanced radiation weapon the U.S. and NATO forces might avoid totally destroying the area which they were defending. As an old saying in NATO goes, "Villages in Germany are three kilotons apart."
The problem is that even if you expose a human to enough rads of radiation to kill them, they will likely still be functional for 24 hours or so before their system begins to break down. In order to incapacitate them immediately through gross tissue damage and energy transfer, you need to expose people to approximately 8 to 10 times the lethal dose, quickly. That works out to around 8000 rads. The neutron bomb allowed a 1 kiloton warhead to expose every armored vehicle within approx. 700 meters to this level of dose, as opposed to the approximately 350 meters of a normal 1 kiloton weapon. The strength of the neutron flux drops off by a factor of 10 or so for every 500 (approximately) meters of atmosphere it traverses, however, so the 'advantage' gleaned by an enhanced radiation weapon is really most pronounced in small (1-2 kiloton or smaller) warheads.
The second use planned was as a warhead-buster. In this case, the enhanced radiation was not intended to allow for smaller warheads, but to better destroy sensitive electronic and nuclear components inside the target silo and/or missile. I believe the first deployed example was the warhead of the Sprint Missile in 1966. The Sprint was designed as an ABM, and its purpose was to destroy/disable incoming nuclear warheads through intercepting them (approximately) and detonating in their vicinity. This, naturally, was the basis for the extremely popular Atari arcade game Missile Command. | 
