The stuff LDO is thinking of is called Peel N Seal (other brands names in other parts of the country) & it's not 1/2" thick. It's a nail through moisture barrier. If you have the generic insulation plain old contact cement might work to hold it down. Before using that stuff I personally would go to a carpet seller and buy some really thin carpet pad & use it. That's what I used under the floor mat in my '38 and love it.
This stuff. It's not standard foam carpet pad.