story identification - Girl sent to defeat planet that uses attacker's own defenses to defeat them

Theodore Sturgeon's The Pod In the Barrier features a defense system that defies all schemes to defeat it until it's broached by a girl who disbelieves everything, including that the system works.

Earth is overcrowded "And there, hanging just out of reach, were the Luana Earths -- eight fine Earth-type planets circling three suns in Galaxy Three." But they are surrounded by the Barrier: "All it did, that Barrier, was draw a line. Anything outside of it was left strictly alone. Anything penetrating it was instantly tracked, hunted, and smashed by Lunanae missiles."

The Barrier is set up by a civilization that suffered a catastrophic attack from aliens. It can't be shut down even by the civilization that set it up, although later in their history they want to. Earth needs the lebensraum and sends out a ship with several people who have schemes to break the barrier. All fail, but a girl whose job is basically to provide sexual relief to the men on the crew ends up destroying the barrier because she can't believe in anything.

It's kind of a weird story to say the least.

I think it's a good match to the question except for the part about the barrier growing. When I skimmed the story I didn't see that part, but I might have missed it.