I'm guessing once you get there, controlled deceleration and getting into an orbit might be a bit of a problem at that speed. If there are enough particles for the nukes to keep pushing the rocket along, the fact that they are extremely sparse isn't going to evade the extraordinary level of heat generated from the friction, and there would be lots of gamma rays (and more) from particle collisions at the leading edges of the rocket. Also, if you hit even a spec of dust on the way, it would obliterate the mission in a spectacular way.

Matter travelling anywhere near the speed of light has a lot to contend with.

The rocket was called Orion. You would probably need more than 200 nukes for it.

Proxima Centauri is ~4 light years away, not a half of a light year.

Project Rho is a good one-stop-shop for all things interstellar travel. Here's their page on the Orion:

http://www.projectrho.com/public_html/rocket/enginelist3.php...

The numbers there indicate that the Orion design doesn't have the sort of exhaust velocity you'd want to get up to 0.95c

That site's also useful reading for all the OTHER downsides: for instance, traveling at 0.95c through space means that everything in your way is hitting the ship at 0.95c. Even stray hydrogen atoms are no picnic when they're arriving at that energy...