And the more time you spend on shooting for perfection of form, the more you will have those days when you hit the Zen Zone. Also for me, there is also an attitude of just not caring. When I start to care about where the arrow goes, then I lose that zone.
Getting that feeling of not caring is the essence of Zen, or most Martial Arts. Usually through years of repetitious body mechanics till you do it with an empty mind. It just happens, and you are left with a "Wow" feeling. Also with all of that training or target shooting you acquire the ability to be able to focus instantly on a small object like, you flicked a switch.
Not many people are willing or have the time to achieve this.