With me, its funny. If a deer is in close that I have no intention of shooting, I'm calm as can be. But then sometimes that little light goes on that says "take it". Its only a natural occurance that the heart rate and breathing will pick up as the body kicks in the autonomic nervous system, releasing adrenaline into the bloodstream.
At this point, we either control it, or it controls us. I watch the body language of the deer. If its jumpy, I relax as the chance of a shot are getting slim. I wait until it relaxes, and work on slowing my breathing. I will close my eyes and take a cleansing breath or two. Or three.
I focus on the spot, and plan for when the angle is right. I breath slow and deep. I look ahead to plan where the animal will be when I strike. Or where he is likely going to be.
I put enough tension on the bowstring to move maybe an inch, allth while burning a hole in the hair I want to hit with my eyes. I play the shot through my minds eye, seeing my arrow arc to the spot, and my arrow disappearing.
When the time comes, I always whisper a silent prayer- Lord- all I ask for is a clean kill, or a clean miss. Then my arrow is gone.....
The real adrenaline rush is held back, but it hits me hard after the shot. Which is fine, I have plenty of time to wait for it to pass before taking up the trail, or searching for my arrow.
I can be quite sure that the mountain lion, the wolf, the bear , any other predator, will have the same adrenaline release prior to striking at their prey. Its a natural reaction, and is desireable in that it provides us that ability to hone our focus on the task at hand. Its how we harness it that makes the difference.
I well remember sitting with my son a few years back as he took his first shot at a deer with his Bear recurve. The adrenaline had him shaking, panting and sweating. I could see him battle to regain control. His eyes narrowed as he picked his spot,but alas his arrow eventually did miss the mark. afterwards, he told me he felt his heart was about to come out his shirt.
I welcomed him to bowhunting with a hug and a pat on the back and told him- you will learn to control it, or it will control you. When you gain control, that arrow will be where it should be. He's still workin on it, but it sure is fun to watch.