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The only reason Luke, Leia, Han and Chewbacca were able to escape the Death Star is because the Stormtroopers left their stations and ran like kids to watch the lightsaber duel between Vader and Kenobi.

Why didn't the stormtroopers act like professionals?

If they were so interested, they could have watched a hologram or video of the duel later.

Though whether Darth Vader actually held rank in the Imperial military was unclear, he is still at the very least a VIP aboard the Death Star. The stormtroopers choosing to provide such an important figure with backup when he is engaged in combat with an unknown foe is perfectly reasonable.

In addition, the stormtroopers aboard the Death Star were specifically instructed to allow the Millennium Falcon to escape after the tracking device was installed so that they could be tracked to the location of the rebel base. Leaving their posts to provide aid to Darth Vader is a perfect excuse to do so.

According to the film's original novelisation (written by Alan Dean Foster George Lucas himself), the guards were originally attracted to observe the fight, then moved into position to help Vader.

Illuminated by the flare from contacting energy fields, Ben Kenobi and Darth Vader were backing toward the bay. The fight attracted the attention of others beside the Senator. Every one of the guards moved in for a better view of the Olympian conflict.

“Now’s our chance,” Solo observed, starting forward.

All seven of the troopers guarding the ship broke and rushed toward the combatants, going to the Dark Lord’s aid. Threepio barely ducked aside as they ran past him. Turning back into the alcove, he yelled to his companion.

_{^{A New Hope: Official Novelisation}}

This tallies nicely with the film's script

Vader and Ben Kenobi continue their powerful duel. As they hit their lightsabers together, lightning flashes on impact. Troopers look on in interest as the old Jedi and Dark Lord of The Sith fight. Suddenly Luke spots the battle from his group's vantage point.

...

Threepio ducks out of sight as the seven stormtroopers who were
guarding the starship rush past them heading towards Ben and The Sith
Knight. He pulls on Artoo.

...

They start for the Millennium Falcon. Ben sees the troops charging toward him and realizes that he is trapped. Vader takes advantage of Ben's momentary distraction and brings his mighty lightsaber down on the old man. Ben manages to deflect the blow and swiftly turns around.

_{A New Hope: Script}

Stormtroopers act like professionals? What fictional universe do you inhabit? Certainly not the "Star Wars" universe. Let's go right back to the very first episode. As Obi-Wan remarks, "The Force can have a strong influence on the weak-minded."

Stormtroopers are naturally weak-minded, so of course they act unprofessionally, even without nudging from the Force. As the saying goes, "I can do stupid all on my own." The first episode demonstrates that they can't even shoot straight, so there's no particular reason to think they can anything else right - at least, not if such failure advances the plot.

EDIT - I think I should expand on my last point.

First, we need to step out of canon. The first Star Wars was clearly intended as essentially a comic book come to life. Harrison Ford's classic, "George! You can type this shit, but you sure can't say it!" does rather describe the dialog. And George Lucas wanted what he wanted from the visuals - and he got it. This was fine until folks started taking it seriously and attempting to incorporate the movie into a "real" (whatever that means) world.

So let's take the Stormtroopers at face value. How are they as soldiers?

1) They wear armor which does not seem to actually work. I've not watched the original in quite a while, but I do not recall ever seeing a stormtrooper's armor deflecting a shot. If they get hit, they go down. Also, just as a nitpick, you might notice that nobody ever gets hit in the arms, legs, or head. What are the odds?

2) They carry "laser" weapons with optical sights - and they never use the sights. It's all shoot from the hip, and with terrible accuracy. Green beams flying all over the place and the occasional casualty. Any US Marine today would be ashamed to do it that way. The only reason they don't get slaughtered is that the rebels are just as incompetent.

3) While #2 might possibly be excused for close-in shootouts, where close range and stress can cause people to do all sorts of funny stuff, the same does not apply, for instance, to the escape of the Millennial Falcon. Here, the troopers are relatively far from the ship and only Han Solo is providing covering fire. He should have been chopped about 3 seconds after the shooting started.

(Stepping out of canon for a moment, all of this is necessary to advance the plot, while looking good at the same time. Shootouts with laser beams all over the place, heroic covering fire, etc. Pity it doesn't make any sense.)

So, what have we got? Soldiers who are burdened by inappropriate equipment, and who are incapable of hitting exposed targets at close range and/or completely exposed. In other words, amateurs. And these are supposed to be elite troops?

Well, yes. Yes they are. And since they are supposed to be elite, they ARE elite - the movies and novelizations say they are.

There is an old saying about movies: "Show, don't tell." And what the movies show are a bunch of wankers. Apparently the rest of the Star Wars universe is made up of even worse troops, so they are elite wankers, but wankers nonetheless.

While not disagreeing with the other answers, another point is:

Because lightsaber duels are the stuff of legend

Back twenty years ago when there were actual Jedi, an exceptionally lucky person might have got to see a Jedi from afar once every few years, and see them fight maybe once in a lifetime. Anyone who saw such a thing would have told stories of it, and dined out on the anecdote for years. Now Vader is pretty much the only lightsaber user, and there hasn't been a lightsaber duel anywhere in years. They have passed from 'something you might see if you were very lucky' to 'something that nobody has ever seen in our lifetime', or even 'that thing my uncle's friend told me his father saw once that I'm not sure I actually believe'. To actually see one would be by far the most exciting and interesting thing that has ever happened to these stormtroopers, or anyone they know.