Accelerator’s arm did not actually make contact.

However, an explosive wind of unknown origin appeared and blew Hamazura away. He flew more than 2 meters through the air before slamming into the hallway wall. Unnatural strength entered his finger holding the trigger and he fired a meaningless shot into the ceiling.

[...]

Accelerator pulled Hamazura closer and then casually threw him aside. That was all it had been, but Hamazura’s body shot away like a bullet. He rolled over and over along the hard floor until he finally came to a stop. Dull damage had permeated even the areas between his bones and the very depths of his organs, so he could not even stand up. He had never been more shocked that his exhalations were not accompanied by blood.

Toaru Majutsu no Index vol.19