Frank Belknap Long's "The Trap" (short story, first contact, free): Life can exist as pure shape too!

A shape whose food is someone else "appreciating" it! Alien here is actually incomprehensible. And I got a feeling there is a vampire-derivation here - an alien that feeds on its victims seeking something other than their blood.

Story happens on a far off world - an interstellar refueling station, with two attendants, of a star faring humanity. An unusual alien ship has arrived with which all previous attempts to communicate have failed. But attendants of the station will "meet" the aliens.

See also.

1. Incomprehensible aliens: Terry Carr's "The Dance of Changer & the Three" (download).
2. Vampire-derivations: C L Moore's "Shambleau" (download) & "Black Thirst"; Eric Frank Russell's "Sinister Barrier".

Fact sheet.

First published: Astounding, May 1945.
Download full text as part of the scans of Astounding issue where it originally appeared.
Among the stories from Astounding/Analog issues edited by John W Campbell, Jr.
Rating: B.
Related: First contact fiction.