The most common and most likely answer to this crossword clue is the 4 plus 4 letter word BETA RAYS
I've seen this crossword clue in The Sunday Telegraph
B
E
T
A
R
A
Y
S
Buddy explains!
The straight part
We know that "signs of radioactive emissions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case signs of radioactive emissions = beta rays.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.