Step 1: Understand the effect of X-rays on the charge.
X-rays can ionize the air around the gold leaf electroscope. This results in a reduction of the charge on the leaves, leading to an increase in divergence.
Step 2: Explanation of the answer.
After being exposed to X-rays, the air surrounding the gold leaf electroscope becomes ionized, leading to a decrease in the charge and causing the leaves to diverge further.
Final Answer:
\[
\boxed{\text{B) Diverge further}}
\]