Neutron golf balls can be acquired through the ball collection album.
When you have collected all golf balls available in a generation, you will receive 5 Neutron golf balls.
You will also receive additional Neutron golf balls when all golf balls available in a generation reach the same prestige level. For example - you will receive 10 Neutron balls when all golf balls in a generation reach the bronze prestige level.
Be sure to check out the Ball Collection Album FAQs for more information.