What is our liability and obligation for the falling pine cones?

Our backyard neighbor has been complaining about the pine needles and pine cones that fall from our 65-foot tall pine tree, which has some branches that hang over her yard. Three years ago, we pruned the tree back to the maximum extent recommended by an Arborist, and even paid our neighbor about $180 to compensate her for a year's worth of gardening service to clean up the pine needles. Now, she is complaining about the pine needles again, as well as expressing her fears that pine cones may come down and injure her or her grandchildren. We have again consulted with an Arborist, who has agreed to do some extensive pruning and clean up of the tree. This, however, seems unlikely to satisfy our neighbor whom, it appears, won't be completely assuaged until we completely cut the tree down. What I am most curious about is whether we would have any real liability in the unlikely event of that, a pine cone did happen to fall and injure someone in our neighbor's yard. It seems that whether it was a mature, opened pine cone that fell of its own accord, or a hard, green pine cone that fell by the mischief of squirrels, that these would be considered acts of nature and would not create a liability on our part, as owners of the tree. What exactly are our liabilities and obligations? Thank you.