JQuery :: Reference Unordered List Item As An Array?

I have an unordered list that I am using as a menu. This list contains sub lists.

I found out how to get the index of the primary unordered list item that is being hovered but I am not getting the syntax correct to reference the individual items of this listto get the HTML, the position, height and lengthof this item.

$(" #nav li").hover(function(){
// Locate the index of the singular list item that is being hovered
var index = $(this).parent().children('li').index(this);
// This is incorrect
var $itemObject = $(this).parent().children('li')[index];