i'd like posts modified in pending status

Hello,
What i would like :
Author can modify their own post but are not allowed to post new
When any author modify his own posts, these posts stay live until new modification is approved.
I tryed something like :

$le_role = get_role( "author" );
$le_role->add_cap("edit_published_posts");
$le_role->remove_cap("publish_posts");
$le_role->remove_cap("edit_posts");

author cannot post new OK
they still can publish modification ??
thanks for any explanation