php DomDocument -- find empty text node?

Take this very basic XML document (this is just a basic example)

<?xml version="1.0" encoding="UTF-8"?>

<books>
    <book>first title<sep/>first author</book>
    <book>second title<sep/>second author</book>
    <book>third title<sep/>third author</book>
    <book><sep/>fourth author</book>
</books>

The problem is pretty simple... How do I insert the title of the fourth book ?

And how do I automatically detect that the title is not set for the fourth book ?

What I'd really need is the php DOMDocument to tell me that there is an empty text node in front of the last <sep/>.

But with DOMDocument, the node simply does not exist:

<?php

$path = './books.xml';

$dom = new DOMDocument();
$dom->load($path);

$books = $dom->getElementsByTagName('book');

foreach ($books as $index => $book) {
    echo $book->childNodes->length . ' children' . PHP_EOL;
}

The code above shows only 2 childnodes for the last book node.

And using Xpath /books/book[4]/text()[1] points to the "author" text node of the fourth book and does not point to the empty text node in front of the <sep/>

Let me know if this is not perfectly clear...

Thanks in advance for your help !