<p>OP - to second @gravitas2…</p>
<ol>
<li> Do it because you like it.</li>
<li> That will show through in your some of your essays (there is one just on intellectual vitality) as well as your EC list. But don’t have all your essays talk about that one aspect.</li>
<li> They don’t want you to send them a paper as was stated earlier, but, you can send in one additional recommendation - that can obviously come from that prof. If you build a good relationship with the prof and s/he strongly supports you, then you should sit down with them and explain how important a quality recommendation is (e.g. they may not know how competitive admissions are now a days and may not realize they have to write a super recommendation).</li>
</ol>