Using recaptcha on php form within Wordpress template

Form changes

<form class="form" method="POST" action="index.php" onsubmit="return validateCaptcha()"><input type="hidden" name="valid" value="0" />

Below the form

<script type="text/javascript">function validateCaptcha(){    if ($('input[name="valid"]')) return true;    if ($('input[name="recaptcha_response_field"]').val() == "")    {        alert("Fill in the captcha field");        return false    }    $.ajax({        url: "verify.php",        type: "POST",        async:"false",        data: {            recaptcha_response_field: $('input[name="recaptcha_response_field"]').val(),            recaptcha_challenge_field: $('input[name="recaptcha_challenge_field"]').val()        },        success: function(data){            if (data == "OK")            {                $('input[name="valid"]').val(1);                $('.form').submit();            }            else            {                alert(data);            }        },        error: function(){            alert("An error occured, please try again later");        }    });    return false;};</script>

verify.php

if (!$resp->is_valid) {    die ("The reCAPTCHA wasn't entered correctly. Go back and try it again. (reCAPTCHA said: " . $resp->error . ")");} else {    echo "OK";}