I have a date field that can be searched in the detail page, while i would like to search for a period of time , instead of only search by one single day.

Is there a way I can solve it?

I don't know this helps but you can edit the XA_SEARCH_OP line in web/codelib/asc/df.fl.(table-name).inc.php to change the search operator.
For example,

XA_SEARCH_OP=>'s>=',