How to send document in database to multiple persons listed?

I have a form and in this form, there is an editable Readers field - AuthorizedReader with default value - @UserName.
I created a button - MailSend so that when the author create this document, he/she will click on this button to send to all the person listed in the AuthorizedReader field.
My formula for the button works only when 1 username is in this field. If there are multiple users in this AuthorizedReader field, it give me this msg-> Document has been send to authorized readers! and follow by this error -> Unable to send mail, no match found in Name & Address Book(s). But the names listed are correct.

Formula for MailSend button:
Sub Click(Source As Button)
      Dim ws As New NotesUIWorkspace
      Dim uidoc As NotesUIDocument
      Set uidoc=ws.CurrentDocument
      Call uidoc.save
      Dim session As New NotesSession
      Dim db As NotesDatabase
      Dim newDoc As NotesDocument
      Dim curdoc As notesdocument
      Dim rtitem As NotesRichTextItem
      Dim dateTime As New NotesDateTime("")
      Set db = session.CurrentDatabase
      Set curdoc = uidoc.document
      Set newDoc = New NotesDocument( db )
      Set rtitem = New NotesRichTextItem( newDoc, "Body" )
      Call rtitem.AppendText( "New Meeting document added! Please follow this document link to view the meeting details" )
      Call rtitem.AddNewLine( 2 )
      Call rtitem.AppendDocLink( curdoc, db.Title )
      Messagebox ("Document has been send to authorized readers!")
      Call uidoc.Close
      Call newdoc.Send(False,uidoc.FieldGetText("AuthorizedReader"))
      Call ws.ViewRefresh
End Sub

Pls help.
Thank you very much.