The ten days between the Feast of Trumpets and the Day of Atonement are called the Days of Awe.  Also known as the Days of Repentance.  The fast day of Atonement is considered the most sacred day among many Jews.  

Five years ago almost exactly I gave a sermon on the Day of Atonement in Cincinnati, Ohio about our visit to an event in Washington D.C. known as The Return which featured Jonathan Cahn who spoke along with many others about the need for our nation to return to God. 

See full video version on YouTube at https://youtu.be/p4mS8qfQOxE