Tried using the density tool with kernel density but cannot seem to refine the "red" areas to the required spread??
I would start by making a copy of your input feature layer and work with
the copy. The tool I propose in your first step, Integrate, changes the
geometry of your input file. So be careful.
So open Integrate, and set the distance at which you would like to
summarise your points i.e. your input distance will be 100 m. After running
this tool, all your accident incidents within 100 m of one another will
have the same geometery.
Next run a Spatial Join on your input layer, using the same layer for
both your Target Features and Join Features inputs. The join operation
should be one to one. The resulting output will contain a field called
Join_Count. This field will contain the number of points (accidents)
occurring at each point on the map.
Have you looked at:
Hot Spot Analysis (Getis-Ord Gi*)—Help | ArcGIS for Desktop
There are a number of you tube videos on hot spot mapping as well.
Retrieving data ...