This probably has nothing to do directly with the '\\', it's probably about the nature of the data you're storing and the stats that Oracle collects.
I'd guess that you have a lot of rows starting '\\domain\' and that Oracle has created a histogram on the column. Histograms are only accurate to the first 6 bytes for part of the calculation and 32 or 64 characters maximum for the rest. This makes it very easy for bad cardinality estimates (hence bad execution plans) to appear when you have a column that stores things like URLs (here's a link to a blog posting that describes the issue: https://jonathanlewis.wordpress.com/2010/10/13/frequency-histogram-5/ ). For URLs it's a good idea to adopt a strategy of using a two-column (domain / file), or three-column (domain / directory / file) implementation to workaround the problem.
I would say there are many table rows with:
AID=382 AND AF = '\\domain\test\1123.pdf';
So the CBO has decided it's quicker to do a full-table scan rather than an index.
There are no table rows with this combination:
AID=382 AND AF = 'a\\domain\test\1123.pdf';
So the index is used.
Many thanks you for your tips, you are right.
I dropped the histogram and disabled the recreation for the specified field. Now the CBO uses the indexes and
the query finishes in miliseconds.