And incidentally a lot of things in modern accelerators are only detected indirectly as well. The famous Higgs boson which physicists now believe they've "seen" was actually detected by putting together thousands of observations of things that were predicted to happen if a Higgs boson was created and then immediately decayed.
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It has a magnetic moment, but that's not typically how it is detected. This Wikipedia article covers the bases
http://en.wikipedia.org/wiki/Neutron_detection
The basic answer is "indirectly", for instance by noticing that something uncharged is bouncing off something else we can detect.
That's how James Chadwick, the person first credited with "observing" the neutron in 1932, did it. Pretty detailed technical description here:
http://hyperphysics.phy-astr.gsu.edu/hbase/particl...
And incidentally a lot of things in modern accelerators are only detected indirectly as well. The famous Higgs boson which physicists now believe they've "seen" was actually detected by putting together thousands of observations of things that were predicted to happen if a Higgs boson was created and then immediately decayed.