The Collaborative International Dictionary of English v.0.48:

Unconcern \Un`con*cern"\, n.
   Want of concern; absence of anxiety; freedom from solicitude;
   indifference.
   [1913 Webster]

         A listless unconcern,
         Cold, and averting from our neighbor's good. --Thomson.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

83 Moby Thesaurus words for "unconcern":
   accidia, acedia, aloofness, apathy, ataraxia, ataraxy,
   benumbedness, blah, blahs, boredom, carelessness, casualness,
   comatoseness, detachment, disinterest, disinterestedness,
   dispassion, disregard, disregardfulness, dullness, easygoingness,
   heartlessness, hebetude, heedlessness, hopelessness, impassiveness,
   impassivity, inappetence, inattention, incuriosity, incuriousness,
   indifference, indifferentism, indifferentness, indiscrimination,
   inexcitability, insouciance, intellectual inertia, lack of affect,
   lack of appetite, lack of interest, lackadaisicalness, languidness,
   lassitude, lethargicalness, lethargy, listlessness, mindlessness,
   negligence, nonchalance, numbness, offhandedness, passiveness,
   passivity, phlegm, phlegmaticalness, phlegmaticness, plucklessness,
   pococurantism, recklessness, regardlessness, resignation,
   resignedness, sloth, sluggishness, sopor, soporifousness,
   spiritlessness, spunklessness, stolidity, stupefaction, stupor,
   supineness, torpidity, torpidness, torpor, unanxiousness,
   uninquisitiveness, uninterestedness, unmindfulness,
   unsolicitousness, withdrawal, withdrawnness