Unconcern, n.
Want of concern; absence of anxiety; freedom from solicitude; indifference. A listless unconcern, Cold, and averting from our neighbor's good. Thomson.
Shades of meaning
Fernald has no entry of its own for unconcern; he lists it under apathy.
Where he writes about it:
Indifference is a want of interest; insensibility is a want of feeling; unconcern has reference to consequences. — from apathy