I apologize that this isn't actually an answer, but the comment section is too limiting and I believe the explanation is valuable.
You're doing something very common in every language. You're making a comparison or a judgement. There are a great many ways to do this, but the grammar should be consistent.
Don't give a...
This form of the comparison is comparing the reference object (in your case, radioactive decay) to a referent object. I apologize that I don't use coarse language, so let's use a phrase popular in my family, "hill of beans."
I don't give a hill of beans about that!
An astute observer would point out that the market value of a hill of beans could potentially be quite high. The reason "hill of beans" is used is that, historically, beans are a cheap source of food. However, there's a very long story behind this that isn't approrpriate to go into here. So, please help me out by accepting the idea that a hill of beans has little perceived value in the context of the phrase. Thanks!
This is the form of comparison you should use were you to continue to use the expletive. The article "a" invites you to use a physical, countable object. You could convert the phrase to use the article "the" as in "I don't give the vastness of outer space!" but the phrase can quickly become awkward and the comparison unclear (outer space is basically empty and therefore has not value... yuck). I believe this version of the comparison is best understood when using physical, low-value objects.
Don't care a...
This version of the comparison does not compare the reference to a physical referent. In its simplest form, the referent is a trivially small measurement of the verb "to care." This is why words like "bit" and "whit" work so well with it. For example, "bit" is (among many other things) a "small quantity of something." You could less eloquently say, "because you don't care about radioactive decay" and obtain the same meaning.
It's worth noting that you have as much flexibility with this form as you do the other, because you can make the comparison against any human virtue. Care, love, hope, even hate.
I don't love you even the tiniest bit!
It's all about Emphasis
Why do we use comparative phrases like these? Because humans love emphasizing things — both positively and negatively. "I don't care a bit" has the same basic meaning as "I don't care," but it's lacking the emphasis "a bit" lends to the statement. The added phrase brings no additional clarity to the basic meaning of the statement. It only makes an attempt to express the extent of your emotional state at the time the statement was made. You don't care either way, but in one instance you look calm and peaceful and in the other you're huffing with veins popping out on your head. :-)
So, remember that you "don't give a [low-value physical object]" and you "don't care a [trivially small measurement]." Whichever you choose will work fine in your poem.