The half shekel and atonement for the soul

Question

In parashas Ki Sissa, G-d instructs Moshe to collect from all the people, half a shekel:

When thou dost take the sum of the children of Yisra᾽el after their number, then shall they give every man a ransom for his soul to the Lord, when thou dost number them; that there be no plague among them, when thou dost number them.

The Torah uses different words to describe what the half shekel is for.

1. a ransom for his soul to the L-rd (v.12)
2. an atonement for the soul (v. 15/16)

However, the words "atonement for the soul" seems to be used more than "ransom for his soul".

In posuk 12, the Torah writes:

that there be no plague among them, when thou dost number them.

However, the Sifsei Chakhamim seems to understand this to mean that it does not serve as an atonement for the soul.

So that you not be struck. . . But it does not mean to atone for your sins, like other atonements mentioned in the Torah. [Rashi knows this] because [otherwise,] why is the atonement connected to the counting?

Are there meforshim that explain why the Torah uses the words "atonement for the soul" and what this implies? What is the deeper meaning behind this? Was it really atonement for the soul, atonement for the golden calf? And how to reconcile the words of the Sifsei Chakhamim with the posuk itself?

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^{I've thought about the Yerushalmi that teaches us that the gold of the cover of the Ark was an atonement for the golden calf. So I thought, maybe the half shekel was also an atonement for the golden calf, since everybody needed to give his part (however, the gold was used, and the half shekel was not made from gold. The Chasam Sofer on that Yerushalmi seems to explain that it would be logical that since the people gave their gold for the egel to be made, that the cover of the ark was also made from gold, as an atonement. So it seems logical to me that other objects could also serve as an atonement, including the half shekel).}

Answer 1

There are many sources that interpret atonement in the ordinary sense. The Yerushalmi and Tanchuma link it to the golden calf (also hinted to in Rashi). Some say that it's an atonement for the evil eye caused by counting, or to counteract the additional scrutiny brought about when individuals are singled out from the community.

But Rashi seems to take a novel approach in his main interpretation. He reads "when you count them" as implying that the counting itself was done via the coins, so as to avoid the issue of counting people altogether, which requires him to loosely define "atonement"as a sort of preventative measure. Perhaps that's why he offers the second explanation, that it's called an atonement because it funded the communal sacrifices which brought atonement.

On a deeper level, the Lubavitcher Rebbe explains that these sacrifices are uniquely related to the golden calf since it was a communal sin. The world was originally created in a state of perfection, but it was ruined by the sin of the Tree of Knowledge, which impacted not only Adam and Chava, but the entire world and all future generations. The Jews were cleansed of this contamination when they received the Torah at Sinai, but with the sin of the golden calf, they reverted to a state of contamination at the community level, affecting even those who had no part in it, like the tribe of Levi and Moshe himself. That's why the half-shekel went specifically toward communal sacrifices (and why it was a fixed rate for everyone), because it was a communal atonement.

But this is only skimming the surface of a classic topic in Chassidus. There are many in-depth Maamarim and Sichos on the subject; see here and here for some translated examples.