Need help about the verbal form +て いた … です

Hi all,

I'm studying the sentences like "This is the thing I'm looking for", that is translated in this way:

これ は 探して いた もの です

I would need help to understand the chunks of this sentence, because I'd have naturally translated it like

これ は もの を 探している

but I've understood that this would be wrong (google traslator says that its meaning is "This is looking for something").

I think that the focal point of the sentence is the いた between 探して and もの です. First of all, I'd need to understand why もの is between the two verbs and not before 探す joined with を, and then which verbal form is the て form + いた. I mean if it's something similar to a nominalizaiton (but it doesn't actually seem like that) or if it's a verbal form "tout court" that I have to learn by memory without asking too much about its construction.

I have also understood that this construction is not related to the noun もの, because it's the same with other nouns, like for example 本 for a sentence like "This is the book I'm looking for", to make a generic example.

Thanks to who will help me to understand this better.