The phrase "after a deeper" is correct and usable in written English.
It can be used when discussing a more thorough or profound examination or understanding of a subject.
Example: "After a deeper analysis of the data, we found significant trends that were previously overlooked."
Alternatives: "following a more thorough" or "after a more profound".
Readers sometimes found this perplexing, but after a deeper reading it became clear that this was what gave him his unique value".
After three days spent on the ground here in New Hampshire, however — and after a deeper look at the polls — it certainly does not seem as though Mr. Romney is in any real danger.
The plea for big business to support the recovery came as official data on Monday showed Japan's economy shrank by an annualised 0.8% in July to September after a deeper than previously estimated 0.7% contraction in the previous three months, providing the two consecutive quarters of declines needed to mark a recession.
What Lyon, like many before her, fails to see is that the idea of "Nature," as she describes it, perpetuates the misbegotten project of amateur anthropologists like Lady Raglan, who lusted after a deeper past than could ever be available to them.
After all, why not go after a deeper pocket for some real money?
Indeed, what we are dealing with here is a bimodal logic, which is properly treated only after a deeper understanding of the semantical subtleties of mixing alethic and deontic logics.
After a deep rumble, a plume of smoke rose skyward and people rushed into the streets.
Not infrequently, when they reach the surface after a deep dive they pass out.
After a deep slump, Latvia has the fastest-growing economy in the European Union.
Second, bold austerity measures can restore public finances even after a deep recession.
After a deep slump at the end of last year, the wind industry is picking up.
