Mexican Hat Function that Converges to 1

Question

The Ricker wavelet, also known as the Mexican Hat function, converges to 0 for negative and positive infinity.

I'm looking for a function with the same shape in the center, but that converges back to 1 (or a value really close to 1) when approaching negative or positive infinity.

P.S: Obviously $f(x) + 1$ does not work, as the new maximum will be close to 2.

Answer 1

Something like this seems to work: $$f(x)=1-0.1e^{-0.36x^2}-1.3x^2e^{-x^2}$$