Can we "fill" an atom with alpha particles? The following passage has been extracted from the book "Modern's abc of Chemistry":  

..Heisenberg in 1927, put forward a principle known as Heisenberg's uncertainty principle. It states that, it is not possible to measure simultaneously both the position and momentum (or velocity) of a microscopic particle, with absolute accuracy.   

Lets fill an isolated atom by subatomic "Rutherford projectiles"-alpha particles. I hope it is possible. This doesn't seem to be a limit of our technology. Isn't it?  
If we are successful in filling the an atom with alpha particles, we are decreasing the space for the electron and confining them to a least distance, isn't it?   
Doesn't this experiment, give us belief of measuring simultaneously both the position and momentum with little greater (or even complete) certainty than what predicted by Heisenberg's principle? This doesn't seem to allow us to fill an atom with alpha particles.  
So, can we fill an atom with alpha particles?
 A: Apart from the good answer from @dmckee, the "filling up an atom" is somehow what happens in very massive stars. With enough gravitation, you can squeeze atoms. Well, the heart of a star is too hot to have true "atoms" in the mundane sense; the electrons and nuclei are free-moving (that's called a plasma). The electrons have no problem sharing space with the nuclei, but they take issue at one another; this is Pauli's exclusion principle at work. If you push too hard, electrons, like angry teenagers, will prefer to merge with protons instead of getting along together (but cramped for space). That's the reverse of the beta decay; a proton and an electron, if forced to meet, fuse into a neutron.
Push hard enough and all the star "atoms" will become neutrons, yielding a neutron star. If you push even more, the whole thing collapses as a black hole, at which point it quits the game and we can stop talking about it.
So that's how you fill an atom (with a lot of gravitation); and what happens is a neutron star, not because the electrons don't like the nuclei, but because they don't like each other. Presumably, if you could first remove all the electrons, then you could get a massive "proton star", but it would not be electrically neutral, so removing the electrons would be hard.
A: 
Lets fill an isolated atom by subatomic "Rutherford projectiles"-alpha particles.

That would be every even-even nucleus for which $A = 2Z$. You'll note that there is a stability limit above which you must add extra neutrons to hold the whole thing together, and another limit beyond which even adding extra neutrons won't help.

If we are successful in filling the an atom with alpha particles, we are decreasing the space for the electron and confining them to a least distance, isn't it? 

No. Electrons can happily co-occupy space with nucleons. Remember that these are fully quantum objects, not little billiard balls. The wave-function for all s-shell electron states has them with non-zero probability density inside the nucleus.
You might be thinking that this could manifest as a small correction, but in the case of highly ionized heavy atoms it would have to be a quite significant correction, but the spectroscopy agrees with the (relativistic) theory quite well. Electrons really do co-occupy the same space as the nucleons without trouble.

Your premise is not really correct, so the question you want to ask is moot. Bu the Heisenberg limit is fundamental to the way we believe quantum mechanics works. It can't be beaten without completely overthrowing the theory.
