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The symbol for the alpha particle is α or $α^{2+}$, it can be written as $He^{2+}$. What I want to know is that, are they same? I mean alpha particle and helium nucleus are same or any subtle difference exists?

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As you say $\alpha$ and $He^{2+}$ are same , so it's $\alpha$ particle. Not $\alpha^{2+}$ –  Mr.ØØ7 Apr 29 '13 at 6:38
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2 Answers

They are exactly the same, with the different notations arising in different contexts. You could start with a bunch of helium gas and heat it up or shine UV light on it to turn it into a plasma, and then you'd probably say you have $\mathrm{He}^{2+}$ (or $\mathrm{He}\ \mathrm{III}$ if you are an astronomer). The symbol $\alpha$ is more often reserved for when the particle was just ejected in a nuclear reaction, as in ${}^{238}\mathrm{U} \to {}^{234}\mathrm{Th} + \alpha$.

This also applies to protons, where $\mathrm{H}^+$, $\mathrm{H}\ \mathrm{II}$, $p$, and $p^+$ all refer to the same particle.

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Noe, however, that if you inject your highly ionized helium gas into a particle accelerator it is then described as a alpha beam. The distinguishing feature may be better described as having significant kinetic energy in the frame of [whatever interaction you are interested in]. –  dmckee Apr 28 '13 at 20:14
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They are the same particles. When $\alpha$-radiation eventually gets stopped by an object (a sheet of paper or simply a meter or so of air will do the trick) it attracts two electrons and becomes elementary Helium.

Most of the world's Helium actually originates from reserves underground where Uranium and other $\alpha$ radiators have been creating He for millenia.

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