is it possible to break the bonds of diatomic elements such as fluorine or iodine and create positive and negative ions by electron bombardment?

If I had a container in vacuum filled with $\ce{I2}$ gas and then I bombarded it with high speed electrons using an electron gun, would be able to get both $\ce{I+}$ and $\ce{I-}$ ions or would I only get $\ce{I2+}$ plus an ejected electron?




Sure, why not. It's just the question of your bombarding electrons having the right energy. At low energies, a bombarding electron will likely be captured by one of the iodine atoms:
$$
\ce{I2 + e- -> I- + I} \, .
$$
But somewhere around $8.62 \pm 0.06 \, \mathrm{eV}$ according to [this study](http://www.nrcresearchpress.com/doi/abs/10.1139/v60-057#.VVHO8mBmMUU), you'll indeed have the ion pair formation:
$$
\ce{I2 + e- -> I- + I+ + e-} \, .
$$
There are some other processes which contribute to the ion pair formation. For details, read the paper quoted above.




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With respect to the formation of $\ce{I2+}$ note that to form it a bombarding electron have to, formally speaking,


* Either first break the $\ce{I-I}$ bond homolyticly and then remove two electrons from one of the $\ce{I}$ atom which requires it to carry about 30 eV of energy (the sum of the homolytic bond dissociation energy and of the first and the second ionization energies).
* Or break the $\ce{I-I}$ bond heteroliticly and then remove the second electron from $\ce{I-}$ ion which requires it to carry also about 30 eV of energy (the sum of the heterolytic bond dissociation energy and of the second ionization energy).


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