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When alpha particles hit the gold nucleus shouldn't they form thallium. More over shouldn't it also ionize the gold or any atom it hits how does it remain unchanged unionized?

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  • $\begingroup$ How does titanium not form in Rutherford gold foil experiment? $\endgroup$ – compenthusiast Jun 15 '20 at 5:06
  • $\begingroup$ en.m.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment $\endgroup$ – compenthusiast Jun 15 '20 at 5:11
  • $\begingroup$ Update your question rather than add comments. Use the edit option. Also be specific in your question to get quality answers otherwise. $\endgroup$ – M. Farooq Jun 15 '20 at 5:13
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    $\begingroup$ We don't care if a few gold atoms turned into thallium. Ditto for ionization. This is not what we measure here. $\endgroup$ – Ivan Neretin Jun 15 '20 at 9:50
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    $\begingroup$ @Poutnik - you need another particle (likely a neutron) departing the compound nucleus, so the likely isotope formed is 200Tl. In fact, the reverse reaction, TL-200(N,A)AU-197, can be found in the Evaluated Nuclear Data files, although one needs a fairly energetic (> 3MeV) neutron to make it happen. $\endgroup$ – Jon Custer Jun 15 '20 at 13:41
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The Rutherford formula, as derived, assumes purely elastic scattering from the Coulomb force. No formation of a compound nucleus is considered. Generally, for most of the initial experiments, the available alpha particle energies from various decays (in the range of a few MeV) were not high enough for large deviations from pure Rutherford scattering. Of course, folks rapidly wanted both other energies (or controlled energies) or other charged particles (such as the protons used by Cockroft and Walton for their first accelerator measurements).

These days, much higher energy particles are available, and are commonly used in nuclear physics. A nice recent paper on the topic is in Physics Review C, "Cross section of $\alpha$-induced reactions on $^{197}$Au at sub-Coulomb energies". Here, the authors measure the reaction cross-sections for $^{197}$Au($\alpha$,$\gamma$)$^{201}$Tl, $^{197}$Au($\alpha$,n)$^{200}$Tl, and $^{197}$Au($\alpha$,2n)$^{199}$Tl. Although mainly of interest to astrophysical heavy-element nucleosynthesis, the results bear on this question.

The bottom line is that high (> 13MeV) $\alpha$ energies are needed to drive these reactions. At the lowest energy used (~ 13.7 MeV), the cross-section for the $^{197}$Au($\alpha$,n)$^{200}$Tl reaction is 0.67 $\mu$b (micro barns). At 20 MeV it has increased to 37 mb (milli barns).

Anyway, it is quite clear that these reactions do not occur to any measurable extent in the few MeV regime.

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