How do alpha particles emit the heleum spectrum without electrons? By definition, alpha particles do not have any electrons. This, in turn, should mean they do not emit a spectrum because a light spectrum is caused by electrons jumping between orbitals. Yet it is by alpha particles emitting a spectrum that Rutherford determined them to be helium nuclei (see here for details https://history.aip.org/exhibits/rutherford/sections/alpha-particles-atom.html). 
 A: The paper usually referenced (e.g. by Wikipedia) as the identification of the $\alpha$ particle as the Helium nucleus is "XXIV. Spectrum of the Radium Emanation", E. Rutherford and T. Royds, Phil. Mag. Vol. 16. No. 92 (Aug. 1908 - DOI link). Details on how the $\alpha$ particles were isolated and purified are given in "XXIII. Experiments with the radium emanation. (1) The volume of the emanations", E. Rutherford, Phil. Mag. 16(92) 300-312 (1908, DOI link). Now, the possible linking of the $\alpha$ particle and He had existed for a while, such as in "XLI. The mass and velocity of the $\alpha$ particles expelled from radium and actinium", E. Rutherford, Phil. Mag. Vol. 12 No. 70  348-371 (Oct. 1906 - DOI link). However, such indirect proof was not considered sufficient.
The experiment is described in the 1908 paper pretty well. The "radium emanations" where captured in a glass tube. After various purifying steps (condensation with liquid air, reaction with potash to remove carbon dioxide, ...). What was left was sealed in a glass tube with platinum electrodes. The electrodes were used to excite the remaining gas. The spectrum of the discharge was observed visually and photographed as well. 
To quote the 1908 paper:

In order to photograph
  the spectrum, a spectrograph with a glass prism of two inches
  base was used. The length of the spectrum on the plate
  between $\lambda$ 5000 and $\lambda$ 4000 was 1.5 cms. Arrangements
  were made so that visual observations of the wave-lengths
  could be made by the Hilger spectroscope while the plate
  was being exposed. Two photographs were taken before the
  emanation spectrum ran out. The first (photograph 1) showed
  about thirty of the more intense emanation lines. The second
  (photograph 2), which had a much longer exposure, showed
  over a hundred lines. A helium tube was used for comparison
  purposes, and its spectrum obtained above and below the
  emanation spectrum. The plates were measured up with the
  aid of a Kayser's measuring machine. The wave-lengths
  were deduced with the aid of the Hartmann dispersion
  formula

So, the emission spectrum of the $\alpha$ particles was not measured as they were emitted. Instead, the $\alpha$s were released from the radium into a glass tube, separated through purification, and then used in a discharge tube. The direct comparison with a He lamp seals the deal. (As for the 'emanation spectrum' running out, recall that He diffuses quite easily through glass so it leaks out quickly.)
A: Protons or neutrons can also emit photons. You don’t necessarily need electrons. https://www.quora.com/Can-an-accelerated-proton-emit-electromagnetic-radiation 
