A strontium iodide crystal doped by europium (SrI2(Eu)) was produced by using the Stockbarger growth technique. The crystal was subjected to a characterization that includes relative photoelectron output and energy resolution for gamma quanta. The intrinsic radioactivity of the SrI2(Eu) crystal scintillator was tested both by using it as scintillator at sea level and by ultra-low background HPGe gamma spectrometry deep underground. The response of the SrI2(Eu) detector to alpha particles (alpha/beta ratio and pulse shape) was estimated by analysing the 226Ra internal trace contamination of the crystal. We have measured: alpha/beta=0.55 at E_alpha=7.7 MeV, and no difference in the time decay of the scintillation pulses induced by alpha particles and gamma quanta. The application of the obtained results in the search for the double electron capture and electron capture with positron emission in 84Sr has been investigated at a level of sensitivity: T_1/2 sim 10^{15}-10^{16} yr. The results of these studies demonstrate the potentiality of this material for a variety of scintillation applications, including low-level counting experiments.
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