The study of fusion reactions $$\hbox {D}(\hbox {d}, \hbox {p})^{3}\hbox {H}$$, $$\hbox {D}(\hbox {d}, \hbox {n})^{3}\hbox {He}$$, $$\hbox {T}(\hbox {d}, \hbox {n})^{3}\hbox {He}$$, $$^{3}\hbox {He}(\hbox {d}, \hbox {p})^{4}\hbox {He}$$, and $$\hbox {D}(^{3}\hbox {He}, \hbox {p})^{4}\hbox {He}$$ at astrophysical energies is of interest for both basic and applied physics. These studied provide information on electron screening of nuclear reactions that provide important information on the role of electrons in reactions induced by deuterons, tritons, and nuclei of helium isotopes that proceed in reactors. The $$\hbox {D}(^{3}\hbox {He}, \hbox {p})^{4}\hbox {He}$$ reaction was investigated at the pulsed plasma Hall accelerator (Tomsk) in the $$^{{3}}\hbox {He}^{{+}}$$ ion energy range $$E_{\mathrm{He}} =16\div 34$$ keV (laboratory reference frame) with a step of 2 keV. The goal of this work was to determine experimentally the enhancement factor of the $$\hbox {D}(^{{3}}\hbox {He}, \hbox {p})^{{4}}\hbox {He}$$ reaction and the electron screening potential $$U_{\mathrm {e}}$$ using a TiD targets with Miller indices [111] and [100]. A strong impact of the target crystal structure on reaction enhancement factor was discovered. We believe that solid-state effects make the largest contribution to the behavior of the enhancement factor $$\hbox {D}(^{{3}}\hbox {He, p})^{{4}}\hbox {He}$$ of the reaction as a function of energy. One of these effects is the particle channeling in crystal structures. An unexpected increase of the enhancement factors for the $$\hbox {D}(^{{3}}\hbox {He, p})^{{4}}\hbox {He}$$ reaction in the energy range $$16\div 22$$ keV probably indicates the emergence of some new mechanism that increases the yield of the reaction with lowering energy.