New determination of proton spectroscopic factors and reduced widths for $^{8}$Be states in the $16.5-18.0$ MeV excitation energy region via the study of the $^{7}$Li($^{3}$He,d)$^{8}$Be transfer reaction at E$_{lab}$ $=\ 20$ MeV

The angular distributions of $^{8}$Be states in the excitation energy region, E$_{x}$ $\ \sim$($16.5-18.2$) MeV, produced in the $^{7}$Li($^{3}% $He,d)$^{8}$Be proton transfer reaction have been measured at the Orsay 14.8$-$MV tandem accelerator for $^{3}$He$^{2+}$ ion bombarding energy, E$_{lab}$ $=20$ MeV, and forward anglular range, $\theta_{lab}=5^{\circ}-50^{\circ}$. A high energy resolution detection system composed of a split-pole magnetic spectrometer and a $\Delta E-E$,\ position-sensitive drift chamber was used to record the energy spectra of outgoing deuterons. The measured cross section data for the direct reaction component have been separated from the compound nucleus one, then analyzed in the framework of the non local, FR-DWBA theory. New values of the $C^{2}S$ and ($S_{p1/2},$ $S_{p3/2})$ proton absolute and partial spectroscopic factors and related $\gamma_{p}^{2}(a)$\ proton reduced widths versus the p $+$ $^{7}$Li channel radius have been extracted for the $2^{+}(16.626)$ and $2^{+}(16.922),T=0+1$ isospin-mixed loosely bound states of astrophysical interest and the $1^{+}(17.640)$, $T=1$ unbound state of $^{8}$Be. They are compared to sparse earlier experimental values and to shell-model predicted ones from the literature, and are discussed. In particular, the status of the spectroscopic information on the $2^{+}$ isospin-mixed doublet is reviewed and up-dated. The application in nuclear astrophysics of the DWBA derived results is emphasised.