High-resolution radioactive beam study of the $$^{26}\hbox {Al}(d,p$$) reaction and measurements of single-particle spectroscopic factors

We present a detailed comparison of shell model calculations with inverse kinematic transfer reaction data, obtained using a radioactive beam. Experimentally extracted spectroscopic factors from the $$^{26}\hbox {Al}(d,p)^{27}\hbox {Al}$$26Al(d,p)27Al reaction for both even and odd parity states are found to be exceptionally well reproduced by the shell model and a high level of consistency is observed between bound isobaric analog states in $$^{27}\hbox {Al}$$27Al and $$^{27}\hbox {Si}$$27Si, populated via (d, p) and (d, n) transfer, respectively. Furthermore, an evaluation of key resonances in the astrophysical $$^{26}\hbox {Al}(p,\gamma )^{27}\hbox {Si}$$26Al(p,γ)27Si reaction indicates that shell model calculations provide relatively accurate predictions for the existence of strong resonances and mirror nucleus comparisons appear to hold exceptionally well for proton-unbound levels. Consequently, we expect that the utilization of both techniques will likely be a very effective tool in the investigation of stellar processes outside the current reach of experiment.