Elastic breakup cross sections of well-bound nucleons

The ${}^9\mathrm{Be}\left({}^{28}\mathrm{Mg},{}^{27}\mathrm{Na}\right)$ one-proton removal reaction with a large proton separation energy of $S_p\left({}^{28}\mathrm{Mg}\right)=16.79$ MeV is studied at intermediate beam energy. Coincidences of the bound ${}^{27}\mathrm{Na}$ residues with protons and other light charged particles are measured. These data are analyzed to determine the percentage contributions to the proton removal cross section from the elastic and inelastic nucleon removal mechanisms. These deduced contributions are compared with the eikonal reaction model predictions and with the previously measured data for reactions involving the removal of more weakly bound protons from lighter nuclei. The role of transitions of the proton between different bound single-particle configurations upon the elastic breakup cross section is also quantified in this well-bound case. The measured and calculated elastic breakup fractions are found to be in good agreement.

Figure 1

Missing-mass spectra of the one-proton removal reaction residues ${}^7\mathrm{Be}$ (a), ${}^8\mathrm{B}$ (b), and ${}^{27}\mathrm{Na}$ (c) and a proton detected in coincidence. The beam energies are shown in each panel. The arrows show the position of the target mass, $M{(}^9\text{Be})$, and indicate events associated with proton removal by the elastic breakup mechanism. The ${}^{28}\mathrm{Mg}$ spectrum is from the current measurement and the ${}^8\mathrm{B}$ and ${}^9\mathrm{C}$ spectra were extracted from the data sets of Ref. [12].

Figure 2

Computed fractional contribution (%) of the elastic breakup (diffraction) reaction mechanism to the proton removal cross section as a function of the proton separation energy. The lines show the predictions of the eikonal model for proton removal from $1d_{5/2}$ (solid black), $1d_{3/2}$ (dotted red), and $2s_{1/2}$ (dashed green) orbitals. The theoretical prediction, 18%, when using spectroscopic factors calculated from the shell model (see text and Table 1), is shown by the filled black circle.

Figure 3

Experimental (black squares) and theoretical (green circles) fractional contribution (%) of the elastic breakup (diffraction) reaction mechanism to the proton removal cross section as a function of the proton separation energy. In addition to the present study the figure also shows the previously measured cases of weakly bound proton removals from ${}^9\mathrm{C}$ and ${}^8\mathrm{B}$ [12].