Structure of the exotic neutron-rich nuclei 42Si, 52Ti, and 54Ti

The modification of magic numbers and the shell structure of very neutron-rich systems is one of the most intriguing subjects to be studied with present and future exotic beam facilities. In a number of recent experiments, the modification of shell structure for both the neutron and proton-systems was studied for the very neutron-abundant nuclides $^{52,54}$Ti and $^{42}$Si; The excited level structure of $^{52,54}$Ti show evidence for a sub-shell closure at N=32 [1], while a recent measurement of Coulomb excitation of the 2$^+_1$ in $^{56}$Ti [2] shows that the sub-shell closure at N=34 is weaker than expected. In order to investigate the character of $^{42}$Si, we performed an experiment using a $^{44}$S beam, generated in fragmentation of 140 MeV/u $^{48}$Ca at the Coupled-Cyclotron Facility at the NSCL. This beam was delivered to the target position of the S800 spectrograph, where secondary reactions occurred. The one-proton and two-proton knockout reaction products, $^{43}$P and $^{42}$Si, were identified using the S800 spectrograph and coincident $\gamma$ rays were detected with the segmented Germanium array, SeGA, surrounding the S800 target position. We measured one-proton knockout populating the ground and first excited state of $^{43}$P. The direct reaction character of one-proton [3] knockout and two-proton knockout [4] allows to compare the observed cross-section to calculations using the eikonal-approach. We find large cross sections for the single-proton knockout, corresponding to single-particle spectroscopic factors for the $^{43}$P = $^{42}$Si + p system. Simultaneously, the measured two-proton knockout cross section corresponds to a Z=14 closed shell $^{42}$Si. Both of these aspects support the magic character of $^{42}$Si. [1] R.V.F. Janssens {\em et al.} Phys. Lett. B 546 (2002) [2] D.C. Dinca {\em et al.} Phys. Rev. C{\bf 71}, 041302R (2005) [3] Hansen, P.G. \& Tostevin, J.A., Direct Reactions with Exotic Nuclei. Annu. Rev. Nucl. Part. Sci. 53, 219-261 (2003). [4] D. Bazin {\em et al.} Phys.~Rev.~Lett. {\bf 91} 012501 (2003)