Analysis of the Structure of Nuclei from (d, t) Reactions

The following work illustrates the use of experimentally determined reduced widths from ($d, t$) reactions in analyzing the structure of the ground state of the target nuclei. The ($d, t$) reaction is an especially sensitive and almost unique experimental technique for measuring small components of nuclear wave functions. In this role it becomes a valuable tool in investigating the presence of strong pairing forces in nuclei. This analysis demonstrates the strong mixture of the $2p_{\frac{3}{2}}$ and $1f_{\frac{5}{2}}$ neutron states in the region around $A=60\mathrm{}$. In contrast to this, nuclei with 28 neutrons show no observable mixing of states. Special attention is given to ${\mathrm{Fe}}^{57}$ and a shell-model wave function is derived that gives the observed magnetic moment as well as the observed ($d, t$) reduced widths. In this connection a simple general formula is presented for the magnetic moment of any shell-model wave function.