Shell-Model Continuum in Nuclear Bound States

Shell-model calculations are performed for bound $0^{+}$ states of ${\mathrm{Ca}}^{42}$ and ${\mathrm{Ni}}^{58}$. The neutron configurations $1f_{\frac{7}{2}}$, $2p_{\frac{3}{2}}$, $2p_{\frac{1}{2}}$, $1f_{\frac{5}{2}}$, and $1g_{\frac{9}{2}}$ are included, as well as states in which one of the neutrons is in the shell-model continuum. These continuum contributions have little effect on energy eigenvalues, but modify the wave functions in the vicinity of the nuclear surface. The calculated wave functions yield one-particle-transfer form factors whose logarithmic derivatives at large radius are consistent with the neutron separation energies. Comparison is made with other procedures for calculating form factors within the framework of the ordinary shell model. It is found that the conventional well-depth procedure underestimates the ($p, d$) cross sections for populating highly excited states, relative to low-lying states, by about 50%. Two-neutron-transfer cross sections are also calculated and are found to be in agreement with those yielded by the well-depth procedure. However, some of our form factors exhibit an extra node at 8 F, showing that they do not decay like a Hankel function.