Toward a New Theory of Spherical Nuclei. II

A study is carried out of one of several possible mechanisms contributing to the quadrupole moment of the first excited ($2^{+}$) state of spherical nuclei. The possibility of a deformed solution is investigated for a set of Hartree-Bogoliubov equations describing the $2^{+}$ state in an angular-momentum-conserving approximation. In the pairing-plus-quadrupole-quadrupole model, a sharp transition from spherical to deformed density distribution is shown to occur just beyond the value of the quadrupole coupling strength necessary to yield the $2^{+}$ excitation energy.