  Inspired by the recent results of the WASA-at-COSY Collaboration, in which
they found a resonance pole in the coupled $^{3}D_{3}$ - $^{3}G_{3}$ partial
waves as expected from the $d^{*}$ resonance hypothesis, we calculated the
resonance structure in the coupled $^{3}D_{3}$ - $^{3}G_{3}$ partial wave phase
shifts of nucleon-nucleon scattering in the framework of two constituent quark
models: the quark delocalization color screening model and the chiral quark
model. Our results show that there is a resonance $^{7}S_{3}^{\Delta\Delta}$ in
the coupled $^{3}D_{3}^{NN}$ and $^{3}G_{3}^{NN}$ partial waves in both of
these two models, which is in accordance with the expectation from the $d^{*}$
resonance structure. The resonance shape in the $^{3}D_{3}^{NN}$ partial wave
is remarkable, whereas in the $^{3}G_{3}^{NN}$ phase shifts there is a small
rise around the resonance energy. This result is in agreement with the recent
experimental observations of WASA-at-COSY Collaboration.
