Nuclear deformation effects in photoproduction of $\rho$ mesons in ultraperipheral isobaric collisions

We have investigated the ${\rho }^0$ meson photoproduction in ultraperipheral isobaric collisions between ${}_{44}^{96}\text{Ru}{+}_{44}^{96}\text{Ru}$ and ${}_{40}^{96}\text{Zr}{+}_{40}^{96}\text{Zr}$ at $\sqrt{s_{NN}}=200$ GeV, employing the dipole model with the equivalent photon approximation. By implementing the Woods-Saxon distribution to represent the nuclear mass density, which is derived from density functional theory with an inclusion of nuclear deformation effects, we have calculated the transverse momentum $q_T$ spectra in isobaric collisions. We observe the characteristic dip behavior in these spectra, indicative of diffraction phenomena in high-energy physics. We notice that the deformation effects cause a nearly linear increase with $q_T^2$ for $q_T^2\lesssim 0.015$ ${\text{GeV}}^2$, aligning with experimental observations. We offer a simple explanation for the observed behavior in these spectra by introducing the effective width of the nuclei in the thickness function. We also extend our discussion on the ${\rho }^0$ meson photoproduction with the targets ${}^{63}\text{Cu}$,${}^{197}\text{Au}$, and ${}^{238}\text{U}$.