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 $_{44}^{96}\textrm{Ru}+_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+_{40}^{96}\textrm{Zr}$ 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 $q_{T}^{2}\lesssim0.015$ $\textrm{GeV}^{2}$, 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 $^{63}\textrm{Cu}$,$^{197}\textrm{Au}$, and $^{238}\textrm{U}$.