Accessing the shape of atomic nuclei with relativistic collisions of isobars

Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to gain precise knowledge of the geometric shape of atomic nuclei.

Figure 1

Anisotropic overlap regions in nuclear collisions. Left: a collision of spherical nuclei breaks anisotropy in the transverse plane due to the finite impact parameter. Right: a central collision of deformed nuclei breaks anisotropy due to the non-spherical shape of the colliding bodies.

Figure 2

Rms elliptic flow in X+X collisions divided by the rms elliptic flow in Y+Y collisions as a function of collision centrality. The ratio of flow coefficients is estimated following Eq. (8) and the TRENTo model. The shaded band represents a 1% deviation from unity. Any deviation from unity which falls outside the shaded band can be considered as a significant signature that ${\beta }_{\mathrm{X}}\ne {\beta }_{\mathrm{Y}}$.