Orientational average in nuclear shape imaging: densities, correlations, and eccentricity in Ne-20

Abstract

The orientational treatment of deformed nuclei in high-energy nuclear collisions have two ways, a rigid rotor and a wave-function rotor, in which nuclear densities in laboratory frame are constructed differently. We calculate the one- and two-body densities (including Pauli blocking effects), body-axis contour multipoles, and geometric eccentricity variances under a leading-order ultracentral mapping for Ne-20 in a deformed harmonic-oscillator model in the rigid and wave-function rotors. At fixed deformation parameter $κ$ in the model, the two constructions can give different laboratory radial moments and pair correlations. The body-axis transition-kernel contours in the wave-function rotor are generally more compact along the symmetry axis, and $β_{20}$, $β_{40}$, $\langle\varepsilon_2^2\rangle$ and $\langle\varepsilon_4^2\rangle$ lie below the rigid-rotor results in a wide range of $κ$. The relations among these quantities in each rotor are nevertheless similar in most scanned parameter space: $β_{40}$ and $\langle\varepsilon_2^2\rangle$ depend linearly on $β_{20}^{2}$, while the hexadecapole baseline-subtracted variance follows an approximate quadratic trend in the quadrupole one. The method can be extended to seek more sensitive quantities for rotational effects in the wave-function rotor.