Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Abstract

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β2 and triaxiality γ. The deformation can be accessed in high-energy heavy-ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ε2 and the density gradient d⊥ in the initial state. Using analytical estimate and a Glauber model, we show that the variances, ⟨ε 2 2 ⟩ or ⟨(δd⊥ d⊥) 2 ⟩, and skewnesses, ⟨ε 2 2 δd⊥ d⊥⟩ or ⟨(δd⊥ d⊥From these, we constructed several normalized skewnesses to isolate the γ dependence from that of β2, and show that the correlations between a normalized skewness and a variance can constrain simultaneously the β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [p T ] of final state particles, v2 ∝ ε2 and δd⊥ d⊥ ∝ δ[p T ] [p T ], similar conclusions are also expected for the variances and skewnesses of v2 and [p T ], which can be measured precisely in top RHIC and LHC energies. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate, cos(3γ) = 1, and oblate nuclei, cos(3γ) = −1, with well known β2 values to calibrate the coefficients b ′ and c ′ , followed by collisions of species of interest especially those with known β2 but unknown γ.

Scaling approach to nuclear structure in high-energy heavy-ion collisions

“…is the value for spherical nuclei with the reference radius and diffuseness, and b 1 -b 4 are centrality-dependent response coefficients that are encoded in the final-state dynamics. Note that the leadingorder contribution from deformation appears as β 2 n instead of β n because these observables do not depend on the sign of β n [20,34] 1 . The b n coefficients depend on the mass number but otherwise are the same between isobars.…”

“…The first calculation is based on the quark Glauber model discussed in Refs. [20,34], where each nucleon is replaced by three constituent quarks. The distribution of quark-participants p(N quark ) generated for the parameter set of 96 Ru in Table I is then convoluted with a negative binomial distribution that describes the production of charged particle for each participant,…”

“…1 For higher-order correlators, such as skewness of p T fluctuation and v 2 n −p T correlation, the leading order term scales with β 3 n[34].modified…”

An overview of new measurements of flow, chirality, and vorticity from STAR experiment

“…The analytical estimation of shape and size are strongly correlated with nuclear deformation as illustrated in Ref. 52 So far, experimental measurements are limited to the mean transverse momentum and and its variance. [54][55][56][57][58] To save the computational overhead from loop-calculations, a framework for calculating the higher-order dynamical p T cumulants up to fourth-order using the standard and subevent methods is established and detailed in Ref.…”

Search for the chiral magnetic effect in collisions between two isobars with nuclear structures

“…It is worth noting that the Cases 4-6 and the effect of β 3 have been studied in detail in Refs. [35,48,51], and their recent study suggested that the ratios calculated at the same N ch provide a better baseline for the non-CME background [52]. For simplicity, we choose the halo-type neutron skin case for doing our following study related to the CME.…”