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 ${\beta }_2$ and triaxiality $\gamma$. 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 ${\epsilon }_2$ and the density gradient $d_{\perp }$ in the initial state. Using analytical estimate and a Glauber model, I show that the variances, $⟨{\epsilon }_2^2⟩$ or $⟨(\delta d_{\perp }/d_{\perp }{)}^2⟩$, and skewnesses, $⟨{\epsilon }_2^2\delta d_{\perp }/d_{\perp }⟩$ or $⟨(\delta d_{\perp }/d_{\perp }{)}^3⟩$, have a simple analytical form of $a^{\prime }+b^{\prime }{\beta }_2^2$ and $a^{\prime }+(b^{\prime }+c^{\prime }\cos (3\gamma )){\beta }_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $\gamma$ dependence from that of ${\beta }_2$, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the ${\beta }_2$ and $\gamma$. Assuming a linear relation with elliptic flow $v_2$ and mean-transverse momentum $[p_{\mathrm{T}}]$ of final state particles, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. 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, $\cos (3\gamma )=1$, and oblate nuclei, $\cos (3\gamma )=-1$, with well known ${\beta }_2$ values to calibrate the coefficients $b^{\prime }$ and $c^{\prime }$, followed by collisions of species of interest especially those with known ${\beta }_2$ but unknown $\gamma$. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

20 pages, 14 figures, plus 3 appendix, published version

References in corpus (18)

• Glauber Modeling in High Energy Nuclear Collisions
• 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid
• Elliptic and triangular flow in p+Pb and peripheral Pb+Pb collisions from parton scatterings
• A transverse momentum differential global analysis of Heavy Ion Collisions
• Evidence of quadrupole and octupole deformations in ${}^{96}$Zr+${}^{96}$Zr and ${}^{96}$Ru+${}^{96}$Ru collisions at ultra-relativistic energies
• Shape of atomic nuclei in heavy ion collisions
• Triangular flow in heavy ion collisions in a multiphase transport model
• Transverse-momentum fluctuations in relativistic heavy-ion collisions from event-by-event viscous hydrodynamics
• Evidence of the triaxial structure of ${}^{129}$Xe at the Large Hadron Collider
• Long-range azimuthal correlations in proton-proton and proton-nucleus collisions from the incoherent scattering of partons
• Measurement of the azimuthal anisotropy of charged-particle production in Xe+Xe collisions at $\sqrt{s_{\mathrm{NN}}}=5.44$ TeV with the ATLAS detector
• Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions
• Accessing the shape of atomic nuclei with relativistic collisions of isobars
• Scaling approach to nuclear structure in high-energy heavy-ion collisions
• Collision Energy Dependence of $p_{\mathrm{t}}$ Correlations in Au+Au Collisions at RHIC
• Nuclear deformation at finite temperature
• Non-flow effects in correlation between harmonic flow and transverse momentum in nuclear collisions
• Using local nuclear scaling of initial condition parameters to improve the system size dependence of transport model descriptions of nuclear collisions

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