Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

Abstract

In heavy ion collisions, elliptic flow v2 and radial flow, characterized by event-wise average transverse momentum [p T ], are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between v2 and [p T ], ρ2, was found to be particularly sensitive to the quadrupole deformation parameter β that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation β > 0 reduces the ρ2 in ultra-central collisions (UCC), we show that the prolate deformation β < 0 enhances the value of ρ2. As β > 0 and β < 0 are the two extremes of triaxiality, the strength and sign of v 2 2 − [p T ] correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale (< 10 −24 s).

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

“…Note that the off-diagonal coefficients ⟨p 0;m ′ p 0;m ′ ⟩ m≠m ′ and ⟨p n;m p * n;m ′ ⟩ m≠m ′ may not vanish especially in the noncentral collisions. These mixing contributions have been observed in our previous study of ⟨ε 2 n ⟩ [14], and are expected to influence all other cumulants discussed above. We leave this interesting topic to a future study.…”

“…The AMPT model has been demonstrated to qualitatively describe the harmonic flow v n in p+A and A+A collisions [49,50], so it can be use to predict the β 2 dependence of v n . A previous study has demonstrated a robust simple quadratic dependence ⟨v 2 2 ⟩ = a + bβ 2 2 in the final state as a result of a linear response to a similar dependence in the initial state ⟨ε 2 2 ⟩ = a ′ + b ′ β 2 2 [13,14]. However this model is known to have the wrong hydrodynamic response for the radial flow, i.e.…”

“…1 discussed above. A few model studies on the feasibility of constraining triaxiality in heavy ion collisions appeared recently [14][15][16]. In light of these measurements and model work, we aim to clarify, via a Monte-Carlo Glauber model and a transport model, the influence of deformation on the cumulants of ε 2 and [p T ].…”

“…Information about nuclear deformation is primarily extracted from spectroscopic measurements and models of reduced transition probability B(En) between low-lying rotational states, which involves nuclear experiments with energy per nucleon less than few 10 MeVs. Recently, the prospects of probing the nuclear deformation at much higher beam energy, energy per nucleon exceeding hundreds of GeVs, by taking advantage of the hydrodynamic flow behavior of large number of produced final-state particles, have been discussed [6][7][8][9][10][11][12][13][14][15][16], several experimental evidences have been observed [17][18][19][20][21].…”

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

“…Experimental information of nuclear structure is primarily obtained by spectroscopic or scattering measurements at low energies. But studies show that nuclear structure can be probed in high-energy nuclear collisions [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and experimental evidences have been observed [22][23][24][25][26].…”