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 an analytical estimate and a Glauber model, I show that the variances $$\langleε^{2}_{2}\rangle$$ or $$\langle$$(δd⊥/d⊥)2$$\rangle$$ and skewnesses $$\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$$ or $$\langle(δd_{⊥}/d_{⊥})^{3}\rangle$$ have a simple analytical form of a'+b'β$$^{2}_{2}$$ and a'+[b'+c' cos(3γ)]β$$^{3}_{2}$$, respectively. From these, I 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 β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [pT] of final-state particles, v2 ∝ ε2 and δ [pT] / [pT] ∝ δd⊥/d⊥, similar conclusions are also expected for the variances and skewnesses of v2 and [pT], i.e., a + bβ$$^{2}_{2}$$ for $$\langle v^{2}_{2}\rangle$$ and $$\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$$ and a + [b + c cos (3γ)] β$$^{3}_{2}$$ for $$\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$$ or $$\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$$. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos (3γ) ≈ 1, and near oblate nuclei, cos (3γ) ≈ –1 , with known β2 values, followed by collisions of other species of interest with similar mass number. The (β2, γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.
- Authors:
-
[1]
- Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1871832
- Report Number(s):
- BNL-223052-2022-JAAM
Journal ID: ISSN 2469-9985; TRN: US2306810
- Grant/Contract Number:
- SC0012704; FG0287ER40331
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. C
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 4; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; collective flow; relativistic heavy-ion collisions; collective models; nuclear structure and decays; nuclear distribution; particle correlations and fluctuations; quark-gluon plasma; strong interaction
Citation Formats
Jia, Jiangyong. Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions. United States: N. p., 2022.
Web. doi:10.1103/physrevc.105.044905.
Jia, Jiangyong. Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions. United States. https://doi.org/10.1103/physrevc.105.044905
Jia, Jiangyong. Wed .
"Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions". United States. https://doi.org/10.1103/physrevc.105.044905. https://www.osti.gov/servlets/purl/1871832.
@article{osti_1871832,
title = {Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions},
author = {Jia, Jiangyong},
abstractNote = {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 an analytical estimate and a Glauber model, I show that the variances $\langleε^{2}_{2}\rangle$ or $\langle$(δd⊥/d⊥)2$\rangle$ and skewnesses $\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$ or $\langle(δd_{⊥}/d_{⊥})^{3}\rangle$ have a simple analytical form of a'+b'β$^{2}_{2}$ and a'+[b'+c' cos(3γ)]β$^{3}_{2}$, respectively. From these, I 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 β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [pT] of final-state particles, v2 ∝ ε2 and δ [pT] / [pT] ∝ δd⊥/d⊥, similar conclusions are also expected for the variances and skewnesses of v2 and [pT], i.e., a + bβ$^{2}_{2}$ for $\langle v^{2}_{2}\rangle$ and $\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$ and a + [b + c cos (3γ)] β$^{3}_{2}$ for $\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$ or $\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos (3γ) ≈ 1, and near oblate nuclei, cos (3γ) ≈ –1 , with known β2 values, followed by collisions of other species of interest with similar mass number. The (β2, γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.},
doi = {10.1103/physrevc.105.044905},
journal = {Physical Review. C},
number = 4,
volume = 105,
place = {United States},
year = {Wed Apr 20 00:00:00 EDT 2022},
month = {Wed Apr 20 00:00:00 EDT 2022}
}
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