Nuclear Physics Confronts Relativistic Collisions Of Isobars

Anatoli Afanasjev; Andreas Kirchner; Andr\'e V. Giannini; Benjamin Bally; Bj\"orn Schenke; Chunjian Zhang; Chun Shen; Dean Lee; Derek Teaney; Eduardo Grossi

REVIEW 3 major objections 4 minor 4 cited by

Nuclear Physics Confronts Relativistic Collisions Of Isobars

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Isobar collision ratios are explained by nuclear shapes, not magnetic fields.

desk verdict A comprehensive and mostly honest task-force report that makes the nuclear-structure interpretation of the isobar data credible, but rests its sharpest quantitative claim on a flagged and unresolved assumption about octupole deformation in 96Zr. read the letter →

arxiv 2507.01454 v1 pith:KBBOVWOW submitted 2025-07-02 nucl-ex hep-exhep-phnucl-th

Giuliano Giacalone , Jiangyong Jia , Vittorio Somà , You Zhou , Anatoli Afanasjev , Massimiliano Alvioli , Benjamin Bally , Federica Capellino

show 38 more authors

Jean-Paul Ebran Hannah Elfner Fernando G. Gardim André V. Giannini Frédérique Grassi Eduardo Grossi Jan Hammelmann Andreas Kirchner Dean Lee Matthew Luzum Hadi Mehrabpour Emil G. Nielsen Govert Nijs Tamara Nikšić Jacquelyn Noronha-Hostler Jean-Yves Ollitrault Takaharu Otsuka Kevin P. Pala Udeshika C. Perera Luis M. Robledo Tomás R. Rodríguez Wouter Ryssens Nils Sa{ss} Wilke van der Schee Björn Schenke Willian M. Serenone Pragya Singh Chun Shen Noritaka Shimizu Huichao Song Seyed Farid Taghavi Derek Teaney Yusuke Tsunoda Kathrin Wimmer Kota Yanase Chunjian Zhang Shujun Zhao Wenbin Zhao

This is my paper

classification nucl-exhep-exhep-phnucl-th

keywords isobarcollisionsnucleardeformationoctupolechiralmagneticeffectcollectiveflowneutronskinheavy-ionstructure

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This report argues that the measured deviations from unity in ratios of observables from collisions of the two A=96 isobars, ruthenium-96 and zirconium-96, are naturally explained by differences in the two nuclei's ground-state shapes and skin thicknesses. If that is right, the deviations are not primarily a magnetic-field effect: the nuclear-structure background masks any relative variation genuinely driven by the chiral magnetic effect, so a sound conclusion about that effect depends on knowing the ground states. The report further establishes isobar collision ratios as a quantitative imaging tool for nuclear ground-state properties, including quadrupole deformation, octupole deformation, and neutron skin. The central technical claim is that a large static octupole deformation in zirconium-96 is the source of the measured enhancement of triangular flow in its collisions.

What carries the argument

The load-bearing object is the deformed Woods-Saxon density of each colliding nucleus, $\rho(r,\theta,\phi) = \rho_0/(1+\exp[(r-R(\theta,\phi))/a])$ with $R(\theta,\phi) = R_0(1+\beta_2 Y^0_2 + \beta_3 Y^0_3 + \cdots)$, whose parameters $R_0$ (radius), $a$ (diffuseness or skin), $\beta_2$ (quadrupole), $\beta_3$ (octupole), and $\gamma$ (triaxiality) are sampled event-by-event to build initial conditions. The argument works through the near-linear mapping from initial eccentricities ($\varepsilon_2$, $\varepsilon_3$) computed from these densities to final harmonic flow coefficients ($v_2$, $v_3$), combined with a Taylor-expansion relation for isobar ratios, $\mathcal{O}_{\mathrm{Ru}}/\mathcal{O}_{\mathrm{Zr}} \approx 1 + c_1\Delta\beta_2^2 + c_2\Delta\beta_3^2 + c_3\Delta a + c_4\Delta R_0$, which isolates how each nuclear parameter shows up in each observable. Octupole deformation mainly feeds triangular flow in central collisions, while the diffuseness difference drives the non-monotonic multiplicity and flow-ratio trends.

What would settle it

A decisive test would be a model-independent measurement of zirconium-96's ground-state shape, for instance a precision Coulomb-excitation or laser-spectroscopy experiment that determines whether the ground state carries a static octupole deformation $\beta_3 \approx 0.2$ without assuming equality of the $0^+$ and $3^-$ wave functions. Alternatively, an ab initio calculation that yields a spherical or vibration-only octupole picture for the ground state, or a hydrodynamic simulation that reproduces the measured $v_3$ ratio without any static $\beta_3$, would falsify the report's central explanation.

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Extended reading notes

Core claim

The paper's central claim is that the measured isobar ratios of multiplicity, elliptic flow, and triangular flow are reproduced by initial-state and hydrodynamic calculations once the two nuclei are given different intrinsic shapes: ruthenium-96 more quadrupole-deformed, zirconium-96 with a larger neutron skin and a significant octupole deformation. This picture is consistent with low-energy nuclear structure information, in particular a strong E3 transition in zirconium-96 that can be read as a static octupole deformation $\beta_3 \approx 0.2$–$0.27$. Consequently, the report concludes that the isobar run does not provide evidence for the chiral magnetic effect; the nuclear-structure background dominates the ratios and must be quantified before magnetic-field effects can be isolated. It also concludes that the same measurements, once understood, turn isobar collisions into a precision probe of nuclear shapes and skins.

Load-bearing premise

The load-bearing assumption is that zirconium-96's ground state really is octupole-deformed in the static sense, inferred by assuming that the ground state and the $3^{{-}}$ excited state are formed from the same intrinsically deformed shape; if that conversion is wrong, the triangular-flow excess needs another source.

Editorial extensions

If this is right

If the central claim is correct, the ratio of triangular flow between the isobars serves as a quantitative measure of octupole deformation in zirconium-96.
The measured elliptic-flow and multiplicity ratios can be used to extract the quadrupole deformation of ruthenium-96 and the difference in skin thickness between the two nuclei.
A sound conclusion about the chiral magnetic effect requires nuclear-structure uncertainty quantification; without it, isobar ratios cannot be read as magnetic-field signals.
Future isobar runs intended to probe magnetic-field effects should use a pair in which at least one nucleus is near-spherical, since the A=96 pair is particularly geometry-sensitive.
Isobar ratio data can also constrain the short-range nucleon-nucleon repulsion parameter in initial-state models, which is poorly determined by existing global analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial: if the report's method is sound, isobar ratios become a new high-energy handle on ground-state properties of isotopes that are hard to study at low energy, including nuclei relevant to neutrinoless double beta decay.
Editorial: the octupole-deformation interpretation predicts specific centrality and multiplicity dependence of higher-order cumulant ratios, such as $v_3\{4\}/v_3\{2\}$, which future isobar data could test.
Editorial: the Taylor-expansion identity suggests a general experimental strategy: measuring ratios of observables across isobar pairs cancels much of the unknown bulk dynamics, isolating geometry parameters; this could be applied to other isobar pairs beyond A=96.
Editorial: the report leaves open whether the large correlation energy that beyond-mean-field methods attribute to octupole shapes is physical; if it is not, the value of $\beta_3$ extracted from flow will need reinterpretation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

You should know this for what it is: a genuinely useful task-force report, and the strongest statement so far that the RHIC isobar ratios are dominated by nuclear structure rather than the chiral magnetic effect. The central qualitative claim holds up well. No matter which way you slice the initial-state or hydrodynamic models, the observed ratios are naturally explained by different intrinsic shapes, with a larger quadrupole deformation in 96Ru and a larger skin in 96Zr.

What is actually new here is the breadth. The report ships a large set of original calculations: a 17-parameterization Skyrme survey, BSkG searches over the full gamma range with finite octupole deformation, new Gogny PGCM and Monte Carlo shell model results, plus systematic TRENTo, free-streaming, SMASH, AMPT, and Trajectum scans. The Taylor-expansion framework in Sec 5.3.2 is a clean way to organize which nuclear parameter drives which observable. The report also deserves credit for its honesty: the authors repeatedly flag preliminary status, missing uncertainty quantification, and their own load-bearing assumption.

That load-bearing assumption is the soft spot, and it is the one you should worry about. The entire v3 ratio explanation rests on converting the measured B(E3; 3- -> 0+) in 96Zr into a static ground-state octupole deformation beta3 ~ 0.2-0.27. As the report itself says in Sec 3.5.2, this requires the 0+ ground state and the 3- state to share the same intrinsic octupole-deformed shape. No alternating-parity band is observed in 96Zr, most mean-field and ab initio results put the ground-state beta3 lower (0 to 0.175), and there is no simple experimental test of the assumption. If 96Zr is instead an octupole vibrator, the large initial-state triangularity driving the central v3 excess has no demonstrated explanation within the mechanisms the report tested.

The partial circularity is real but less damaging than it looks. Several simulation sets take beta3 = 0.2 from Ref. [99], which was itself inferred from STAR data, and then reproduce STAR data. The independent low-energy B(E3) evidence and the diversity of models mitigate this, but the report would be stronger if it clearly separated inputs derived from STAR from inputs derived from low-energy data.

Who is this for? Anyone working on the RHIC isobar program, the CME search, or nuclear structure imaging from heavy-ion collisions. It is long, but as a reference document it is valuable. It absolutely deserves a serious referee; the quantitative claims need tightening, but the central conclusion that nuclear structure dominates the isobar ratios is well supported.

My recommendation: send it to peer review, with the expectation that the octupole assumption and the circularity get addressed head-on.

Referee Report

3 major / 4 minor

Summary. This paper is the report of the EMMI Rapid Reaction Task Force on isobar collisions at RHIC. It combines low-energy nuclear structure calculations (mean-field, beyond-mean-field, shell model, ab initio PGCM, lattice EFT prospects) with high-energy initial-state and full dynamical simulations (T RENTo, SMASH, AMPT, iEBE-VISHNU, Trajectum) to understand the STAR measurements of 96Ru+96Ru and 96Zr+96Zr collisions. The central claim is that the measured isobar ratios are naturally explained if the two nuclei have different intrinsic shapes, in particular a large octupole deformation in 96Zr, and that the corresponding differences qualitatively agree with low-energy nuclear information. A corollary is that nuclear-structure effects mask relative magnetic-field-driven variations, so a sound conclusion about the chiral magnetic effect requires proper uncertainty quantification of nuclear ground-state properties. The report also recommends using the 136Xe-136Ce pair for future CME searches and argues that isobar collisions can serve as a precision probe of nuclear shapes and skins.

Significance. If the central claim holds, this report establishes a genuinely cross-disciplinary result: high-energy isobar collision ratios become a quantitative imaging tool for nuclear ground-state shapes and surface properties, and CME conclusions become contingent on nuclear-structure uncertainties. The report is strengthened by the diversity of independent model comparisons, by its explicit engagement with low-energy experimental data, and by the unusually candid self-assessment of limitations, including the unresolved static-vs-vibrational octupole interpretation and the absence of uncertainty quantification. The Taylor-expansion approach and the correlated-sampling method of Sec. 4.6 are practically valuable methodological contributions. The significance is high for both the heavy-ion and nuclear-structure communities, provided the load-bearing octupole assumption is settled or explicitly downgraded.

major comments (3)

[Sec. 3.5.2 and Sec. 3.2] The quantitative explanation of the v3 excess rests on converting B(E3; 3- -> 0+) = 42-53 W.u. into a static ground-state octupole deformation beta3 ~ 0.2-0.27, but the report itself states in Sec. 3.5.2 that this assumes the ground state and the 3-1 state share the same intrinsic state with static octupole deformation, and Sec. 3.1.2 notes that no alternating-parity band built on the ground state is observed. The independent many-body results in Tables 1-2 and in Secs. 3.4 and 3.6 give ground-state beta3 values of 0, 0.05-0.125, or at most 0.175, all below the 0.2-0.27 used in Table 3 and in the hydrodynamic/AMPT comparisons. Because the central v3 excess in Secs. 4 and 5 is generated by the large beta3(96Zr) input, the conclusion that the STAR observations are naturally explained by low-energy structure is contingent on an assumption that the report itself identifies as unresolved.
[Sec. 5.5 (Table 9), Sec. 4.2 (Cases 3-6), Sec. 5.3] There is partial circularity in the validation chain: beta3(96Zr) = 0.2 is taken from Ref. [99], a value inferred from STAR isobar data, and is then used as input to simulations that reproduce those same STAR data. This applies to the Trajectum case-5 setup, the T RENTo default/cases 3-6, and the AMPT default. As a validation of the nuclear-structure explanation, the agreement with STAR data in these sections is therefore not independent. The paper should either repeat the comparisons with beta3 values derived solely from low-energy data (including the smaller values predicted by the calculations in Sec. 3), or explicitly demonstrate that the reproduced ratios are insensitive to the provenance of beta3; without this, the 'naturally explained' claim is weakened.
[Secs. 4-6] No uncertainty bands are attached to the theoretical isobar ratios, despite the experimental precision of about 0.4% and the report's own recommendation in Sec. 6 that quantitative conclusions about the magnetic-field effects require uncertainty quantification. Propagated uncertainties on beta2, beta3, a, R0, dmin, and the transport parameters would be needed to assess whether the agreement with STAR data is statistically supported or merely a visual match. The final conclusions should either include such uncertainty quantification or explicitly downgrade the 'naturally explained' statement to a plausibility argument.

minor comments (4)

[Sec. 4.3.3] In the sentence 'the largest effect is observed when we move from case 4 to vase 5', 'vase' should read 'case'.
[Sec. 3.3.1 and Tables 3, 5, 9] The distinction between the Woods-Saxon deformation parameter beta_WS used in the simulation tables and the multipole moment beta_l0 of Eq. (20) should be applied consistently; for the values used here the difference is about 0.02 and should be accounted for when comparing high-energy extractions with low-energy results.
[Sec. 5.3.2, Table 7] The row 'Case 1 and 5 difference' lists Delta_beta2^2 and Delta_beta3^2 alongside Delta R0 and Delta a, but Eq. (81) uses Delta beta_n^2 notation; the table would be clearer if it explicitly stated that the tabulated deformation differences are already squared.
[Sec. 5.5.2 and Fig. 37] The quantity N^off_trk,raw and the meaning of the 'off' superscript are not defined in the text; a brief definition would help readers interpret the inverse-correction procedure.

Circularity Check

3 steps flagged · score 6.0 of 10

The v3-excess explanation recycles the fitted input: beta3(96Zr) ~ 0.2 enters every simulation from a STAR-data-based work (Ref. [99]) and is then found to 'reproduce' the same STAR v3 ratio; the low-energy B(E3) anchor is real but yields static beta3 only under an assumption the paper itself flags as unverified.

fitted input called prediction [Sec. 1.2.1; Sec. 4.2 Table 3 (Case 6); Sec. 5.5.1 Table 9 (Case 5)]
"The v3 of 96Zr+96Zr collisions is indeed higher by about 10% in the central limit. This was not predicted by any kind of calculations, and points to an effect that is akin to the presence of a large octupole deformation in the ground state of 96Zr. … Case 5 mirrors case 4 but incorporates β2 and β3 values in 96Zr in accordance to Ref. [99]."

The ~10% central v3 excess is the paper's headline observation ('This was not predicted by any kind of calculations'), yet the explanation is generated by simulations initialized with β3 = 0.20–0.202 for 96Zr (TRENTo Table 3 Case 6; AMPT Table 7; Trajectum Table 9 Case 5), a value the report says is 'in accordance to Ref. [99]', and Sec. 3.5.2 itself describes Refs. [99, 123] as 'based on STAR data'. The STAR v3 ratio motivated the large-β3 hypothesis; the same STAR ratio is then 'reproduced' by simulations whose key input is that hypothesis. The reproduction is a consistency check of the fit rather than an independent prediction, so for the v3 channel the claim that isobar observations are 'naturally explained' by nuclear shape reduces, by construction, to the fitted input.
self citation load bearing [Sec. 3.5.2 (MCSM results)]
"This is consistent with the large values of octupole deformation indicated in theoretical works [99, 123] based on STAR data [14]."

The MCSM result (B(E3) = 52 W.u., β3 = 0.27) is offered as low-energy support for the large octupole deformation used in the collision simulations, but the text explicitly locates the comparison value in 'theoretical works [99, 123] based on STAR data' — i.e., in analyses of the very isobar ratios the report aims to explain. The 'consistency' between β3 ≈ 0.27 and β3 ≈ 0.2 is therefore partly a comparison of STAR-derived quantities with STAR-derived quantities, and the simulation input (β3 ≈ 0.2, from Ref. [99]) is not independently verified outside this self-referential chain. Genuinely external evidence — the measured B(E3) = 42–53 W.u.

1 more flagged steps

self definitional [Sec. 3.5.2; see also Sec. 3.2]
"The present value, 0.27, is obtained based on the assumption that the ground state and the 3−1 state are formed from the same intrinsic state with static octupole deformation. This assumption has to be further studied, as it is in contrast with the traditional picture of the octupole vibration assuming a spherical ground state."

To reach the 'qualitative agreement with low-energy data' claimed in the conclusions, the measured B(E3; 3−→0+) = 42–53 W.u. must be converted into a ground-state β3 ≈ 0.2–0.27. The paper admits this conversion is valid only 'based on the assumption that the ground state and the 3−1 state are formed from the same intrinsic state with static octupole deformation' — the very property the high-energy analysis invokes to explain the v3 excess. Sec. 3.2 records that no alternating-parity band is observed in 96Zr and that there is no simple experimental procedure to test equal deformations of the 0+ and 3− states; Sec. 3.5.1 notes the traditional picture is octupole vibration around a spherical ground state.

full rationale

The derivation chain largely decomposes into independent channels and one self-referential channel. The multiplicity and v2 ratios are driven by differences in surface diffuseness a and quadrupole deformation β2, anchored to low-energy measurements (B(E2; 2+→0+) = 2.3 vs 18.2 W.u.) and to EDF/mean-field predictions, and these explanations were in the literature before the 2021 data release (Shou et al., Xu et al.). The report also contains genuine forward predictions (longitudinal decorrelation r3, cumulant ratios, ac2{3}, [pT] ratios) and is internally honest: it flags the B(E3)→β3 conversion assumption in Sec. 3.5.2, reports that most mean-field functionals give β3 = 0 for 96Zr, and notes the absence of an alternating-parity band. The circularity is confined to the v3 channel, which is nevertheless the report's most emphasized novelty: the 'completely nontrivial' 10% central v3 excess was 'not predicted by any kind of calculations', yet every simulation that 'explains' it is initialized with β3(96Zr) = 0.20–0.202 taken 'in accordance to Ref. [99]', a work the text explicitly describes as 'based on STAR data'. Reproducing the data with an input derived from that same data is a fitted-input-called-prediction loop; the independent low-energy B(E3) strength is real evidence of octupole collectivity, but it fixes a static ground-state β3 only through the contested same-intrinsic-state assumption the paper itself says 'has to be further studied'. The overall conclusion — that isobar data are sensitive to nuclear shapes — survives, but the specific quantitative explanation of the v3 excess, and the claim of qualitative agreement with low-energy data for this channel, are partially circular.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a modest set of shape parameters (beta2, beta3, a, R0, gamma) plus the Glauber factorization and linear-response assumptions. No new particles or forces are introduced. The main circularity-sensitive input is beta3(96Zr), which in part of the report is taken from a fit to the same STAR data it is used to explain.

free parameters (7)

beta2 (quadrupole deformation) of 96Ru = 0.12 to 0.16 in different cases
Value chosen from low-energy B(E2) measurements and EDFs, not fit to STAR data in most cases; but the shell-model and SOM papers use values consistent with the isobar data.
beta3 (octupole deformation) of 96Zr = 0.2 (Ref [99]) or 0.27 (MCSM)
The 0.2 value used in many simulations of this report was inferred from STAR v3 data in Ref [99]; the 0.27 from B(E3) under the equal-intrinsic-state assumption. This is the main circularity-sensitive parameter.
a (surface diffuseness) for 96Ru and 96Zr = 0.46 fm and 0.52 fm
Chosen from electron scattering and EDF predictions; the difference drives the multiplicity and v2 ratio shapes.
R0 (half-density radius) for 96Ru and 96Zr = 5.09 fm and 5.02 fm
From electron scattering and liquid-drop systematics; the 1% difference matters for volume effects.
gamma (triaxiality) = 0 to 30 degrees
Varied to test sensitivity; shown to have little effect on the observables considered.
dmin (minimum inter-nucleon distance) = 0 to 1.0 fm
Varied in TRENTo scans; found to affect the epsilon2 ratio in central collisions.
hydrodynamic transport parameters (eta/s, tau_FS) = e.g., eta/s=0.05, tau_FS=1 fm/c
Taken from Bayesian fits to other systems; ratios shown to be insensitive at the percent level.

assumptions (5)

domain assumption Instantaneous snapshot of nucleon positions from ground-state wavefunction (position-space factorization)
Sec. 2.1 argues the collision timescale is 10^-24 s, much shorter than nuclear excitation timescales, so the interaction samples |Psi|^2.
domain assumption Woods-Saxon form with spherical-harmonic expansion describes the nuclear density for collision simulations
Eqs. (10)-(11), (43)-(46), (79) parametrize shape with beta2, beta3, gamma, R0, a; this form is assumed to capture the relevant structure.
domain assumption Linear (or near-linear) mapping between initial eccentricities and final flow harmonics
Sec. 5.1.1 invokes V2 = kappa2 E2 + ... and Pearson coefficients Qn; the report checks this for beta2 but explicitly leaves beta3, beta4, a variations for future work.
domain assumption EDF ground-state shapes are reliable inputs for these transitional nuclei
Sec. 3.2 and 3.3 note large model spread; e.g., SV-mas07 gives beta30=0.10 for 96Zr while SLy4 gives 0, so the report relies on the spread as an uncertainty band.
domain assumption B(E3) strength can be interpreted as static octupole deformation assuming identical intrinsic states for 0+ and 3-
Sec. 3.5.2 states this assumption explicitly and says it must be studied further.

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Pith. "Pith review of Nuclear Physics Confronts Relativistic Collisions Of Isobars." pith.science (2026). https://pith.science/paper/KBBOVWOW

@misc{pith2026250701454,
  author       = {Pith},
  title        = {Pith review of: Nuclear Physics Confronts Relativistic Collisions Of Isobars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBBOVWOW}},
  note         = {Machine review of arXiv:2507.01454}
}

abstract

High-energy collisions involving the $A=96$ isobars $^{96}$Zr and $^{96}$Ru have been performed in 2018 at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) as a means to search for the chiral magnetic effect in QCD. This would manifest itself as specific deviations from unity in the ratio of observables taken between $^{96}$Zr+$^{96}$Zr and $^{96}$Ru+$^{96}$Ru collisions. Measurements of such ratios (released at the end of 2021) indeed reveal deviations from unity, but these are primarily caused by the two collided isobars having different radial profiles and intrinsic deformations. To make progress in understanding RHIC data, nuclear physicists across the energy spectrum gathered in Heidelberg in 2022 as part of an EMMI Rapid Reaction Task Force (RRTF) to address the following question. Does the combined effort of low-energy nuclear structure physics and high-energy heavy-ion physics enable us to understand the observations made in isobar collisions at RHIC?

Figures

Figures reproduced from arXiv: 2507.01454 by the authors.

**Figure 2.** Left: Minimum bias charged multiplicity distribution in 238U+238U collisions at top RHIC energy, for 238U nuclei with a = 0.60 fm (Original, red line) and a = 0.42 fm (New, green line). Right, New/Original ratio for the eccentricities of 238U+238U collisions as a function of the collision centrality (where each integer number should be multiplied by 5%). Figures adapted from Ref. [21]. participant nucleons within th… view at source ↗

**Figure 3.** Left: Ratio of multiplicity distributions, P(Ntrack) taken between 96Ru+96Ru and 96Zr+96Zr collisions as measured by the STAR collaboration. Right: Isobar ratio of anisotropic flow coefficients as a function of the collision centrality. Black points are for v2, while red points for v3. Note that the limit of central collisions is in both panels on the right-hand side of the plots. The data is from Ref. [14]. the pos… view at source ↗

Figures from the paper (36 more)

**Figure 4.** Figure 4: Illustration of an intrinsic nuclear density presenting an ellipsoidal deformation [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

**Figure 5.** Figure 5: The figure illustrates nuclear collisions involving different types of deformation: [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

**Figure 6.** Figure 6: Level schemes of (a) 96Zr and (b) 96Ru at low excitation energy. States are labeled with their excitation energy in keV, known transitions are given in Weisskopf units for E2 and E3 transitions and electric monopole transition strength ρ 2 (E0) are given in 10−3 . inva…

**Figure 7.** Figure 7: The comparison of experimental and calculated differential charge radii of the [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]

**Figure 8.** Figure 8: Multipole deformations β20 and β30 for a WS density for 96Zr with βWS 20 = 0.062, βWS 30 = 0.2 and varying hexadecapole deformation. The faint horizontal lines indicate βℓ0 = βWS ℓ0 to guide the eye. where R0 = 1.2 fm, ρ0(r) is the matter density and Yℓm is a spherical…

**Figure 9.** Figure 9: Hartree-Fock-Bogoliubov total energy surfaces as a function of quadrupole ( [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]

**Figure 10.** Figure 10: Total energy surfaces as a function of β2 and γ for 96Zr (left column) and 96Ru (right column) at fixed values of β30 as obtained with BSkG2. Top row: calculations for reflection symmetric configurations, β30 = 0.0. Bottom row: calculations at the value of β30 corresp…

**Figure 11.** Figure 11: Visualization of the nuclear shapes corresponding to the minima depicted in [PITH_FULL_IMAGE:figures/full_fig_p029_11.png]

**Figure 12.** Figure 12: (a)-(b) Particle number projected and particle number and angular momentum [PITH_FULL_IMAGE:figures/full_fig_p033_12.png]

**Figure 13.** Figure 13: (a)-(b) HFB and particle number and angular momentum projected, (g)-(h) [PITH_FULL_IMAGE:figures/full_fig_p034_13.png]

**Figure 14.** Figure 14: Experimental (black squares) [65] and theoretical excitation energies for the ground state (positive) band computed with the parity-conserving triaxial PGCM method (red bullets) and the parity-breaking axial PGCM method (blue triangles) for (a) 96Ru and (b) 96Zr. In t…

**Figure 15.** Figure 15: Calculated level energies of some lowest states of [PITH_FULL_IMAGE:figures/full_fig_p038_15.png]

**Figure 16.** Figure 16: Hartree-Fock-Bogoliubov (HFB) total energy surfaces for [PITH_FULL_IMAGE:figures/full_fig_p039_16.png]

**Figure 17.** Figure 17: Differential HFB (circles) and symmetry-projected (crosses) total energy curves [PITH_FULL_IMAGE:figures/full_fig_p040_17.png]

**Figure 18.** Figure 18: The left panel shows the insertion of pinholes with spin and isospin indices in [PITH_FULL_IMAGE:figures/full_fig_p042_18.png]

**Figure 19.** Figure 19: Average energy ratio as a function of entropy for all different configurations of [PITH_FULL_IMAGE:figures/full_fig_p048_19.png]

**Figure 20.** Figure 20: Second harmonic eccentricity ϵ2 ratio as a function of entropy for all different configurations of nuclear and TRENTo parameters. 49 [PITH_FULL_IMAGE:figures/full_fig_p049_20.png]

**Figure 21.** Figure 21: Third harmonic eccentricity ϵ3 ratio as a function of entropy for all different configurations of nuclear and TRENTo parameters. 50 [PITH_FULL_IMAGE:figures/full_fig_p050_21.png]

**Figure 22.** Figure 22: Second harmonic eccentricity (ε2) ratio as a function of charge multiplicity for seven points in the parameter space (w, d, p). The black curve is the same in all panels. 4.3 Role of the free streaming time 4.3.1 Objective State-of-the-art simulations of heavy-ion col…

**Figure 23.** Figure 23: Isobar ratios of various quantities for different nuclear structure parametrizations. [PITH_FULL_IMAGE:figures/full_fig_p054_23.png]

**Figure 24.** Figure 24: One (left) and two (right) body density of nuclear configurations of Ruthenium [PITH_FULL_IMAGE:figures/full_fig_p058_24.png]

**Figure 25.** Figure 25: Energy density profile in the transverse plane of one event of a [PITH_FULL_IMAGE:figures/full_fig_p059_25.png]

**Figure 26.** Figure 26: Ratio of ε2 (left), ε3 (center) and ε4 (right) as a function of the total entropy S. In the upper row, the ratio is taken of the results of case 1-5 with respect to case 6 (see Tab. 5). In the lower row the ratio is taken between the nuclear configurations without and…

**Figure 27.** Figure 27: Ratio of number of paricipants Npart (left), probability distribution P(S) (center), total energy E and inverse radius 1/R (right). In the upper row ratios of case 1-5 with respect to case 6 are presented, whereas the lower row highlights the effect of the NN SRC. inv…

**Figure 28.** Figure 28: JIMWLK evolution of the trace of the Wilson line, 1 [PITH_FULL_IMAGE:figures/full_fig_p063_28.png]

**Figure 29.** Figure 29: Geometric eccentricities εn = p ⟨|εn(y)| 2⟩ (left) and its ratio (right) for the isobars 96Ru and 96Zr as a function of collision energy profile and growth in the impact parameter space (see the recent Ref. [202] for a dedicated study on the subject). In the left pane…

**Figure 30.** Figure 30: Vector plot of shift d⃗x in x-z plane for case of axial quadrupole and octupole deformation, β2,0 = 0.06, β3,0 = 0.2. The axis scales correspond to Woods-Saxon radius R = 5.09 fm. The curves represent the Woods-Saxon radius R(θ, ϕ) for the starting spherical distribut…

**Figure 31.** Figure 31: Isobar ratios of rms eccentricities, εn {2}, for n = 2 (left) and n = 3 (right), computed from the initial conditions of the v-USPhydro simulations. parameter p = 0, gamma fluctuation parameter k = 1.6, and the nucleon width σ = 0.51 fm. The normalization constant for…

**Figure 32.** Figure 32: Pearson coefficient Qn, as defined by Eq. (70), for the linear mapping of En to Vn for n = 2 (left) and n = 3 (right) in 96Ru+96Ru collisions. Different line styles represent different choices of the deformation parameter β2. shown in the previous sections. Although w…

**Figure 33.** Figure 33: Isobar ratio of the Pearson coefficients [PITH_FULL_IMAGE:figures/full_fig_p071_33.png]

**Figure 34.** Figure 34: The longitudinal flow decorrelation coefficients for elliptic flow [PITH_FULL_IMAGE:figures/full_fig_p072_34.png]

**Figure 35.** Figure 35: Isobar ratios of p (Nch) (left panel), rms v2 (middle panel), and rms v3 (right panel) obtained from AMPT simulations with the nuclear structure parameters in Tab. 7 or calculated by means of Eq. (81) from the response coefficients [144] (labeled ”direct calculation”)…

**Figure 36.** Figure 36: Multiplicity dependence of R(⟨pT ⟩), R(v2{2}) and R(v3{2}) computed from all charged hadrons in 96Ru+96Ru and 96Zr+96Zrcollisions at √sNN = 200 GeV, calculated by the iEBE-VISHNU model with the deformation parameters-I for 96Ru and 96Zr. lant ac2{3} = ⟨⟨e i(2φ1+2φ2−4φ…

**Figure 37.** Figure 37: We show the comparison between (inversely-corrected) multiplicity distributions [PITH_FULL_IMAGE:figures/full_fig_p080_37.png]

**Figure 38.** Figure 38: We show hydrodynamic results for v2{2} (left), v3{2} (center), and ⟨pT ⟩ (right) in 96Ru+96Ru collisions (top) and 96Zr+96Zr collisions (middle) at RHIC energy for all WS parameter sets considered in Tab. 9. The isobar ratios of these observables are shown in the bott…

**Figure 39.** Figure 39: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p082_39.png]

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Cited by 4 Pith papers

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