TGSW2022 online seminar

Imaging the nuclear structure and initial condition ofheavy-ion collisions across the nuclei chart
Jiangyong Jia
Nuclear structure

based partially onarXiv:2209.11042
9/27/2022

High-energy collisions

Landscape of nuclear physics
Quark-gluon
plasmahadrons

nucleiMost nuclear experiments starts with nuclei

2

Rich structure of atomic nuclein3Collective phenomena of many-body quantum systemnnnclustering, halo, skin, bubble…
β2-landscapequadrupole/octupole/hexdecopole deformations
Nontrivial evaluation with N and Z.
Radii-landscapen

Understanding via effective nuclear theoriesnnn

Lattice, Ab.initio (starting from NN interaction)
Shell models (configuration interaction)
DFT models (non-relativistic and covariant)

High-energy heavy ion collision

400 nucleonsin 10-23 seconds

30000 hadrons

4

High-energy heavy ion collision

1) Are nuclear structures important for HI initial condition and final state evolution?
2) What HI experimental observables can be used to infer structure information?
3) Can HI provides competitive constraints on nuclear shape and radial profile? canconsideration of nuclear structure improves understanding of HI initial condition?

56From nuclear structure to Quark Gluon Plasma
Nucleus

Final state

Initial condition
ε2hydro?

ε3ε4
Fixed impact parameter

Nuclear structureHigh energy: approx. linear
response in each event:Collective structure of nuclei

Quadrupole:

Octupole:
Prolate: a=b<c à β2, γ=0
Hexadecapole:

Oblate: a<b=c à β2, γ=π/3
Triaxial: a<b<c à β2, γ=π/67How deformation influence HI initial state
Body-Body

Tip-Tipyyyx

ε2~0.95β2xx

ε2~0.48β2

ε2~0Shape depends on Euler angle Ω=φθψ8

Expected structure dependencies
arXiv:2106.08768

Central collisions
QGPQGP

Non-Central collisions

a0The shape and size the overlap,
therefore v2 and pT, also depend ondiffuseness a0 and radius R0
At fixed Nparta0↘

v2↗ pT↗

R0↘

pT↗

9

Isobar collisions at RHIC

arXiv:2109.00131

10Voloshin, hep-ph/0406311•Designed to search for the chiral magnetic effect: strong P & CP violation ofQCD in the presence of EM field. Turns out the CME signal is small, andisobar-differences are dominated by the nuclear structure differences.

•<0.4% precision is achieved in ratio of many observables between
96Ru+ 96Ru and 96Zr+96Zr systemsà precision imaging tool

Isobar collisions as a precision tooln

A key question for any HI observable O:

Deviation from 1 must has origin in the nuclear structure, which
impacts the initial state and then survives to the final state.
nExpectation
2109.00131

Only probes isobar differences

11Structure influences everywhere

We can ask the same question for isobar ratios for hard probes

12Nuclear structure via vn-ratio

2 1 0.2%

52 1 0.2%

Ratio

Ratio

513v 2,Ru / v 2,Zr STAR Data

11.1

STAR Preliminary
0.95

1.05

STAR Preliminaryv 3,Ru / v 3,Zr STAR Data

0.9

10100

200300Nofflinetrk(|h|<0.5)0100

200300Nofflinetrk(|h|<0.5)

Simultaneously constrain these parameters using different Nch regions

Nuclear structure via vn-ratio
nβ2Ru~0.16 increase v2, no influence on v3 ratio

2 1 0.2%

52 1 0.2%

Ratio

5Ratio14v 2,Ru / v 2,Zr STAR Datav 2,Ru / v 2,Zr AMPT b
211.1

STAR Preliminary
0.95

1.05

0.9

10100

200300Nofflinetrk(|h|<0.5)

0STAR Preliminaryv 3,Ru / v 3,Zr STAR Data
v 3,Ru / v 3,Zr AMPT b
2100200300

Nofflinetrk(|h|<0.5)

Simultaneously constrain these parameters using different Nch regions

Nuclear structure via vn-rationnβ2Ru~0.16 increase v2, no influence on v3 ratio
β3Zr~0.2 decrease v2 in mid-central, decrease v3 ratio

2 1 0.2%

52 1 0.2%Ratio

Ratio

5v 2,Ru / v 2,Zr STAR Datav 2,Ru / v 2,Zr AMPT b2v 2,Ru / v 2,Zr AMPT b

12,31.1

15STAR Preliminary
0.95

1.05

0.9

10100200300

Nofflinetrk(|h|<0.5)

0STAR Preliminaryv 3,Ru / v 3,Zr STAR Data
v 3,Ru / v 3,Zr AMPT b2v 3,Ru / v 3,Zr AMPT b
2,3100200300

Nofflinetrk(|h|<0.5)

Simultaneously constrain these parameters using different Nch regions

Nuclear structure via vn-rationnn

β2Ru~0.16 increase v2, no influence on v3 ratio
β3Zr~0.2 decrease v2 in mid-central, decrease v3 ratio
Δa0= -0.06fm increase v2 mid-central, small influ. on v3.

2 1 0.2%

52 1 0.2%

Ratio

Ratio

51.116v 2,Ru / v 2,Zr STAR Datav 2,Ru / v 2,Zr AMPT b2v 2,Ru / v 2,Zr AMPT b2,3v 2,Ru / v 2,Zr AMPT b a 0

12,3STAR Preliminary
0.95

1.05

0.9

1STAR Preliminaryv 3,Ru / v 3,Zr STAR Data
v 3,Ru / v 3,Zr AMPT b2v 3,Ru / v 3,Zr AMPT b2,3v 3,Ru / v 3,Zr AMPT b a 02,30100

200300Nofflinetrk(|h|<0.5)0100200

300

Nofflinetrk(|h|<0.5)

Simultaneously constrain these parameters using different Nch regions

Nuclear structure via vn-rationβ2Ru~0.16 increase v2, no influence on v3 ratio
β3Zr~0.2 decrease v2 in mid-central, decrease v3 ratio
Δa0= -0.06fm increase v2 mid-central, small influ. on v3.

nRadius ΔR0=0.07fm only slightly affects v2 and v3 ratio.

nRatio52 1 0.2%

52 1 0.2%

Ratio

n1.1

17v 2,Ru / v 2,Zr STAR Datav 2,Ru / v 2,Zr AMPT b2v 2,Ru / v 2,Zr AMPT b
2,3v 2,Ru / v 2,Zr AMPT b a 02,3v 2,Ru / v 2,Zr AMPT b a 0 R012,3STAR Preliminary
0.95

1.05

0.9

1STAR Preliminaryv 3,Ru / v 3,Zr STAR Data
v 3,Ru / v 3,Zr AMPT b2v 3,Ru / v 3,Zr AMPT b2,3v 3,Ru / v 3,Zr AMPT b a 02,3v 3,Ru / v 3,Zr AMPT b a 0 R02,30100

200300Nofflinetrk(|h|<0.5)0100200300

Nofflinetrk(|h|<0.5)

Simultaneously constrain these parameters using different Nch regions

Nuclear structure via p(Nch), <pT>-ratio

18Earlier studies on this from H.Li, H.J Xu, PRL125, 222301 (2020) arXiv:2111.14812

For Nch ratio:nnn

Strong influence from Δa0 and ΔR05

2 1 0.2%

AMPT b)1.05

trk

AMPT b2,32,3a02,3a 0 R0/ ápTñZrAMPT b2AMPT b
AMPT b

AMPT báp ñAMPT b5AMPT b2 1 0.2%

22,32,3a02,3

a 0 R01.002

p(Noffline

For <pT> ratio:

STAR dataofflinep(N)Ru /trkZrnβ2Ru~0.16 decrease ratio, increase after considering β3Zr~0.2
The bump structure in non-central region from Δa0 and ΔR0T Run1

10100

200

300

Noffline(|h|<0.5)
trk

Δa0 and ΔR0 influences add up

0100

200300Ntrk (|h|<0.5)

Δa0 and ΔR0 influences cancel

Isobar ratios not affected by final statenVary the shear viscosity via partonic cross-sectionn

Flow signal change by 30-50%, the vn ratio unchanged.

Robust probe ofinitial state!

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Low-energy vs high-energy HI methodnnShape from B(En), radial profile from e+A or ion-A scattering

Shape frozen in crossing time (<10-24s), probe entire mass distribution
via multi-point correlations.

Collective flow response to nuclear structure

20

Triaxility
Prolate21

1910.04673, 2004.14463
v2↘ pT↗
v2↗ pT↘

Need 3-point correlators to probe the 3 axes
TriaxialOblate

2109.00604

Triaxility

221910.04673, 2004.14463

Prolatev2↘ pT↗
v2↗ pT↘

Need 3-point correlators to probe the 3 axes
Triaxial2109.00604
Compare U+U vs Au+Au: β2U ~ 0.28, β2Au~ 0.13:

v2-[pT] covarianceOblate8%[pT] skewness

Influence of triaxiality: Glauber model
Skewness super sensitive
Described by

U+U

2109.00604

variances insensitive to γ

Use variance to constrain β2, use skewness to constrain γ23

(β2,γ) diagram in heavy-ion collisions
The (β2,γ) dependence in 0-1%
U+U Glauber model can beapproximated by:
Map from (β2,γ) plane to HI observables

How about

Collision system scan to map out this trajectory: calibrate coefficientswith species with known β,γ, then predict for species of interest.

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What future collisions can bring?
Future well-motivated system-scan to use heavy-ion collisions
into a precision tool for both nuclear structure and initialcondition, and ultimately improve the study of QGP.

More than 250 stable (longlived nuclei), about 140 of themin isobar pairs or triplets25

What future collisions can bring?
Future well-motivated system-scan to use heavy-ion collisions
into a precision tool for both nuclear structure and initialcondition, and ultimately improve the study of QGP.
Representative cases were identified in a dedicated EMMI
taskforce among HI and structure experts.
https://indico.gsi.de/event/14430/contributions/64193/

A~200
Stress test small system collectivity
with extreme deformability

Imaging strong shape evolution of144−154Sm isotopic chain

26

27

Exploiting the lever-arm provided by nuclear structure

Flow observable =k

QGP response,a smooth function of N+ZQGP⨂initial condition (structure)

Structure of colliding nuclei,
non-monotonic function of N and Z

Stress-testing small system collectivity with 20Ne
Geometric origin of small system program is rather qualitative.
Very subtle effects if one only have 16O+16O collisions

Benjamin Ballyratio

20Ne with 5 alpha has the most extreme ground state shape: %2~0.7, %3~0.5. Use O+O
and Ne+Ne to observe “strong” purely-geometric effects at dN/dy~100.

Trajectum framework
Ratio 20Ne+20Ne /16O+16O

Wilke van der Schee28

Imaging strong shape evolution of 144−154Sm isotopic chain
Transition from nearly-spherical to well-deformednuclei when size increase by less than 7%. Using
HI to access the multi-nucleon correlations leading
to such shape evolution, as well as dynamical %3and %4 shape fluctuations.

29

Application in 197Au+197Au vs 238U+238U
Ultra-central Collisions at√sNN=193-200 GeV

30

arXiv:2105.01638

b~0.014

Need to correct for slightly different size:
A linear relation for β2U and β2Au :β2Au=0.18

Suggests |β2|Au~0.18+-0.02, larger than NS model of 0.13+-0.02

Summarynnn

31

Constrain QGP initial condition with nuclear structure input and heavy ion observables
è Improve the extraction of QGP properties in the Bayesian approaches
Understanding how initial condition responds to nuclear structure, in turn enables probing
novel nuclear structure properties and compliments low-energy experiments.
Collisions of carefully-selected isobar species will help us to understand the many-bodynucleon correlations of atomic nuclei from small to large system

A lot of work is needed to firm-up this science casearXiv:2102.08158