Free system of four correlated neutrons

Meytal Duer, TU Darmstadt
CLUSHIQ2022
November 3rd, 2022

3.11.2022
FB Physik| Institut
Institut
11/09/2022 | Fachbereich BBBBB | Institut AAAA
| Prof.
TTTTTT| 1 für Kernphysik | Meytal Duer

Sublogo1

At and beyond the neutron drip-line

proton number Z

β+ unstablestable nuclei
β- unstablen-star●neutron number N●●

Figure from Marqués, EPJP 136 (2021)●●

Most extreme conditions:large N/Z asymmetry and low-density
Neutron halo/skin
Correlations: di-neutron, neutron droplets
Neutron matter...

3.11.2022
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J. Kahlbow| 2 Institut für Kernphysik | Meytal Duer2

At and beyond the neutron drip-line

proton number Z

β+ unstablestable nuclei
β- unstable

4
0n

6
0n

8
0n

n-star●neutron number N●●

Figure from Marqués, EPJP 136 (2021)●●

Most extreme conditions:large N/Z asymmetry and low-density
Neutron halo/skin
Correlations: di-neutron, neutron droplets
Neutron matter...

3.11.2022
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J. Kahlbow| 3 Institut für Kernphysik | Meytal Duer2

Outline➊ The tetra-neutron context●●

experimental quest
theoretical predictions

40n➋ 4n experiment at SAMURAI:

quasi-free -knockout reaction●●

experimental method
results and discussion➌ Future perspectives

next-generation experiments

3.11.2022
Physik | Institut
21.04.2020 | BM@N Collaboration Meeting | FB
J. Kahlbow| 4 Institut für Kernphysik | Meytal Duer3

A 60-year quest
XX century:●

fission of uranium

XX century:●e.g. Schiffer & Vandenbosch, Phys. Lett. 5 (1963)●

transfer reactions

e.g. Cerny et al., Phys. Lett. 53B (1974)●

e.g. Cerny et al., Phys. Lett. 53B (1974)●

transfer reactions
double-charge-exchange 4He(π-,π+) reaction
e.g. Ungar et al., Phys. Lett. B 144 (1984)

double-charge-exchange 4He(π-,π+) reaction➢

No indication for a tetra-neutron

3.11.2022
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J. Kahlbow| 5 Institut für Kernphysik | Meytal Duer4

A 60-year quest
XX century:●

fission of uranium

XX century:●e.g. Schiffer & Vandenbosch, Phys. Lett. 5 (1963)●

transfer reactions

e.g. Cerny et al., Phys. Lett. 53B (1974)●

e.g. Cerny et al., Phys. Lett. 53B (1974)●

transfer reactions
double-charge-exchange 4He(π-,π+) reaction
e.g. Ungar et al., Phys. Lett. B 144 (1984)

double-charge-exchange 4He(π-,π+) reaction➢

No indication for a tetra-neutron

XXI century:
radioactive-ion beams➢

first positive signals

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4

The elusive tetra-neutron
GANIL 2002
Breakup on a C target:

6 candidates: bound 4n or
low-energy resonance (Er<2 MeV)
Marqués et al., PRC 65 (2002)
Marqués et al., arXiv:nucl-ex/0504009 (2005)

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5

The elusive tetra-neutron
GANIL 2002
Breakup on a C target:

6 candidates: bound 4n or
low-energy resonance (Er<2 MeV)RIKEN 2016
Double-charge-exchange:

4 candidates for 4n resonance:
Er=0.8±1.4 MeV, Γ<2.6 MeV

Marqués et al., PRC 65 (2002)

Kisamori et al., PRL 116 (2016)

Marqués et al., arXiv:nucl-ex/0504009 (2005)

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5

Can a bound tetra-neutron exist?
Overall historical consensus: no bound tetra-neutron
unrealistic modifications of Vnn
Glöckle PRC 18, 1978; Offermann, NPA 318, 1979...

Pieper PRL 90, 2003:
AA

H =∑ T i + ∑ V ij +
i=1

●
●
●

i < j= 1A∑ V ijki < j<k= 1

ab initio Green’s function Monte Carlo calculations
using modern realistic NN and NNN potentials
good description for light nuclei

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6

Can a bound tetra-neutron exist?
Overall historical consensus: no bound tetra-neutron
unrealistic modifications of Vnn
Glöckle PRC 18, 1978; Offermann, NPA 318, 1979...

Pieper PRL 90, 2003:
AA

H =∑ T i + ∑ V ij +
i=1

●
●
●

i < j= 1A∑ V ijki < j<k= 1

ab initio Green’s function Monte Carlo calculations
using modern realistic NN and NNN potentials
good description for light nuclei“it does not seem possible to change modern nuclear
Hamiltonians to bind a tetraneutron without destroying
many other succesful predictions... our understanding of
nuclear forces will have to be significantly changed”

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6

What about a resonance ?
Pieper PRL 90, 2003:
A

A

H=∑ T i + ∑ V ij +
i=1

●

●
●

i < j =1

AA

∑ V ijk +∑ V WS (r i)i < j<k =1

i=1

neutrons trapped in Woods-Saxon potential
with radius R and depth V0
resonance energy by extrapolation to V 0→0
possible resonance around 2 MeV

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What about a resonance ?
Pieper PRL 90, 2003:
A

A

H=∑ T i + ∑ V ij +i=1

i < j =1

A

Hiyama et al., PRC 93, 2016:
A∑ V ijk +∑ V WS (r i)i < j<k =1

Full treatment of continuum

i=1

●
●

●
●

neutrons trapped in Woods-Saxon potential
with radius R and depth V0
resonance energy by extrapolation to V 0→0
possible resonance around 2 MeV●

absence of a four-neutron resonanceresonance behaviour only for remarkably (unrealistic)
attractive 3N force in T=3/2 channel➢➢

15 times larger than T=1/2
inconsistent with known light nuclei

Exp.

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What about a resonance ?

All studies agree on:●●

dominance of V nn (1S 0) in multi-neutron systems
negligible contribution of 3N force

Contradictory results:●●

From bound state to the continuum
example: 2n (1S0) confined in a trap
Importance of near threshold region(Analytic Continuation on the Coupling Constant Method)

do not origin from different interactions
methods to solve the few-neutron problem
and/or treatment of the continuum
nn state

Modified from Deltuva & Lazauskas, PRL 123 (2019)

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8

The elusive tetra-neutron

Experiment:●●a long-standing quest for tetra-neutron system
so far, three (weak) positive signals:➢
GANIL 2002, RIKEN 2016, TUM 2022➢
indications for bound / unboundTheory:●●no bound tetra-neutron
no consensous about a resonant state

Modified from Marqués & Carbonell, EPJA 57 (2021)

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9

Outline➊ The tetra-neutron context●●

experimental quest
theoretical predictions

40n➋ 4n experiment at SAMURAI:

quasi-free -knockout reaction●●

experimental method
results and discussion➌ Future perspectives

next-generation experiments

3.11.2022
Physik | Institut
21.04.2020 | BM@N Collaboration Meeting | FB
J. Kahlbow| 15 Institut für Kernphysik | Meytal Duer

10

Present experimental work
QFS knockout 8He(p,p4He) at 156 MeV/nucleon●

Large momentum transfer p-4He➢

elastic p-4He @ 156 MeV
V. Comparat et al., PRC (1975)

dσ/dΩc.m. [mb/sr]➢“recoil-less” production
minimizes final-state interactions (FSI)
between neutrons and charged particles

thisexperimentθc.m. [deg.]

3.11.2022
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11

Present experimental work
QFS knockout 8He(p,p4He) at 156 MeV/nucleon●

Large momentum transfer p-4He
➢
➢

●

8

“recoil-less” production
minimizes final-state interactions (FSI)
between neutrons and charged particles

He is a good starting point:➢

elastic p-4He @ 156 MeV
V. Comparat et al., PRC (1975)

dσ/dΩc.m. [mb/sr]➢

pronounced -core structure
large overlap ⟨8He|4n⟩

thisexperimentθc.m. [deg.]

3.11.2022
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11

Present experimental work
QFS knockout 8He(p,p4He) at 156 MeV/nucleon
Large momentum transfer p-4He
➢
➢

●

8

He is a good starting point:➢➢●“recoil-less” production
minimizes final-state interactions (FSI)
between neutrons and charged particles

pronounced -core structure
large overlap ⟨8He|4n⟩

4n energy spectrum via missing mass➢precise measurement of charged particles
Pmiss =P He + P p (tgt)−P He −P p
8

E 4 n= √ E

4

2
miss

E 4 n <0 : bound

−P

2
miss

elastic p-4He @ 156 MeV
V. Comparat et al., PRC (1975)

dσ/dΩc.m. [mb/sr]●

thisexperiment−4 mn

E 4 n >0 : unbound3.11.2022
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11

The Radioactive Ion Beam Factory

Access to exotic nuclei
●

●

➢

ECR
RILAC

Superconducting Ring Cyclotron (SRC):
CSM
primary 18O beam
RILAC2BigRIPS fragment separator:
AVF
RIPS
production and selection of RIB

SCRIT
2013

GARIS &GARISIIRRC

SAMURAI

ZDS

2012

2008

SLOWRISAMURAI setup

SRC

2014

2014

fRC

SHARAQKISSBigRIPS

2009

2007

He

8

IRC

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12

SAMURAI setup at the RIBF
SAMURAI dipole magent: up to 3 T (1.25 T)
Tracking & identification of secondary beam (8He)
Tracking & identification of fragments (p, 4He)
Neutrons (not possible in this experiment)

1.25 T

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SAMURAI setup at the RIBF
SAMURAI dipole magent: up to 3 T (1.25 T)
Tracking & identification of secondary beam (8He)
Tracking & identification of fragments (p, 4He)
Neutrons (not possible in this experiment)

1.25 T

Reaction vertex reconstruction at target

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13

SAMURAI setup at the RIBF
SAMURAI dipole magent: up to 3 T (1.25 T)
Tracking & identification of secondary beam (8He)
Tracking & identification of fragments (p, 4He)
Neutrons (not possible in this experiment)

1.25 T

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13

SAMURAI setup at the RIBF
SAMURAI dipole magent: up to 3 T (1.25 T)
Tracking & identification of secondary beam (8He)
Tracking & identification of fragments (p, 4He)
Neutrons (not possible in this experiment)

In this measurement:

1.25 T

small p-4He cross section ~1 µb➢➢

relatively low statistics 8He(p,p4He)
4n detection impossible

NEBULASAMURAI
NeuLAND

1n2n3.11.2022
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Benchmark measurement
QFS knockout 6He(p,p4He)●●

2n relative-energy spectrum is expected to bewell described by theory

6

✗
✗

2n

✗
✗

di-neutron is unbound by ~100 keV

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Benchmark measurement
QFS knockout 6He(p,p4He)●●

2n relative-energy spectrum is expected to bewell described by theory

6

✗
✗

2n

✗
✗

di-neutron is unbound by ~100 keV

Theoretical input:●

w/o FSI: 3-body (4He+n+n) cluster model
➢
➢
➢

●

nn interaction in 1S0 wave
nα interactions in s-, p-, d-wave
phenomenological 3-body force

w/ FSI: nn final-state interaction➢
t-matrix approach

M. Göbel et al., “Neutron-neutron scattering length from the 6He(p,p)nn reaction”, PRC 104 (2021)

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Benchmark measurement
QFS knockout 6He(p,p4He)●●

2n relative-energy spectrum is expected to bewell described by theory

6

✗
✗

2n

✗
✗

di-neutron is unbound by ~100 keV

Theoretical input:●

w/o FSI: 3-body (4He+n+n) cluster model
➢
➢
➢

●

nn interaction in 1S0 wave
nα interactions in s-, p-, d-wave
phenomenological 3-body force

w/ FSI: nn final-state interaction➢
t-matrix approacha nn=−18.7 fm
wide energy range E2n>>1 MeV
a nn±2 → <2 % deviation

M. Göbel et al., “Neutron-neutron scattering length from the 6He(p,p)nn reaction”, PRC 104 (2021)

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14

Results: missing-mass spectraHe(p,p4He)2n6

confirms the expected di-neutron
low-energy peak ~100 keV
MD et al., Nature 606, 678 (2022)
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Results: missing-mass spectraHe(p,p4He)4n8He(p,p4He)2n6

confirms the expected di-neutron
low-energy peak ~100 keV
MD et al., Nature 606, 678 (2022)
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Continuum component

continuum spectrum w/o FSI

He

8

●

4n

Five-body (4He+4n) COSMA model
A source term for the reaction mechanism:➢“sudden removal of an
α-particle from 8He”

= 5.6, 7.3, 8.9 fm➢➢

initial structure (8He)
sensitive to the hyperradius of the source 
5.6 fm reproduces experimental 8He radius

Zhukov et al., PRC (1994); Grigorenko et al., EPJA (2004)

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Results: missing-mass spectraHe(p,p4He)2nHe(p,p4He)4n68resonance like-structure:
Er = 2.37±0.38(stat.)±0.44(sys.) MeV
Γ = 1.75±0.22(stat.)±0.30(sys.) MeV

confirms the expected di-neutron
low-energy peak ~100 keV

MD et al., Nature 606, 678 (2022)
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A tetra-neutron correlation?
Predictions for a tetra-neutron

Shirokov PRL 117 (2016);

Gandolfi PRL 118 (2017);

Fossez PRL 119 (2017);

Li PRC 100 (2019);

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A tetra-neutron correlation?
Predictions for a tetra-neutron

Full treatment of continuum → No tetra-neutron
A recent overview: Marqués & Carbonell, EPJA 57 (2021)

Low-energy structures“the four-neutron system is studied using exact continuum equations fortransition operators... This indicates the absence of an observable 4n resonance,in contrast to a number of earlier works. Even without an observable
resonance the transition operators exhibit pronounced low-energy peaks”➢

may be seen in nuclear reactions➢

must be combined with reaction mechanism

Deltuva, PLB 782 (2018)
Shirokov PRL 117 (2016);

Gandolfi PRL 118 (2017);

Fossez PRL 119 (2017);

Li PRC 100 (2019);

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A tetra-neutron correlation?
Predictions for a tetra-neutron

Full treatment of continuum → No tetra-neutron
A recent overview: Marqués & Carbonell, EPJA 57 (2021)

Low-energy structures●

Reaction model to describe the sudden removal of -core from 8He:
transition from (4He+4n) initial state and 4 interacting neutrons in the final state

Consequence of:two-dineutron FSI andpresence of dineutron clusters in 8He●●●

Independent of the nn interaction
Strong inverse correlation with thenn scattering length

Laszauskas, Hiyama, Carbonell, arXiv:2207.07575 [nucl-th] (2022)
Shirokov PRL 117 (2016);

Gandolfi PRL 118 (2017);

Fossez PRL 119 (2017);

Li PRC 100 (2019);

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Outline➊ The tetra-neutron context●●

experimental quest
theoretical predictions

40n➋ 4n experiment at SAMURAI:

quasi-free -knockout reaction●●

experimental method
results and discussion➌ Future perspectives

next-generation experiments

3.11.2022
Physik | Institut
21.04.2020 | BM@N Collaboration Meeting | FB
J. Kahlbow| 34 Institut für Kernphysik | Meytal Duer

19

Future perspectives
Correlations in multi-neutron systems [Proposal 2022, K. Miki, MD, T. Uesaka et al.]●Neutron detection: 8He(p,p)4n with all four neutrons in coincidence

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20

Future perspectives
Correlations in multi-neutron systems [Proposal 2022, K. Miki, MD, T. Uesaka et al.]●Neutron detection: 8He(p,p)4n with all four neutrons in coincidencep=0.5 mb

=1 μb●●GAGG

Cross section:> two orders of magnitude larger

Si

Detection efficiency for 4n: 0.9%

LH2

4

He

xn

p

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Future perspectives
Correlations in multi-neutron systems [Proposal 2022, K. Miki, MD, T. Uesaka et al.]●Neutron detection: 8He(p,p)4n with all four neutrons in coincidencep=0.5 mb

=1 μb

GAGG
p

●

●

Cross section:> two orders of magnitude larger

Si

Detection efficiency for 4n: 0.9%

LH2

4

p

●

He

xn

p
p

Reaction mechanism: 6He(p,3p)4n knockout reaction➢➢(p,3p) cross sections measured for heavy nuclei
two sequential p-p collisions A. Frotscher et al., PRL 125 (2020)

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20

Future perspectives
nn scattering length from 6He(p,p)nn reaction[T. Aumann et al. SAMURAI55R1]●●

nn scattering length not known precisely experimentally
HIME neutron detector → aa nn
nn within 0.2 fm
HIME demonstrator

M. Göbel et al., PRC 104 (2021)

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21

Future perspectives
nn scattering length from 6He(p,p)nn reaction[T. Aumann et al. SAMURAI55R1]●●

nn scattering length not known precisely experimentally
HIME neutron detector → aa nn
nn within 0.2 fm

Multi-neutron 4n and 6n states in extremely
n-rich nuclei [T. Nakamura et al. SAMURAI47, Jan. 2023]
10

He

●

Li(p,2p) knockout reaction:

He → 8He + 2n / 6He + 4n / 4 He + 6n
Mainly missing-mass: (p,2p) + fragment
two neutrons in coincidence➢
nn correlations
10●

HIME demonstrator

11●

M. Göbel et al., PRC 104 (2021)

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Thank you!

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