Study of Neutron-Proton Correlations via �Two-Nucleon Removal Reactions

Outline:

1. Importance of np-correlations in nuclei
2. Probe: Two-nucleon knockout reactions
3. First exclusive np-removal measurement from ¹²C with

heavy-ion target

4. Ongoing analysis of np-removal data with proton target

5. Summary

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Hongna Liu, Beijing Normal University

IWND2026, Shanxi, China, Aug. 21-25, 2026

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Woods-Saxson+ Spin-Orbital Interaction

Important ingredient：np Correlations

Neutron-Proton Correlations

4 types of Nucleonic pairs

Well defined from the

isospin symmetry

T = 1, S = 0

T = 0, S = 1

Isoscalar

Isovector

(deutron-like)

A lot of uncertainties

Neutron-Proton Correlations

Isoscalar (T=0, S=1) np pair

(deuteron-like)

🡪 new phase of nuclear matter

(e, eꞌp) reactions

R. Subedi et al., Science 320, 1476(2008)

¹²C( e, eꞌ pN )

@4.627GeV JLAB

IPM

SRC

S. Paschalis et al., PLB 800, 135110 (2020) .

L. Lapikas et al., NPA 553, 297c(1993).

30%～40%压低

M. Duer, et al., Nature 560, 7720 (2018) .

In Stable nuclei:

Mean-filed contribution: ~60%-70%

SRC contribution:22%±8% LRC:14%±10%

np Dominance in SRC correlations

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🡺T = 0 np tensor

interaction

O. Hen et al., Science (2014),

Neutron-Proton Correlations

J. Engel et al.,.Phys. Lett.B 389, 211(1996). 

T = 1 components

Nature, 654, 619(2026)

Stronger high-momentum enhancement

n & p in the same valence shell

N = Z system is good to study np correlations

(e,e’pN)

6 protons

8 protons

Shell evolution

0s_1/2

0p_3/2

0p_1/2

1s_1/2

0d_5/2

0d_3/2

1p_3/2

0f_7/2

1p_1/2

0f_5/2

0g_9/2

2

8

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Neutron-Proton Correlations in unstable nuclei

Driving force behind the shell evolution?

Properties of heavy N = Z nuclei (waiting point)

• Key ingredients in rapid-proton capture

(rp) nucleosynthesis

Reduced T = 0 np interaction

np correlations:

• Fundamental nuclear force
• Nuclear structure
• Heavy element production in universe

T. Otsuka et al., PRL 95, 232502(2005).

Two-nucleon Knockout Reactions in Inverse Kinematics

High incident energy🡪 Spectator

E.C. Simpson et al., PRL 102,132502(2009)

🡪 Is it a good tool for systematic study of np correlations with RI beams?

Beam energy (>100 MeV/u)

Target

proton/ Heavy-ion target

Stripping-Stripping

Target

A-2

A-2

Target

Free nucleon1

Free nucleon2

Diffraction-Diffraction

Stripping-Diffraction

Target

A-2

Free nucleon

Direct 2N-removal

Be/C target: 2p-removal from neutron-rich nuclei

~10%

~30%

~60%

K. Wimmer et al., PRL 109 (2012)

Pair knockout

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56(12)% “di-proton” correlated events

²⁸Mg(-2p) on Be target @ 93 MeV/u

Suppress two-step evaporation contribution

²⁸Mg🡪²⁷Na* (S_n=6.7 MeV) 🡪 ²⁶Ne+p

(S_p=13.3 MeV)

-1p

1p-Evaporation

²⁶Ne+2p coincidence

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M. Yasue et al., JPSJ. 42, 367 (1977)

“Unusual” neutron-proton Correlations in ¹²C (N = Z = 6)

Behavior of T = 0 interaction:

function of pair relative momentum

High-momentum transfer

🡪 Short-range correlations

p

n

p

~

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p

σ-np

σ-nn

For ¹²C

pair counting ratio:

Different mechanisms

🡪 Sensitive to different range of 2N forces

🡪To obtain of a complete picture of np correlations

Inclusive 2N-removal data from ¹²C

p

p

T=1

T=0&1

T = 0 & 1

E. C. Simpson et al., PRC 83, 014605(2011)

For pp & nn (T = 1) removal, calculations are broadly consistent with data.

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For np (T = 0 & 1) removal, calculations underestimate data by a factor of 2.

What do we find with inclusive data?

First Calculation：np-removal from ¹²C @ 2.1 GeV/u with ¹²C target

Indicate insufficient T = 0 np-spatial correlations in p-shell SM

Need to disentangle the T = 0 & T = 1

More exclusive data is necessary.

What do we need in next step?

To provide a clear answer

Due to Interactions or Model space?

Observables: np-removal from ¹²C

Partial cross sections in np removal🡪 Sensitive to the interaction used

E. C. Simpson et al., PRC 86, 054609 (2012)

Structure of ¹²C &¹⁰B can be described using NCSM (NN + 3N).

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Experimental Setup

⁹Be(¹²C,¹⁰Be) ⁹Be(¹²C,¹⁰B) @190MeV/u

¹⁸O primary beam: 250MeV/u , ~0.08pnA

Production target: ⁹Be (5mm)

Secondary beam: ¹²C 190MeV/u 12k cps

Purity: 97%

Secondary target: ⁹Be (1.879g/cm² )

Beam on Target: 10.7 h

TOF − ΔE

¹¹B

¹²C

¹³N

BigRIPS PID

SAMURAI

Superconducting Analyser for Multi-particles from RAdioIsotope beams

W/O proton detection

σ_np= σ_np-direct + σ_np-indirect

Indirect contribution is negligible (High particle separation energy)

Indirect: -1n knockout followed by 1p evaporation & Sequential knockout

Experimental Setup around SAMURAI

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BDCs: Tracking of ¹²C beam

DALI2 (NaI): Gamma rays

NEBULA: Neutrons

FDCs: Tracking of ¹⁰B, ¹⁰Be residues

Hodoscope: TOF & ΔE of ¹⁰B, ¹⁰Be residues

Multi-particle Detector Systems

Large Acceptance

Bρ_max/ Bρ_min = 2 ~ 3

Measured in one setting.

SAMURAI Spectrometer

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DALI2

⁹Be(¹²C,¹⁰Be + γ) X

⁹Be(¹²C,¹⁰B+ γ) X

Experimental Challenges

Apply Hardware Cut to Exclude Unreacted ¹²C

SBT

High Trigger Counting Rate

• N = Z system A/Q(¹²C)=A/Q(¹⁰B)

Unreacted ¹²C beam will be accepted by SAMURAI.

¹²C beam

SAMURAI Magnet

Target

PID of Fragments & Inclusive cross sections

PID without HODP5

With target

empty target

After subtraction

Clear identification of ¹⁰B

P. J. Lindstrom et al., PRC 28,1602(1938)

J. M. Kidd et al., PRC 37,2613(1998)

np removal from ¹²C

Counts/ 20keV

J, T, E, T_1/2 & decay branching ratios are known.

⁹Be(¹²C,¹⁰B + γ) X

Add-back Reconstruction was applied to improve the peak-to-noise ratio & photo-peak efficiency.

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Fit function: Response functions(GEANT4) + Exponential background (Error of efficiency from GEANT4: 4%)

First exclusive np-removal data

🡪Strong splin-aligned (p3/2)

np pair configurations in ¹²C?

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🡪Unclear reaction process?

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¹²C ¹¹C* ¹⁰B

-n

-p

S_p=16 MeV

S_n=19 MeV

Evaporation

n-evaporation

p-evaporation

n

p

Diff-Diff

n

½ Strp-Diff

n

X

¹²C🡪¹⁰B+n

Difficult to subtract two-step process from the measured E_rel spectrum

E_rel (MeV)

¹⁰B

Contaminations in E_rel(¹⁰B+n)

¹⁰B

¹⁰B

Be/C target: np removal

Two-step process: neutron evaporation

Target

After the reaction

Proton target: Quasi-free scattering reaction

¹²C(p,2p)¹¹B @ 400 MeV/u

Before the reaction

Quasi-free scattering

with specific kinemtics

V. Panni et al., PLB 753, 204 (2016).

Y.L. Lu@BNU

V. Panin@GSI

Proton target: Indirect contribution measured from ¹²C(p,2p)

¹²C(p,2p)

(17%)

(n+¹⁰B) Decay ratio of the s-hole state in ¹¹B: 17(2)%

V. Panni et al., PLB 753, 204 (2016).

Excitation Energy of ¹¹B

Two step process to ¹⁰B:

～80% goes to the ground state

Proton target: Indirect contribution measured from ¹²C(p,2p)

Gamma spectrum of ¹²C(p,2p)(¹⁰B+n)

Evaporation to ¹⁰B: 8(1) mb out of 42(2) mb

0s-hole state in ¹²C: C²S = 1.62

Calculated by C.X. Yuan

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Be target: Indirect contribution in two-nucleon removal

¹⁰Be: 1.6 (6) mb out of 9.2(5) mb

Measured decay branching ratios to individual final states of ¹⁰B from ¹²C(p,2p)¹¹B*

(assuming same contribution from n & p evaporation)

20% contribution

SM calculations with WBP interactions describe well T = 1 but underestimate T = 0

p

T = 1

p

T = 0&1

p

n

First exclusive np-removal data to ¹⁰B

np removal

While that to T = 0 states are broadly underestimate by the theory by a factor of 2

🡪 Insufficient treatment of T = 0 np

correlations in WBP calculations

SM calculations with WBP interactions describe well T = 1 but underestimate T = 0

Clear enhancement of T = 0 than T = 1 np correlations was observed.

T = 1 5.6(4) mb

T = 0 29(2) mb

R(σ_{T = 0}/σ_{T = 1})

= 5.6(5)

ab initio no-core shell model (NCSM)

⁹Be(¹²C,¹⁰B ) X

Proton target

Two types of Hammer

Probe: Knockout Reactions in Inverse Kinematics

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Analysis of the ¹²C(p, pd)¹⁰B reaction

Deuteron kinetic energy:

Where

Determine whether it is a deuteron.

Extracting (p, pd) reaction pathways using kinematic conditions

(p,pd)

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R. Subedi et al., Science 320, 1476(2008)

Pair knockout

Sequential

Multiple possible process

Could we see np pair?

• 1n evaporation from neutron-rich residue

• n/p sequential removal as (p,3p)
• pair knockout (p, pd)

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(p, 2pn) from neutron-rich nuclei @ 250 MeV/u

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⁵²Ca🡪⁵⁰K Multiple comp.

(p, 2pn) from neutron-rich nuclei @ 250 MeV/u

Geant4 Simulations

• 1n evaporation

• n/p sequential removal as (p,3p)
• pair knockout (p, pd)

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Sequential

Sequential

(p,pd)

C.L. Hao

⁵²Ca(p,2p)⁵¹K*🡪⁵⁰K+n

Evaporation

1n-evap.

sequen. + Pair

MINOS+SAMURAI @ RIBF

MINOS@RIBF

STRASSE @ RIBF

LH2+Si tracker

Decent angular resolution

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Missing-mass & gamma Spe.

Development of the LH2 target for HIAF

H.N. Liu et al., EPJA 59, 121 (2023)

MF4

Stable Nuclei

Unstable

Primary beam from Booster

External target Area

SRC study along isotopic chain with (p, 2pn), (p, pd)

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Under construction @BNU

Cold head

Target cell

Condensor

Changeable target arm

HIRIBL

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Summary

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Partial cross sections (Disentangle T = 0 & T = 1 np pair)

1. R(σ_{T = 0}/σ_{T = 1}) = 5.6(5), suggesting a stronger T = 0 np correlations.

2. Compared with the theory:

SM calculations with WBP interactions describe well T = 1 NN removal.

but underestimate the T = 0 np removal by a factor close to 2.

🡺 Insufficient treatment of T = 0 np correlations in the p-shell

NCSM calculations with NN+3N provide a much better description of the

measured partial cross sections to the T = 0 states than the p-shell model.

• 3N is necessary to describe the measured trend of the cross sections.

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⁹Be(¹²C,¹⁰Be + γ) X

⁹Be(¹²C,¹⁰B+ γ) X

Probe: Two-nucleon knockout reactions from ¹²C at 190 MeV/u

Obtain the first exclusive np-removal data with the γ+residue measurement

Evaporation contribution in np-removal is significant and such components could not be directly identified when using HI target.

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QFS with proton target is a promising tool, the (p,2pn) data analysis is ongoing…

Backup slides

Counts/ 30keV

⁹Be(¹²C,¹⁰Be + γ) X

Add-back Reconstruction was also performed.

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Fit function:

Response functions(GEANT4)+Exponential background

pp removal from ¹²C

J, T, E, T_1/2 & decay branching ratios are known. (Only states with positive parity are considered)

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Analysis of gamma spectrum

Consider fitting the ¹⁰B gamma spectrum：

Response function of the excited state of ¹⁰B

Background

Low-energy background caused by protons produced in the reaction

Low-energy background caused by beam bombardment of the target (primarily bremsstrahlung) .

Simulated using R3BROOT

Consider using a double-exponential background

Gamma spectrum of ¹¹B following ¹²C(p,2p) ¹¹B*

Constraining the Shape and Counts of a Double-Exponential Background Using the Gamma Spectrum of ¹¹B

Uncertainty of the fitting:

Statistical Error in Experimental Spectrometer Counting

Errors Resulting from Different Constraint Methods for Dual-Exponential Background

Uncertainty arising from the inclusion of the proton background

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(p, 3p) reactions in neutron-rich

nuclei @ 250 MeV/u

Pair K.O. + Breakup =5～15%

A. Frotscher et al., PRL 125, 012501(2020).

Only Angular distribution

🡺Dominance of sequential

R. Subedi et al., Science 320, 1476(2008)

First exclusive np-removal data

p

T = 0&1

p

n

T = 1

Partial cross sections

Large cross section to T = 0 3+ state in np removal (20/42 mb)

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🡪Indicate a strong

splin-aligned np paired

configurations in ¹²C

np-removal:

T = 1 6.2(4) mb

T = 0 36(1) mb

R(σ_{T = 0}/σ_{T = 1}) = 5.9(4)

🡪Shown stronger T = 0 np correlations

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v

R(σ_-np/σ_-pp) = 4.6(3)

pp-removal:

T = 1 9.1(3) mb

p

Comparison with Theory

R(σ_np/σ_pp) = 4.6(3)

Structure:

TNA from p-shell SM

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Reaction: Eikonal theory

Theoretical cross sections:

Data: 190 MeV/u@⁹Be

Theory: 250 MeV/u @¹²C

pp removal

np removal

Partial cross sections to T = 1 states could be reasonably reproduced by the theory.

While that to T = 0 states are broadly underestimate by the theory by a factor of 2.

• T = 1 NN correlations are well

described in p-shell shell model.

🡪 Insufficient treatment of T = 0 np

correlations in SM or Eikonal theory

ab initio no-core shell model (NCSM)

⁹Be(¹²C,¹⁰B ) X

Role of 3N Forces

⁹Be(¹²C,¹⁰B ) X

However, NCSM with NN+3N still cann’t reproduce the data quantitatively.

3N forces

3N is also necessary to predict the right trend of the measured partial cross sections.

3N is necessary to describe the energy level of ¹⁰B.

Eikonal Theory for 2N Removal

Eikonal model:

Only consider the interactions between (β₁,Target), (β₂,Target) & (Residue,Target)

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Interaction between (β_1, β₂) are missing.

¹²C( e, epN )@4.627GeV

1N removal in Eikonal theory

2N removal in reality

R. Subedi et al., Science 320, 1476(2008)

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Summary

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Partial cross sections (Disentangle T = 0 & T = 1 np pair)

1. R(σ_{T = 0}/σ_{T = 1}) = 5.9(4), suggesting a stronger T = 0 np correlations.

2. Compared with the theory:

T = 1 NN removal: σ_exp~ σ_th T = 0 np removal: σ_exp~ 2σ_th

Such discrepancy shows that either the T = 0 np correlations in the SM is

insufficient or the reaction mechanism of SRC pairs removal is missing

in the Eikonal model.

3. NCSM calculations: Discrepancy between data and theory mainly arises

from the T = 0 3⁺ GS. 3N is necessary to predict the right trend of the measured partial cross sections.

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⁹Be(¹²C,¹⁰Be + γ) X

⁹Be(¹²C,¹⁰C+ γ) X

⁹Be(¹²C,¹⁰B+ γ) X

Probe: Two-nucleon knockout reactions from ¹²C at 190 MeV/u

Obtain the first exclusive np-removal data with the γ+residue measurement

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Collaborators

RIKEN J. Lee, H. Liu, P. Doornenbal, N. Inabe, T. Isobe, T. Kubo, S. Kubono, T. Motobayashi, M. Nishimura, H. Otsu, H. Sakurai, H. Sato, Y. Shimizu, H. Wang, S. Takeuchi, K. Yoneda

CNS/ Unvi. Of Tokyo

M. Matsushita, D. Steppenbeck

NSCL/ MSU B. A. Brown

TRIUMF P. Navratil

Tohoku Univ.

T. Kobayashi

Tokyo Tech.

Y. Kondo, N. Kobayashi, R. Minakata, T. Nakamura, S. Ogoshi, Y.Togana

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RCNP, Osaka U.

N. Aoi

LPC de CAEN

J. Gibelin, S. Leblond�

Univ. of Kyoto

Y. Matsuda R. Minakata

Seoul National Univ.

J. Hwang

Theory Collaboration:

Univ. of Surrey

J. A. Tostevin, E.C.Simpson

LBNL

A. O. Macchiaveli, P. Fallon

PKU H. Liu, Yanlin Ye

Thank you very much for your attention!

4 types of Nucleonic pairs

Neutron-Proton Pair Correlations

Isoscalar (T=0, S=1) np pair

(deuteron-like)

🡪 new phase of nuclear matter

Well defined from the

isospin symmetry

T = 1, J = 0

T = 0, J > 0

Isoscalar

Isovector

Long-standing ambitions:

Obtaining direct information of T = 0 np pair correlations

(e, eꞌp) reactions

Mean Field

Important ingredient：Pair Correlations

n & p in the same valence shell

(deutron-like)

A lot of uncertainties

N = Z system: A dominance of np pair

Correlations

L. Lapikas et al., NPA 553, 297c(1993).

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Drip-line nucleus

Nuclear Structures Driven by Nuclear Forces

How do nuclear forces evolve with Isospin asymmetry?

How do nuclear structures change with Isospin asymmetry?

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Mean field: Woods-Saxson

+ Spin-Orbital Interaction

Stable Nuclei

S_p S_n~8 MeV

20MeV

S_n < 1 MeV

Two-nucleon Knockout Reactions in Inverse Kinematics

Core survival and nucleon “removal”🡪

Only affect the nucleon near surface

High incident energy🡪

Spectator (eikonal reaction model)

E.C. Simpson et al., PRL 102,132502(2009)

Fig. 1 Calculated P_// of ²⁶Ne after pure π[d_5/2]² two proton removal from ²⁸Mg at 82 MeV/u

🡪 A promising tool for systematic study of np correlations in N=Z nuclei

Electron-induced 2N removal reactions : study stable nuclei.

Cross section of 2N transfer reaction is small.

Beam energy (>100 MeV/u)

Background shape of γ spectrum

¹²C(⁹Be, X)⁹Be

Only the ground state of ⁹Be is bound.