Study on 1n halo nuclei from light to medium mass region

Shi-Sheng Zhang (张时声)

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Beijing University of Aeronautics and Astronautics (Beihang University)

The 8th International Workshop on Nuclear Dynamics in Heavy-ion Reactions,

Taiyuan, Shanxi, August 21^st-24^nd, 2026.

Background & Motivations：Nuclear physics under extreme conditions

• Exotic nuclei (extreme N/Z ratio)

​

Heaviest

halo nucleus

stable

N halo

P halo

1n halo

2n halo

4n halo

N

Y

N

N

Y

N

Y

narrow dσ/dp_//

soft dipole resonance

Y

Y

N

HALO

Observables:

• S_n
• soft dipole resonance
• large σ_R
• narrow dσ/dp_//
• _……

​

structure

reaction

Part I: CDFT + Glauber model for medium mass region�1n halo description from structure to reaction observables

³⁷Mg

³¹Ne

^43,45Si

The 8th International Workshop on Nuclear Dynamics in Heavy-ion Reactions,

Taiyuan, Shanxi, August 21^st-24^nd, 2026.

History of p-wave 1n halo nuclei ³¹Ne & ³⁷Mg

T. Nakamura, et al., PRL 103, 262501 (2009).

History of p-wave 1n halo nuclei ³¹Ne & ³⁷Mg

A unified description of the halo nucleus ³⁷Mg from microscopic structure to reaction observables

J. L. An, …, S.S. Zhang, PLB 849, 138422（2024）

AMD+DFM+RGM FAILED!

A unified description from structure to reaction applicable for medium-mass region halo nuclei is strongly desired!

Goals

Spherical structure

(RAB)

Deformed structure

(DRHBc、D-RHFB )

Deformed reaction

(Glauber)

• Reaction cross section (CS)
• One-neutron removal CS
• Momentum distribution

Spherical reaction

(Glauber)

Spherical reaction

(Glauber)

Deformed reaction

(D/TRHBc、NLEFT )

Step 1

Step 2

Step 3

Observables

JPG 2022. 01 cover article

SCPMA 2022.06

submitted

Radius, density distribution

cannot be directly detected

ZSS, MSS, ZSK, ZJ, PLB 730, 30 (2014).

Neutron density distributions (DD)

3/2^-

RAB (RMF+ACCC+BCS) approach:

Glauber model

• Lippmann-Schwinger equation

• Eikonal Approximation

• Scattering amplitude

Spherical Glauber model

B. Abu-Ibrahim, et al. CPC., 151(3) (2003) 369-386. 　　　　　　　　　　　

Phase shift χ

Reaction CS σ

Longitudinal momentum distribution dσ/dp_//

Longitudinal Momentum distribution

Step 1 :

spherical + spherical

• Multi-set of Gaussian functions fit (×)
• RAB density

Gaussian function fit

RAB density

deviations

ZSS, ZSY, SB, and MSS, JPG 49 (2022) 025102

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Halo hints

JPG cover article

Density distribution

50 mb deviation

CDFT：RAB (s.p. resonant states + pairing) + spherical Glauber model

Solving the Dirac-Hartree(-Fock)-Bogoliubov equations have been achieved!

deformed

B. Abu-Ibrahim, et al. CPC., 151(3) (2003) 369-386. 　　　　　　　　　　　J. Hong, et al, PRC, 96(6) (2017) 064603.

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Phase shift χ

Reaction CS σ

Longitudinal momentum distribution dσ/dp_//

spherical

Step 2:

deformed + spherical

Improved

• Removal CS：30%
• Momentum distribution：26%

ZSY, ZSS*, et al. SCPMA, 65 (2022) 262011

​

Reaction CS

CDFT：DRHBc (axial deformed + pairing + continuum) + spherical Glauber model

DRHBc theory + Glauber model：

​

​

AJL, ZKY*, LQ, ZSY, ZSS*, PLB 849 (2024) 138422.

deformation + pairing + continuum

K. Y. Zhang, et al., PLB 844 (2023) 138112.

Highly cited in 2024

PC-F1

Exp. Data are taken from

Kobayashi N, et al.

PRL 112(24): 242501(2014).

momentum distribution

Reaction CS

Observables for 1n halo ³⁷Mg

Step 3:

deformed + deformed

Impact

• Reaction CS：20 mbarn
• Momentum distribution：in between

CDFT：DRHBc (axial deformed + pairing + continuum) + deformed Glauber model

In between

β₂=0.25

Summary I

• Spherical structure + Spherical reaction
• Reaction CS：RAB density vs. Gaussian density

​

• Momentum distribution: narrow
• Deformed structure + Spherical reaction
• Reaction CS ：
• 1n removal CS： 　　
• Momentum distribution:
• Deformed structure + Deformed reaction
• Reaction CS ：
• Momentum distribution ：

Gaussian fitting

RAB densities

Realize a unified description of halo nuclei with medium masses�from microscopic structure to reaction observables

the best

JPG 49 (2022) 025102 cover

SCPMA 65 (2022) 262011

Improved by 50 mb

↔ dilute in coordinate space

PC, AJL,…, ZSS*, ZKY*, PLB 877: 140487 (2026).

Predict deformed halo candidates

Exp. Data:

B. Hue, et al., Phys. Conf. Ser 934: 012058 (2017).

Y. Penionzhkevich, et al., KnE Energy 3: 21 (2018).

Same energy in center of mass coordinate

Key points in the reply to the PLB’s referee

​

Triaxial Relativistic Hartree-Bogoliubov theory in continuum（TRHBc）

Exp. Data:

M. Wang, et al., CPC 45: 030003 (2021).

H. Heylen, et al., PRC 103: 014318 (2021).

ZKY, etal.

PRC 108: L014301 (2023);

PRC 112: 044308 (2025).

CDFT：TRHBc (triaxial deformed + pairing + continuum) + spherical Glauber model

AJL, ZSS*, ZKY*, JPG 53(7): 075105 (2026).

Part II: NLEFT + Glauber model for light mass region�1n halo description from structure to reaction observables

https://arxiv.org/abs/2608.01131

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The 8th International Workshop on Nuclear Dynamics in Heavy-ion Reactions,

Taiyuan, Shanxi, August 21^st-24^nd, 2026.

NLEFT(Nuclear Lattice Effective Field Theory): ¹¹Be halo

Shihang Shen, et al., PRL 134, 162503 (2025)

Parity Inversion: ¹¹Be J^π (1/2⁺ )

From microscopic structure to reaction observables

NLEFT configurations

Deformed Glauber

Intrinsic density

Reaction observables

correlated A-body samples

configuration alignment

orientation-resolved S(b)

No fitted density parametrization

NLEFT + deformed Glauber model is valid for elastic scattering!

For p + ¹²C,

• Minima can be reproduced
• correct angular scale

Predictions for ¹¹Be + ¹²C,

• First minimum shifts to lower q

⇒ Larger transverse interaction radius

⇒ Signal of halo ¹¹Be with spatially extended valence neutron

Elastic differential cross sections for p + ¹²C and ¹¹Be + ¹²C at 800 MeV/A as a function of the momentum transfer q

Deformation can largely reduce σ_R(^7-12Be + ¹²C / ⁹Be) by ~50 mb

• σ_R​ can be systematically reduced by deformation and agree with measured data
• Pronounced increase of σ_R​ ¹⁰Be→¹¹Be appear

⇒ clear signal of 1n halo for ¹¹Be

• Independ on the selection of the targets

Narrow longitudinal momentum distributions at 63 MeV/A and 790 MeV/A

790 MeV/A — predictions for future measurement!

the dσ/dp_// for ¹⁰Be+n residues after 1n removal reactions are narrower than those for ⁸Be+n.

63 MeV/A — calculated shape agrees with the data

Colored band: uncertainty from S_n(exp)​ – S_n(NLEFT)

​

¹¹Be: S_n ​= 0.5–1.9 MeV

​

¹⁰Be:​ S_n ​= 0.9–1.7 MeV

For light nuclei, NLEFT+deformed Glauber model works!

• Elastic differential cross sections for p + ¹²C agree with data and predict those for ¹¹Be + ¹²C
• Deformation reduce σ_R(^7-¹²Be) by ~ 50 mb
• A sudden increase of σ_R from ¹⁰Be to ¹¹Be is recovered and independent on both targets ⁹Be & ¹²C
• Narrow momentum widths suggest halo structure at 63 MeV/A & 790 MeV/A

unpublished

1n halo

2n halo

JPG2026

PLB2026

SCPMA2022

JPG2022

JPG2025

EPJA2024

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PLB2024

PLB2023

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Systematic study on neutron-rich isotopes with 15<A<50 & 6<Z<14

https://arxiv.org/abs/2608.01131

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Thanks for your attention!

NLEFT(Nuclear Lattice Effective Field Theory)

S. Elhatisari, et al., Nature 630, 59 (2024).

Densities from Pinhole Algorithm

S. Elhatisari et al., PRL 119, 222505 (2017)