In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

China

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

Possible deformed neutron halos in silicon isotopes are investigated from both structure and reaction perspectives using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) combined with the Glauber model. The experimental neutron separation energies of silicon isotopes are well reproduced by the DRHBc theory. Multiple halo criteria are examined, including the global ones based on root-mean-square radii and density profiles, as well as the microscopic ones based on single-particle orbitals and their spatial distributions. Calculations employing different density functionals and pairing strengths consistently indicate the emergence of <italic>p</italic>-wave neutron halos in 43,45Si, accompanied by pronounced shape decoupling between the halo and the core. Moreover, the enhanced reaction cross sections and the narrow longitudinal momentum distributions of one-neutron removal residues provide additional evidence supporting the halo structures in 43,45Si.

C. Pan (潘琮)

J.L. An (安嘉琳)

Germany

P. Ring

X.H. Wu (吴鑫辉)

South Korea

P. Papakonstantinou

M.H. Mun

Y. Kim

S.S. Zhang (张时声)

K.Y. Zhang (张开元)

Prediction of deformed halo nuclei 43,45Si from multiple criteria based on structure and reaction analyses

Quasi-elastic (QEL) scattering measurements have been performed using the 28,30Si projectiles off the 90Zr target at energies around the Coulomb barrier. Coupled-channels (CC) calculations were carried out in a large parameter space of quadrupole and hexadecapole deformations for the N=Z, 28Si and N=Z+2, 30Si nuclei. 28Si at the N=Z line is observed to be uniquely oblate shaped in its ground state. In contrast, for 30Si with just two additional neutrons- oblate, prolate, and spherical CC descriptions are equally compatible with the measurements. To further investigate the nuclear structure evolution with varying neutron number, shell-model calculations were performed. These calculations reveal a sudden change in the nuclear structure aspects at 30Si in going from 28Si to 32Si. Combined reaction and structure analyses consistently indicate that 30Si does not possess a well-defined intrinsic shape, and it is a potential candidate for &#8220;shape fluctuations&#8221; in its ground state.

India

Y.K. Gupta

France

B. Maheshwari

G.K. Prajapati

A.K. Jain

Japan

K. Hagino

B.N. Joshi

A. Pal

N. Sirswal

Pawan Singh

S. Dubey

V.V. Desai

V. Ranga

V.B. Katariya

D. Patel

H. Vyas

S. Panwar

B.V. John

I. Mazumdar

B.K. Nayak

United States

U. Garg

Quasi-elastic scattering for the nuclear ground state structure: An intriguing case of 30Si

The sub-barrier fusion hindrance phenomenon is systematically observed in heavy-ion systems, but its evidence for light-mass cases of astrophysical interest, like C+C, C+O and O+O, is controversial. Their low-energy behaviour may be clarified by studying slightly heavier systems, so to extrapolate their trend to the lighter cases. In this work, fusion of 12C + 28Si has been measured down to deep sub-barrier energies, using 28Si beams from the XTU Tandem accelerator of LNL on thin 12C targets. Two different set-ups were employed: 1) the fusion-evaporation residues were identified by a detector telescope following an electrostatic beam separator, and 2) coincidences between the <italic>&#947;</italic>-ray array AGATA and segmented silicon detectors DSSD were performed, where the evaporated light charged particles were identified by pulse shape analysis. Fusion cross sections have been obtained in the wide range <italic>&#963;</italic>&#8239;&#8776;&#8239;150 mb &#8211; 42&#8239;nb. Coupled-channel (CC) calculations using a Woods-Saxon potential reproduce the data above &#8239;&#8771;&#8239;0.1 mb. Below that, hindrance shows up and the CC results overestimate the cross sections which get close to the one-dimensional potential tunnelling limit. This suggests that the coupling strengths gradually vanish, as predicted by the adiabatic model. The hindrance threshold follows a recently updated phenomenological systematics.

Italy

A.M. Stefanini

G. Montagnoli

M. Del Fabbro

A. Goasduff

P.A. Aguilera Jorquera

G. Andreetta

F. Angelini

L.V. D’Auria

M. Balogh

D. Bazzacco

J. Benito

G. Benzoni

United Kingdom

M.A. Bentley

N. Bez

A. Bonhomme

S. Bottoni

A. Bracco

D. Brugnara

Croatia

L. Busak

S. Capra

S. Carollo

Spain

S. Casans

E. Clément

P. Cocconi

A. Cogo

Poland

G. Colucci

A. Conte

E. Coradin

L. Corradi

S. Courtin

G. Deangelis

J.M. Deltoro

G. Del Piero

R. Depalo

J. Dudouet

A. Ertoprak

E. Fioretto

A. Gadea

F. Galtarossa

A. Gambalonga

A. Giaz

B. Gongora Servin

V. González

A. Gottardo

A. Gozzelino

G. Harmant

M. Heine

Hungary

I. Kuti

M. Labiche

S.M. Lenzi

S. Leoni

M. Mazzocco

R. Menegazzo

D. Mengoni

T. Mijatović

B. Million

E. Monpribat

A. Nannini

D.R. Napoli

A.E. Navarro-Antón

R. Nicolas Del Alamo

Sweden

J. Nyberg

S. Paschalis

J. Pellumaj

R.M. Pérez-Vidal

M. Petri

E. Pilotto

S. Pigliapoco

Z.S. Podolyak

M. Polettini

A. Pullia

L. Ramina

M. Rampazzo

W. Raniero

M. Rebeschini

F. Recchia

P. Reiter

K. Rezynkina

M. Rocchini

D. Rosso

E. Sanchis

M. Scarcioffolo

D. Scarpa

Türkiye

M. Şenyiğit

J. Simpson

D. Sohler

O. Stezowski

D. Stramaccioni

S. Szilner

C. Theisen

N. Toniolo

A. Trzcinska

J.J. Valiente Dobon

F. Veronese

Slovenia

J. Vesic

V. Volpe

K. Wimmer

L. Zago

I. Zanon

M. Zielińska

Fusion of 12C+ 28Si at deep sub-barrier energies

Proton-rich nuclei beyond the proton drip line are of great interest in nuclear structure physics, due to exotic phenomena such as proton emissions and the Thomas-Ehrman shift (TES). In this work, we employ the Gamow shell model (GSM) to investigate the structure and decay of 20Si, a candidate for six-proton (6 <italic>p</italic>) emission, which can be produced via two-neutron knockout from the drip line nucleus 22Si. We predict that its ground state decays via 6 <italic>p</italic> emission to the ground state of 14O, with a decay energy <math altimg='si21.svg'><mrow><msub><mi>E</mi><mrow><mn>6</mn><mi>p</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>10.125</mn></mrow></math> MeV and a width of 371 keV. A <math altimg='si22.svg'><msup><mn>2</mn><mo>+</mo></msup></math> state is predicted at 1.7 MeV, comparable with that in 18Mg, indicating the disappearance of the <math altimg='si23.svg'><mrow><mi>Z</mi><mo linebreak='goodbreak'>=</mo><mn>14</mn></mrow></math> magic number in 20Si. Instead, analyses of the many-body configurations and the average occupancies of the mirror states suggest the presence of <italic>dynamic</italic> TES in low-lying states of 19Al/ 19C and 20Si/ 20C. Further evidence is provided by analyzing the contributions of different components of the GSM Hamiltonian. Moreover, this study offers the first theoretical description of 20Si and guidance for future experiments.

J.L. Wang

M.R. Xie

K.H. Li

P.Y. Wang

N. Michel

Q. Yuan

J.G. Li

Gamow shell model predictions for six-proton unbound nucleus 20Si

The proton-rich nucleus <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si is studied using Nuclear Lattice Effective Field Theory with high-fidelity chiral forces. Our results indicate that <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si is more tightly bound than <math altimg='si2.svg'><msup><mrow /><mn>20</mn></msup></math>Mg, thereby excluding the possibility of two-proton emission. The <math altimg='si18.svg'><mrow><mi>Z</mi><mo linebreak='goodbreak'>=</mo><mn>14</mn></mrow></math> shell closure in <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si is investigated through the evolution of the <math altimg='si8.svg'><msup><mn>2</mn><mo>+</mo></msup></math> state in the neighboring nuclei. We then focus on the charge radius and spatial distribution information of <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si, considering the novel phenomena that may emerge due to the small two-proton separation energy and the shell closure. We present the distribution of the 14 protons and 8 neutrons obtained from our lattice simulation, revealing insights into the spatial arrangement of the nucleons. Moreover, the spatial localization of the outermost proton and neutron suggests that <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si is a doubly magic nucleus. Furthermore, we develop the pinhole method based on the harmonic oscillator basis, which gives insight into the nuclear structure in terms of the shell model picture from lattice simulations. Our calculated occupation numbers support that <math altimg='si18.svg'><mrow><mi>Z</mi><mo linebreak='goodbreak'>=</mo><mn>14</mn></mrow></math> and <math altimg='si6.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>8</mn></mrow></math> are the shell closures and show that the <math altimg='si19.svg'><mrow><mi>&#960;</mi><mn>1</mn><msub><mi>s</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> orbital component is minor in <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si.

Shuang Zhang

Saudi Arabia

Serdar Elhatisari

Ulf-G. Meißner

Shihang Shen

Lattice simulation of nucleon distribution and shell closure in the proton-rich nucleus <math altimg='si1.svg'><msup><mrow /><mn>22</mn></msup></math>Si

We report on the first measurement of the elemental fragmentation cross sections (EFCSs) of <math><mmultiscripts><mrow><mi>Si</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>29</mn><mo>−</mo><mn>33</mn></mrow></mmultiscripts></math> on a carbon target at ∼230 MeV/nucleon. The experimental data covering charge changes of ΔZ = 1-4 are reproduced well by the isospin-dependent quantum molecular dynamics (IQMD) coupled with the evaporation GEMINI (IQMD+GEMINI) model. We further explore the mechanisms underlying the single-proton removal reaction in this model framework. We conclude that the cross sections from direct proton knockout exhibit an overall weak dependence on the mass number of Si projectiles. The proton evaporation induced after the projectile excitation significantly affects the cross sections for neutron-deficient Si isotopes, while neutron evaporation plays a crucial role in the reactions of neutron-rich Si isotopes. It is presented that the relative magnitude of one-proton and one-neutron separation energies is an essential factor that influences evaporation processes. Therefore, proton evaporation should be incorporated into the reaction model in addition to the direct proton knockout in analyses of Gade-Tostevin systematic for single-proton removal reactions.

Guang-Shuai Li

Bao-Hua Sun

Jun Su

Isao Tanihata

Satoru Terashima

Jian-Wei Zhao

Er-Xi Xiao

Ji-Chao Zhang

Liu-Chun He

Ge Guo

Wei-Ping Lin

Wen-Jian Lin

Chuan-Ye Liu

Chen-Gui Lu

Bo Mei

Dan-Yang Pang

Ye-Lei Sun

Zhi-Yu Sun

Meng Wang

Feng Wang

Jing Wang

Shi-Tao Wang

Xiu-Lin Wei

Xiao-Dong Xu

Jun-Yao Xu

Li-Hua Zhu

Yong Zheng

Mei-Xue Zhang

Xue-Heng Zhang

Single-proton removal reaction in the IQMD+GEMINI model benchmarked by elemental fragmentation cross sections of Si on carbon at ∼230 MeV/nucleon