The <italic>&#946;</italic>-delayed <italic>&#947;</italic>-ray spectroscopy of neutron-rich 117,119Rh isotopes has been investigated at the Radioactive Isotope Beam Factory of RIKEN. The <math altimg='si7.svg'><mrow><mn>1</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> isomers in 117,119Rh have been identified for the first time. The systematics of energy differences between the <math altimg='si8.svg'><mrow><mn>9</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> and <math altimg='si7.svg'><mrow><mn>1</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> states have been extended up to <math altimg='si9.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>74</mn></mrow></math>, which shows a tendency to first increase with the neutron number <italic>N</italic>, then reach a maximum at <italic>N</italic>&#8239;&#8776;&#8239;68, and subsequently decrease. Self-consistent triaxial relativistic Hartree-Bogoliubov (TRHB) calculations highlight the crucial role of triaxial deformation, particularly in the positive-parity states, in driving the observed evolution of energy differences. A shape transition from axially symmetric to triaxial and back to axially symmetric deformation is suggested along the Rh isotopic chain. These findings provide new insights into the structure of neutron-rich nuclei in the <italic>A</italic>&#8239;&#8764;&#8239;110 region and motivate further studies of exotic isotopes in this region to explore the interplay between triaxiality and shell evolution.

China

J.Z. Zhang

Germany

Z.Q. Chen

T. Qu

Y.K. Wang

Z.H. Li

H. Hua

P.W. Zhao

Japan

H. Watanabe

United Kingdom

G. Lorusso

C.X. Yuan

S. Nishimura

H. Baba

Italy

G. Benzoni

F. Browne

South Korea

K.Y. Chae

F.C.L. Crespi

P. Doornenbal

N. Fukuda

R. Gernhäuser

France

G. Gey

C.Y. Guo

N. Inabe

T. Isobe

D.X. Jiang

Y. Jin

United States

H.S. Jung

Spain

A. Jungclaus

D. Kameda

G.D. Kim

Y.K. Kim

I. Kojouharov

F.G. Kondev

T. Kubo

N. Kurz

Australia

G.J. Lane

X.Q. Li

J.L. Lou

D.W. Luo

A. Montaner-Pizá

K. Moschner

F. Naqvi

L. Ni

M. Niikura

H. Nishibata

A. Odahara

Belgium

R. Orlandi

Z. Patel

Zs. Podolyák

H. Sakurai

H. Schaffner

G.S. Simpson

P.-A Söderström

K. Steiger

T. Sumikama

H. Suzuki

H. Takeda

Hungary

J. Taprogge

A. Wendt

H.Y. Wu

J. Wu

C. Xu

Hong Kong

Z.Y. Xu

A. Yagi

Y.L. Ye

K. Yoshinaga

S.Q. Zhang

S.Y. Zhang

Z.X. Zhou

Shape evolution in neutron-rich Rh isotopes: First measurement of negative-parity isomers in 117,119Rh

Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

One compelling way to probe dark matter is by looking for its gravitational effects on black holes. Inspired by the study of Cardoso et al. (Phys. Rev. D 105, 6, L061501 (2022)) on black holes in galaxies, this work investigates static, spherically symmetric black holes surrounded by Dekel-Zhao-type dark matter halos and influenced by a quintessential field. By adopting a double power-law profile, we derive explicit expressions for the cumulative mass, tangential velocity, and the modified metric, providing a coherent description of the horizon structure and thermodynamic properties. Depending on the core density, the spacetime may feature multiple horizons or even a naked singularity. Our analysis of null geodesics reveals that both dark matter and quintessence significantly affect photon trajectories and the resulting black hole shadow. By combining theoretical modeling with EHT observations of Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>, we place constraints on the halo density and quintessence parameter, directly connecting them to observable features. However, a stability analysis of circular photon orbits confirms that the photon sphere is inherently unstable, with its location and sensitivity strongly influenced by the surrounding matter. Finally, we analyze how the impact parameter <math altimg='si39.svg'><mover accent='true'><mi>b</mi><mo>&#732;</mo></mover></math> shapes photon trajectories around a black hole, determining the bending of null geodesics, the photon sphere location, and the event horizon structure, thereby illustrating the influence of spacetime geometry on light paths. This work highlights the intricate interplay between dark matter, quintessence, and black hole observables, bridging theoretical predictions with astrophysical measurements.

South Africa

Azerbaijan

A. Errehymy

Null geodesics and shadows of Dekel-Zhao-type dark matter black holes with a quintessential field: Constraints from EHT observations of M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>

Time-dependent covariant density functional theory (TD-CDFT) combined with angular momentum projection is developed and applied to study multinucleon transfer (MNT) reactions, with a focus on the intrinsic angular momentum distributions of the final fragments. Using the illustrative reaction <math altimg='si23.svg'><msup><mrow /><mn>40</mn></msup></math>Ca + <math altimg='si24.svg'><msup><mrow /><mn>208</mn></msup></math>Pb across a range of impact parameters, we find that the MNT process generates broad distributions of intrinsic spins. These distributions arise from the conversion of relative orbital angular momentum into intrinsic spin due to frictional interactions between the colliding nuclei. Additionally, mutual information (entanglement Shannon entropy) is employed to analyze correlations between the intrinsic spins of the fragments.

D.D. Zhang

Croatia

D. Vretenar

T. Nikšić

J. Meng

Intrinsic spin distributions in multinucleon transfer reactions

Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

The shape of $^{286}$No is investigated with the relativistic density functional theory on a three-dimensional lattice space without any symmetry restriction in a microscopic and self-consistent way. It is found that the ground state of $^{286}$No has a pure non-axial octupole shape and coexists with a tetrahedral isomeric state. The energy difference between the two states is only 0.12 MeV, and they are separated by a potential barrier of about 0.5 MeV. The occurrence of the octupole correlations is analyzed with the evolution of the single-particle levels near the Fermi surface driven by the octupole deformations.

F.F. Xu

B. Li

P. Ring

Coexistence of pure octupole shapes in the superheavy nucleus No

The chirality in soft triaxial nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. Taking the puzzling chiral nucleus $^{106}$Ag as an example, the experimental energies of the observed nearly degenerate bands are well reproduced without any free parameters beyond the well-defined density functional. A novel chiral mode in soft triaxial nuclei is newly revealed from the microscopic dynamics of the total angular momentum. This opens a new research area for the study of chirality, particularly in relation to soft nuclear shapes.

Chiral dynamics in soft triaxial nuclei

A multi-task learning (MTL) framework, called gradient kernel ridge regression, for nuclear masses and separation energies is developed by introducing gradient kernel functions to the kernel ridge regression (KRR) approach. By taking the WS4 mass model as an example, the gradient KRR network is trained with the mass model residuals, i.e., deviations between experimental and theoretical values of masses and one-nucleon separation energies, to improve the accuracy of theoretical predictions. Significant improvements are achieved by the gradient KRR approach in both the interpolation and the extrapolation predictions of nuclear masses and separation energies. This demonstrates the advantage of the present MTL framework that integrates the information of nuclear masses and separation energies and improves the predictions for both of them.

X.H. Wu

Y.Y. Lu

Multi-task learning on nuclear masses and separation energies with the kernel ridge regression

The neutrinoless double-β (<math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>) decay and the double Gamow-Teller (DGT) transition are investigated with the state-of-the-art Relativistic Configuration-interaction Density functional theory. A strong linear correlation between the nuclear matrix elements (NMEs) of the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> decay and the DGT transition is demonstrated. This linear correlation is found to originate from the similarity of the leading-order term of the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>-decay operator and the DGT-transition one, as revealed by expanding the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>-decay operator in terms of the spherical harmonics. The present results provide a strong support to constrain the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>-decay NMEs through the double charge-exchange reactions.

Correlation between neutrinoless double- decay and double Gamow-Teller transitions

Nuclear level density is calculated with the combinatorial method based on the relativistic density functional theory including pairing correlations. The Strutinsky method is adopted to smooth the total state density in order to refine the prediction at low excitation energy. The impacts of pairing correlations and moments of inertia on the nuclear level density are discussed in detail. Taking <math><mmultiscripts><mrow><mi>Cd</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>112</mn></mrow></mmultiscripts></math> as an example, it is demonstrated that the nuclear level density based on the relativistic density functional PC-PK1 can reproduce the experimental data at the same level as or even better than the previous approaches.

X.F. Jiang

Nuclear level density from relativistic density functional theory and combinatorial method