176Lu is the key nucleus for understanding the evolution of planetary bodies in the solar system, and the temperature and nucleosynthesis of the <italic>s</italic> process, due to its very long terrestrial half-life <italic>T</italic> <inf>1/2</inf>&#8239;&#8776;&#8239;3.7&#8239;&#215;&#8239;10 10 years. The very long half-life is caused by two anomalous first-forbidden transitions from the <math altimg='si2.svg'><msup><mn>7</mn><mo>&#8722;</mo></msup></math> state with extremely large comparative half-life log <italic>ft</italic>&#8239;&#8776;&#8239;19 which have never been appeared in other cases of the existing nuclear databases. We analyze the underlying mechanism and reason for the anomaly in first-forbidden transitions of 176Lu for the first time, which is based on the projected shell model. It is found that the possible <italic>K</italic>-forbidden nature is indispensable for describing the two extremely weak first-forbidden transitions, and the transition strengths are very sensitive to the detailed configuration mixing and <italic>K</italic> mixing in the nuclear wave functions. The half-life of the <math altimg='si2.svg'><msup><mn>7</mn><mo>&#8722;</mo></msup></math> state is calculated to be <italic>T</italic> <inf>1/2</inf>&#8239;&#8776;&#8239;1.95&#8239;&#215;&#8239;10 10 years. The sensitive dependence of the stellar <math altimg='si1.svg'><msup><mi>&#946;</mi><mo>&#8722;</mo></msup></math>-decay rate of 176Lu on <italic>s</italic>-process temperature is discussed as well.

China

Jing-Wen Ran

Long-Jun Wang

Anomaly in first-forbidden transitions of 176Lu

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

The dineutron as a bound chargeless nucleus of two identical nucleons has been attracting attention for many decades. In addition to the study of the formation of a bound dineutron in the outgoing channel of specific nuclear reactions, cross-section estimates have been gaining interest as research targets. We used a traditional neutron activation technique to irradiate Lu samples followed by measurements of the induced activity with HPGe spectrometer in order to detect gamma-peaks of the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu reaction product when this reaction channel is not open for incident neutron energies. Based on two measurements of the instrumental gamma-ray spectra of Lu samples we reliably identified the presence of the 174 gLu isotope in the outgoing channel of the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu nuclear reaction. Also, the cross-section for this nuclear reaction was obtained and to be equal <math altimg='si1.svg'><mrow><mn>33</mn><mo>.</mo><msubsup><mn>5</mn><mrow><mo>&#8722;</mo><mn>6.7</mn></mrow><mrow><mo>+</mo><mn>7.0</mn></mrow></msubsup></mrow></math> mb. For the first time, the dineutron as a nuclearreaction product was indirectly detected via statistically significant observation of the induced activity of 174 gLu with a corresponding cross-section estimate.

Ukraine

Ihor Kadenko

Hungary

Barna Biró

Mihály Braun

András Fenyvesi

Kateryna Okopna

Nadiia Sakhno

Loránd Zakàny

Formation of bound dineutrons in the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu nuclear reaction and its cross-section

We revisit the proton emitter $^{149}$Lu utilizing the recently developed triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc). By incorporating the microscopic nuclear structure properties from the TRHBc theory into the WKB approximation, we successfully reproduce the measured proton-emission half-life of $^{149}$Lu within experimental uncertainties. A triaxial ground state characterized by (<math><mi>β</mi><mo>=</mo><mn>0.17</mn><mo>,</mo><mi>γ</mi><mo>=</mo><msup><mrow><mn>31</mn></mrow><mrow><mo>∘</mo></mrow></msup></math>) has been clarified for $^{149}$Lu. The inclusion of triaxiality significantly changes nuclear density distributions and potentials, which results in enhanced binding of both the nuclear system and the proton-emitting orbital. As a result, a slightly extended half-life for the proton emission of $^{149}$Lu is achieved after considering triaxial deformation degrees of freedom. The examination of the dependence of the decay width on triaxial deformation parameters highlights the significance of microscopic description of nuclear deformation beyond the proton dripline.

Qi Lu

Kai-Yuan Zhang

Shi-Sheng Zhang

Triaxial shape of the one-proton emitter Lu

One-proton radioactivity in $^{149}$Lu, the latest identified proton emitter, is studied in the Wentzel-Kramers-Brillouin (WKB) approach with the proton-nucleus potential extracted from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for the first time. The predicted half-life turns out to be consistent with the experimental measurement within uncertainties and (almost) independent of the density functionals in the DRHBc theory. Such a microscopic self-consistent calculation reveals that $^{149}$Lu is oblately deformed with a quadrupole deformation <math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≈</mo><mo>−</mo><mn>0.18</mn></math>, and rules out the possibility of a prolate quadrupole deformation suggested in the nonadiabatic quasiparticle model. We also check the validity of this approach in the description of $^{150,151}$Lu and their isomeric states. The deviations of the predicted half-lives from their experimental counterparts are mostly smaller than those of the theoretical studies without considering deformation effects. Furthermore, we predict $^{148}$Lu to be a more oblately deformed proton-emitter with a longer half-life than that of $^{149}$Lu, which can be checked in the future. Our studies show that the DRHBc + WKB approach provides a new alternative method to evaluate the half-lives of well-deformed proton emitters.

Yang Xiao

Si-Zhe Xu

Ru-You Zheng

Xiang-Xiang Sun

Li-Sheng Geng

One-proton emission from Lu in the DRHBc+WKB approach

Inspired by recent progresses in observations of the fully charmed tetraquark states by LHCb, CMS, and ATLAS collaborations, we perform a systematic study of the ground states and the first radial excitations of the S- and P-wave $$\textrm{cc}\bar{\textrm{c}}\bar{\textrm{c}}$$ <math> <mrow> <mtext>cc</mtext> <mover> <mrow> <mtext>c</mtext> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mtext>c</mtext> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> system. Their mass spectra, root mean square (r.m.s.) radii and radial density distributions are studied with the relativized quark model. The calculations show that there is no stable bound states for the fully charmed tetraquark states, and the r.m.s. radii of these tetraquark states are smaller than 1 fm. Our results support assigning X(6600) structure, M $$_{X(6600)}=6552\pm 10\pm 12$$ <math> <mrow> <msub> <mrow></mrow> <mrow> <mi>X</mi> <mo>(</mo> <mn>6600</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mn>6552</mn> <mo>±</mo> <mn>10</mn> <mo>±</mo> <mn>12</mn> </mrow> </math> MeV, as one of the $$0^{++}$$ <math> <msup> <mn>0</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math> (1S) and $$2^{++}$$ <math> <msup> <mn>2</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math> (1S) states or their mixtures. Another structure also named as X(6600) by CMS Collaboration, M $$_{X(6600)}=6.62\pm 0.03^{+0.02}_{-0.01}$$ <math> <mrow> <msub> <mrow></mrow> <mrow> <mi>X</mi> <mo>(</mo> <mn>6600</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mn>6.62</mn> <mo>±</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>03</mn> <mrow> <mo>-</mo> <mn>0.01</mn> </mrow> <mrow> <mo>+</mo> <mn>0.02</mn> </mrow> </msubsup> </mrow> </math> GeV, may arise from the lowest 1P states with $$J^{PC}=0^{-+}$$ <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </mrow> </math> , $$1^{-+}$$ <math> <msup> <mn>1</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </math> , and $$2^{-+}$$ <math> <msup> <mn>2</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </math> . The possible assignments for X(6900) include the $$0^{++}$$ <math> <msup> <mn>0</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math> (2S), $$2^{++}$$ <math> <msup> <mn>2</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math> (2S) states, and the highest 1P state with $$J^{PC}=0^{-+}$$ <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </mrow> </math> . As for X(7200), it can be interpreted as one of the highest 2P states with $$J^{PC}=0^{-+}$$ <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </mrow> </math> , $$1^{-+}$$ <math> <msup> <mn>1</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </math> , and $$2^{-+}$$ <math> <msup> <mn>2</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </math> , and the 3S states can not be completely excluded from the candidates.

Guo-Liang Yu

Zhen-Yu Li

Zhi-Gang Wang

Lu Jie

Yan Meng

The S- and P-wave fully charmed tetraquark states and their radial excitations

Motivated by great progresses in experiments in searching for the heavy baryons, we systematically analyze the mass spectra and root mean square radius of single heavy baryons <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>Q</mi></mrow></msub></math>, <math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>Q</mi></mrow></msub></math> and <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>Q</mi></mrow></msub></math>. The calculations of the mass spectra are carried out in the frame work of relativized quark model, where the baryon is regarded as a three-body system of quarks. Our results show that the mass of single heavy baryon with λ-mode is lower than those of the ρ-mode and λ-ρ mixing mode, which indicates that the lowest state is dominated by the λ-mode. Basing on this research, we systematically calculate the mass spectra and the root mean square radius of the baryons with λ excited mode. With these predicated mass spectra, the Regge trajectories in the (J, <math><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup></math>) plane are constructed, and the slopes, intercepts of the Regge trajectories are obtained by linear fitting. It is found that all available experimental data are well reproduced by model predictions and fit nicely to the constructed Regge trajectories.

Systematic analysis of single heavy baryons Λ , σ And ω

The quenching of the experimental spectroscopic factor for proton emission from the short-lived d3/2 isomeric state in 151 m Lu was a long-standing problem. In the present work, proton emission from this isomer has been reinvestigated in an experiment at the Accelerator Laboratory of the University of Jyväskylä. The proton-decay energy and half-life of this isomer were measured to be 1295(5) keV and 15.4(8) μs, respectively, in agreement with another recent study. These new experimental data can resolve the discrepancy in the spectroscopic factor calculated using the spherical WKB approximation. Using the R-matrix approach it is found that the proton formation probability indicates no significant hindrance for the proton decay of 151 m Lu.

F. Wang

B.H. Sun

United Kingdom

Z. Liu

R.D. Page

Sweden

C. Qi

Finland

C. Scholey

S.F. Ashley

L. Bianco

I.J. Cullen

Austria

I.G. Darby

S. Eeckhaudt

A.B. Garnsworthy

W. Gelletly

Spain

M.B. Gomez-Hornillos

T. Grahn

P.T. Greenlees

D.G. Jenkins

G.A. Jones

South Africa

P. Jones

D.T. Joss

R. Julin

S. Juutinen

S. Ketelhut

S. Khan

A. Kishada

M. Leino

Japan

M. Niikura

Belgium

M. Nyman

J. Pakarinen

S. Pietri

Z. Podolyak

P. Rahkila

S. Rigby

J. Saren

T. Shizuma

J. Sorri

S. Steer

J. Thomson

N.J. Thompson

J. Uusitalo

P.M. Walker

Netherlands

S. Williams

H.F. Zhang

W.Q. Zhang

L.H. Zhu

Spectroscopic factor and proton formation probability for the d 3/2 proton emitter 151 m Lu