Recently, resonance-like signals for 4 <italic>n</italic> system were reported by M. Duer et al. (2022) <cross-ref refid='br0040' id='crf0170'>[4]</cross-ref>. Here the properties of 3 <italic>n</italic> and 4 <italic>n</italic> systems are further investigated, where their artificial bound states confined by external wells are studied with tensor-optimized antisymmetrized molecular dynamics and possible resonances are extrapolated by inverse analytical continuation in the coupling constant method. The results agree with previous theoretical predictions and recent experimental data. However, evident dependence on external attraction is observed for the resultant resonances.

China

Niu Wan

Japan

Takayuki Myo

Hiroki Takemoto

Mengjiao Lyu

Qing Zhao

Hisashi Horiuchi

Masahiro Isaka

Akinobu Doté

Investigation on resonances for 3 <italic>n</italic> and 4 <italic>n</italic> systems using realistic nuclear interaction and inverse analytical continuation in the coupling constant method

This work introduces a new Control Neural Network (Ctrl.NN) method to uncover evidence of exotic quantum state, <italic>i.e.</italic>, the breathing modes in 3- <italic>&#945;</italic> resonant states of <sup>12</sup>C nucleus. We provide the most precise microscopic description to date for the <sup>12</sup>C energy spectrum, identify two new exotic breathing states, and uncover strong evidence that directly connects the recent experimental observations to the breathing modes. The Ctrl.NN method significantly simplifies numerical calculations of quantum systems under multiple constraints and offers a new perspective for solving the nuclear many-body problem.

Zheng Cheng

Hiroshi Toki

Zhongzhou Ren

Mengyun Mao

Wenlong You

Evidence for three- <italic>&#945;</italic> breathing modes uncovered by control neural network

We investigate the hypernuclear cluster states of <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>B</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>12</mn></mrow></mmultiscripts></math> using a neural-network-driven microscopic model. We extend the Control Neural Networks (Ctrl.NN) method and systematically calculate the positive-parity spectrum of <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>B</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>12</mn></mrow></mmultiscripts></math>. By incorporating <italic>sd</italic>-shell excitations and parity-coupling effects into the <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>B</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>12</mn></mrow></mmultiscripts></math> hypernuclear system, we reveal structural changes, including clustering effects and new configurations such as isosceles-triangle and <italic>&#945;</italic>- <italic>t</italic>- <italic>&#945;</italic> linear-chain structures. Furthermore, by comparing with experimental data, we identify that many peaks (#6 and #8) can be interpreted as <math altimg='si19.svg'><msub><mrow><mi>p</mi></mrow><mrow><mi mathvariant='normal'>&#923;</mi></mrow></msub></math> dominant states, which is consistent with shell-model predictions. Notably, based on our analysis of the excited states of <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>B</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>12</mn></mrow></mmultiscripts></math>, we propose possible candidates for previously unexplained or controversial experimental peaks.

Jiaqi Tian

Hypernuclear cluster states of <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>B</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>12</mn></mrow></mmultiscripts></math> unveiled through neural network-driven microscopic calculation

We investigate the Λ particle motion and cluster states of <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>9</mn><mo>−</mo><mn>11</mn></mrow></mmultiscripts></math> using a novel multiple cooling approach guided by the Control Neural Networks method (Ctrl.NN). The numerical results are well reproduced, and the Ctrl.NN method shows rapid convergence concerning the set of the basis states in comparison to traditional generator coordinate method (GCM) calculations. Taking advantage of this merit, we calculate ground state energies and rotational bands of <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>9</mn><mo>−</mo><mn>11</mn></mrow></mmultiscripts></math> which agree well with experimental observations. By analyzing the density distributions of the main basis, a slight short-range repulsive correlation between Λ particle and α clusters in directions perpendicular to the axis of the <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></math> core is revealed. The Λ particle presents a significant broad distribution as a consequence of this correlation, which we call an “analog π-orbit” structure. Furthermore, we prove that this correlation originates from the competition between kinetic energy and Λ-N interaction, as indicated by the energy curves for different configurations of <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>9</mn></mrow></mmultiscripts></math>. In the ground states of <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>10</mn></mrow></mmultiscripts></math> and <math><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>Λ</mi></mrow><mrow><mn>11</mn></mrow></mmultiscripts></math>, the Λ particle is confined in a cage-like structure of core nuclei formed by two α clusters and valence neutrons. These structures lead to the development of more compact Λ particle configurations, and the shrinkage of α-α relative distance is also well reproduced.

Changjian Yu

Lambda motion and cluster states of Predicted via Neural Networks Guided Microscopic Calculation

We propose a new approach to probe the spatial extension of the valence neutron orbital in the $^{9}$Be nucleus via the $^{9}$Be(<math><mi>p</mi><mo>,</mo><mi>p</mi><mi>n</mi></math>)$^{8}$Be knockout reaction. This property of the nuclear molecular orbital has not been established in previous experimental studies and divergence exists between the theoretical descriptions of $^{9}$Be from different perspectives, i.e., the antisymmetrized molecular dynamics and the container pictures of cluster dynamics. These pictures are represented by two different well-proven microscopic models, the antisymmetrized molecular dynamics (AMD) and Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave functions. The corresponding reduced width amplitudes (RWAs) in the $^{8}$Be+n channel are extracted from both the AMD and THSR wave functions, and they are found to describe drastically different valence-nucleon motion, which shows the theoretical ambiguity in describing the π-orbitals in $^{9}$Be. Using the RWAs as input, the physical observables of the $^{9}$Be(<math><mi>p</mi><mo>,</mo><mi>p</mi><mi>n</mi></math>)$^{8}$Be knockout reaction are predicted by the distorted-wave impulse approximation (DWIA) framework. The magnitudes of the triple-differential cross sections (TDX) are found to be highly sensitive to the RWA input. It is concluded that the $^{9}$Be(<math><mi>p</mi><mo>,</mo><mi>p</mi><mi>n</mi></math>)$^{8}$Be knockout reaction could provide a feasible probing for the subtle differences between several structure models manifesting through the spatial extension of the π-orbital in the $^{9}$Be nucleus.

Vietnam

Nguyen Tri Toan Phuc

Yohei Chiba

Kazuyuki Ogata

Manifestation of the divergence between antisymmetrized-molecular-dynamics and container pictures of Be via Be( , ) Be knockout reaction

High-momentum components of nuclei are essential for understanding the underlying inter-nucleon correlations in nuclei. We perform the comprehensive analysis for the origin of the high-momentum components of $^{4}$He in the framework of Tensor-optimized High-momentum Antisymmetrized Molecular Dynamics (TO-HMAMD), which is a completely variational approach as an ab initio theory starting from the bare nucleon-nucleon interaction. The analytical derivations are provided for the nucleon momentum distribution of the Antisymmetrized Momentum Dynamics (AMD) wave functions, with subtraction of center-of-mass motion. The nucleon momentum distribution for $^{4}$He is calculated by applying a new expansion technique to our ab initio wave function, and agrees with the values extracted from experimental data up to the high-momentum region. Fine-grained analysis is performed for the high-momentum components in $^{4}$He with respect to different nucleon correlations. Contributions from tensor, central with short-range, and many-body correlations are extracted from the nucleon momentum distributions. The manifestation of tensor correlation around 2 fm$^{−1}$ region is explicitly confirmed by comparing the momentum distributions predicted using different types of NN interactions with and without the tensor force.

Chang Xu

High-momentum components in the He nucleus caused by inter-nucleon correlations