Alpha clustering is an important dynamic in nuclear physics, with growing interest to its study in heavy nuclei in recent years. Theoretically, the microscopic cluster models taking nucleons as relevant degrees of freedom have been widely used to study <italic>&#945;</italic>-cluster structures in light nuclei. However, a straightforward application on same footing in heavy nuclei is obstructed by the complexity of handling numerous nucleons. As a simplified alternative, the macroscopic cluster models built upon cluster degrees of freedom are usually employed in heavy nuclei, though these approaches typically lose several critical structural details. In this work, we propose to study the <italic>&#945;</italic>-cluster structures within the framework of valence-space microscopic cluster model (VS-MCM), which is a hybrid between microscopic and macroscopic cluster models and inherits features from both models, making it capable to investigate the <italic>&#945;</italic>-cluster structures in heavy nuclei from a relatively microscopic viewpoint. In VS-MCM, the valence <italic>&#945;</italic> clusters are described by antisymmetrized microscopic wave functions, with single-particle orbits in core nuclei removed systematically from the model space via the Pauli projection to simulate the antisymmetrization between <italic>&#945;</italic> clusters and doubly magic cores. As a proof of principle, we apply the VS-MCM to study the <italic>&#945;</italic>-cluster structures in 20Ne and 44Ti at first, with the theoretical energy levels of the <math altimg='si1.svg'><msup><mrow><mi>K</mi></mrow><mrow><mi>&#960;</mi></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>&#177;</mo></mrow></msubsup></math> bands for 20Ne and 44Ti showing reasonable agreement with experimental data. These calculations lay the foundation for future applications of VS-MCM in general cluster structures across the nuclide chart, where more <italic>&#945;</italic> clusters and valence nucleons can exist outside the heavy doubly magic core, opening new avenues to study the <italic>&#945;</italic> and cluster decays in heavy nuclei microscopically.

China

Zhen Wang

Dong Bai

Zhongzhou Ren

Nuclear <italic>&#945;</italic>-cluster structures from valence-space microscopic cluster model

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 12C nucleus. We provide the most precise microscopic description to date for the 12C 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

Mengjiao Lyu

Japan

Takayuki Myo

Hisashi Horiuchi

Hiroshi Toki

Masahiro Isaka

Mengyun Mao

Hiroki Takemoto

Niu Wan

Wenlong You

Qing Zhao

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

The nuclear contact characterizes the nucleon-nucleon pairs in close proximity and serves as an important tool for studying the short-range correlations (SRCs) within atomic nuclei. While they have been extracted for selected nuclei, the investigation of their behavior across the nuclear chart remains limited. Very recently, Yankovich, Pazy, and Barnea have proposed a set of universal laws (YPB laws) to describe the correlation between nuclear contacts and nuclear radii and tested their laws for a small number of nuclei by using the Woods-Saxon mean-field model Yankovich et al. (2021) <cross-ref refid='br0320' id='crf0420'>[32]</cross-ref>. In this Letter, we extend their study to a majority part of the nuclear chart within the framework of the Skyrme Hartree-Fock-Bogolyubov model, which incorporates several essential beyond-mean-field features and offers a more accurate description of the bulk properties of atomic nuclei. Our results suggest that the YPB laws hold as a good approximation for different nuclear mass regions, with minor deviations attributed to, e.g., isospin-breaking effects. Our work lays a firm foundation for future applications of the YPB laws in finite nuclei and provides new evidence for the long-range nature of the relative abundance of short-range pairs.

Tongqi Liang

Universal laws for nuclear contacts

Nucleon-nucleon short-range correlations (SRCs) describe the formation of nucleon pairs with high-momentum components, representing an essential issue in nuclear physics, yet their implications for inspiral gravitational waves remain underexplored. In this study, we employ three different nucleon-nucleon SRC models in neutron star interiors to assess their effects on gravitational waves during binary neutron star (BNS) inspiral phase. Our findings indicate that SRC-affected BNS systems exhibit lower gravitational wave frequencies, with a characteristic reduction of approximately 200 Hz compared to the traditional BNS systems. Additionally, SRCs appear to accelerate the BNS inspiral process, leading to a shorter retarded time and notable deviation in the gravitational waveform. These results underscore the critical role of SRC in shaping the features of inspiral gravitational waves and propose that inspiral gravitational waves could potentially serve as an effective probe for detecting SRC phenomena within neutron stars.

Bin Hong

Nucleon-nucleon short-range correlations: A hidden driver in binary neutron star inspiral gravitational waves

Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling, standard quantum computing cannot solve for complex eigenvalues directly. Therefore, it is necessary to embed the non-Hermitian operator into a larger dimensional unitary operator. Additionally, for the case of two basis vectors, we improve the traditional direct measurement method and optimize the quantum circuit. Ultimately, using the <math><mi>α</mi><mo>+</mo><mi>α</mi></math> system as an example, we obtain the complex eigenenergies from the quantum computer that are consistent with those obtained from direct Hamiltonian diagonalization.

Hantao Zhang

Quantum computing for extracting nuclear resonances

Gravitational waves from binary neutron star merger events have shown unparalleled advantages in deciphering the stellar internal structure, yet it remains underexplored to seek clues about kaon meson condensations inside massive neutron stars through these events. To address this gap, this study examines the binary star inspiral processes with kaon meson condensations, employing various kaon meson potential wells to probe unique imprints in the inspiral gravitational waves. Our analysis reveals that the inspiral process of kaon meson condensation binary stars exhibits lower gravitational wave frequencies and shorter retarded times compared to traditional neutron stars. Furthermore, a deeper kaon meson potential well in these systems further shortens the inspiral duration time, resulting in distinctive gravitational waveforms and notable orbital phase deviations. These findings underscore the pivotal role of kaon meson condensations in modulating the inspiral gravitational waves, suggesting the inspiral gravitational waves could serve as a powerful tool for probing potential signals of kaon mesons within neutron stars.

Probing kaon meson condensations through gravitational waves during neutron star inspiral phases

We present a novel scattering emulator utilizing the complex scaling method to enhance nuclear reaction analysis. This approach leverages a single set of reduced bases, allowing for efficient and simultaneous emulation across multiple channels and potential parameters, significantly reducing computational storage and accelerating calculations. Demonstrated through n+$^{40}$Ca and $^{11}$Be+$^{64}$Zn elastic scattering, our method achieves high accuracy and efficiency. This emulator exhibits stable and reliable performance without anomalies inherent in other techniques, showcasing its robustness.

Junzhe Liu

Jin Lei

A complex scaling method for efficient and accurate scattering emulation in nuclear reactions

Nuclear contact is a key quantity to describe the nucleon-nucleon short-range correlations (SRCs). While they have been determined by electron scattering experiments for selected stable nuclei, nuclear contacts are largely unknown for unstable nuclei. In this work, we study nuclear contacts for a number of nuclei in the vicinity of the doubly magic $^{132}$Sn from the theoretical perspective, with special emphasis on unstable nuclei. We find that the proton-proton contact generally gets suppressed by the excess neutrons for the Sn isotopes, resembling the suppression of α-cluster formation reported recently for the same isotopic chain (J. Tanaka et al., 2021 [46]). This might suggest a hidden universal aspect of SRCs and α clustering, two different kinds of nuclear correlations. Moreover, we reveal a model-independent correlation between the proton-proton contact and the root-mean-square radius of proton density distributions for Sn isotopes. Meanwhile, a linear relation is found between the proton-proton contact and the proton number for the <math><mi>N</mi><mo>=</mo><mn>82</mn></math> isotones. Our results can be helpful for future experimental studies of SRCs in unstable nuclei at advanced facilities worldwide.

Nuclear contacts of unstable nuclei

The trap method has been successfully applied in the nuclear community to address scattering problems involving particles interacting through real potentials. However, many situations require dealing with the complex potential that includes an imaginary part, which is incorporated to describe the absorption effect, annihilation effect and so on. In this letter, we propose a novel method based on the analytic continuation to deal with the complex potentials in the trap method. The reliability of the method is validated using an example of antinucleon-nucleon complex spherical well scattering. This work lays the key foundation for future ab initio studies on antinucleon scattering process based on the trap method.

Harmonic trap method for complex short-range potentials

The trap method provides a novel way to extract phase shifts of neutral-particle scattering from bound-state calculations. It has been adopted successfully in several ab initio calculations to study neutron-nucleus scattering, where there is no long-range Coulomb interaction between the target and projectile. How to incorporate the effects of Coulomb interaction is a crucial problem in the trap method. In this Letter, we examine the robustness of the new proposed Coulomb-corrected Busch-Englert-Rzażewski-Wilkens (BERW) formula Guo (2021) [25] by taking proton-proton scattering as the test ground. While the numerical results are generally well consistent with conventional methods, a number of anomalous scattering energies are identified, where the Coulomb-corrected BERW formula gives less satisfactory results. The underlying theoretical reasons are analyzed in depth, which contributes to a more complete understanding of the applicable scope of the Coulomb-corrected BERW formula. Our study lays the key foundation for future ab initio studies of scattering processes between proton and light nuclei based on the trap method.