In this Letter, I work out spin entanglement properties of neutron-proton scattering using the exact S-matrix, generalizing previous works based on S wave. The dependence of spin entanglement on momentum, scattering angle, and initial spin configuration is investigated for realistic nuclear forces, while low-energy properties of spin entanglement are analyzed within the framework of pionless effective field theory at leading order. New connections are found between spin entanglement and symmetry enhancement of strong interactions. These results lead to a more complete understanding of how spin entanglement is generated via neutron-proton interaction. They also lay the theoretical foundation for controllable production of entangled nucleon-nucleon pairs in future experiments.
The calculable $R$-matrix theory has been formulated successfully for regular boundary conditions with vanishing radial wave functions at the coordinate origins [P. Descouvemont and D. Baye, Rep. Prog. Phys. 73, 036301 (2010)]. We generalize the calculable $R$-matrix theory to the incoming-wave boundary condition (IWBC), which is widely used in theoretical studies of low-energy heavy-ion fusion reactions to simulate the strong absorption of incoming flux inside the Coulomb barriers. The generalized calculable $R$-matrix theory also provides a natural starting point to extend eigenvector continuation (EC) [D. Frame et al., Phys. Rev. Lett. 121, 032501 (2018)] to fusion observables. The $^{14}\mathrm{N}+^{12}\mathrm{C}$ fusion reaction is taken as an example to validate these new theoretical tools. Both local and nonlocal potentials are considered in numerical calculations. Our generalizations of the calculable $R$-matrix theory and EC are found to work well for IWBC.
Nuclear entanglement is a flagship in the interdisciplinary direction of nuclear physics and quantum information science. Spin entanglement, a special kind of nuclear entanglement, is ubiquitous in nuclear structures and dynamics. Based on the idea of quantum state tomography, the problem of experimental determination of spin entanglement of two-nucleon pure states is studied directly within the scope of nuclear physics. It is shown that the amount of spin entanglement can be obtained by measuring three spin polarizations of one nucleon in polarization experiments. The errors from imperfect preparation of nucleon pairs are also analyzed. This work not only complements the existing literature of nuclear entanglement but also provides new opportunities for nuclear physics with polarized particles.
We study the possibility to use the cluster-daughter overlap as a new probe of alpha-cluster formation in medium-mass and heavy even–even nuclei. We introduce a dimensionless parameter O, which is the ratio between the root-mean-square (rms) intercluster separation and the sum of rms point radii of the daughter nucleus and the alpha particle, to measure the degree of the cluster-daughter overlap quantitatively. By using this parameter, a large (small) cluster-daughter overlap between the alpha cluster and daughter nucleus corresponds to a small (large) O value. The alpha-cluster formation is shown explicitly, in the framework of the quartetting wave function approach, to be suppressed when the O parameter is small, and be favored when the O parameter is large. We then use this O parameter to explore systematically the landscape of alpha-cluster formation probabilities in medium-mass and heavy even–even nuclei, with O being calculated from experimentally measured charge radii. The trends of alpha-cluster formation probabilities are found to be generally consistent with previous studies. The effects of various shell closures on the alpha-cluster formation are identified, along with some hints on a possible subshell structure at N=106 along the Hg and Pb isotopic chains. The study here could be a useful complement to the traditional route to probe alpha-cluster formation in medium-mass and heavy even–even nuclei using alpha-decay data. Especially, it would be helpful in the cases where the target nucleus is stable against alpha decay or alpha-decay data are currently not available.
Coal gangue is the main solid waste in coal mining areas, and its annual emissions account for about 10% of coal production. The composition information of coal gangue is the basis of reasonable utilization of coal gangue, and according to the composition information of coal gangue, one can choose the appropriate application scene. The reasonable utilization of coal gangue can not only effectively alleviate the environmental problems in mining areas but also produce significant economic and social benefits. Chemical analysis techniques are the principal ones used in traditional coal gangue analysis; however, they are slow and expensive. Many researchers have used machine learning techniques to analyze the spectral data of coal gangue, primarily random forests (RFs), extreme learning machines (ELMs), and two-hidden-layer extreme learning machines (TELMs). However, these techniques are heavily reliant on the preprocessing of the spectral data. This research suggests a quick analysis approach for coal gangue based on thermal infrared spectroscopy and deep learning in light of the drawbacks of the aforementioned methodologies. The proposed deep learning model is named SR-TELM, which extracts spectral features using a convolutional neural network (CNN) consisting of a spatial attention mechanism and residual connections and implements content prediction with TELM as a regressor, which can effectively overcome the dependence on preprocessing. The usefulness and speed of SR-TELM in coal gangue analysis were demonstrated by comparing several models in order to verify the proposed coal gangue analysis model. The experimental findings show that, for the prediction tasks of moisture, ash, volatile matter, and fixed carbon content, respectively, the SR-TELM model attained an R2 of 0.947, 0.972, 0.967, and 0.981 and an RMSE of 0.274, 4.040, 1.567, and 2.557 with a test time of just 0.03 s. It offers a method for the analysis of coal gangue that is low cost, highly effective, and highly reliable.
The Maryland model is a critical theoretical model in quantum chaos. This model describes the motion of a spin-1/2 particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field. In this work, we propose the linearly delayed quantum relativistic Maryland model (LDQRMM) as a novel generalization of the original Maryland model and systematically study its physical properties. We derive the resonance and antiresonance conditions for the angular momentum spread. The “characteristic sum” is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters. In addition, different topological patterns emerge in the LDQRMM. It predicts some additions to the Anderson localization in the corresponding tight-binding systems. Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.
The density-dependent cluster model (DDCM) is one of the successful theoretical models for $\ensuremath{\alpha}$-decay studies. It gives a good description of the experimental $\ensuremath{\alpha}$-decay half-lives for a wide range of $\ensuremath{\alpha}$ emitters. Nuclear surface diffuseness, one important quantity in determining the nucleon density profiles, is extremely sensitive to deformation, Bohr, Mottelson et al. proposed an anisotropic feature of the surface diffuseness for the deformed nuclei. In this work, an improved version of the density-dependent cluster model, abbreviated as $\mathrm{DDCM}+$, is developed to optimize $\ensuremath{\alpha}$-decay calculations on half-lives, by accounting for the anisotropy and polarization effects of surface diffuseness due to nuclear deformation. Within a deformation-dependent diffuseness correction, the response of $\ensuremath{\alpha}$-decay dynamics to the diffuseness anisotropy is first investigated in detail. It demonstrates that such an anisotropic deformation-dependent diffuseness would change the shape of nucleon density profile and effective $\ensuremath{\alpha}$-core interactions, yielding longer calculated $\ensuremath{\alpha}$-decay half-lives, as well as suggesting larger estimated $\ensuremath{\alpha}$-preformation factors. The systematic calculations on $\ensuremath{\alpha}$-decay half-lives are subsequently performed for 157 even-even nuclei with $52\ensuremath{\le}Z\ensuremath{\le}118$, which reproduce the experimental data within an average factor of 1.88, and drastically reduce the root-mean-square deviations between theoretical results and experimental data by about $41.4%$ in contrast to conventional DDCM. Noticeably, the theoretical result of new isotope $^{214}\mathrm{U}$ [Zhang et al., Phys. Rev. Lett. 126, 152502 (2021)] given by $\mathrm{DDCM}+$ also shows good agreement with the latest reported experimental data, demonstrating the high reliability of the improved model. It is expected that this improved model could be useful for future experimental and theoretical studies of $\ensuremath{\alpha}$ decays.
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