Reliable calculations of nuclear binding energies by the Gaussian process of machine learning

Reliable calculations of nuclear binding energies are crucial for advancing the research of nuclear physics. Machine learning provides an innovative approach to exploring complex physical problems. In this study, the nuclear binding energies are modeled directly using a machine-learning method called the Gaussian process. First, the binding energies for 2238 nuclei with Z > 20 and N > 20 are calculated using the Gaussian process in a physically motivated feature space, yielding an average deviation of 0.046 MeV and a standard deviation of 0.066 MeV. The results show the good learning ability of the Gaussian process in the studies of binding energies. Then, the predictive power of the Gaussian process is studied by calculating the binding energies for 108 nuclei newly included in AME2020. The theoretical results are in good agreement with the experimental data, reflecting the good predictive power of the Gaussian process. Moreover, the α-decay energies for 1169 nuclei with 50 ≤ Z ≤ 110 are derived from the theoretical binding energies calculated using the Gaussian process. The average deviation and the standard deviation are, respectively, 0.047 MeV and 0.070 MeV. Noticeably, the calculated α-decay energies for the two new isotopes ^ (204 )Ac(Huang et al. Phys Lett B 834, 137484(2022)) and ^ (207) Th(Yang et al. Phys Rev C 105, L051302(2022)) agree well with the latest experimental data. These results demonstrate that the Gaussian process is reliable for the calculations of nuclear binding energies. Finally, the α-decay properties of some unknown actinide nuclei are predicted using the Gaussian process. The predicted results can be useful guides for future research on binding energies and α-decay properties.

Contributions of optimized tensor interactions on the binding energies of nuclei

The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting between proton h11=2 and g7=2 single-particle orbits along the Z=50 isotopes.With the optimized tensor interactions,the binding energies of spherical or weakly deformed nuclei with A=54-228 are studied systematically.The present results show that the global effect of tensor interaction is attractive and systematically increases the binding energies of all these nuclei and makes the nuclei more bound.The root mean squared deviation of the calculated binding energies from the experimental values is significantly improved by the optimized tensor interactions,and the contribution of the tensor interaction to the binding energy is estimated.

Binding energies of impurity states in strained wurtzite GaN/Al_xGa_(1-x)N heterojunctions with finitely thick potential barriers

Ground state binding energies of donor impurities in a strained wurtzite GaN/AlxGal_xN heterojunction with a po- tential barrier of finite thickness are investigated using a variational approach combined with a numerical computation. The built-in electric field due to the spontaneous and piezoelectric polarization, the strain modification due to the lattice mismatch near the interfaces, and the effects of ternary mixed crystals are all taken into account. It is found that the binding energies by using numerical wave functions are obviously greater than those by using variational wave functions when impurities are located in the channel near the interface of a heterojunction. Nevertheless, the binding energies using the former functions are obviously less than using the later functions when impurities are located in the channel far from an interface. The difference between our numerical method and the previous variational method is huge, showing that the former should be adopted in further work for the relevant problems. The binding energies each as a function of hydrostatic pressure are also calculated. But the change is unobvious in comparison with that obtained by the variational method.

On Dineutron and Deuteron Binding Energies

The binding energy of the deuteron is estimated from the scalar strong interaction hadron theory SSI. The predicted value is 7.7% lower than the measured value. Existence of a spin 1 dineutron with a binding energy 4/5 that of the deuteron or 1.78 MeV is predicted. This is verified by the dineutron, first observed in 2012, in 16Be decay. No free dineutrons are expected to exist in nature as they can decay into deuterons. These binding energies are limited by short range strong interaction internucleon forces but consist of long range electrostatic energies from quark charges.

Global Impact and Balancing Act:Deciphering the Effect of Fluorination on B 1s Binding Energies in Fluorinated h‑BN Nanosheets

X-ray photoelectron spectroscopy(XPS)is an important characterization tool in the pursuit of controllable fluorination of two-dimensional hexagonal boron nitride(h-BN).However,there is a lack of clear spectral interpretation,and seemingly conflicting measurements exist.To discern the structure−spectroscopy relation,we performed a comprehensive first-principles study on the boron 1s edge XPS of fluorinated h-BN(F-BN)nanosheets.By gradually introducing 1−6 fluorine atoms into different boron or nitrogen sites,we created various F-BN structures with doping ratios ranging from 1 to 6%.Our calculations reveal that fluorines landed at boron or nitrogen sites exert competitive effects on the B 1s binding energies(BEs),leading to red or blue shifts in different measurements.Our calculations affirmed the hypothesis that fluorination affects 1s BEs of all borons in theπ-conjugated system,opposing the transferability from h-BN to F-BN.Additionally,we observe that BE generally increases with higher fluorine concentration when both borons and nitrogens are nonexclusively fluorinated.These findings provide critical insights into how fluorination affects boron’s 1s BEs,contributing to a better understanding of fluorination functionalization processes in h-BN and its potential applications in materials science.

Binding Energy, Root Mean Square Radius and Magnetic Dipole Moment of the Triton Nucleus

The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.

Influence of binding energies of electrons on nuclear mass predictions

Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However, the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted from the theoretical mass predictions, the rms deviations of nuclear mass predictions with respect to the known data are increased by about 200 keV for nuclei with Z, N ~〉 8. Furthermore, by using the Coulomb energies between protons to absorb the binding energies of electrons, their influence on the rms deviations is significantly reduced to only about 10 keV for nuclei with Z, N ≥ 8. However, the binding energies of electrons are still important for the heavy nuclei, about 150 keV for nuclei around Z = 100 and up to about 500 keV for nuclei around Z = 120. Therefore, it is necessary to consider the binding energies of electrons to reliably predict the masses of heavy nuclei at an accuracy of hundreds of keV.

Binding and Adsorption Energies of Heavy Metal Ions with Hapli-Udic Argosol and Ferri-Udic Argosol Particles

Gibbs free binding energy and adsorption energy between cations and charged soil particles were used to evaluate the interactions between ions and soil particles. The distribution of Gibbs free adsorption energies could not be determined experimentally before the development of Wien effect measurements in dilute soil suspensions. In the current study, energy relationships between heavy metal ions and particles of Hapli-Udic Argosol （Alfisol） and Ferri-Udic Argosol were inferred from Wien effect measurements in dilute suspensions of homoionic soil particles （〈 2 μm） of the two soils, which were saturated with ions of five heavy metals, in deionized water. The mean Gibbs free binding energies of the heavy metal ions with Hapli-Udic Argosol and Ferri-Udic Argosol particles diminished in the order of Pb^2＋ 〉 Cd^2＋ 〉 Cu^2＋ 〉 Zn^2＋ 〉 Cr^3＋, where the range of binding energies for Hapli-Udic Argosol （7.25-9.32 kJ mol^-1） was similar to that for Ferri-Udic Argosol （7.43-9.35 kJ mol^-1）. The electrical field-dependent mean Gibbs free adsorption energies of these heavy metal ions for Hapli-Udic Argosol and for Ferri-Udic Argosol descended in the order： Cu^2＋ 〉 Cd2^＋ 〉 Pb^2＋ 〉 Zn^2＋ 〉 Cr^3＋, and Cd^2＋ 〉 Cu^2＋ 〉 Pb^2＋ 〉 Zn^2＋ 〉 Cr^3＋, respectively. The mean Gibbs free adsorption energies of Cu^2＋, Zn^2＋, Cd^2＋, Pb^2＋, and Cr^3＋ at a field strength of 200 kV cm^-1, for example, were in the range of 0.8-3.2 kJ mo1^-1 for the two soils.

Rapid and accurate evaluation of the binding energies and the individual N H…O=C, N H…N, C H…O=C, and C H…N interaction energies for hydrogen-bonded peptide-base complexes

The binding energies of thirty-six hydrogen-bonded peptide-base complexes, including the peptide backbone-ase complexes and amino acid side chain-base complexes, are evaluated using the analytic potential energy function established in our lab recently and compared with those obtained from MP2, AMBER99, OPLSAA/L, and CHARMM27 calculations. The comparison indicates that the analytic potential energy function yields the binding energies for these complexes as reasonable as MP2 does, much better than the force fields do. The individual N H…O=C, N H…N, C H…O=C, and C H…N attractive interaction energies and C=O…O=C, N H…H N, C H…H N, and C H…H C repulsive interaction energies, which cannot be easily obtained from ab initio calculations, are calculated using the dipole-dipole interaction term of the analytic potential energy function. The individual N H…O=C, C H…O=C, C H…N attractive interactions are about 5.3±1.8, 1.2±0.4, and 0.8 kcal/mol, respectively, the individual N H … N could be as strong as about 8.1 kcal/mol or as weak as 1.0 kcal/mol, while the individual C=O…O=C, N H…H N, C H…H N, and C H…H C repulsive interactions are about 1.8±1.1, 1.7±0.6, 0.6±0.3, and 0.35±0.15 kcal/mol. These data are helpful for the rational design of new strategies for molecular recognition or supramolecular assemblies.

Investigation of Nuclear Binding Energy and Charge Radius Based on Random Forest Algorithm

The random forest algorithm was applied to study the nuclear binding energy and charge radius.The regularized root-mean-square of error(RMSE)was proposed to avoid overfitting during the training of random forest.RMSE for nuclides with Z,N>7 is reduced to 0.816 MeV and 0.0200 fm compared with the six-term liquid drop model and a three-term nuclear charge radius formula,respectively.Specific interest is in the possible(sub)shells among the superheavy region,which is important for searching for new elements and the island of stability.The significance of shell features estimated by the so-called shapely additive explanation method suggests(Z,N)=(92,142)and(98,156)as possible subshells indicated by the binding energy.Because the present observed data is far from the N=184 shell,which is suggested by mean-field investigations,its shell effect is not predicted based on present training.The significance analysis of the nuclear charge radius suggests Z=92 and N=136 as possible subshells.The effect is verified by the shell-corrected nuclear charge radius model.

Binding Energy and Photoionization of Hydrogenic Impurities in GaAs/Ga_(1-x)Al_xAs Quantum Well Wires

The binding energy and the photon energy dependence of the photoionization cross-section are calculated for a hydrogenic impurity in GaAs/Ga 1-xAl xAs quantum well wires.The correlation between confined and non-confined direction of the wire in the variational wave function is taken into account.The results show that the photoionization cross-sections are affected by the width of the wire and that their magnitudes are larger than those in infinite potential quantum well wires.In comparison with previous's results,the variational wave function improves the binding energy and decreases the value of photoionization cross-sections of the hydrogenic impurities,which makes the results more reasonable.

Mechanism of inhibitor ADS-J1 and ADS-J2 binding to HIV-1 gp41

In order to analyze and explain the mechanism of the two small inhibitors （ADS-JI and ADS-J2） binding to HIV-1 gp41, a computational study is carried out to help identifying possible binding modes by docking these compounds onto the hydrophobic pocket on gp41 and characterize structures of binding complexes. The binding interactions of gp41-molecule and free energies of binding are obtained through molecular dynamics simulation and molecular mechanic/Poisson- Boitzmann surface area （ MM/PBSA ） calculation. Specific molecular interactions in the gp41-inhibitor complexes are identified. The present computational study complements the corresponding experimental investigation and helps establish a good starting point tbr further refinement of small molecular gp41 inhibitors.

XPS Studies on Electroless As-Deposited and Annealed Ni-P Films

Electroless deposition has been used to deposit Ni-P films on glass slides using the reducing agent sodium hypophosphite. This has been done with a purpose to use Ni-P films as back contact for silicon carbide radiation detectors. By keeping deposition time, temperature, pH and concentration of the precursor solution constant, the film deposition has been done. XPS studies were done to analyze the composition and stoichiometry of Ni-P thin films.

Calibration of Binding Energy Positions with C1s for XPS Results

The adventitious carbon located at 284.8 eV was used to calibrate samples without the carbon themselves.When the carbon is as a major part of the inorganic material,the adventitious carbon should be identified and used as the reference.There is no adventitious carbon on the surfaces of the polymer materials,so using C1s of the carbon in the polymer itself to calibrate the charging effect is reasonable.Furthermore,compared with gold and argon,a more practical and convenient method based on C1s is proposed to get the right positions for binding energy peaks.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3^+ Cluster

The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method of a modified arrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a. u at R = 1.55 a(0). The binding energy of He-3(+) with respect to He+He++He was calculated to be 0.1064 a.u. (about 2.89 eV). This means that the He-3(+) cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two helium atoms.

Formation Mechanism and Binding Energy for Body-Centered Cubic Structure of He^＋9 Cluster

The formation mechanism for the body-centered cubic structure of cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between the nuclei at the center and an apex of the body-centered cubic structure. The result of the calculation shows that the curve has a minimal energy . The binding energy of with respect to was calculated to be 0.8857 a.u. This means that the cluster ofmay be formed in the body-centered cubic structure of .

Correlation between catalytic activity of supported gold catalysts for carbon monoxide oxidation and metal–oxygen binding energy of the support metal oxides

The effect of a wide variety of metal oxide （MOx） supports has been discussed for CO oxidation on nanoparticulate gold catalysts. By using typical co‐precipitation and deposition–precipitation methods and under identical calcination conditions, supported gold catalysts were prepared on a wide variety of MOx supports, and the temperature for 50%conversion was measured to qualita‐tively evaluate the catalytic activities of these simple MOx and supported Au catalysts. Furthermore, the difference in these temperatures for the simple MOx compared to the supported Au catalysts is plotted against the metal–oxygen binding energies of the support MOx. A clear volcano‐like correla‐tion between the temperature difference and the metal–oxygen binding energies is observed. This correlation suggests that the use of MOx with appropriate metal–oxygen binding energies （300–500 kJ/atom O） greatly improves the catalytic activity of MOx by the deposition of Au NPs.

The binding energy of a hydrogenic impurity in self-assembled double quantum dots

The binding energy of a hydrogenic impurity in self-assembled double quantum dots is calculated via the finitedifference method. The variation in binding energy with donor position, structure parameters and external magnetic field is studied in detail. The results found are： （i） the binding energy has a complex behaviour due to coupling between the two dots; （ii） the binding energy is much larger when the donor is placed in the centre of one dot than in other positions; and （iii） the external magnetic field has different effects on the binding energy for different quantum-dot sizes or lateral confinements.

Formation Mechanism and Binding Energy for Body-Centred Regular Icosahedral Structure of Li_(13) Cluster

The formation mechanism for the body-centred regular icosahedral structure of Li13 cluster is proposed. The curve of the total energy versus the separation R between the nucleus at the centre and nuclei at the apexes for this structure of Li13 has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of-96.951 39 a.u. at R = 5.46ao. When R approaches to infinity, the total energy of thirteen lithium atoms has the value of-96.564 38 a.u. So the binding energy of Lii3 with respect to thirteen lithium atoms is 0.387 01 a.u. Therefore the binding energy per atom for Lii3 is 0.029 77 a.u. or 0.810 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, 0.494 eV for Li3, 0.7878 eV for Li4. 0.632 eV for Lis, and 0.674 eV for Liv calculated by us previously. This means that the Li13 cluster may be formed stably in a body-centred regular icosahedral structure with a greater binding energy.

Conformations and Metal Ion Affinities of Glutamine Binding with Alkali and Alkaline Earth Metal Cations： an ab initio Study

Conformations and reaction energetics are important for understanding the interactions be- tween biomolecules and metal ions. In this work, we report a systematic ab initio study on the conformations and metal ion affinities of glutamine （Gln） binding with alkali and alkaline earth metal ions. An efficient and reliable method of searching low energy conformations of metalated Gln is proposed and applied to the complexes of Gln.Gln.M^＋/＋＋（M＋/＋＋=Li^＋、Na^＋、K^＋、Rb^＋、Cs^＋、Be^＋＋、Mg^＋＋、Ca^＋＋、Sr^＋＋ and Ba^＋＋）.. In addition to all conformers known in literatures, many new important conformations are located, demonstrating the power of the new method and the necessity of the conformational search performed here. The metal coordination modes, relative energies, dipole moments, and equilibrium distributions of all important conformations of Gln.M^＋/＋＋ are calculated by the methods of B3LYP, BHandHLYP, and MP2. IR spectra and metalation enthalpies and free energies are also presented and compared with the available experiments. The results form an extensive database for systematic examination of the metalation properties of Gln.