Theoretical uncertainties of(d,^(3)He)and(^(3)He,d)reactions owing to the uncertainties of optical model potentials

The theoretical uncertainties of single proton transfer cross sections of the(^(3)He,d)and(d,^(3)He)reactions,owing to the uncertainties of the entrance-and exit-channel optical model potentials,are examined with the^(30)Si(^(3)He,d)^(31)P,^(13)B(d,^(3)He)^(12)Be,and^(34)S(^(3)He,d)^(35)Cl reactions at incident energies of 25,46,and 25 MeV,respectively,within the framework of the distorted wave Born approximation.The differential cross sections at the first peaks in the angular distributions of these reactions are found to have uncertainties of approximately 5%,owing to the uncertainties in the optical model potentials from 20,000 calculations of randomly sampled parameters.This amount of uncertainty is found to be nearly independent of the angular momentum transfer and the target masses within the studied range of incident energies.Uncertainties in the single proton spectroscopic factors obtained by matching the theoretical and experimental cross sections at different scattering angles are also discussed.

The Nucleon-Actinide Global Optical Model Potential Below 300 MeV

A set of new global phenomenological optical model potential parameters has been obtained in the mass range of target nuclei 220≤A≤260 with incident energies below 300 MeV, by simultaneously fitting the experimental data of 232Th and 23Su, and these potential parameters are analyzed and used to calculate the reaction cross sections, energy spectra and double differ- ential cross sections for p＋232Th reaction. Comparison of calculated results using these potential parameters with available experimental data shows that the present form of global optical model potential could reproduce experimental data for both the neutron and the proton.

Systematic investigation of nucleon optical model potentials in(p,d)transfer reactions

The consistent three-body model reaction methodology(TBMRM)proposed by J.Lee et al.[Phys.Rev.C 69,064313(2004);Phys.Rev.C 73,044608(2006);Phys.Rev.C 75,064320(2007)],which includes adopting the simple zero-range adiabatic wave approximation,constraining the single-particle potentials using modern Hartree-Fock calculations,and using global nucleon optical model potential(OMP)geometries,are widely applied in systematic studies of transfer reactions.In this study,we investigate the influence of different nucleon OMPs in extracting spectroscopic factors(SFs)from(p,d)reactions.Our study covers 32 sets of angular distribution data of(p,d)reactions on four targets and a large range of incident energies(20-200 MeV/nucleon).This study uses two semi-microscopic nucleon OMPs,i.e.,Jeukenne,Lejeune,and Mahaux(JLM)[Phys.Rev.C 16,80(1977);Phys.Rev.C 58,1118(1998)]and CTOM[Phys.Rev.C 94,034606(2016)],and a pure microscopic nucleon potential,i.e.,WLH[Phys.Rev.Lett.127,182502(2021)].The results are compared with those using the phenomenological global optical potential KD02[Nucl.Phys.A 713,231(2003)].We find that the incident energy dependence of spectroscopic factors extracted from(p,d)reactions is evidently suppressed when microscopic OMPs are employed for ^(12)C,^(28)Si,and 40Ca.In addition,spectroscopic factors extracted using the systematic microscopic optical potential CTOM based on the Dirac-Brueckner-Hartree-Fock theory are more in line with the results obtained from(e,e′p)measurements,except for 16O and ^(40)Ca at high energies(>100 MeV),necessitating an exact treatment of double-magic nuclei.The results obtained by using the pure microscopic optical potential,WLH,based on the EFT theory show the same trend as those of CTOM but are generally higher.The JLM potential,which relies on simplified nuclear matter calculations with old-fashioned bare interactions,produces results that are very similar to those of the phenomenological potential KD02.Our results indicate that modern microscopic OMPs are reliable tools for probing the nuclear structure using transfer reactions across a wide energy range.

Systematic study of global optical model potentials in(d,p)transfer reactions

In the T-matrix form of the transfer reaction,the optical model potentials(OMPs)are used to compute the scattering wave function and transition operator.For most cases,the elastic scattering cross sections,normally used to generate the OMPs,are not directly given in the same experiment.Then,the global OMPs,which fit the experimental data over a broad mass and energy range,are widely used in the theoretical calculations.Different sets of global OMPs with different parameter sets can reproduce the scattering cross section equally well within the uncertainty.Here,we apply different global OMPs to calculate the(differential)cross sections of(d,p)transfer reactions on the target nuclei^(12)C,^(48)Ca,^(124)Sn,and^(208)Pb at different energies.The results demonstrate that the effects of deuteron and nucleon global OMPs on transfer(differential)cross sections vary with energy and target mass.Furthermore,the influences of the spin-orbit coupling term of deuteron and nucleon global OMPs on the transfer cross sections are not negligible.

Application of a microscopic optical potential of chiral effective field theory in (p, d) transfer reactions

The microscopic global nucleon–nucleus optical model potential(OMP)proposed by Whitehead,Lim,and Holt,the WLH potential(Whitehead et al.,Phys Rev Lett 127:182502,2021),which was constructed in the framework of many-body per-turbation theory with state-of-the-art nuclear interactions from chiral effective field theory(EFT),was tested with(p,d)transfer reactions calculated using adiabatic wave approximation.The target nuclei included both stable and unstable nuclei,and the incident energies reached 200 MeV.The results were compared with experimental data and predictions using the phenomenological global optical potential of Koning and Delaroche,the KD02 potential.Overall,we found that the micro-scopic WLH potential described the(p,d)reaction angular distributions similarly to the phenomenological KD02 potential;however,the former was slightly better than the latter for radioactive targets.On average,the obtained spectroscopic factors(SFs)using both microscopic and phenomenological potentials were similar when the incident energies were below approxi-mately 120 MeV.However,their difference tended to increase at higher incident energies,which was particularly apparent for the doubly magic target nucleus 40Ca.

An accurate analytical surface potential model of heterojunction tunnel FET

Based on the accurate and efficient thermal injection method, we develop a fully analytical surface potential model for the heterojunction tunnel field-effect transistor(H-TFET). This model accounts for both the effects of source depletion and inversion charge, which are the key factors influencing the charge, capacitance and current in H-TFET. The accuracy of the model is validated against TCAD simulation and is greatly improved in comparison with the conventional model based on Maxwell–Boltzmann approximation. Furthermore, the dependences of the surface potential and electric field on biases are well predicted and thoroughly analyzed.

Helium-3 global optical model potential with energies below 250 MeV

A new set of global phenomenological optical model potential parameters has been obtained for helium-3 projectile, by simultaneously fitting the experimental data of helium-3 total reaction cross sections and elastic scattering angular distributions in the mass range of target nuclei 20〈〈A〈209 at incident energies below 250 MeV. A comparison has been made between the extracted helium-3 global optical model potential parameters and the existing ones. The calculated results of total reaction cross sections and elastic scattering angular distributions are also agreement. compared with experimental data with their satisfactory

What kind of optical model potentials should be used for deuteron stripping reactions?

This paper presents the results of a study that compares CTOM, a microscopic optical model potential(OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP.The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and(d,p) transfer reactions involving14C,36S, and58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from(e,e′p) reactions as well as with more recent(p,2p) and(p,pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP;accordingly,phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.

Test of the notch technique for determining the radial sensitivity of the optical model potential

Detailed investigations on the notch technique are performed on ideal data generated by the optical model potential parameters extracted from the 16O＋208spb system at the laboratory energy of 129.5 MeV, to study the sensitivities of this technique to the model parameters as well as the experimental data. It is found that for the perturbation parameters, a sufficiently large reduced fraction and an appropriate small perturbation width are necessary to determine the accurate radial sensitivity; while for the potential parameters, almost no dependence was observed. For the experimental measurements, the number of data points has little influence for heavy target systems, and the relative inner information of the nuclear potential can be derived when the measurement is extended to a lower cross section.

Two-colour coherent control of multiphoton ionization： a comparison between long-range and short-range potential model atoms

Using the numerical solution of the time-dependent SchrSdinger equation of a one-dimensional model atom in a two-colour laser field, we have investigated the effects of the potential models on coherent control of atomic multiphoton ionization. It is found that the photoelectron spectra are obviously different for the long-range （Coulomb-like） and short-range （with no excited bound states） potential model atoms, which are produced by two-colour coherent control of atomic multiphoton ionization in a few laser cycles. Our results indicate that two-colour coherent control of atomic multiphoton ionization can be observed in simulations, depending on the choice of the model potentials.

Global optical model potential describing 12C-nucleus elastic scattering

We construct a new global optical model potential to describe the elastic scattering of 12C.The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are considered below 200 MeV within the framework of the optical model.The results calculated using the derived global optical potential are then compared with the existing experimental data.The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges,within which the global potential parameters are determined,and reasonable results are also obtained.

Structure and Properties of Hydrotalcite Using Electrostatic Potential Energy Model

The electrostatic potential energy model of hydrotalcites was based on the theory of crystallography. The anionic potential energy of MgAl-hydrotalcites, with 20 layers and 2107 anions per layer, was calculated, and the anionic stability of the hydrotalcites was investigated. The charge density of the layer and the distance between the adjacent anions varied with the molar ratio of Al^3＋/（Mg^2＋ ＋ Al^3＋）. Anionic potential energy depended on the charge and size of the anions. Calculation results remained consistent with thermal stability and the ion exchange ability reported. This model is able to predict anionic stability of the hydrotalcites.

A Fully Flexible Potential Model for Carbon Dioxide

A fully flexible potential model for carbon dioxide has been developed to predict the vapor-liquid coexistence properties using the NVT-Gibbs ensemble Monte Carlo technique(GEMC).The average absolute deviation between our simulation and the literature experimental data for saturated liquid and vapor densities is 0.3% and 2.0%,respectively.Compared with the experimental data,our calculated results of critical properties(7.39 MPa,304.04 K,and 0.4679 g?cm-3) are acceptable and are better than those from the rescaling the potential parameters of elementary physical model(EPM2).The agreement of our simulated densities of supercritical carbon dioxide with the experimental data is acceptable in a wide range of pressure and temperature.The radial distribution function estimated at the supercritical conditions suggests that the carbon dioxide is a nonlinear molecule with the C O bond length of 0.117 nm and the O C O bond angle of 176.4°,which are consistent with Car-Parrinello molecular-dynamics(CPMD),whereas the EPM2 model shows large deviation at supercritical state.The predicted self-diffusion coefficients are in agreement with the experiments.

Comparison of Ten Potential Evapotranspiration Models and Their Attribution Analyses for Ten Chinese Drainage Basins

Potential evapotranspiration(EPET)is usually calculated by empirical methods from surface meteorological variables,such as temperature,radiation and wind speed.The in-situ measured pan evaporation(ETpan)can also be used as a proxy for EPET.In this study,EPET values computed from ten models are compared with observed ETpan data in ten Chinese river basins for the period 1961−2013.The daily observed meteorological variables at 2267 stations are used as the input to those models,and a ranking scheme is applied to rank the statistical quantities(ratio of standard deviations,correlation coefficient,and ratio of trends)between ETpan and modeled EPET in different river basins.There are large deviations between the modeled EPET and the ETpan in both the magnitude and the annual trend at most stations.In eight of the basins(except for Southeast and Southwest China),ETpan shows decreasing trends with magnitudes ranging between−0.01 mm d−1 yr−1 and−0.03 mm d−1 yr−1,while the decreasing trends in modeled EPET are less than−0.01 mm d−1 yr−1.Inter comparisons among different models in different river basins suggest that PETHam1 is the best model in the Pearl River basin,PETHam2 outperforms other models in the Huaihe River,Yangtze River and Yellow River basins,and PETFAO is the best model for the remaining basins.Sensitivity analyses reveal that wind speed and sunshine duration are two important factors for decreasing EPET in most basins except in Southeast and Southwest China.The increasing EPET trend in Southeast China is mainly attributed to the reduced relative humidity.

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

A Potential Model for Cylindrical Pores

An analytical potential for cylindrical pores has been derived by introducing a variational method into the integration for the calculation of the interaction energy between the wall molecules and a test molecule, all of which are represented by Lennard-Jones potential. The model proposed gives good fit to the results from the cylindrical surface model and the pseudoatom model. To test the potential proposed rigorously, we have carried out grand canonical ensemble Monte Carlo(GCMC) simulation of nitrogen in the MCM-41 pore at 77 K, and compared the simulated adsorption isotherm with the experimental data reported in the literature. The simulated isotherm from our model is in almost qualitative agreement with experiment. Consequently, the model proposed provides an explicit and accurate description of cylindrical pores represented by the Lennard-Jones potential. Moreover, the model can be easily applied to a variety of cylindrical pores, ranging from cylindrical surface to finite thickness walls, in both theoretical studies and computer simulations.

πN Elastic Scattering and Resonances in Quark Potential Model

The quark potential model is used to investigate the low-energy elastic scattering of πN system. The model potential consists of the t-channel and s-channel one-gluon exchange potentials and the harmonic oscillator confining potential. By means of the resonating group method, a nonlocal effective potential for the πN system is derived from the interquark potentials and used to calculate the πN elastic scattering phase shifts. By considering the effect of QCD renormalization, the suppression of the spin-orbital coupling and the contribution of the color octet of the clusters （qq） and （qqq）, the numerical results are in fairly good agreement with the experimental data. The same model and method are employed to investigate the possible πN resonances. For this purpose, the resonating group equation is transformed into a standard Schrodinger equation in which the nonlocal effective πN interaction potential is included. Solving the Schrodinger equation by the variational method, we are able to reproduce the masses of some currently concerned πN resonances.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Astrophysical S-factor and reaction rate for 15N(p,γ)16O within the modified potential cluster model

We study radiative p^(15)N capture on the ground state of ^(16)O at stellar energies within the framework of a modified potential cluster model(MPCM)with forbidden states,including low-lying resonances.The investigation of the ^(15)N(p,γ0)^(16)O reaction includes the consideration of ^(3)S_(1) resonances due to E1 transitions and the contribution of the ^(3)P_(1) scattering wave in the p+^(15)N channel due to the ^(3)P_(1)→^(3)P_(0)M1 transition.We calculated the astrophysical low-energy S-factor,and the extrapolated S(0)turned out to be within 34.7−40.4 keV·b.The important role of the asymptotic constant(AC)for the ^(15)N(p,γ0)16O process with interfering ^(3)S_(1)(312)and ^(3)S_(1)(962)resonances is elucidated.A comparison of our calculation for the S-factor with existing experimental and theoretical data is addressed,and a reasonable agreement is found.The reaction rate is calculated and compared with the existing rates.It has negligible dependence on the variation of AC but shows a strong impact of the interference of ^(3)S_(1)(312)and ^(3)S_(1)(962)resonances in reference to the CNO Gamow windows,especially at low temperatures.We estimate the contribution of cascade transitions to the reaction rate based on the exclusive experimental data from Phys.Rev.C.85,065810(2012).The reaction rate enhancement due to the cascade transitions is observed from T_(9)>0.3 and reaches the maximum factor~1.3 at T_(9)=1.3.We present the Gamow energy window and a comparison of rates for radiative proton capture reactions ^(12)N(p,γ)^(13)O,^(13)N(p,γ)^(14)O,^(14)N(p,γ)^(15)O,and ^(15)N(p,γ)^(16)O obtained in the framework of the MPCM and provide the temperature windows,prevalence,and significance of each process.