Improved nuclear mass formula with an additional term from the Fermi gas model

Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the complexity of atomic nuclei and nonperturbative strong interactions,conventional physical models cannot completely describe nuclear binding energies.In this study,the mass formula was improved by considering an additional term from the Fermi gas model.All nuclear masses in the Atomic Mass Evaluation Database were reproduced with a root-mean-square deviation(RMSD)of -1.86 MeV(1.92 MeV).The new mass formula exhibits good performance in the neutron-rich nuclear region.The RMSD decreases to 0.393 MeV when the ratio of the neutron number to the proton number is≥1.6.

Machine learning the nuclear mass

Background:The masses of-2500 nuclei have been measured experimentally;however,>7000 isotopes are predicted to exist in the nuclear landscape from H(Z=1)to Og(Z=118)based on various theoretical calculations.Exploring the mass of the remaining isotopes is a popular topic in nuclear physics.Machine learning has served as a powerful tool for learning complex representations of big data in many fields.Purpose:We use Light Gradient Boosting Machine(LightGBM),which is a highly efficient machine learning algorithm,to predict the masses of unknown nuclei and to explore the nuclear landscape on the neutron-rich side from learning the measured nuclear masses.Methods:Several characteristic quantities(e.g.,mass number and proton number)are fed into the LightGBM algorithm to mimic the patterns of the residual δ(Z,A)between the experimental binding energy and the theoret-ical one given by the liquid-drop model(LDM),Duflo–Zucker(DZ,also dubbed DZ28)mass model,finite-range droplet model(FRDM,also dubbed FRDM2012),as well as the Weizsacker–Skyrme(WS4)model to refine these mass models.Results:By using the experimental data of 80%of known nuclei as the training dataset,the root mean square devia-tions(RMSDs)between the predicted and the experimental binding energy of the remaining 20%are approximately 0.234±0.022,0.213±0.018,0.170±0.011,and 0.222±0.016 MeV for the LightGBM-refined LDM,DZ model,WS4 model,and FRDM,respectively.These values are approximately 90%,65%,40%,and 60%smaller than those of the corresponding origin mass models.The RMSD for 66 newly measured nuclei that appeared in AME2020 was also significantly improved.The one-neutron and two-neutron separation energies predicted by these refined models are consistent with several theoretical predictions based on various physical models.In addition,the two-neutron separation energies of several newly measured nuclei(e.g.,some isotopes of Ca,Ti,Pm,and Sm)pre-dicted with LightGBM-refined mass models are also in good agreement with the latest experimental data.Conclusions:LightGBM can be used to refine theoretical nuclear mass models and predict the binding energy of unknown nuclei.Moreover,the correlation between the input characteristic quantities and the output can be inter-preted by SHapley additive exPlanations(a popular explainable artificial intelligence tool),which may provide new insights for developing theoretical nuclear mass models.

Modification of Even-A Nuclear Mass Formula

In this paper we obtain an empirical mass formula of even-A nuclei based on residual proton-neutron interactions. The root-mean-squared deviation (RMSD) from experimental data is at an accuracy of about 150 Kev. While for heavy nuclei, we give another formula that fits the experimental data better (RMSD ≈ 119 Kev). We have successfully described the experimental data of nuclear masses and predicted some unknown masses (like 200Ir not involved in AME2003, the deviation of our predicted masses from the value in AME2012 is only about 82 keV). The predictive power of our formula is more competitive than other mass models.

Principal components of nuclear mass models

Principal component analysis(PCA)is employed to extract the principal components(PCs)present in nuclear mass models for the first time.The effects from different nuclear mass models are reintegrated and reorganized in the extracted PCs.These PCs are recombined to build new mass models,which achieve better accuracy than the original theoretical mass models.This comparison indicates that using the PCA approach,the effects contained in different mass models can be collaborated to improve nuclear mass predictions.

Nuclear mass predictions based on a deep neural network and finite-range droplet model(2012)

A neural network with two hidden layers is developed for nuclear mass prediction,based on the finiterange droplet model(FRDM12).Different hyperparameters,including the number of hidden units,choice of activation functions,initializers,and learning rates,are adjusted explicitly and systematically.The resulting mass predictions are achieved by averaging the predictions given by several different sets of hyperparameters with different regularizers and seed numbers.This can provide not only the average values of mass predictions but also reliable estimations in the mass prediction uncertainties.The overall root-mean-square deviations of nuclear mass are reduced from 0.603 MeV for the FRDM12 model to 0.200 MeV and 0.232 MeV for the training and validation sets,respectively.

Comparative study of nuclear masses in the relativistic mean-field model

With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field model,the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA,especially for the neutron-deficient nuclei.The corresponding rms deviation with respect to the known masses falls to 1.4 MeV.Furthermore,it is found that the RMF mass model better describes the nuclei with large deformations.The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93,crossing the 1 MeV accuracy threshold for the PC-PK1,which may indicate the new model is more suitable for those largely-deformed nuclei.In addition,the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.

High precision nuclear mass predictions towards a hundred kilo-electron-volt accuracy

Mass is a fundamental property and an important fingerprint of atomic nucleus.It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy elements synthesized in stellar explosions.Nuclear physicists have been attempting at developing a precise,reliable,and predictive nuclear model that is suitable for the whole nuclear chart,while this still remains a great challenge even in recent days.Here we employ the Fourier spectral analysis to examine the deviations of nuclear mass predictions to the experimental data and to present a novel way for accurate nuclear mass predictions.In this analysis,we map the mass deviations from the space of nucleon number to its conjugate space of frequency,and are able to pin down the main contributions to the model deficiencies.By using the radial basis function approach we can further isolate and quantify the sources.Taking a pedagogical mass model as an example,we examine explicitly the correlation between nuclear effective interactions and the distributions of mass deviations in the frequency domain.The method presented in this work,therefore,opens up a new way for improving the nuclear mass predictions towards a hundred kilo-electron-volt accuracy,which is argued to be the chaos-related limit for the nuclear mass predictions.

Ability of the radial basis function approach to extrapolate nuclear mass

The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27),finite-range droplet model(FRDM12)and Weizsäcker-Skyrme(WS4)mass models.It is found that when the RBF approach is employed with a simple linear basis function,different mass models have different performances in extrapolating nuclear masses in the same region,and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions.The WS4 and FRDM12 models(two macroscopic–microscopic mass models),combined with the RBF approach,may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.

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.

Improved isochronous mass spectrometry with tune measurement

In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.However,the resolution of T inevitably deteriorates due to the magnetic rigidity spread of the ions,limiting the mass-resolving power.In this study,we used the betatron tunes Q(the number of betatron oscillations per revolution)of the ions and established a correlation between T and Q.From this correlation,T was transformed to correspond to a fixed Q with higher resolution.Using these transformed T values,the masses of ^(63)Ge,^(65)As,^(67)Se,and ^(71)Kr agreed well with the mass values measured using the newly developed IMS(Bρ-IMS).We also studied the systematics of Coulomb displacement energies(CDEs)and found that anomalous staggering in CDEs was eliminated using new mass values.This method of T transformation is highly effective for conventional IMS equipped with a single time-of-flight detector.

Βρ-defned isochronous mass spectrometry at the storage ring CSRe

A novel technique of isochronous mass spectrometry(IMS),termed Bρ-defned IMS,was developed at the experimental cooler-storage ring CSRe in Lanzhou for the frst time.Two time-of-fight detectors were installed in a straight section of the CSRe,thereby enabling simultaneous measurements of the velocity and revolution time of each stored short-lived ion.This technique boosts the broadband precision,efciency,sensitivity,and accuracy of mass measurements of short-lived exotic nuclides.Using Bρ-defned IMS,the masses of^(22)Al,^(62)Ge,^(64)As,^(66)Se,and^(70)Kr were measured for the frst time,and the masses of^(65)As,^(67)Se,and other 21 nuclides were redetermined with improved accuracy.Mass data have been used in studies of relevant issues regarding nuclear structures and nuclear astrophysics.Herein,we review the development of experimental techniques and main physical results and outline plans for future experiments.

Improved mass relations of mirror nuclei

In this study,we revisit the previous mass relations of mirror nuclei by considering 1/N-and 1/Z-dependent terms and the shell effect across a shell.The root-mean-squared deviation is 66 keV for 116 nuclei with neutron number N≥10,as com-pared with experimental data compiled in the AME2020 database.The predicted mass excesses of 173 proton-rich nuclei,including 98 unknown nuclei,are tabulated in the Supplemental Material herein with competitive accuracy.

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three- dimensional coordinate transformation. In addition, Singh＇s analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross- cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross-cutting joints along the deflection-axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.

Density isomer of nuclear matter in an equivalent mass approach

The equation of state of symmetric nuclear matter is studied with an equivalent mass model.The equivalent mass of a nucleon has been expanded to order 4 in density.We first determine the first-order expansion coefficient in the quantum hadron dynamics,then calculate the coefficients of the second to fourth order for the given binding energy and incompressibility at the normal nuclear saturation density.It is found that there appears a density isomeric state if the incompressibility is smaller than a critical value.The model dependence of the conclusion has also been checked by varying the first-order coefficient.

New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

In this study, a new lumped-mass-stick model （LMSM） is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the ＂frequency adaptive lumped-massstick model,＂ hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model （FEM） for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of floor response spectra at certain elevations are also in good agreement.

Nuclear Fusion Research and Development Need New Relativistic Mass and Energy Corrections Given by the Information Relativity Theory

Hundred years after the conjecture of the British astronomer Eddington that the sun is powered by nuclear fusion of hydrogen, new physics theory may help make energy harvesting by nuclear fusion soon a reality. Researchers as well as investors funding fusion megaprojects are asked to deal with new relativistic corrections for mass and energy proposed by Suleiman in his Information Relativity Theory (IRT). These corrections were calculated in this contribution. It will help to decide whether a venture will be successful and to save big investments when in doubt. The assumed optimal kinetic energy for controlled nuclear fusion must be corrected to a somewhat higher level. At very high kinetic energy in the upper GeV range, it remains not enough baryonic mass to be transformed in energy. The fusion probability faded out to zero already at the golden limit of the recession speed of between target nucleon and projectile nucleon. Cold nuclear fusion, if ever possible, is recommended for protons rather than deuterons at highest experimental possible temperatures around 1000 (K) and needs fine-tuned kinetic nucleon energy. It would be also of interest whether a golden ratio based nuclear fuel confinement chamber could be beneficial. In this connection, also cold nuclear fusion setups should be discussed. Nature is governed by the golden ratio and criticality of physical systems influenced by it, and nuclear physics is not an exception. Computer simulations of the underlying controlled nuclear fusion processes should gain profit from IRT corrected starting information and may tackle anew possible low energy nuclear transmutations considering the wave-like dark components of matter and energy.

Structural Characteristics and Mechanical Properties of Rock Mass in the Field of Tianwan Nuclear Power Plant, China

The structural characteristics and mechanical properties of the rock mass are important parts of the feasibility study on the nuclear power engineering field. In this study, by means of in situ investigation and statistics, the structural plane and joint fissure features of the rock mass were analyzed and discussed at different plots and different depth scopes in the Tianwan Nuclear Power engineering field, the rock mass integrality and its weathered degree were evaluated respectively, and especially, the unfavorable geological phenomena of strongly-weathered cystid existing in the field were studied. According to the results of indoor rock mechanical tests, in combination with drilling, the shallow seismic prospecting, sonic logging and point load tests, the statistical results of physical and mechanical indices of rocks at key plots of the field were analyzed, and the design parameters of the field were calculated. It provided scientific basis for the foundation design of the nuclear power plant.

A New View of the Mass Extinctions and the Worldwide Floods

In this study, the reasons for mass extinction in Jurassic were investigated. It was shown that galactic compression led to the activation of terrestrial nuclear reactors, which in turn led to the changes in tectonic activity, volcano eruptions, LIPs, MORBs, paleoclimate change, drift of continents, narrowing of the Earth, worldwide floods, tsunami, changes in mantle and core structures, in magnetic fields and in sedimentary isotopes. It was shown that the mass extinctions occurred during worldwide floods, caused by the narrowing of the Earth at the time of galactic gravitational compression. It was shown that the average statistical altitude distribution of dinosaurs has a bimodal distribution and corresponds to permanent migrations between the plains and the hills. It has been suggested that the skeletons of dinosaurs are well preserved as a result of covering the bodies of dinosaurs with mud flows of coastal sediments and the soil layers at worldwide tsunami. It was formulated the requirement to paleontology, consisting in the obligatory registration of altitudes of the actual place of the fossils found. The simple explanation of the presence of boundaries in the structure of the Earth is given: the 40K nuclear layer corresponds to the boundary between upper and lower mantle;the 137Cs layer located on the boundary between the lower mantle and the outer core;the Th-U nuclear layer is a border between outer and inner core. The previously abstract theories of subduction and continents drift have a clear and obvious physical sense. It was shown that the standard geological table is a registration book of galactic events during Paleozoic. It is proposed to restore the structure of the galactic arms by the geological deposits on the Earth. It was suggested to create the stations on elevated hills for rescue and regeneration of biological forms in the future.

Intra-Atomic Gravitational Shielding (Lensing), Nuclear Forces and Radioactivity

The discovery by the author of real magnetic charges and true anti-electrons in the atomic structures allowed him to establish that the gravitational field (GF) in reality is the vortex electromagnetic field. Depending on the vector conditions the gravitational fields can be either paragravitational (PGF) or ferrogravitational (FGF). Masses (atoms, nucleons, etc.) emitting PGF manifest so-called attraction to each other. In fact, this process is the pressing of atoms or nucleons to each other by the forces of gravitational “Dark energy”. Namely the gravitational “Dark energy” which is formed between the masses emitting PGF and compressing of nucleons in atomic nuclei is the main force factor determining the formation of nuclear forces. Masses that emit FGF are repelled from PGF sources, for example, from the Earth. The last gravitational manifestation, discovered by the author, this is of the effect of the gravitational levitation. The atomic shell and atomic nucleus are autonomous sources of gravitational field in atomic compositions. The gravitational fields emitted these sources, by its physical parameters, are different gravitational fields, what associated with differences in the magnitudes charges of magnetic and electric particles in their compositions. The noted differences in the parameters of the GF are of reason that in atoms the process of extrusion of foreign gravitational field from the region of given gravitational source is realized. This effect should be called the effect of intra-atomic gravitational shielding (IAGS). Within the framework of this effect the shell of the atom is a kind of gravitational “insulator” that prevents the PGF of the nucleons from leaving beyond of the atom. As result of the IAGS effect, the concentration PGF of nucleons is realized only in the region of the nucleus, which leads to an increase in nuclear forces. However, the resistance of the marked “insulator” is finite and if the critical voltage PGF on the nucleus is exceeded, the complete shielding of the nucleon fields by the atomic shell is broken. As result of the leakage of a part of the PGF of nucleons beyond the atom, the density of this field in the region of the nucleus decreases significantly, which leads to a weakening of the nuclear forces and often leads to radioactivity. The effect of gravitational shielding is directly related to such a well-known concept as the mass defect of the nucleus. It is the exclusion of the gravitational field formed by the nucleons in the composition of the atomic nucleus as a result of the full IAGS effect that creates the illusion of atomic mass defect.

Coupling a Gas Chromatography Unit to an Inductively Coupled Plasma Mass Spectrometer

Although the eminent threat of a terrorist group detonating an improvised nuclear device (IND) in an urban environment is low, it is crucial that countries develop modern nuclear forensic capabilities to expedite response in a post-detonation scenario. In particular, new instruments need to be created to shorten dissolution time, expedite chemical separation, and improve forensic analysis of the nuclear melt glass that is created during the detonation of the device. To expedite this process, an instrument was designed to thermally couple a gas chromatograph (GC) to a time-of-flight inductively coupled plasma time-of-flight mass spectrometer (ICPTOFMS) In order to couple these two instruments, another instrument was designed to provide an isothermal atmosphere between the GC and TOFICPMS to expedite rapid gas separations processes. By using gas separations instead of the current wet chemistry processes, the required separation and analysis time of the melt glass significantly decreases. The new instrument would also provide a more detailed analysis of the elemental and isotopic composition of the melt glass. By completing these tasks simultaneously, this significantly decreases the required time to conduct these separations and improves the elemental and isotopic analysis.