Showing papers on "Mass formula published in 2022"

Upsilon decay widths in magnetized asymmetric nuclear matter

Abstract: The in-medium partial decay widths of [Formula: see text] in magnetized asymmetric nuclear matter are studied using a field theoretic model for composite hadrons with quark (and antiquark) constituents. [Formula: see text] is the lowest bottomonium state which can decay to [Formula: see text] in vacuum. The medium modifications of the decay widths of [Formula: see text] to [Formula: see text] pair in magnetized matter arise due to the mass modifications of the decaying [Formula: see text] as well as of the produced [Formula: see text] and [Formula: see text] mesons. The in-medium masses of the open bottom meson in magnetized nuclear matter are computed from their interactions with the nucleons and the scalar mesons within a chiral effective model. The mass modification of the [Formula: see text] arises due to the medium modification of a scalar dilaton field, which is introduced in the model to simulate the gluon condensates of QCD. The effects of the anomalous magnetic moments for the proton and neutron are taken into consideration in the present investigation. The presence of the external magnetic field is observed to lead to different mass modifications within the [Formula: see text] as well as the [Formula: see text] doublets, even in isospin symmetric nuclear matter. This is due to the difference in the interactions of the proton and the neutron to the electromagnetic field. The charged [Formula: see text] mesons have additional contributions from the Landau energy levels, leading to positive shifts in their masses in the presence of a magnetic field. In the presence of an external magnetic field, there are contributions to the masses of the B, [Formula: see text] mesons and [Formula: see text] state (longitudinal component) due to the pseudoscalar meson–vector meson (PV) mixing ([Formula: see text], [Formula: see text] and [Formula: see text] mixings), which are also considered in this study. The PV mixing effects are observed to be the dominant contributions to the mass shifts of these mesons, which lead to appreciable modifications in the decay widths of [Formula: see text] to the neutral ([Formula: see text]) and the charged ([Formula: see text]) pairs in the presence of a magnetic field. These should have observable consequence in the production of open bottom mesons and bottomonium states at LHC and RHIC, where huge magnetic fields are produced in ultra-relativistic peripheral heavy-ion collisions.

Uncertainty analysis for the nuclear liquid drop model and implications for the symmetry energy coefficients

Abstract: Background: Despite its age, the nuclear liquid drop (LD) model, plus the microscopic corrections, still plays an important role in nuclear mass studies. Especially, the LD model readily correlate the finite nucleus and the nuclear matter through the symmetry energy term.Purpose: To systematically analyze the model uncertainty of the LD mass formula and check the corresponding symmetry energy coefficients.Method: The Monte Carlo bootstrap approach, based on the nonparametric sampling, is applied to determine the statistical uncertainties of the parameter set in two popular LD formulas. The dependence between these parameters is also quantified via the correlation coefficients.Results: The least required proportion of the experimental mass data is fixed for the fitting process of the LD formula. After the statistical deviation is determined for each parameter in the LD formula, the model uncertainty is evaluated as illustrated for one heavy isotopic chain. The Pearson coefficients between each two parameters involved in the LD mass formula are tabulated and figured plus the detailed discussions on the surface and volume symmetry energy coefficients.Conclusion: The uncertainties of the fitted parameters and the LD model itself are smooth, leading to a relatively stable extrapolation. It is necessary to include the Wigner energy term in the LD model when yielding the reasonable symmetry energy coefficients.

Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes

Abstract: In our previous work, a novel idea that the NUT charge can be thought of as a thermodynamical multi-hair has been advocated to describe perfectly the thermodynamical character of the generic four-dimensional Taub-NUT spacetimes. According to this scheme, the Komar mass M, the gravito-magnetic charge and/or the dual (magnetic) mass N, together with a new secondary hair J_N=MN, namely, a Kerr-like conserved angular momentum, enter into the standard forms of the first law and Bekenstein-Smarr mass formula. Distinguished from other recent attempts, our consistent thermodynamic differential and integral mass formulae are both obtainable from a meaningful Christodoulou-Ruffini-type squared mass formula of almost all of the four-dimensional NUT-charged spacetimes. As an excellent consequence, the famous Bekenstein-Hawking one-quarter area-entropy relation can be naturally restored not only in the Lorentzian sector and but also in the Euclidian counterpart of the generic Taub-NUT-type spacetimes without imposing any constraint condition. However, only purely electric-charged cases in the four-dimensional Einstein-Maxwell gravity theory with a NUT charge have been addressed there. In this paper, we shall follow the simple, systematic way proposed in that article to further investigate the dyonic NUT-charged case. It is shown that the standard thermodynamic relations continue to hold true provided that no new secondary charge is added, however, the so-obtained electrostatic and magneto-static potentials are not coincident with those computed via the standard method. To rectify this inconsistence, a simple strategy is provided by further introducing two additional secondary hairs: Q_N=QN and P_N=PN, together with their thermodynamical conjugate potentials, so that the first law and Bekenstein-Smarr mass formula are still satisfied.

The generation of mass in a non-linear field theory

Abstract: Abstract The mass spectrum of elementary particles is calculated in a new approach, based on B. Heim’s quantum field theory, which manifests in a non-linear eigenvalue equation and merges into the Einstein field equation in the macroscopic limit. The poly-metric of the theory allows spacetime and matter to be described in a unified formalism, representing a radical geometrisation of physics. The calculated mass energies are in very good agreement with the empirical data (error < 1 % ${< }1\%$ on average) if the mass scale is gauged to the electron as lowest mass and the second main parameter, determining the strength of obtained mass hierarchy levels, is close to the half inverse of the fine structure constant, describing the difference in strength between the electromagnetic and the strong interaction. The obtained hierarchy levels are not identical to the particle generations of the Standard Model; however, show a self-similarity typical for non-linear theories. For higher values of the main quantum number N, the calculated mass formula becomes identical to the phenomenological formulae of Nambu, respectively, Mac Gregor.

On the masses of $A = 54$ Isospin Septet and the Isobaric Multiplet Mass Equation

Abstract: Using the ground-state mass of $^{52}$Ni and two-proton decay energy of $^{54}$Zn, the ground-state mass excess of $^{54}$Zn is deduced to be $-6504(85)$ keV. This value is about $\sim 2$~MeV lower than the prediction of quadratic form of isobaric multiplet mass equation (IMME). A cubic fit to the existing mass data of the $A=54$, $T=3$ isospin multiplet yields a surprisingly large $d$ coefficient of IMME, i.e., $d=18.6(27)$ being $6.9\sigma$ deviated from zero, and the resultant $|b/c|$ ratio significantly deviates from the systematics. This phenomenon is analyzed in this paper and we conclude that the breakdown of the quadratic form of IMME could be likely due to mis-assignment of the $T=3$ isobaric analog state (IAS) in the $T_z=1$ nucleus $^{54}$Fe or extremely strong isospin mixing.

AMC 12 atomic mass compilation data extrapolated for atomic masses of nuclei far from the valley of stability

Abstract: The experimental mass data from the Atomic Mass Compilation - 2012 (AMC12) has been analyzed for two-neutron separation energies ([Formula: see text]), two-proton separation energies ([Formula: see text]), double-beta decay energies ([Formula: see text]), and four-beta decay energies ([Formula: see text]) and plotted against neutron number and mass number, respectively. A new weighted slope method of extrapolation, tested for known and new mass measurements, has been used to obtain the extrapolated mass values with better precision for more than 1100 nuclei far from the valley of stability, out of which more than 100 are being reported for the first time. A comparison has been made with five of the popular mass models with reference to experimental extrapolated masses from the present work and the Atomic Mass Evaluation 2016 (AME16). The extrapolated experimental atomic mass data will be very useful for both experimentalists and mass-model theoreticians, as well as in simulations of astrophysical r-processes.

Effective mass of α-cluster in 12C nucleus

Abstract: Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3[Formula: see text] states in [Formula: see text]C nucleus. A three-body potential is used to describe the known breaking of the 3[Formula: see text]-cluster structure in the nucleus. We show that the contribution of the three-body potential to the Hamiltonian can be compensated by increasing/decreasing the [Formula: see text]-particle free mass. The effective-mass values are adjusted to reproduce the experimental data for the [Formula: see text]C nucleus. The energy dependence of the effective mass and the correlation to a three-body potential are discussed. We show that the coupling between the [Formula: see text] ([Formula: see text]) levels forms a specific picture of anti-crossing on the energy/effective-mass plane.

Revisiting Macro-microscopic Mass Formula using Atomic Mass Evaluation-2020 Data

Abstract: Background: The macro-microscopic model has been succesful in nuclear mass predictionsand in obtaining various other properties of nuclear and nucleon matter. The present statusof generalised liquid drop model (GLDM) has been based on atomic mass evaluation (AME)-2003 data.Purpose: In this work, the co-efficients of most efficient mass formulae from Royer et.al.,have been re-optimised for 2451 selected nuclei from AME-2020 data.Methods: The root mean squared deviation (RMS) is minimized to optimize seven modelparameters that correspond to various terms in the nuclear binding energy that come inpowers of mass number A and square of relative neutron excess I = N −Z/A .Results: The RMS between the theoretical and experimental binding energies has beenobtained as 0.65 using both the formulae.Conclusions: The best possible formula for nuclear binding energy has been obtained usingAME-2020 data and it needs to be seen how this would effect the various nuclear propertiesand predictions.

A new relation for nuclear masses based on the nuclide chain with the same number of neutrons

Abstract: There are many studies in Odd–Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. In this work, we analyze the relationship among the four neighboring nuclei based on the OES of nuclide chain with the same number of neutrons in atomic mass evaluation database (AME2016 database). Our purpose in this paper is to describe an empirical formula with one constant for OES of nuclear masses that can be useful in describing and predicting nuclear masses with mass number [Formula: see text]. With the empirical formula and AME2016 database, the root-mean-square deviation (RMSD) of the nuclei that we have successfully obtained 172[Formula: see text]keV for [Formula: see text] (the RMSD is 140[Formula: see text]keV for [Formula: see text]). This paper also uses Levenberg–Marquart (L-M) neural network approach to study the OES of nuclear masses ([Formula: see text], RMSD [Formula: see text][Formula: see text]keV; [Formula: see text], RMSD [Formula: see text][Formula: see text]keV). The results show that the RMSD of nuclear masses for [Formula: see text] based on neural network approach 30[Formula: see text]keV decreases than that based on empirical formula (the accuracy is increased by about 17%). In addition, the predicted values based on the empirical formula and L-M neural network approach are consistent with the values in AME2020 database, and the difference between our predicted values based on AME2016 database and experimental values measured in recent years is small. These results show that the new relation for nuclear masses has good simplicity, accuracy and reliability. Accurate nuclear mass is helpful to the research of nuclear physics, nuclear technology and astrophysics.

On the masses of A = 54 isospin septet and the isobaric multiplet mass equation

Abstract: Using the ground-state mass of 52Ni and two-proton decay energy of 54Zn, the ground-state mass excess of 54Zn is deduced to be –6504(85) keV. This value is about 2 MeV lower than the prediction of the quadratic form of the isobaric multiplet mass equation (IMME). A cubic fit to the existing mass data of the , isospin multiplet yields a surprisingly large d coefficient of IMME, i.e., , being deviated from zero, and the resultant ratio significantly deviates from the systematics. This phenomenon is analyzed in this study, and we conclude that the breakdown of the quadratic form of IMME could be likely due to the mis-assignment of the isobaric analog state (IAS) in the nucleus 54Fe or extremely strong isospin mixing.

AMC 12 atomic mass compilation data extrapolated for atomic masses of nuclei far from the valley of stability

Abstract: The experimental mass data from the Atomic Mass Compilation - 2012 (AMC12) has been analyzed for two-neutron separation energies ([Formula: see text]), two-proton separation energies ([Formula: see text]), double-beta decay energies ([Formula: see text]), and four-beta decay energies ([Formula: see text]) and plotted against neutron number and mass number, respectively. A new weighted slope method of extrapolation, tested for known and new mass measurements, has been used to obtain the extrapolated mass values with better precision for more than 1100 nuclei far from the valley of stability, out of which more than 100 are being reported for the first time. A comparison has been made with five of the popular mass models with reference to experimental extrapolated masses from the present work and the Atomic Mass Evaluation 2016 (AME16). The extrapolated experimental atomic mass data will be very useful for both experimentalists and mass-model theoreticians, as well as in simulations of astrophysical r-processes.