Mass formula

About: Mass formula is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22043 citations.

Baryon Mass Splitting in a Boson-Fermion Model

Abstract: A model is proposed in which a baryon consists of a boson and fermion deeply bound in a potential. The fermion can be regarded as a quark and the boson as a bound state of two quarks. In the model, the mass splitting of the different isospin multiplets among the baryons arises partly from mass splittings within the boson and fermion multiplets and partly from a symmetry-breaking interaction. The isospin-conserving mass splittings within the boson and fermion multiplets, as well as the symmetry-breaking interaction, are assumed to be proportional to the hypercharge. Under the assumption that these mass splittings and symmetry-breaking interactions are small, it is found that the seven baryon mass splittings which conserve isospin are given in terms of four parameters, and that the Gell-Mann-Okubo mass formula holds. Some effects of representation mixing are considered.

Modification of nuclear mass formula by considering isospin effects

Abstract: We propose a semiempirical nuclear mass formula based on the macroscopic-microscopic method in which the isospin and mass dependence of model parameters are investigated with the Skyrme energy density functional. The number of model parameters is considerably reduced compared with the finite range droplet model. The rms deviation with respect to 2149 measured nuclear masses is reduced by 21%, falling to 0.516 MeV. The new magic number $N=16$ in light neutron-rich nuclei and the shape coexistence phenomena for some nuclei have been examined with the model. The shell corrections of superheavy nuclei are also predicted.

Towards a Hartree-Fock mass formula

Abstract: A ten-parameter Skyrme force, along with a four-parameter $\ensuremath{\delta}$-function pairing force, have been fitted, using the Hartree-Fock-BCS method, to the masses of 1719 nuclei, both spherical and deformed, with an rms error of 0.754 MeV. The corresponding value of the symmetry coefficient J is 28.0 MeV, and that of the effective nucleon mass ${M}^{*}$ is $1.05M.$

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. II: Role of the effective mass

Abstract: We have constructed four new complete mass tables, referred to as (Hartree-Fock-Bogoliubov) HFB-4 to HFB-7, each one including all the 9200 nuclei lying between the two drip lines over the range of $Z$ and $N\ensuremath{\geqslant}8$ and $Z\ensuremath{\leqslant}120$. HFB-4 and HFB-5 have the isoscalar effective mass ${M}_{s}^{*}$ constrained to the value $0.92M$, with the former having a density-independent pairing, and the latter a density-dependent pairing. HFB-6 and HFB-7 are similar, except that ${M}_{s}^{*}$ is constrained to $0.8M$. The rms errors of the mass-data fits are 0.680, 0.675, 0.686, and $0.676\phantom{\rule{0.3em}{0ex}}\text{MeV}$, respectively, almost as good as for the HFB-2 mass formula, for which ${M}_{s}^{*}$ was unconstrained. However, as usual, the single-particle spectra depend significantly on ${M}_{s}^{*}$. This decoupling of the mass fits from the fits to the single-particle spectra has been achieved only by making the cutoff parameter of the $\ensuremath{\delta}$-function pairing force a free parameter. An improved treatment of the center-of-mass correction was adopted, but although this makes a difference to individual nuclei it does not reduce the overall rms error of the fit. The extrapolations of all four new mass formulas out to the drip lines are essentially the same as for the original HFB-2 mass formula.