A.K. Dutta

Nuclear mass formula via an approximation to the Hartree-Fock method

We present the first nuclear mass table to be based entirely on microscopic forces. The calculations are performed using the extended Thomas-Fermi plus Strutinsky integral method, a semiclassical approximation to the Hartree-Fock method that includes full Strutinsky shell corrections; BCS pairing corrections are added. The eight active parameters of the underlying Skyrme and δ-function pairing forces are fitted to all the 1492 mass data (1988 compilation) for A ≥ 36; the rms error of this fit is 0.736 MeV. Our tabulation covers the range 36 ≤ A ≤ 300 and reaches beyond the neutron- and proton-drip lines. In addition to the calculated masses, we show the calculated neutron- and proton-separation energies and beta-decay energies. We also give for each nucleus in the table the model predictions for the deformation parameters and deformation energy at equilibrium (with axial and left-right symmetry assumed) and for the charge radii.

Thomas-Fermi approach to nuclear-mass formula. (IV). The ETFSI-1 mass formula

Abstract We summarize the main features of the first nuclear-mass table to be based entirely on microscopic interactions. A semi-classical approximation to the HF-BCS method is adopted, with full Strutinsky shell corrections included. The 9 parameters of the underlying Skyrme and δ-function pairing forces are fitted to all 1492 mass data for A ⩾ 36; the r.m.s. error of this fit is 0.730 MeV. Our tabulation covers the range 36 ⩽ A ⩽ 300, goes out to the neutron-drip line and extends beyond the proton-drip line. Equilibrium deformations of all nuclei are calculated, with axial symmetry assumed. We also calculated several fission barriers using the same force with no further adjustment of parameters; a satisfactory agreement with experiment is obtained.

Thomas-Fermi approach to nuclear mass formula: (III). Force fitting and construction of mass table

Abstract The ETFSI method, developed in two earlier papers, is here used to construct a complete mass table. Since the method allows for interpolation both in the ( N , Z ) plane and with respect to deformations, without losing the characteristic shell-model fluctuations, it is some 2000 times faster than the HF-BCS method for a given force. The present table is calculated using a preliminary Skyrme-type force with δ-function pairing, fitted to a restricted data set of 491 spherical nuclei. The resulting rms error for all 1492 measured nuclei, spherical and deformed, with A ⩾ 36 is e rms = 0.868 MeV, achieved with just 9 parameters. The main experimental trends in ground-state deformations are well followed. The symmetry coefficient of nuclear matter corresponding to our force is 27.5 MeV. Ways of rapidly improving the fit are indicated.

Thomas-fermi approach to nuclear mass formula

Abstract With a view to having a more secure basis for the nuclear mass formula than is provided by the drop(let) model, we make a preliminary study of the possibilities offered by the Skyrme-ETF method. Two ways of incorporating shell effects are considered: the “Strutinsky-integral” method of Chu et al., and the “expectation-value” method of Brack et al. Each of these methods is compared with the HF method in an attempt to see how reliably they extrapolate from the known region of the nuclear chart out to the neutron-drip line. The Strutinsky-integral method is shown to perform particularly well, and to offer a promising approach to a more reliable mass formula.

Thomas-Fermi approach to nuclear mass formula: (II). Deformed nuclei and fission barriers

Abstract We are developing an approach to the nuclear mass formula based on the Skyrme-ETF method with shell corrections calculated by the “Strutinsky integral” method of Chu, Jennings and Brack. The work of paper I of this series is extended here to deformed nuclei and fission barriers. We find that with a unique set of force parameters the present method can reproduce to within 1 MeV the results of Hartree-Fock calculations for masses and fission barriers in all regions of the nuclear chart. But being much faster than Hartree-Fock the present method will have the advantage of being able to be fitted to the data with greater precision.

Semi-classical equation of state and specific-heat expressions with proton shell corrections for the inner crust of a neutron star

M. Onsi, A. K. Dutta, 2 H. Chatri, S. Goriely, N. Chamel, and J. M. Pearson Dépt. de Physique, Université de Montréal, Montréal (Québec), H3C 3J7 Canada School of Physics, Devi Ahilya University, Indore 452001, India Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles CP226, 1050 Brussels, Belgium Abstract An approach to the equation of state for the inner crust of neutron stars based on Skyrmetype forces is presented. Working within the Wigner-Seitz picture, the energy is calculated by the TETF (temperature-dependent extended Thomas-Fermi) method, with proton shell corrections added self-consistently by the Strutinsky-integral method. Using a Skyrme force that has been fitted to both neutron matter and to essentially all the nuclear mass data, we find strong proton shell effects: proton numbers Z = 50, 40 and 20 are the only values possible in the inner crust, assuming that nuclear equilibrium is maintained in the cooling neutron star right down to the ambient temperature. Convergence problems with the TETF expansion for the entropy, and our way of handling them, are discussed. Full TETF expressions for the specific heat of inhomogeneous nuclear matter are presented. Our treatment of the electron gas, including its specific heat, is essentially exact, and is described in detail.

Droplet models as approximations to the extended Thomas-Fermi method☆

Abstract The conventional droplet model and the “ finite-range” droplet model of Moller et al. are compared with the extended Thomas-Fermi method (ETF) in order to test how reliably these models extrapolate from the region of known nuclei out to the neutron-drip line. We proceed by fitting each of the two droplet models to the binding energies of a large number of nuclei in the known region, calculated by the ETF method. On extrapolating to the neutron-drip line we find that the droplet models can disagree by as much as 10–15 MeV with ETF. However, a dramatic improvement results if higher-order surface-symmetry terms are included in the droplet model; their effect is to “soften” the neutron skin as the neutron excess grows.