Macroscopic-Microscopic

J. Phys. Conference Series 267 012010, 2010

Different Liquid Drop Model mass formulae have been studied. They include a Coulomb diffuseness correction Z 2 /A term and pairing and shell energies of the Thomas-Fermi model. The influence of the selected charge radius, the curvature energy and different forms of the Wigner term has been investigated. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses. The different fits lead to a surface energy coefficient of 17-18 MeV. A large equivalent rms radius (r0 = 1.22 − 1.24 fm) or a shorter central radius may be used. A rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come from the determination of the shell and pairing energies. Mass predictions are given for exotic nuclei.

The European Physical Journal A, 2009

An adjustment to 782 ground state nuclear charge radii for nuclei with N,Z ≥ 8 leads to R0 = 1.2257 A 1/3 fm and σ = 0.124 fm for the charge radius. Assuming such a Coulomb energy Ec = 3 5 e 2 Z 2 /1.2257 A 1 3 , the coefficients of different possible mass formulae derived from the liquid drop model and including the shell and pairing energies have been determined from 2027 masses verifying N,Z ≥ 8 and a mass uncertainty ≤ 150 keV. These formulae take into account or not the diffuseness correction (Z 2 /A term), the charge exchange correction term (Z 4/3 /A 1/3 term), the curvature energy, the Wigner terms and different powers of I = (N − Z)/A. The Coulomb diffuseness correction or the charge exchange correction term plays the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18 MeV. A possible more precise formula for the Coulomb radius is R0 = 1.2332A 1/3 + 2.8961/A 2/3 − 0.18688A 1/3 I fm with σ = 0.052 fm.

Nuclear Physics A, 2008

The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and different powers of the relative neutron excess I = (N − Z)/A have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction Z 2 /A term or the charge exchange correction Z 4/3 /A 1/3 term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an |I| dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an I 4 dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r 0 of 1.22-1.23 fm.

Eur. Phys. J. A. 42 541, 2009

An adjustment to 782 ground-state nuclear charge radii for nuclei with N, Z ≥ 8l e a d st o R0 =1 .2257 A 1/3 fm and σ =0 .124 fm for the charge radius. Assuming such a Coulomb energy Ec = 3 5 e 2 Z 2 /1.2257 A 1 3 , the coefficients of different possible mass formulae derived from the liquid drop model and including the shell and pairing energies have been determined from 2027 masses verifying N, Z ≥ 8 and a mass uncertainty ≤ 150 keV. These formulae take into account or do not the diffuseness correction (Z 2 /A term), the charge exchange correction term (Z 4/3 /A 1/3 term), the curvature energy, the Wigner terms and different powers of I =(N − Z)/A. The Coulomb diffuseness correction or the charge exchange correction term play the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18 MeV. A possible more precise formula for the Coulomb radius is R0 =1.2332A 1/3 +2.8961/A 2/3 − 0.18688A 1/3 I fm with σ =0.052 fm.

Nuclear Physics A, 2010

Different mass formulae derived from the liquid drop model and the pairing and shell energies of the Thomas-Fermi model have been studied and compared. They include or not the diffuseness correction to the Coulomb energy, the charge exchange correction term, the curvature energy, different forms of the Wigner term and powers of the relative neutron excess I = (N − Z)/A. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses [1]. The Coulomb diffuseness correction Z 2 /A term or the charge exchange correction Z 4/3 /A 1/3 term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately but their coefficients are very unstable. The different fits lead to a surface energy coefficient of around 17-18 MeV. A large equivalent rms radius (r 0 = 1.22 − 1.24 fm) or a shorter central radius may be used. A rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come probably mainly from the determination of the shell and pairing energies. Mass predictions of selected expressions have been compared to 161 new experimental masses and the correct agreement allows to provide extrapolations to masses of 656 selected exotic nuclei.

2009

EPJ manuscript No. (will be inserted by the editor) On the liquid drop model mass formulae and charge radii

arXiv: Nuclear Experiment, 2007

The efficiency of different mass formulas derived from the liquid drop model including or not the curvature energy, the Wigner term and different powers of the relative neutron excess I has been determined by a least square fitting procedure to the experimental atomic masses assuming a constant R0;charge/A 1= 3 ratio. The Wigner term and the curvature energy can be used independently to improve the accuracy of the mass formula. The different fits lead to a surface energy coefficient of around 17-18 MeV, a r sharp charge radius r0 of 1.22-1.23 fm and a proton form-factor correction to the Coulomb energy of around 0.9 MeV.

Physical Review C, 1994

We examine the predictions for nuclear charge radii made by an extended Thomas-Fermi mass formula, the first to be built entirely on microscopic forces, and the finite-range droplet model mass formula, the most refined of the droplet-model approaches. The former is highly successful, the parameters emerging from the mass fit giving an optimal fit to charge radii also, without any further adjustment. The latter model in its published form seems to suer from an inappropriate choice for the values of some of the parameters, and we discuss how improvement might be possible.

Physical Review C, 1995

By assuming the existence of a pseudopotential smooth enough to do Hartree-Fock variations and good enough to describe nuclear structure, we construct mass formulae that rely on general scaling arguments and on a schematic reading of shell model calculations. Fits to 1751 known binding energies for N,Z≥ 8 lead to rms errors of 375 keV with 28 parameters. Tests of the extrapolation properties are passed successfully. The Bethe-Weizsäcker formula is shown to be the asymptotic limit of the present one(s). The surface energy of nuclear matter turns out to be probably smaller than currently accepted.

Nuclear Physics A, 1991

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.