ETFSI mass formula

The Extended Thomas-Fermi + Strutinsky Integral (ETFSI) model is a high-speed approximation of the self-consistent Hartree-Fock method based on a Skyrme-type interaction.
The total binding energy is approximated by

Etot = EETF + ESI + Epairing


  • the macroscopic part Eetf is given by the full fourth-order Extended Thomas-Fermi approximation
  • the shell correction is determined by the Strutinsky Integral method where use is made of the same Skyrme interaction as in the macroscopic part
  • the pairing energy is calculated in the BCS approximation with a d-function force

The ground state axial deformations are determined by minimizing the total binding energy.

The parameters of the effective nucleon interaction of Skyrme type (SkSC18) and of the pairing interaction are fitted to the experimentally known masses. The parameters are

t0-1789.81 MeV fm3
t1284.257 MeV fm5
t2-284.257 MeV fm5
t312783.7 MeV fm4
W0123.992 MeV fm5
V-221.0 MeV fm3

The root mean square of the mass fit to 1719 (A>35) nuclei with |N-Z|>1) is 709 keV. The ETFSI-2 mass table for 8244 nuclei (35 < A < 330) between the neutron and the proton drip lines is available . It includes for each nucleus (Z,A):

  • the b2 and b4 deformations (bet2, bet4),
  • the charge radius (Rch),
  • the deformation energy (Edef),
  • the neutron separation energy (Sn),
  • the proton separation energy (Sp),
  • the b-decay energy (Qbet),
  • the nuclear mass excess (Mcal),
  • the deviation from the experimental mass (error).

The corresponding table can be found here (last update 23/06/2000).

More details on the ETFSI model can be found in

- A.K. Dutta, J.-P. Arcoragi, J.M. Pearson, R. Behrman and F. Tondeur (1986) Nucl. Phys. A458, 77;
- F. Tondeur, A.K. Dutta, J.M. Pearson and R. Behrman (1987) Nucl. Phys. A470, 93;
- J.M. Pearson, Y. Aboussir, A.K. Dutta, R.C. Nayak, M. Faine and F. Tondeur (1991) Nucl. Phys. A528, 1;
- Y. Aboussir, J.M. Pearson, A.K. Dutta and F.Tondeur (1992), Nucl. Phys. A549, 155;
- Y. Aboussir, J.M. Pearson, A.K. Dutta and F.Tondeur (1995) At. Data and Nucl. Data Tables 61, 127;
- R.C. Nayak and J.M. Pearson (1995) Phys. Rev. C52, 2254.
- S. Goriely (2000) Proc. Int. Conf. on Capture Gamma-Ray Spectroscopy and Related Topics, (AIP, ed. S. Wender) pp. 287.