HFB-14 mass formula

The force used in the Hartree-Fock-Bogoliubov (HFB) mass model is a conventional 10-parameter Skyrme force, along with a 4-parameter delta-function pairing force.
Pairing correlations are introduced in the framework of the Bogoliubov method with a pairing strength slightly stronger for an odd number of nucleons (V-q) than for an even number (V+q). Deformations with axial and left-right symmetry are admitted.

The total binding energy is given by

Etot = EHFB+ Ewigner


  • EHFB is the HFB binding energy including a cranking correction to the spurious rotational energy and a phenomenological vibration correction energy,
  • Ewigner= VW exp(- lambda ((N-Z)/A)2)+V'W|N-Z| exp(-(A/A0)2) is a phenomenological correction for the Wigner energy.

The final parameter set, labelled BSk14, is determined by constraining the nuclear-matter symmetry coefficient to J=30MeV and the isoscalar effective mass to M*s/M=0.8 and optimizing the fit to the full data set of the 2149 measured masses with N,Z >= 8 (both spherical and deformed) of Audi et al. (Nuc. Phys. A729, 3, 2003): the corresponding root mean square error is 0.729 MeV for this data set.
In addition, HFB-14 has been fitted to the fission data through adjustment of a vibrational term in the phenomenological collective correction. The rms deviation for the 52 primary barriers of nuclei with 88<= Z<= 96, which are always less than 9 MeV high, is 0.67 MeV and for the 52 secondary barriers is 0.65 MeV.
The BSk14 force parameters are given below

t0-1822.670 MeV fm3
t1377.470 MeV fm5
t2-2.411 MeV fm5
t311406.264 MeV fm4
W0135.6 MeV fm5
V+n-240.0 MeV fm3
V+p-265.5 MeV fm3
V-n-252.4 MeV fm3
V-p-275.2 MeV fm3
VW-1.70 MeV

Click HERE for the complete HFB-14 table of 8382 masses including all nuclei with Z,N >= 8 and Z <= 110 and lying between the proton and the neutron drip lines.

The table includes for each nucleus (Z,A):

  • the beta2 and beta4 deformations (bet2, bet4),
  • the rms charge radius (Rch),
  • the deformation energy (Edef),
  • the neutron separation energy (Sn),
  • the proton separation energy (Sp),
  • the beta-decay energy (Qbet),
  • the calculated mass excess (Mcal),
  • the error corresponding to the difference between the experimental and calculated mass excesses (Err).

More details on the HFB model can be found in

  • M. Samyn, S. Goriely, P.-H. Heenen, J.M. Pearson and F. Tondeur (2001) Nucl. Phys. A700, 142;
  • S. Goriely, M. Samyn, P.-H. Heenen, J.M. Pearson, and F. Tondeur (2002) Phys. Rev. C66, 024326;
  • M. Samyn, S. Goriely, and J.M. Pearson (2003) Nucl. Phys. A725, 69;
  • S. Goriely, M. Samyn, M. Bender and J.M. Pearson (2003) Phys. Rev. C68, 054325;
  • M. Samyn, S. Goriely, M. Bender and J.M. Pearson (2004) Phys. Rev. C70, 044309;
  • S. Goriely, M. Samyn, J.M. Pearson, and M. Onsi (2005) Nucl. Phys. A750, 425;
  • S. Goriely, M. Samyn, and J.M. Pearson (2006) Nucl. Phys. A773, 279;
  • S. Goriely, M. Samyn, and J.M. Pearson (2007) Phys. Rev. C75, 064312.

Last update 25/06/2007.