## 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

## E_{tot }= E_{HFB}+ E_{wigner}

where

- E
_{HFB }is the HFB binding energy including a cranking correction to the spurious rotational energy and a phenomenological vibration correction energy, - E
_{wigner}= V_{W}exp(- lambda ((N-Z)/A)^{2})+V^{'}_{W}|N-Z| exp(-(A/A_{0})^{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

t_{0} | -1822.670 MeV fm^{3} |

t_{1} | 377.470 MeV fm^{5} |

t_{2} | -2.411 MeV fm^{5} |

t_{3} | 11406.264 MeV fm^{4} |

x_{0} | 0.302096 |

x_{1} | -0.823575 |

x_{2} | 61.941050 |

x_{3} | 0.473460 |

W_{0} | 135.6 MeV fm^{5} |

gamma | 0.30 |

V^{+}_{n} | -240.0 MeV fm^{3} |

V^{+}_{p} | -265.5 MeV fm^{3} |

V^{-}_{n} | -252.4 MeV fm^{3} |

V^{-}_{p} | -275.2 MeV fm^{3} |

V_{W} | -1.70 MeV |

lambda | 400 |

V^{'}_{W} | 0.75 |

A_{0} | 30 |

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 beta
_{2 }and beta_{4}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.**