HFB-24 mass formula
The force used in the Hartree-Fock-Bogoliubov (HFB) mass model is an extended Skyrme force (containing t4 and t5 terms), along with a 4-parameter delta-function pairing force derived from realistic calculations of infinite nuclear and neutron matter (all details are given in Goriely et al., Phys. Rev. 88, 024308, 2013).
Pairing correlations are introduced in the framework of the Bogoliubov method. 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 BSk24, is determined by constraining the nuclear-matter symmetry coefficient to J = 30 MeV and the isoscalar effective mass to M*s/M = 0.8 and optimizing the fit to the full data set of the 2353 measured masses with N,Z $\ge$ 8
(both spherical and deformed) of the 2012 Atomic Mass Evaluation (Audi et al., Chinese Physics C36, 1287, 2012): the corresponding root mean square error is 0.549 MeV for this data set.
All unphysical instabilities of nuclear matter, including the transition to a polarized state in neutron-star matter, are eliminated with the BSk24 force.
The BSk24 force parameters are given below
|t0||-3970.29 MeV fm3|
|t1||395.766 MeV fm5|
|t2||0 MeV fm5|
|t3||22648.6 MeV fm3+3$\alpha$|
|t4||-100.000 MeV fm5+3$\beta$|
|t5||-150.000 MeV fm5+3$\gamma$|
|t2x2||1389.61 MeV fm5|
|W0||109.622 MeV fm5|
Click here for the complete HFB-24 table of 8392 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).
- the experimental and calculated spins (Jexp and Jth),
- the experimental and calculated parities (Pexp and Pth),
More details on the HFB model can be found in
- M. Samyn, S. Goriely, P.-H. Heenen, J.M. Pearson, and F. Tondeur (2002) 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;
- S. Goriely and J.M. Pearson (2008) Phys. Rev. C77, 031301;
- N. Chamel, S. Goriely, and J.M. Pearson (2008) Nucl. Phys. A812, 72;
- S. Goriely, N. Chamel, and J.M. Pearson (2009) Phys. Rev. Let. 102, 152503;
- N. Chamel, S. Goriely, and J.M. Pearson (2009) Phys. Rev. C80, 065804;
- S. Goriely, N. Chamel, and J.M. Pearson (2009) Eur. J. Phys. A42, 547;
- S. Goriely, N. Chamel, and J.M. Pearson (2010) Phys. Rev. C82, 035804;
- S. Goriely, N. Chamel, and J.M. Pearson (2013) Phys. Rev. C88, 024308;
- S. Goriely, N. Chamel, and J.M. Pearson (2013) Phys. Rev. C88, 061302;
- S. Goriely (2015) Nucl. Phys. A933, 68.
Last update 01/05/2015.