DFT-UNEDF Working Group

Determination of the Nuclear Energy functional:
Database of Experimental Data and Related Software

Introduction Experimental Data Table Software Credits and Documentation

Jun. 28, 2010:

The table and related software have been updated to version 4.
  • For super-deformed states and fission isomers, the table now gives an estimate of the axial deformation beta of the SD state;
  • One nucleus, 240Pu, has been added to the list of fission isomers;
  • Ground-state nuclear masses of actidines in the fission isomers list has been updated to be compatible with those given in the list of deformed nuclei (based onAudi Wapstra 2003 Mass Table Evaluation);
  • Estimates of ground-state deformations for deformed nuclei have been updated: some values were a little too high.

Mar. 13, 2010:

The table and related software have been updated to version 3.
  • For spherical nuclei, the error on the binding energy is now given. Also the nuclear proton and charge radii are both given. The nuclear proton radius was obtained from the charge radius according to:
<Rch>^2 = <Rp>^2 - <rp>^2 - N/Z*<rn>^2

with the proton and neutron form factors taken from the Particle Data Group;
  • For deformed nuclear masses, proton and neutron 3-point Odd-Even Mass differences, and odd-mass nuclei, a flag equal to 0 or 1 has been added to indicate if the mass of the underlying nucleus/nuclei is/are actually measured (=1) or evaluated (=0).

Sep. 22, 2009:

The table and related software have been updated to version 2

  • In version 1, the table listed atomic masses, where the electronic binding energy is implicity included. The programs supplied removed this correction when reading the table. In version 2, the data contained in the table are true nuclear binding energies, and the electronic correction has already been stripped out. The routines have been modified accordingly. The electronic correction implemented is 1.433.10-5 Z2.39 [MeV];
  • All atomic masses given or used in version 1 came from Audi Wapstra 2003 Mass Table Evaluation. Recent mass measurements in Jyvaskyla suggest some of this data could be altered significantly. We used the file given in this page to update our original selection of nuclear masses. The mass of a given nuclide is now given by the weighted average of the original Audi-Wapstra mass and the new JYFLTRAP measurement.


The database contains selected experimental material from published references only. It is aimed at providing a complete set of experimental observables that can be used to fit the parameters of effective interactions or energy functionals. In particular, it should contain enough data to probe most of the terms of a realistic energy functional. Three sets of data can be somewhat arbitrarily distinguished:
  1. Spherical nuclei - The best mean-field candidates where correlations beyond the mean-field are shown to be small or relatively constant over an isotopic chain. Observables: ground-state energy, diffraction radius, charge/proton r.m.s. radius, surface thickness, position of the first 2+ state and B(E2) value, giant monopole resonance and giant dipole resonance in 90Zr, 116Sn and 208Pb.

  2. Deformed nuclei - Available calculations using various effective interaction indicate large ground-state deformations for these nuclei which are good example of a deformed mean-field. Observables: ground-state energy with related experimental uncertainty, position of the first super-deformed state or fission isomer, experimental odd-even mass differences. For deformed nuclei (keyword DEFORM in the file), equilibrium deformations obtained from HFB-SLY4 calculation are given for comparison.

  3. Symmetry-unrestricted - These observables are chosen to probe symmetry-breaking components of a given energy functional, or additional correlations such as pairing correlations. Observables: high-K terminating states, ground-state spins and parity of odd-mass nuclei, 1q.p. excited states of odd-mass heaviest elements

Experimental Data Table

Spherical Nuclei
Axially-deformed Nuclei
  1. The ground-state equilibrium deformation is greater than 0.25 
  2. The experimental mass of the nucleus is known
Software (Version 04, June 28, 2010)

We supply the database itself in the form of an Ascii file (Unix format), as well as the necessary Fortran 77 and Fortran 90 subroutines to read the files. Each of the modules can be used "as is" in existing programs.

File Fortran 77 Fortran 90
Test Program main04.f main04.f90
Input/Output Module input04.f input04.f90
The entire package (fortran source and file) is also available below in the form of gz archive (gunzip *.gz to decompress):

Fortran 77 Fortran 90
ExpDatabase_Fortran77_v04.tar.gz ExpDatabase_Fortran90_v04.tar.gz

The programs supplied here open the data file, read all records and fill out a number of arrays with the data that are read. All the relevant arrays are listed below, together with a short description for each of them. This list can also be found in the form of comments in each source file. In Fortran 77, we use implicit declaration of variables (variables whose name starts by I-N are integers by default, others are real by default). In Fortran 90 the Implicit None instruction is used throughtout and each variable is properly declared. The Fortran 90 code is also explicitly modular for better insertion into other codes.

Spherical nuclei (number of cases NUMsphe):

Deformed nuclei (number of cases NUMdefo):

OEM indicator for neutrons (number of cases NUMd3n):

OEM indicator for protons (number of cases NUMd3p):

Super-deformed states and fission isomers (number of cases NUMsupd):

Giant monopole resonance (number of cases NUMmono):

Giant dipole resonance (number of cases NUMdipo):

Odd-mass nuclei (number of cases NUModds):

One quasi-particle state in odd-mass heaviest nuclei (number of cases NUMqpSH):

Position of the first 2+ state (number of cases NUMtwop):

Vpn (number of cases NUMdvpn):
Terminating states (number of cases NUMterm):

Credits and Documentation

Short presentation of the table with basic formulas for form factors, diffraction radius and surface thickness: Link

We warmly thank the following people who contributed to the selection of these data:

Last Modification: June, 26, 2010

This page is maintained by N. Schunck, in collaboration with J. Dobaczewski and W. Nazarewicz