DFT-UNEDF Working Group
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Determination of the
Nuclear Energy functional:
Database of Experimental
Data and Related Software
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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:
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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.
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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:
-
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.
-
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.
-
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
Spherical Nuclei
- Binding energy, charge and proton r.m.s. radii, diffraction radii and surface
thickness
- Giant monopole and dipole resonance in 90Zr, 116Sn
and 208Pb
- Experimental energy of the first 2+ state and B(E2) value in
Ca, Ni, Sn and Pb isotopes
Axially-deformed Nuclei
- Binding energy of well-deformed even-even nuclei. Candidates
were selected from a HFB mass-table calculation by M. Stoitsov with the
SLy4 interaction according to 2 criteria
- The ground-state equilibrium deformation is greater than
0.25
- The experimental mass of the nucleus is known
- Odd-even mass differences for neutrons and protons. A few
isotopic (for neutrons) and isotonic (for protons) lines have been
selected, essentially in the rare-earth region and in the actinides.
These 2 regions were chosen in order to have well-deformed nuclei, and
avoid transitional and closed-shell systems. The Odd-Even Mass
difference is the 3 point formula of Phys. Rev. C 98, 024308 (2001) and gives a
measure of pairing gaps.
- Super-deformed bandheads and fission isomers
- Vpn(Z,N) = 0.5 * [ B(Z,N) - B(Z,N-2) - B(Z-2,N) +
B(Z-2,N-2) ], see M. Stoitsov, R. B. Cakirli, R. F. Casten, W.
Nazarewicz and W. Satula, Phys. Rev. Lett. 98, 132502 (2007)
Symmetry-unrestricted
- Ground-state spin and parity for odd-mass nuclei (odd-even,
even-odd and odd-odd)
- High-K terminating states in f-p shell nuclei
- 1q.p. excited states of odd-mass heaviest elements
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.
The entire package (fortran source and file) is also available below in
the
form of gz archive (gunzip *.gz to decompress):
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):
- IZsphe, INsphe: proton number Z and neutron number N
- Bsphe: experimental binding energy
- dBsphe: error on experimental energy
- R0sphe: experimental diffraction radius
- SIGsphe: experimental surface thickness
- RMSspheCharge: experimental r.m.s charge radius
- RMSspheProton: experimental r.m.s. proton radius
Deformed nuclei (number of
cases
NUMdefo):
- IZdefo, INdefo: proton number Z and neutron number N
- Bdefo: experimental binding energy
- dBdefo: experimental error in binding energy
- b2defo: beta_2 value of g.s. quadrupole deformation (SLY4
calculation)
- IsOKdefo: status of experimental mass (1: measured, 0, evaluated)
OEM indicator for neutrons
(number of cases
NUMd3n):
- IZd3n, INd3n: proton number Z and neutron number N
- DELd3n: experimental neutron OEM
- ERRd3n: experimental error on the neutron OEM (extracted
from error on masses)
- IsOKdefo: status of experimental masses (1: measured, 0, evaluated)
OEM indicator for protons
(number of cases
NUMd3p):
- IZd3, INd3p: proton number Z and neutron number N
- DELd3p: experimental proton OEM
- ERRd3p: experimental error on the proton OEM (extracted from
error on masses)
- IsOKdefo: status of experimental masses (1: measured, 0, evaluated)
Super-deformed states and fission
isomers (number of cases NUMsupd):
- IZsupd, INsupd: proton number Z and neutron number N
- Bsupd: experimental binding energy
- ESDsupd: energy of the SD bandhead or fission isomer
- b2supd: rough estimate of the axial deformation of the SD state
Giant monopole resonance
(number of
cases NUMmono):
- IZmono, INmono: proton number Z and neutron number N
- Emono: experimental energy
Giant dipole resonance (number
of cases
NUMdipo):
- IZdipo, INdipo: proton number Z and neutron number N
- Emdipo: experimental energy
Odd-mass nuclei (number of
cases
NUModds):
- IZodd, INodd: proton number Z and neutron number N
- SPINodd: experimental g.s. spin
- IPodd: experimental g.s. parity
- IsOKodd: status of experimental mass (1: measured, 0, evaluated)
One quasi-particle state in odd-mass
heaviest
nuclei (number of cases NUMqpSH):
- IZqpSH, INqpSH: proton number Z and neutron number N
- NQPqpSH: number of q.p.
states
- EqpSH: experimental excitation energy
- LABqpSH: experimental Nilsson label
- SPINqpSH: experimental spin
- IPqpSH: experimental
parity
Position of the first 2+ state
(number
of cases NUMtwop):
- IZtwop, INtwop: proton number Z and neutron number N
- Etwop: experimental energy of the 2+ state
- dEtwop: error bar on the energy
- BE2twop: experimental BE2
- dBE2twop: error bar on the BE2
Vpn (number
of cases NUMdvpn):
- IZdvpn, INdvpn: proton number Z and neutron number N
- ExcMASdvpn: Mass excess
- ExcERRdvpn: Error on mass excess
- BnucMASdvpn: binding energy per nucleon B/A
- BnucERRdvpn: error (in %) on B/A
- DelVPNdvpn: delta Vpn
- DelERRdvpn: error on delta Vpn
Terminating states (number of
cases
NUMterm):
- IZterm, INterm: proton number Z and neutron number N
- SPINterm, IP1term: spin Imax and parity for the f7/2 state
- Eterm: energy of the f7/2 state
- SPINdEterm, IP2term: spin Imax and parity for the
d3/2^(-1)*f7/2 stat
- dEterm: experimental energy difference between the two
configurations
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:
- Peter Kluepfel (masses and radii of spherical nuclei)
- Gianluca Colo (giant monopole and dipole resonance)
- Jun Terasaki (2+ states and B(E2) values)
- Mario Stoitsov (axially-deformed nuclei deformations and Vpn)
- Ludovic Bonneau (odd-mass spins and parity)
- Wojtek Satula (terminating states)
Last
Modification: June, 26, 2010
This
page is
maintained by N. Schunck, in collaboration with J. Dobaczewski and W.
Nazarewicz
