GEF | A GEneral description of the Fision process

The model has been developed with the aim to provide dedicated nuclear data for applications in nuclear technology and engineering. The code treates spontaneous fission and fission up to an excitation energy of about 100 MeV (including multi-chance fission) for a wide range of heavy nuclei from polonium to seaborgium. The development of GEF has been supported by the European Union in the framework of the EFNUDAT and the ERINDA projects and by the OECD Nuclear Energy Agency. A detailed description of the code is given in this report and in these articles published in Nuclear Data Sheets and in Reports on Progress in Physics .

#### The authors will be happy about any comments or suggestions:

**The required input of GEF is:**

- Z and A of fissioning nucleus

- Excitation mode and excitation energy

A extended version of GEF that includes delayed processes (output of delayed-neutron multiplicities, delayed-neutron emitters, cumulative fission-fragment yields in ENDF format) is available on demand.

**GEF calculates the folowing quantities:**

- Contributions of fission chances (multi-chance fission)
- Relative yields of fission channels
- Element-yield distribution*
- Isotonic-yield distribution (pre- and post-neutron)
- Isobaric-yield distribution (pre-and post-neutron) *
- Mass-chain yields (pre- and post-neutron) *
- Fragment angular-momentum distributions (for every nuclide)
- Relative independent isomeric yields
- Prompt-gamma spectrum
- Prompt-neutron spectrum
- Neutron-multiplicity distribution
- Fragment total kinetic energy (pre- and post-neutron)
- Energies and directions of pre- and post-scission prompt neutrons

Other quantities are internally calculated and may be listed.

The sequence of a neutron-induced reaction. First a compound nucleus is formed, which then de-excites by the emission of g -rays, a neutron or by fission. The probability P associated with each decay channel is indicated. In a surrogate reaction, the same compound nucleus as in the neutron-induced reaction is produced by a different reaction.

The executable and the source code of GEF can be downloaded below. They are easy to use : Just download the ZIP file, extract the files and run GEF.bat (Windows [1]) or ./GEF (Linux) in a command window on your computer! The file Readme.txt contains further information.

**Download (including copyright information and license):**

GEF-code, Version 2023/1.1 complete package with executables and source (Released 12 January 2023, last update 09 March 2023)

A new set of GEF parameters is used from a Monte-Carlo fit to a set of different kind of measured or evaluated fission data.

#### Binaries for Windows of Version 2023/1.1

Version with nuclear properties from JEFF-3.3 (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 (considers all known isomers).

#### Binaries for Linux of Version 2023/1.1

Version with nuclear properties from JEFF-3.3 32-bit (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 32 bit(considers all known isomers).

Version with nuclear properties from JEFF-3.3 64-bit (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 64-bit (considers all known isomers).

#### Subroutine (Folding method)

The subroutine aims for being used in combination with other nuclear-reaction codes. For a given fissioning nucleus with excitation energy E* and angular momentum I it calculates complete distributions of a number of fission observables before emission of prompt neutrons and prompt gamma radiation with the GEF model.

**Documentation **Technical description of the subroutine

FreeBASIC version, Source files (Released January 12, 2023)

FORTRAN version, Source files (Released January 12, 2023)

GEF-code, Version 2021/1.1 complete package with executables and source (avril 2022) and GEFSUB (7 Decembre 2021)

#### Binaries for Windows of Version 2021/1.1

GEF-2021-V1-1-NUBASE2016-win-bin (considers only long-lived isomers).

GEF-2021-V1-1-JEFF33-win-bin (considers all known isomers).

#### Binaries for Linux of Version 2021/1.1

Version with nuclear properties from JEFF-3.3 64 bit (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 64 bit (considers all known isomers).

#### Subroutine (Folding method)

The subroutine aims for being used in combination with other nuclear-reaction codes. For a given fissioning nucleus with excitation energy *E** and angular momentum *I* it calculates complete distributions of a number of fission observables before emission of prompt neutrons and prompt gamma radiation with the GEF model.

**Documentation **Technical description of the subroutine

**FreeBASIC version **Source files (Released Dec. 3, 2021)**FORTRAN version **Source files (Released Dec. 3, 2021.)

GEF-code, Version 2020/1.2 complete package with executables and source (Release:December 4, 2020. Las update: Januray 4 2021) The description of asymmetric fission in the pre-actinides has been revised.

#### Binaries for Windows of Version 2020/1.2

GEF-2020-V1-1-NUBASE2016-win-bin (considers only long-lived isomers).

GEF-2020-V1-1-JEFF33-win-bin (considers all known isomers).

#### Binaries for Linux of Version 2020/1.2

Version with nuclear properties from JEFF-3.3 (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 (considers all known isomers).

GEF-code, Version 2020/1.1 complete package with executables and source (Release: July 30, 2020. Las update: September 18 2020) The JEFF-3.3 or the NUBASE2016 decay tables are used for the calculation of isomeric yields. Calculations with a filter on a specific fission mode can be performed.

#### Binaries for Windows of Version 2020/1.1

Version with nuclear properties from JEFF-3.3 (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 (considers all known isomers).

#### Binaries for Windows of Version 2020/1.1

Version with nuclear properties from JEFF-3.3 (considers only long-lived isomers).

Version with nuclear properties from NUBASE2016 (considers all known isomers).

GEF-code, Version 2019/1.3 executables and source (Release: February 2, 2020. Last update: 5 July 2020.) Only minor, mostly technical modifications with respect to GEF 2019/1.2.

GEF-code, Version 2019/1.2 executables and source (Release: September 4, 2019) Refined model parameters; calculation of fission probability revised.

GEF-code, Version 2019/1.1 executables and source (Release: February 4, 2019, last update May 5 2019) The parameters of GEF were re-adjusted, using some very accurate mass yields measured at LOHENGRIN and sets of independent yields from JEFF 3.3. An apparent influence of the N=50 shell on the charge polarization was introduced. The calculations of the fission probability and of the gamma spectrum were revised. Calculations outside the recommended validity range of GEF (in A, Z or E* of the fissioning system) have been made possible with a warning.

GEF-code, Version 2018/1.1 executables and source (Release: June 21, 2018) The model parameters were re-adjusted on the basis of recent empirical fission-fragment mass distributions and independent yields. A rather good agreement with the mass yields from the JEFF 3.3 evaluation was achieved, in particular for 235U(nth,f). Isomeric ratios are calculated with the spectroscopic data from NUBASE 2016. Some corrections, improvements and new features were inserted (see the protocol at the beginning of GEF.bas). This new version gives a good description of different kind of fission data for a large variety of systems. Some problems of GEF 2017/1.2 could be solved, e.g. there are no inconsistencies in the description of thermal-neutron-induced and spontaneous fission any more.

GEF-code, Version 2017/1.2 executables and source (Release: October 18, 2017, last modification January 30, 2018) New set of model parameters, improved description of light, neutron-deficient fissioning systems, calculation of fission probabilities modified. Calculation of covariances/correlations between two different systems corrected. Model parameters slightly modified, better adjusted to independent yields of 235U(nth,f).

GEF-code, Version 2017/1.1 executables and source (September 24 2017) This new version is the result of a new fit of the model parameters to experimental data. In particular, the mass distribution of 235U(nth,f) was considered with special care. Experimental masses and appropriately chosen level densities are used in the evaporation routine in order to better model the fine structure in the fission-fragment yields. Moreover, a few inconsistencies in the description of the fluctuations in the division between TKE and TXE were corrected.

GEF-code, Version 2016/1.1 executables and source (October 14 2016) (Handling of multi-threading. Proton-induced fission up to Ep = 30 MeV supported. Neutron emission between saddle and scission added. New adjustment of model parameters. Gamma spectra with condition on fragment mass. Uncertainties available for more fission observables, including the uncertainty due to the fission fragment angular momenta..).

GEF-code, Version 2015/2.2, executables and source (JSeptember 7 2016) (Overflow problems for large event numbers and in utilities.bi removed. Numerical stability improved. Calculation of covariances between different systems corrected. Description of non-statistical prompt gamma energies with a new VMI model. Improved description of fission chances and fission-fragment distributions for highly excited systems. Improved description of fragment distributions for light fissioning systems (Z = 76 to 90). Prompt-neutron spectrum with variable binsize added in folder « /out ». Prompt-gamma spectrum with conditions on fragment mass and with variable binsize added in folder « /dmp/EgammaA ». Accumulation of prompt-neutron spectrum with variable bin size corrected.

NOTE: GEF Version 2015/2.1 should not be used any more.

GEF-code, Version 2015/1.1, executables and source (January 2, 2015. Last modification September 23, 2015: numerical problems with the new FreeBASIC compiler solved.) (Extended output options, covariances between results of different systems.)

GEF-code, Version 2014/2.1, executables and source (March 25, 2014) (New global parameter set, new systematics of fission barriers)

GEF-code, Version 2014/1.2, executables and source (January 25, 2014) (Modified description of multi-chance fission.)

GEF-code, Version 2014/1.1, executables and source (January 4, 2014) (New global parameter set, modifications for better description of multi-chance fission.)

GEF-code, Version 2013/2.2, executables and source (September 18 2013, updated December 6, 2013) (New global parameter set. Even-odd effect in fission-fragment neutron-number distribution revised. Mass distribution at high excitation energies revised. Angular momentum added as input parameter. Calculation of prompt-neutron emission improved. Output of pre-fission neutron and proton emission extended in tables and list-mode. List-mode output of energies and directions of post-scission neutrons. Multi-chance fission corrected and modified. Spurious even-odd effect in fission probabilites due to even-odd effect in theoretical shell correction removed.)

**Supplemental and help information**

Help information for reading a covariance or correlation matrix from the GEF output file. The covariance or correlation matrix of independent yields is listed in a special format. The sample program corrtest is provided that interprets the data structure and lists the 4-dimensional (Z1, A1, Z2, A2) coordinates and the corresponding matrix values. This program may help you to read the matrices from the GEF output with your own software.

The authors will be happy about any comments or suggestions:

Karl-Heinz Schmidt (e-mail: schmidt-erzhausen.at.t-online.de ) and Beatriz Jurado (e-mail: jurado.at.lp2ib.in2p3.fr)

**EXEMPLES**

Here are some examples of the code: (Black: experimental data, see report for references. Coulored: calculations with contributions of the individual fission channels).

**Main ingredients of the model:**

- The mass division and the charge polarization are calculated assuming a statistical population of states in the fission valleys at freeze-out. The freeze-out time considers the influence of fission dynamics and is not the same for the different collective variables.

- The separability principle governs the interplay of macroscopic and microscopic effects.

- Three fission channels are considered. The strengths of the shells in the fission valleys are identical for all fissioning systems. The mean positions of the heavy fragments in the asymmetric fission channels are essentially constant in atomic number, as suggested by experimental data.

- The stiffness of the macroscopic potential with respect to mass asymmetry is deduced from the widths of measured mass distributions.

- The excitation-energy-sorting mechanism [4, 5, 6] determines the prompt neutron yields and the odd-even effect in fission-fragment yields of even-Z and odd-Z systems [7].

- Neutron evaporation is calculated with a Monte-Carlo statistical code using level densities from empirical systematics [8] and binding energies with theoretical shell effects [9] with gamma competition included.

## Publications

**Experimental evidence for the separability of compound-nucleus and fragment properties in fission **K -H Schmidt, A Kelic, M V Ricciardi , Europh. Lett. 83 (2008) 32001

**Nuclear-fission studies with relativistic secondary beams: analysis of fission channels **C Boeckstiegel et al., Nucl. Phys. A 802 (2008) 12

**Shell effects in the symmetric-modal fission of pre-actinide nuclei **S. I. Mulgin, K.-H. Schmidt, A. Grewe, S. V. Zhdanov, Nucl. Phys. A 640 (1998) 375

**Entropy-driven excitation-energy sorting in superfluid fission dynamics **K.-H. Schmidt and B. Jurado, Phys. Rev. Lett. 104 (2010) 212501, see also Maxwell’s demon on the nuclear level

**Thermodynamics of nuclei in thermal contact **K.-H. Schmidt and B. Jurado, Phys. Rev. C 82 (2011) 014607

**Final excitation energy of fission fragments **K.-H. Schmidt, B. Jurado, Phys. Rev. C 83 (2011) 061601(R)

**Influence of complete energy sorting on the characteristics of the odd–even effect in fission-fragment element distributions **B. Jurado and K.-H. Schmidt, J. Phys. G: Nucl. Part. Phys. 42 (2015) 055101

**Inconsistencies in the description of pairing effects in nuclear level densities **K.-H. Schmidt, B. Jurado, Phys. Rev. C 86 (2012) 044322″

**Nuclear ground state masses and deformations **P. Moeller et al., Atom. Data Nucl. Data Tables 59 (1995) 185