NuDEX

NuDEX is a computer toolkit which allows to generate de-excitation cascades of atomic nuclei. The code is available for download from [MCO], together with a manual describing its performance.

For the moment, it has been incorporated into Geant4 to model the emission of \(\gamma \)-rays and electrons following neutron capture reactions, but in the future it is expected to be extended to other types of nuclear de-excitations.

Most neutron capture reactions that are modeled with Geant4 occur through the mechanism known as compound nucleus. In this mechanism, the neutron is absorbed by the target nucleus (^AZ), giving rise to a nucleus with one more neutron (^A+1Z*) and which is in an excited state with typical energies of 5-10 MeV. In a second step, the compound nucleus decays to the ground state or an isomeric state emitting an electromagnetic cascade, which may be modeled by NuDEX.

To model the de-excitation of a nucleus, NuDEX generates the full level scheme, branching ratios and internal conversion coefficients, in a similar way as it is done by the codes DICEBOX [Bec98] and DEGEN [JAT16]. To do this, it takes the known values from a database based mainly in RIPL-3 [CHO+09] and ENSDF [had], and fills in the missing information with statistical models.

The level scheme of a certain nucleus is supposed to be complete up to a certain excitation energy E_crit, provided by RIPL-3. Above E_crit, the level scheme is generated randomly according to level density formulas. The distances between consecutive levels are sampled according to a Wigner distribution. Some of the level density models implemented in the code are the Back-Shifted Fermi Gas Model and the Gilbert-Cameron Model, which depend on some parameters which are taken from RIPL-3.

In order to reduce the computation memory and time, NuDEX has the possibility of grouping the levels into bands. The levels that make up each of these bands all have the same spin and parity. Each of these bands is then characterized by their lower and upper excitation energy, their spin and parity, and the number of levels which contains. The effect of making bands does not have an important impact in the resulting electromagnetic cascades for most practical cases.

Branching ratios not present in the databases are generated according to the so called extreme statistical model [Bec98]. The branching ratio of the transition from a level a to a level b, \(\text{BR}_{a \rightarrow b}\), is computed according to:

\[\text{BR}_{a \rightarrow b} \propto \sum_{X,L}^{}{\xi_{a \rightarrow b}^{2}E_{\gamma}^{2L + 1}\overleftarrow{f^{\text{XL}}}(E_{\gamma},E_{a})}\]

where X is the type of transition (electric or magnetic); L is the multipolarity; \(\xi_{a \rightarrow b}\) is a random variable drawn independently from a normal distribution with zero mean and unit variance, which introduce the Porter-Thomas fluctuations; \(E_\gamma \) is the difference between the energy of the level a, \( E_a \), and the energy of the level b, \( E_b \); and \(\overleftarrow{f^{\text{XL}}}(E_{\gamma},E_{a})\) is the Photon Strength Function (PSF). The branching ratios are normalized so that the sum of all of them starting from the same level equals 1, \(\sum_{i = 0}^{n - 1}\text{BR}_{n \rightarrow i} = 1\). For the moment, only E1, M1 and E2 transitions are considered.

In addition to the branching ratios from the known part of the level scheme, the NuDEX database contains also lists of primary \( \gamma \)-rays from thermal neutron capture, together with the observed intensities, taken from ENSDF. These data are particularly important for simulating thermal neutron capture \( \gamma \)-rays of light nuclei.

Internal conversion coefficients are obtained from the same RIPL-3 database as the known levels, if present. Otherwise they are obtained from the data tables provided by Band et al. in [BTN+02].

To generate the cascades, NuDEX uses default parameters that are mainly found in its database. Users can change these values, if required, in two possible ways:

By editing the file with name GeneralStatNuclParameters.dat, which is located in the NuDEX database. There it is possible to change, for example, the level density or Photon Strength Function models, or the width of the bands where the levels are grouped. Changes can be made for all nuclei (Z=0 A=0) or for some specific ones.
By editing the files or creating new ones inside the folder SpecialInputs. There each file corresponds to a particular nucleus.

More information concerning the performance of NuDEX can be found in the NuDEX manual [MCO] or in [MACO+23, MCOJ+20].

Bibliography

had: Evaluated nuclear structure data file (ensdf). https://www.nndc.bnl.gov/ensdf/. [Online; accessed 3-December-2024].
BTN+02: I.M. BAND, M.B. TRZHASKOVSKAYA, C.W. NESTOR, P.O. TIKKANEN, and S. RAMAN. Dirac–fock internal conversion coefficients. Atomic Data and Nuclear Data Tables, 81(1–2):1–334, May 2002. URL: http://dx.doi.org/10.1006/adnd.2002.0884, doi:10.1006/adnd.2002.0884.
Bec98(1,2): F. Bečvář. Simulation of γ-cascades in complex nuclei with emphasis on assessment of uncertainties of cascade-related quantities. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 417(2–3):434–449, November 1998. URL: http://dx.doi.org/10.1016/S0168-9002(98)00787-6, doi:10.1016/s0168-9002(98)00787-6.
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MACO+23: E. Mendoza, V. Alcayne, D. Cano-Ott, E. González-Romero, T. Martínez, A. Pérez de Rada, A. Sánchez-Caballero, J. Balibrea-Correa, C. Domingo-Pardo, J. Lerendegui-Marco, F. Calviño, and C. Guerrero. Neutron capture measurements with high efficiency detectors and the pulse height weighting technique. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1047:167894, February 2023. URL: http://dx.doi.org/10.1016/j.nima.2022.167894, doi:10.1016/j.nima.2022.167894.
MCO(1,2): E. Mendoza and D. Cano-Ott. Nudex (a nuclear de-excitation code). URL: https://github.com/UIN-CIEMAT/NuDEX.
MCOJ+20: E. Mendoza, D. Cano-Ott, D. Jordan, J.L. Tain, and A. Algora. Nudex: a new nuclear γ-ray cascades generator. EPJ Web of Conferences, 239:17006, 2020. URL: http://dx.doi.org/10.1051/epjconf/202023917006, doi:10.1051/epjconf/202023917006.