A single uranium fission event produces far more than two fragments: it launches a chain of neutron and gamma-ray emissions whose details matter for reactors, medicine, and nuclear astrophysics. This paper makes TALYS follow that chain fragment by fragment. Prompt particle emission from primary fission fragments generates correlated prompt fission quantities.

These include independent fission product yields, prompt fission neutron multiplicities, prompt fission neutron spectra, prompt fission gamma-ray multiplicities, prompt fission gamma-ray spectra, and isomeric yield ratios. The characteristics of these prompt fission quantities contain valuable information for a detailed understanding of fission physics and are beneficial for applications including delayed neutron yields for reactor safety, transmutation systems for nuclear waste management, radioisotope production, and nuclear astrophysics during the fission cycle in the r-process.

Comprehensive modeling of these observables for different fissioning systems at various excitation energies remains challenging, and estimating accurate fission observables still relies on empirical models. For example, Wahl systematics for fission yields and the Madland-England model for isomeric ratios have been used in evaluations, while the Los Alamos, or Madland-Nix, model for prompt fission neutron spectra considers only the most probable fragmentation.

The current modeling of prompt fission observables often does not consider correlations among independent fission product yield and the other prompt fission observables, which partly causes inconsistency in model calculations. Because of this inconsistency, studies are also being conducted to evaluate prompt fission observables consistently.

The proposed approach uses a common, consistent, well-documented, and transparent nuclear deexcitation code to probe biases and systematic errors in the initial assumptions of fission physics. Existing fission fragment generators provide pre-neutron emission fission fragment mass and energy yield distributions, including microscopic and phenomenological models.

TALYS then calculates the evaporation of neutrons and gamma rays from the excited fission fragment to obtain prompt fission observables, using deterministic techniques similar to the HF3D model. Figure one lays out the proposed workflow: fission-fragment generators such as GEF, HF three-D, and SPY provide pre-neutron mass and energy distributions and excitation-energy sharing.

TALYS then takes fragment yields, mean excitation energy, its width, and average total kinetic energy as inputs for a deterministic Hauser–Feshbach calculation, producing observables such as independent yields, prompt fission neutron and gamma emissions, neutron multiplicities, and isomeric yield ratios.

This framework enables consistent comparisons with experiment and other model codes while helping identify model defects and systematic errors. The detailed calculation focuses on neutron-induced fission of 235U. It shows calculated neutron and gamma-ray multiplicities, prompt fission neutron spectra, prompt fission gamma-ray spectra, and independent fission product yields, compared with available experimental and evaluated data.

The emission process starts with an excited fission fragment in a continuum state. The fragment can emit a neutron and move to continuum or discrete states of a fragment with one lower mass number, or emit gamma rays and move among states of the same mass.

This sequential process continues until each state reaches the ground or isomeric state. The statistical Hauser-Feshbach calculation begins from the spin, parity, and excitation energy of a fission fragment with a given charge and mass.

The neutron and gamma-ray results are then weighted using the initial fission yields to calculate the final observables. The sensitivity analysis varies the f two parameter between three and six, and the f s parameter between zero point four and one point zero. The TALYS input comes from fission fragment yields, mean excitation energy, excitation-energy width, and total kinetic energy obtained from HF3D.

The results show that f two equal to four gives better prompt neutron multiplicity values but smaller prompt gamma-ray multiplicity than f two equal to five or six. The average gamma-ray energy decreases as f two and f s increase, while the average neutron energy decreases as f s increases.

The f s value also strongly affects the peak position and shape of the prompt fission neutron spectrum above two megaelectronvolts. Because the priority is accurate neutron observables, particularly prompt neutron multiplicity, the optimal spin cut-off parameters are f two equal to four and f s equal to zero point four.

Figure three compares calculated prompt-fission-neutron spectra with a Maxwellian reference at one point three two megaelectronvolts, for thermal-neutron-induced fission of uranium two hundred thirty-five, using HF three-D input and three hundred events. The curves vary the spin cut-off settings, including f two equal to four and f sub s ranging from zero point four to one point zero, alongside experimental and evaluated-data references.

This matters because the changing spectral shapes, especially at higher outgoing-neutron energies, show how sensitive neutron predictions are to the assumed fragment-spin parameters. The selected input parameter set is f two equal to four, f s equal to zero point four, and N equal to three hundred.

This selection is identified as optimal for accurate prompt neutron multiplicity and better gamma-ray observables at thermal energy. At thermal neutron energy, the calculated mass-dependent prompt neutron multiplicity from TALYS with GEF, TALYS with HF3D, and GEF all shows the saw-tooth shape consistent with experimental data.

TALYS with HF3D agrees fairly well with experimental data around the most probable masses, although larger discrepancies appear for far asymmetric mass splits. TALYS with GEF and GEF overestimate prompt neutron multiplicity for heavy fragments and underestimate it for the light mass region compared with TALYS with HF3D and literature data.

Around double magicity, with atomic number fifty and neutron number eighty-two, prompt neutron multiplicity shows a pronounced minimum. Recent experimental findings indicate a striking shift toward lighter masses. Figure five shows prompt neutron multiplicity as a function of fission-fragment mass for uranium two hundred thirty-five.

Panel a presents thermal-neutron-induced fission, where the calculations and measurements share a pronounced saw-tooth pattern, with a dip near symmetric fragment masses. Panel b compares incident energies of zero point five and five point five five megaelectronvolts, showing how the mass-dependent multiplicity changes with neutron energy and providing a test of the model’s excitation-energy sharing.

The calculated prompt fission neutron spectrum in the laboratory frame is shown as a ratio to a Maxwellian spectrum at a temperature parameter of one point three two megaelectronvolts. Above two megaelectronvolts of outgoing energy, neither TALYS with GEF nor TALYS with HF3D describes the shape of the experimental data.

TALYS with HF3D has a harder tail, while TALYS with GEF has a softer tail. The TALYS with GEF and GEF results also differ substantially, reflecting a difference in the evaporation schemes used by the codes. Figure seven shows the outgoing-neutron spectrum from the thermal-neutron-induced fission of uranium two hundred thirty-five, plotted as a ratio to a Maxwellian spectrum with a temperature of one point three two megaelectronvolts.

Experimental datasets are compared with TALYS calculations using GEF and HF3D, alongside stand-alone GEF. The figure shows that both TALYS results depart from the measured shape above about two megaelectronvolts: HF3D develops a harder tail, while GEF produces a softer one, and the TALYS and stand-alone GEF results also differ substantially.

The mass-dependent gamma-ray multiplicity calculated in this work shows significant differences between TALYS with GEF and GEF. GEF has a flatter gamma-ray multiplicity as a function of fragment mass, while the TALYS results have a more pronounced saw-tooth shape and agree fairly well with experimental data.

The gamma-ray multiplicities are smaller around fragment mass numbers one hundred to one hundred ten, and other contemporary fission codes also verify the saw-tooth shape in several fissioning systems. Figure eight compares prompt gamma-ray multiplicity in uranium-two-thirty-five fission.

Panel a shows multiplicity versus fragment mass, with TALYS calculations, GEF, and experimental data; the TALYS curves display a pronounced saw-tooth pattern, while GEF is flatter, and the calculations broadly follow the measurements. Panel b shows average multiplicity versus incident neutron energy for the same modeling approaches, illustrating how the predicted gamma-ray output changes as neutron energy increases.

Table three summarizes prompt neutron and gamma-ray multiplicities and their average energies for the uranium two hundred thirty-five thermal-neutron fission reaction. It compares TALYS using GEF or HF3D, stand-alone GEF, experimental measurements, and evaluated data, with neutron energies reported in the laboratory frame and gamma-ray energies in the center-of-mass system.

The authors note that the pronounced low-energy gamma-ray peak in the TALYS calculations contributes to their lower average gamma-ray energies. For prompt gamma-ray observables, the TALYS results tend to show a saw-tooth shape of mass-dependent gamma-ray multiplicity, agreeing with recent experimental findings.

Despite that agreement in shape, the prompt gamma-ray multiplicity is underestimated in absolute scale. The total prompt fission gamma-ray spectrum has a strong peak around zero point two megaelectronvolts, believed to be a binning effect in TALYS, and it underestimates experimental data in some regions, including below two megaelectronvolts and after six megaelectronvolts.

Figure ten shows independent fission-product yield as a function of mass number for thermal-neutron-induced fission of uranium two hundred thirty-five. The plot compares TALYS results using GEF and HF3D inputs with the standalone GEF calculation and several experimental or evaluated datasets.

Across the two prominent mass regions, the curves and data points show closely corresponding yield patterns, illustrating how the database-based TALYS procedure reproduces measured fission-product distributions. Figure eleven compares independent fission-product yields calculated with TALYS using GEF and HF3D inputs against Rudstam and colleagues’ experimental data for thermal-neutron fission of uranium two hundred thirty-five.

Across several elements and mass numbers, both calculations broadly follow the measured yield patterns. The lower panel shows calculated-to-experimental ratios, approaching one for yields above zero point zero zero one, while the ratios become more dispersed for smaller yields—highlighting where predictions are less constrained.

TALYS provides a common framework for connecting fission-fragment models to prompt neutron, gamma-ray, and product-yield observables, but the results still show important model-dependent discrepancies, especially in spectra and absolute gamma-ray multiplicities.