Feature Fission: Dynamics & Predictive Models

• Feature fission is a nuclear fission model characterized by a three-body scission configuration of two deformed heavy fragments and an α-particle.
• It rigorously links quantum state densities, fragment deformations, and saddle-point barrier heights to predict mass, charge, and kinetic energy distributions.
• The integrative approach of feature fission enables systematic predictions in neutron-induced actinide reactions, improving analyses of fission fragment characteristics.

Feature fission is a model of nuclear fission dynamics where the scission configuration consists of two deformed heavy fragments and an α-particle, arising from neck nucleons, positioned between them. The process is governed by the traversal of a three-body saddle point in the potential energy surface, resulting in the subsequent fusion of the α-particle with the nearest fragment and yielding two final binary fragments. The model rigorously connects fragment yields and total kinetic energy to quantum state densities above the saddle barrier, fragment deformations, and energy systematics, enabling predictive descriptions of mass, charge, and kinetic energy distributions in neutron-induced actinide fission (Denisov, 2024).

1. Mass and Charge Yield Distributions

The fission yields in the three-body scission-point model are determined by the quantum level densities above the saddle barriers. For a compound nucleus partitioned into two fragments $(A_1,Z_1)$, $(A_2,Z_2)$, and an α-particle, the primary-fragment yield is given by: $$Y_3(A_1,Z_1) = \frac{2}{N_3} \left[ \rho_{12}^{\rm saddle\,1}(A_1,Z_1) + \rho_{12}^{\rm saddle\,2}(A_1,Z_1) \right]$$ where the multiplicity factor accounts for both saddle crossings. The one-body mass and charge yields follow from summation over charge and mass, respectively: $$Y(A) = \sum_Z Y_3(A,Z), \quad Y(Z) = \sum_A Y_3(A,Z)$$

The level density above the barrier at saddle $i$ is: $$\rho_{12}^{\rm saddle\,i}(A_1, Z_1) = \int d\beta_{12} \int d\beta_{22} \ \rho_{A'_1, Z'_1}(E_1^{si}) \, \rho_{A'_2, Z'_2}(E_2^{si})$$ with $(A'_1,Z'_1)$ and $(A'_2,Z'_2)$ determined by the specific saddle configuration. Each fragment's level density adopts the back-shifted Fermi-gas form: $$\rho_{A, Z}(U) = \frac{\sqrt{\pi}}{12} a_{\rm dens}^{-1/4} U^{-5/4} \exp \bigl(2\sqrt{a_{\rm dens} U}\bigr)$$ where $$a_{\rm dens}(A, Z, U) = a_\infty [1 + \delta_{\rm shell}/U (1 - e^{-\gamma U})]$$ and $U = E - \Delta$. Excitation energies $E_1^{si}, E_2^{si}$ are set by equal-temperature and energy conservation constraints at each saddle.

2. Three-Body Scission Configuration and Potential Energy Surface

Immediately prior to scission, the compound nucleus assumes a configuration of two heavy fragments and an α-particle positioned collinearly along the symmetry axis. Characteristic separations are: $$r_{1\alpha},\, r_{2\alpha},\, r_{12} = r_{1\alpha} + r_{2\alpha}$$

The total potential energy is the sum of all interaction terms: $$V_{1\alpha2}^{\rm tot}(r_{1\alpha}, r_{2\alpha}, \beta_{12}, \beta_{22}) = V_{12}^{\rm tot}(r_{12}, \beta_{12}, \beta_{22}) + V_{1\alpha}^{\rm tot}(r_{1\alpha}, \beta_{12}) + V_{2\alpha}^{\rm tot}(r_{2\alpha}, \beta_{22})$$ where two-body potentials decompose into Coulomb, nuclear, and deformation-dependent components.

Saddle-point heights $B_{1\alpha2}^{s1}, B_{1\alpha2}^{s2}$ are the maxima of $V_{1\alpha2}^{\rm tot}$ traced along distinct valleys in the configuration space. These heights directly influence the fragment yield shapes and the energy required for scission.

3. Fragment Deformation and Saddle-Point Barrier Heights

The model incorporates multipole expansions (quadrupole, octupole, hexadecupole) of fragment deformations, post neck-rupture, to accurately assess energy barriers. The two-fragment potential following neck rupture reads: $$V_{12}^{\rm tot}(r, \{\beta_{i\ell}\}) = V_{12}^C(r, \{\beta_{i\ell}\}) + V_{12}^n(r, \{\beta_{i\ell}\}) + E_{\rm def}^{(1)}(\{\beta_{1\ell}\}) + E_{\rm def}^{(2)}(\{\beta_{2\ell}\})$$

Quadrupole deformation energy about the ground state $\beta_{0, i}$ is approximated harmonically: $$E_{\rm def}^{(i)}(\beta_{i2}) = \frac{1}{2} (C_{\rm ld} + C_{\rm sc}) (\beta_{i2} - \beta_{0, i})^2$$ with $$C_{\rm sc} \approx -0.05 C_{\rm ld} \delta_{\rm shell}$$. Locating the saddle requires minimization over higher-order deformations, establishing the subspace $(r, \beta_{12}, \beta_{22})$ for barrier evaluation.

4. Dynamics of α-Particle Fusion and Final Fragment Formation

Following saddle crossing, if $r_{1\alpha}^{s1}$ is sufficiently small, the α-particle is localized in the potential pocket of $V_{1\alpha}^{\rm tot}(r_{1\alpha}, \beta_{12})$ and fuses with fragment 1. The analogous process occurs at the second saddle for fusion with fragment 2. Binary fragments are thus formed subsequent to the collapse of the tri-nuclear configuration.

Rare ternary fission (frequency $\sim 10^{-3}$) results from scenarios where the α-particle either tunnels out of the potential well or a fragment is sufficiently excited that neutron emission is competitive. This highlights the predominant binary outcome for feature fission events.

5. Total Kinetic Energy and Systematics

The total kinetic energy (TKE) of the fission fragments is a direct remnant of the three-body potential at the scission saddle: $$E_{\rm kin}^{si} = V_{12}^{\rm tot}(r_{1\alpha}^{si} + r_{2\alpha}^{si}, \beta_{12}^{si}, \beta_{22}^{si}) + V_{j\alpha}^{\rm tot}(r_{j\alpha}^{si}, \beta_{j2}^{si})$$ The average TKE is: $$\overline{\rm TKE} = \frac{1}{N_3} \sum_{A_1, Z_1} \int d\beta_{12} d\beta_{22} \left[ \rho_{A'_1, Z'_1}(E_1^{s1}) \rho_{A'_2, Z'_2}(E_2^{s1}) E_{\rm kin}^{s1} + \rho_{A'_1, Z'_1}(E_1^{s2}) \rho_{A'_2, Z'_2}(E_2^{s2}) E_{\rm kin}^{s2} \right]$$ The value is taken over all possible partitions and saddle conditions.

6. Integrative Picture and Predictive Scope

Feature fission integrates barrier heights, level densities, deformation energies, and three-body geometry to predict observed binary fragment yields and kinetic energies for neutron-induced fission of actinides. Each model component is functionally linked:

• Barrier heights $\rightarrow$ yield shapes
• Level densities $\rightarrow$ isotopic structure
• Deformation energies $\rightarrow$ shell sensitivity
• Three-body geometry $\rightarrow$ α-particle dynamics
• Saddle potential energies $\rightarrow$ TKE systematics

All quantitative outputs—mass, charge, isotopic yield distributions, and average TKE—for 30 actinide cases are captured without ad-hoc parameterization, using only two-body potentials, α-nucleus pocket energies, and standard nuclear level-density prescriptions (Denisov, 2024). This suggests that the feature fission framework robustly unifies diverse features of fragment distributions and energetics in a single theoretical structure.