Fission path
Fission of a heavy nucleus as the deformation of a charged liquid drop, corrected by shell effects: double-humped barrier, superdeformed isomer and the sequence of shapes down to the two fragments (Cassini ovals). The liquid drop and the energy curves are computed by the Python backend (via gw2py).From the deformed droplet to scission: the same collective droplet of the Bohr–Mottelson nucleus, driven to the large-amplitude deformation that breaks it in two.
Fission of a heavy nucleus as the deformation of a charged liquid drop, corrected by shell effects.
Liquid drop: surface against Coulomb
The deformation energy is the competition between surface energy (which resists) and Coulomb energy (which pushes towards deformation):
\[ \Delta E(\text{shape}) = E_S^0\,[B_S-1] + E_C^0\,[B_C-1], \]with \(E_S^0=a_s A^{2/3}\), \(E_C^0=a_c Z^2/A^{1/3}\) and \(B_S,B_C\) the shape factors (area and Coulomb relative to the sphere).
Fissility
\[ x=\frac{E_C^0}{2E_S^0}=\frac{Z^2/A}{(Z^2/A)_{\rm crit}},\qquad (Z^2/A)_{\rm crit}\simeq 50. \]The double-humped barrier (Strutinsky)
The liquid drop gives a single-humped barrier. Adding the deformation-dependent shell correction makes it double-humped: a superdeformed second minimum opens up (axis ratio 2:1), the fission isomer. Inner barrier \(E_A\), isomeric minimum \(E_{\rm II}\), outer barrier \(E_B\).
Sequence of shapes and scission
Along the path the shape goes from prolate (ground state) to strongly elongated (isomer), develops a neck and finally splits into two fragments, releasing ~200 MeV. Here the surface is parametrized with Cassini ovals, which describe continuously sphere → neck → scission → two fragments.
Fissioning nucleus
Method
The liquid drop is computed by the backend from the shape factors of the Cassini ovals and the fissility \(Z^2/A\); the double hump adds the shell correction (parametrized on the measured values). In the visualization you can slide the deformation by hand or animate the sequence down to scission.
Nuclear shape along the path
Deformation energy
What is computed, what is parametrized, and the thread to the other pages.
Macroscopic computed, microscopic parametrized
Spontaneous fission = tunnelling
Spontaneous fission is quantum penetration through the double-humped barrier: the WKB amplitude \(\exp\!\big[-\tfrac1\hbar\!\int\!\sqrt{2B(V-E)}\,dq\big]\) along the deformation coordinate, with \(B\) the collective mass. It is the same tunnelling physics as the double well page (instantons, WKB), here on the nuclear scale: fission isomers are states trapped in the second well that fission by tunnelling.
Paired with the collective page
This page completes the collective nucleus: there the deformation is a small oscillation (β,γ) around equilibrium; here it is a large-amplitude deformation leading to break-up. Same object (the collective droplet), opposite regimes.
What is missing (honesty)
The model is axially and reflection symmetric; real actinide fission is mass asymmetric (~140/~96), a shell effect in the nascent fragments, and the inner barrier is lowered by triaxiality (~2–3 MeV). The full microscopic dynamics is time-dependent TDHF (a 3D density evolving to scission), out of reach for a browser preview.
References
- N. Bohr, J. A. Wheeler, «The Mechanism of Nuclear Fission», Phys. Rev. 56, 426 (1939). doi.
- V. M. Strutinsky, «Shell effects in nuclear masses and deformation energies», Nucl. Phys. A 95, 420 (1967). doi.
- M. Brack et al., «Funny Hills: The Shell-Correction Approach…», Rev. Mod. Phys. 44, 320 (1972). doi.
- S. Bjørnholm, J. E. Lynn, «The double-humped fission barrier», Rev. Mod. Phys. 52, 725 (1980). doi.
- H. J. Specht, «Nuclear fission», Rev. Mod. Phys. 46, 773 (1974). doi.
WebNIR · CNR-IFAC | demo interface — liquid drop and energy curves from the Python backend (gw2py).
Keywords: fission, double-humped barrier, fission isomer, liquid drop, Strutinsky, Cassini ovals, fissility, scission