Yes, according to the mathematical model of quantum mechanics, there is a non-zero probability for a nuclear fission event to occur spontaneously through the process of quantum tunneling.
Quantum tunneling is a phenomenon in which a particle can penetrate through a potential energy barrier even when its energy is lower than the barrier's height. This effect arises from the wave-like nature of particles in quantum mechanics. In the context of nuclear fission, the nucleus of an atom can be thought of as a particle confined within a potential energy well. When the nucleus has sufficient energy to overcome the barrier, it can tunnel through it, resulting in the spontaneous fission of the nucleus.
The probability of spontaneous fission due to quantum tunneling depends on several factors, including the specific properties of the nucleus involved and the height and width of the potential energy barrier. The phenomenon of spontaneous fission is more likely to occur for heavy nuclei, as they typically have a larger barrier to overcome and exhibit a greater degree of quantum tunneling.
Quantum mechanics provides a mathematical framework to calculate the probability of tunneling events, and these calculations can be applied to understand the likelihood of spontaneous nuclear fission. By solving the relevant quantum mechanical equations, physicists can estimate the probability of such events occurring and compare them with experimental observations.
It is important to note that while quantum mechanics predicts a non-zero probability for spontaneous fission through tunneling, the actual rates of such events can vary significantly depending on the specific system and conditions involved. Experimental measurements are crucial for verifying and refining the theoretical predictions of quantum tunneling and spontaneous fission.