Quantum dissipation in cluster decay phenomena: I. Smoothly joined quadratic potentials

This paper is devoted to the study of quantum dissipation in nuclear cluste r decay phenomena within the framework of the Lindblad approach to quantum open systems. Typical examples of nuclear decay phenomena, such as cluster radioacivity, spontaneous cold fission of actinide nuclei or quasi-fission of super-heavy nuclei tan be described by considering the tunnelling of a m etastable state across a piecewise quadratic potential. Two study cases are considered: (i) a harmonic well smoothly joined to an inverted parabola wh ich simulates the barrier and (ii) the inverted parabola of case (i) is con tinued with a second harmonic well. The width and depth of the second harmo nic oscillator well are varied over a wide range of values in order to enco mpass particular cases of tunnelling in the double-well potential. The evol ution of the averages and covariances of the quantum sub-system is studied in both under- and over-damped regimes. Fora Gaussian initial wavepacket we compute the tunnelling probability for different values of the friction co efficient and fixed values of the diffusion coefficients. The ansatz used f or these coefficients corresponds to the case with temperature T = 0.