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arXiv:0801.2463 · Physical Review C

Assisted tunneling of a metastable state between barriers

German Kälbermann

Published Apr 15, 2008• 16 citations
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Abstract

The assisted tunneling of a metastable state between barriers is investigated analytically by means of a simplified one-dimensional model. A time dependent perturbation changes the pole spectrum of the wave function introducing a larger decay constant. New insights about the decay of a metastable state are found. The scheme is exemplified for parameters corresponding to the nuclear process of \ensuremath{\alpha} decay.

DOI
10.1103/physrevc.77.041601

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The assisted tunneling of a metastable state between barriers is investigated analytically by means of a simplified one-dimensional model. A time dependent perturbation changes the pole spectrum of the wave function introducing a larger decay constant. New insights about the decay of a metastable state are found. The scheme is exemplified for parameters corresponding to the nuclear process of \ensuremath{\alpha} decay.
Recently we outlined an analytical method of solving the time-dependent Schr\"odinger equation for a model which simulates a decaying quantum system such as an $\ensuremath{\alpha}$-decaying nucleus. A particle in the model is initially confined around the origin and leaks out, tunneling through a potential barrier. The solution can be expressed as a linear combination of the Moshinsky functions, each of which is associated with a pole of the scattering S\mathbf{S}S matrix of the model. In this paper we give a full account of the method with a few explicit examples. We examine deviations from the exponential decay law at very large times. We comment on a recent controversy regarding the t dependence of the survival and nonescape probabilities when t is very large.
A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers Classical Descriptions of Tunneling Tunneling in Time-Dependent Barriers Decay Width and Scattering Theory The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems Path Integral and Its Semi-Classical Approximation in Quantum Tunneling Heisenberg's Equations of Motion for Tunneling Wigner Distribution Function in Quantum Tunneling Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation Multidimensional Quantum Tunneling Group and Signal Velocities Time-Delay, Reflection Time Operator and Minimum Tunneling Time More about Tunneling Time Tunneling of a System with Internal Degrees of Freedom Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object Relativistic Formulation of Quantum Tunneling Inverse Problems of Quantum Tunneling Some Examples of Quantum Tunneling in Atomic and Molecular Physics Some Examples from Condensed Matter Physics Alpha Decay.
This study investigates three-dimensional quantum tunneling through analytical solutions of the Schr¨odinger equation in Cartesian and spherical coordinates. By develop ing transmission coefficients for both square and spherical potential barriers, we establish a theoretical framework for α-decay via the Gamow model. The analysis reveals how angular momentum and energy dependence govern tunneling probabilities, with experimental valida tion showing agreement within 15% for high-energy decays. The results bridge fundamental quantum mechanics with nuclear physics applications.