Metastable Potential Research Articles

Metastable decay rates, asymptotic expansions, and analytic continuation of thermodynamic functions

The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series∑nQnzn, whereQn, which depends on the temperatureT, is the “partition function” of a cluster of sizen. At low temperatures this series has a finite radius of convergencezs. Some theorems are proved showing that ifQn, considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromzs to +∞ and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Doring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.

Class of solvable one-dimensional Fokker-Planck and Schrödinger equations with various potentials.

A class of one-dimensional Fokker-Planck and Schr\"odinger equations is defined that are solvable by scalar-continued-fraction calculations for the eigenvalues and for the coefficients in the eigenfunctions. In a selection of preliminary case studies, possibilities and restrictions of the solution method are explored, and a variety of mono-, multi-, and metastable potentials is shown to belong to the class. Different solution-method variants, including the supersymmetry principle, are discussed.

Quantum tunnelling in a high temperature boson bath

Abstract Quantum tunneling of a particle in a high temperature oscillator system is studied. For any potential energy and an arbitrary set of oscillators the instanton action is exactly calculated. As an example tunnelling in the cubic metastable potential is considered.

Sudden theory for tunneling in dissipative systems.

The effect of a low-frequency dissipative medium on the tunneling rate of a particle trapped in a metastable potential is investigated with the aid of a frozen-bath sudden approximation. The sudden theory is formulated for arbitrary time-dependent friction and for all temperatures at which the escape process is dominated by tunneling. The validity criterion of the theory is only that the bath frequency spectrum be substantially lower than the system frequency. It is applicable both in the weak- and strong-damping limits. The sudden theory is applied to tunneling in a cubic potential and a piecewise harmonic potential where the barrier frequency differs from the well frequency. In contrast to the ImF method, the sudden theory, when valid, can provide estimates of tunneling rates from well-defined excited resonance states and is not limited to estimates of only thermal rates. We find that, if the barrier is thin relative to the well, dissipation can serve to enhance tunneling rates from excited states.

Study of argon-based penning gas mixtures for use in proportional counters

Results from an experimental investigation of three Penning gas mixtures, namely argon-acetylene (Ar-C 2H 2), argon-xenon (Ar-Xe) and argon-xenon-trimethylamine (Ar-Xe-TMA), are reported. The measurements, carried out in cylindrical geometry as well as parallel plate geometry detectors, demonstrate that the Ar-C 2H 2 mixtures show a significant Penning effect even at an acetylene concentration of 10% and provide the best energy resolution among all the argon-based gas mixtures (≤13% FWHM at 5.9 keV and 6.7% at 22.2 keV). In the parallel plate detector the Ar-C 2H 2 fillings provide a resolution of ≈ 7% FWHM at 22.2 keV up to a gas gain of at least ⋍10 4 . The nonmetastable Penning mixture Ar-Xe provides the highest gas gain among all the argon-based gas mixtures and is well suited for use in long-duration space-based experiments. Best results are obtained with 5% and 20% Xe in Ar, the energy resolution being ⋍ 7% FWHM at 22.2 keV and ⋍ 4.5% at 59.6 keV for gas gain ⪅10 3. Addition of ≥1% TMA to an 80% Ar-20% Xe mixture produces a dramatic increase in gas gain but the energy resolution remains unaffected (≈ 7% FWHM at 22.2 keV). This increase in gas gain is attributed to the occurrence of a Penning effect between Xe and TMA, the ionization potential of TMA being 8.3 eV, just below the xenon metastable potential of 8.39 eV.

Potassium adsorption on hydrogen-covered Ru(0001) studied by metastable quenching spectroscopy, thermal desorption, and electron-stimulated desorption

Metastable quenching spectroscopy, thermal desorption spectroscopy, and electron stimulated desorption spectroscopy were used to study how potassium adsorption affects hydrogen binding to the Ru(0001) surface. Potassium causes the appearance of Penning ionization peaks from H/Ru surface states, which are found to be more prominent with Ne ∗ than with He ∗. This intensity difference is explained qualitatively by a model in which the competition between metastable quenching by resonance ionization or by Penning ionization is examined in terms of surface work function, the metastable atom ionization potential, and the image-charge potential. Potassium adsorption on Ru(0001) precovered with hydrogen leads to the appearance of a narrow high temperature peak in the H 2 thermal desorption spectrum. At that temperature H 2 desorbs simultaneously with the last of the adsorbed potassium left on the surface. This peak is increased and broadened if the Ru surface is sputtered prior to H 2 and K coadsorption. The presence of potassium increases the ESD H + yield by a factor of up to 30 times that without potassium, with the yield peaking at the potassium coverage giving the minmum work function, and sharply decreasing as the potassium coverage is increased further. This effect is discussed in terms of a model proposed by Lanzillotto, Dresser, Alvey and Yates for similar results on the H/K/Ni(111) system.

Use of propane as a quench gas in argon-filled proportional counters and comparison with other quench gases

An experimental investigation of propane and six other quench gases was carried out in argon-filled proportional counters. The objective of the study was to find the best gas mixture for optimizing the gas gain and the energy resolution as well as to understand the role of the ionization potential of quench gases in determining these parameters. It was found that the best gas gains and energy resolutions are obtained with propane, ethane, and isobutane in that order. The ionization potentials of these three lie below the argon metastable potentials and have the lowest value of resonance defect compared to the other quench gases. The better results obtained with these mixtures can be explained by an increased ionization yield resulting from the Penning effect. Propylene and trans-2-butene give inferior performance compared to the above three gases. Methane and carbon dioxide, the most commonly used quench gases in the argon-filled detectors, provide the worst results.

Decay and resonance tunneling in a small ac field: Two-level approximation

In the presence of a periodic external field a particle confined in a well may occupy one of the quasienergy states. We investigate the tunneling decay of such a state in a metastable potential as well as resonance tunneling via it in the double barrier case. The decay rate as function of the magnitude of the ac field and the form of the resonance peak are calculated under the assumption that the applied field is small and its frequency is close to the spacing between two energy levels of the unperturbed system. The resonance peak in the transparency of a double barrier is shown to be doubled due to the splitting of the quasienergies in the well.

Boundary-layer theory for the extremely underdamped Brownian motion in a metastable potential

A theory for the boundary layer near the critical trajectory for the extremely underdamped Brownian motion in a metastable potential is presented. The probability distribution function in phase space near this critical trajectory, the average escape energy, and the correction terms for the zero-friction-limit escape rate are calculated.

Phenomenological shortcut to dissipative tunneling

A phenomenological approach to dissipative tunneling, originally put forth by Pollak [Phys. Rev. A 33, 4244 (1986)], is discussed and contrasted with the bounce formalism. This phenomenological approach is based on the WKB theory for parabolic barrier tunneling. It is quite simple and readily evaluated. We study the results for the leading exponential dissipative decay rate in metastable potentials and contrast them with previous instanton-type (bounce-technique) calculations. In doing so, we compare the zero-temperature decay rate in various metastable potentials, different dissipation mechanisms, and also consider the rate enhancement at very low temperatures. One finds between the two methods unexpected good agreement at weak to moderate dissipation strength; the accuracy decreases with increasing dissipation strength and increasing deviation from a harmonic barrier shape.

Quantum decay into a continuum at weak bias.

We consider the quantum decay from the locally stable ground state of a one-dimensional metastable potential. We consider the case where the metastable minimum is almost degenerate with the vacuum level. In this case, the quantum decay probability is influenced by backscattering from the continuum states; a feature which is not accounted for in standard WKB theory. We evaluate the decay rates, from the ground state and the higher-resonance states, by the use of complex-time path-integral methods. The decay rate from the low-lying states of the metastable well is characterized by two quasi-zero-modes and a transmission factor, which approaches zero proportional to the square root of the potential drop. Moreover, we present a useful set of rules for the complex-time path-integral phase factors. These rules considerably simplify the calculation of decay rates (i.e., the pole condition of the Fourier-transformed Green's function).

Thermal enhancement of the quantum decay rate in a dissipative system

The quantum decay of a metastable system which interacts with an environment at temperatureT is considered. A general formula for the decay rate at finite temperatures is obtained by a method which is based on the framework recently described by Caldeira and Leggett. The thermal enhancement of the tunnelling rate at low temperatures is discussed for arbitrary metastable potentials, and it is found that the exponent of the rate obeys a power law in a dissipative system. The power law exponent is shown to be a characteristic feature of the dissipative mechanism. Finally, a universally valid formula for the thermal enhancement factor is given, where the form of the potential enters only through the frequency of small oscillations about the metastable minimum and the “length” of the zero temperature bounce trajectory.

Ionization in Argon Mixtures by Electrons in an Electric Field

A systematic investigation has been made on ionization in argon mixtures by electrons in a convergent field. Total filling pressure is 760 mmHg and the added impurities are organic vapors and inert gases. The ionization current increases by the addition of these impurities even when their ionization potentials are higher than the metastable potential of argon. The increase in ionization seems to become more remarkable as the ionization potential of the impurity lowers and the optimum concentration that gives a maximum ionization decreases with the effectiveness of the added impurities. From the result of a series of our measurement possibility of direct impact ionization and photoeletric ionization is suggested.