Optical and mechanical properties of electron bubbles in superfluid helium-4
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ptical and Mechanical Properties of Electron Bubbles in Superfluid Helium41 Z. Xie, W. Wei, Y. Yang, and H. J. Maris* Department of Physics, Brown University, Providence, Rhode Island, 02912 USA *email: [email protected] Received May 14, 2014
Abstract—A series of experiments has revealed the existence of a large number (about 18) of different types of negative ions in superfluid helium4. Despite much effort, the physical nature of these “exotic ions” has still not been determined. We discuss possible experiments which may be able to help determine the structure of these objects. Contribution for the JETP special issue in honor of A.F. Andreev’s 75th birthday DOI: 10.1134/S1063776114120103 1
1. INTRODUCTION
At first sight, it appears that it should be easy to understand the behavior of an electron immersed in liquid helium. Because a helium atom has a closed shell of electrons, there is a strong repulsion between a helium atom and an electron. As a result, in order to enter liquid helium, an electron has to overcome an energy barrier of approximately 1 eV [1a]. An experi ment performed earlier [1b] gave the result 1.3 eV. This barrier, together with the very low surface energy α of the liquid (0.375 erg cm–2) [2], makes it favorable for an electron to force open a cavity in the liquid and become trapped there, rather than moving freely through the bulk liquid. The size of this bubble can be estimated, to a reasonable accuracy, from the approx imate expression for the energy 2
2 4π 3 h E bubble = 2 + 4πR α + R P, (1) 3 8mR where R is the bubble radius, m is the electron mass, and the last term represents the energy associated with forming the bubble when a pressure P is applied to the liquid. In the absence of an applied pressure, we find from Eq. (1) that the energy should be a minimum for the radius 2
1/4
h ⎞ ≈ 19 Å. R 0 = ⎛ (2) ⎝ 32πmα⎠ These “electron bubbles” have been studied in many experiments. 1—Measurements have been made of the photon energies required to excite the electron to a higher 1 The article is published in the original.
energy state [3–5]. Since these energies are dependent on the bubble size (approximately proportional to the inverse square of the radius), the experiments provide information about the radius. 2—The mechanical properties of the bubble can be studied by applying a negative pressure [6]. If a nega tive pressure larger than a critical value Pc is applied, the bubble becomes unstable and grows rapidly. It can then be detected optically. From Eq. (1), the critical pressure is found to be [7] 16 2πm 1/4 5/4 P c = – ⎛ 2⎞ α . (3) 5 ⎝ 5h ⎠ 3—Measurements have been made of the mobility μ of these bubbles [8–10]. The mobility is limited by the drag force exerted on a moving bubble by thermally excited phonons and rotons. In superfluid helium4 above 1 K, the drag is primarily due to rotons and the mobility can be expected to vary as (4) μ ∝ exp ( Δ/kT ), where Δ is the roton energy gap. The results of the mobility experiments
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