Electron bubble

Connect the tubing from the electronic bubble meter to the inset of the impinger/bubbler. 

Figure 2. For calibration, the cassette is attached to an electronic bubble meter as shown in the illustration.

Calibrate personal sampling pumps before and after each day of sampling, using either the electronic bubble meter method or the precision rotameter method (that has been calibrated against a bubble meter). 

The electronic bubble meter method consists of the following ... 

Press the button on the electronic bubble meter. Visually capture a single bubble and electronically time the bubble. The accompanying printer will automatically record the calibration reading in liters per minute. 

The precision rotameter is a secondary calibration device. If it is to be used in place of a primary device such as a bubble meter, care must be taken to ensure that any introduced error will be minimal and noted. The precision rotameter may be used for calibrating the personal sampling pump in lieu of a bubble meter provided it is (a) Calibrated with an electronic bubble meter or a bubble meter, (b) Disassembled, cleaned as necessary, and recalibrated. It should be used with care to avoid dirt and dust contamination which may affect the flow, (c) Not used at substantially different temperature and/or pressure from those conditions present when the rotameter was calibrated against the primary source, (d) Used such that pressure drop across it is minimal. If altitude or temperature at the sampling site are substantially different from the calibration site, it is necessary to calibrate the precision rotameter at the sampling site where the same conditions are present. 

Electronic Flow Calibrators These units are high accuracy electronic bubble flowmeters that provide instantaneous air flow readings and a cumulative averaging of multiple samples. These calibrators measure the flow rate of gases and report volume per unit of time. The timer is capable of detecting a soap film at 80... 

D. Threshold Size Effects for Superfluidity Energetics of Electron Bubbles in ( He) Clusters... 

D. Motion of the Electron Bubble in the Image Potential in Superfluid and Normal Fluid... 

How can one use macroscopic probes (i.e., excess electron bubbles) to interrogate superfluidity in finite ( He)jy clusters ... 

N > 10 ) at 0.4 K involves a transport probe—that is, electron tunneling from the electron bubble (Chapter IV)—which provided evidence for vanishingly low viscosity of the superfluid finite system. 

The excess electron surface state and the electron bubble state constitute two distinct ground states and two electronic manifolds of bound electronic states, with the surface states converging to the vacuum level, while the bubble states converge to the hquid conduction band (Fig. 9). The two electronic manifolds... 

R — Rc), converging to the bulk value (cxd) = —0.74 meV [178]. The huge mean radius (r) of this halo state diverges when R Rc (Fig. 11). The internal electron bubble state was predicted to be realized in sufficiently large He clusters [208, 209]. The experimental genesis of this field rested on... 

Figure 12. Artist s view of the excess electron bubble localized state in a (He)jy cluster.

Figure 13. The cluster size dependence of the calculated binding energies per atom for a He) cluster (N = 6.5 x 103 to 1.88 x lO ) of radius R without a bubble (marked as cluster) and for a cluster with a bubble at the equilibrium electron bubble radius Rf, (marked as cluster + bubble). The experimental binding energy per atom in the bulk [232, 248], E /N = —0.616 meV (R, N = cxd), is presented (marked as bulk). Previous computational results for the lower size domain N = 128-728 [51-54, 106, 128, 129] are also included. The calculated data for the large (N = 10 —10 ) clusters (A = 6.5 x 1Q3 to 1.88 x 10 ), as well as the bulk value of Ec/N without a bubble, follow a linear dependence versus 1 /R and are represented by the liquid drop model, with the cluster size equation [Eq. (58)] (solid line). The dashed curve connecting the E /N data with a bubble was drawn to guide the eye. The calculated data for the smaller clusters (N = 128) manifest systematic positive deviations from the liquid drop model, caused by the curvature term, which was neglected.

In Fig. 13 we also present the energetics of the ( He) cluster with a bubble at the equilibrium electron bubble radius, with inferred (Section III.C) from the electron bubble. These results manifest the marked increase of Ec/N upon bubble formation, which is due to cluster deformation. Data were obtained on the bubble radius Rb, the cluster deformation energy per atom Ea/N [Eq. (57)], the cluster mean density n, and the cluster radius R for ( He)jy clusters. These results reflect on the energetic implications (i.e., the increase of E /N) and on the structural manifestations (i.e., cluster expansion with increasing the bubble radius). 

Figure 15. The potential energy surfaces for the excess electron bubble states in C He) clusters portraying the total energy EtiRi, R, N) versus the bubble radius Rf, for fixed values of N marked on the curves. The open and full points represent the results of the computations for the clusters using the density functional method for Ej Ri, R, N) and the quantum mechanical treatment for Ee(Ri, R, N), while for the bulk we took Ed Rb, R — oo, iV oo) = AttyR. The black point ( ) on each configurational diagram represents the equilibrium bubble radius. The Rj-dependence of the energy of the quasi-free electron state Vo(Rt, R, N) in the cluster of the smallest size of N = 6.5 X 10 (dashed line) and the bulk value of To (solid line) are also presented. The To values for each Rj, for iV = 8.1 x 10 to 1.88 x 10 fall between these two nearly straight fines.

Figure 16. The cluster size dependence of the equilibrium electron bubble radii and the total ground-state energies E , corresponding to the minima of the potential curves of Fig. 15.

Figure 17. The dependence of the energy gap (To — Ef) between the quasi-free electron energy and the total ground-state energy at the equilibrium configuration of the electron bubble on the reciprocal value of the cluster radius at this equilibrium configuration 1 /B for clusters in the range N = 6.5 x 10 to 1.86 x 10 and for the bulk. A crude extrapolation of this linear dependence of Vo — E to zero leads to a localization threshold at 1 < 39 A, which corresponds to A = 5 x 10. ...

It is of considerable interest to use the electron bubble as a probe for elementary excitations in finite boson quantum systems—that is, ( He)jy clusters [99, 128, 208, 209, 243-245]. These clusters are definitely liquid down to 0 K [46 9] and, on the basis of quantum path integral simulations [65, 155], were theoretically predicted (see Chapter II) to undergo a rounded-off superfluid phase transition already at surprising small cluster sizes [i.e., Amin = 8-70 (Table VI)], where the threshold size for superfluidity and/or Bose-Einstein condensation can be property-dependent (Section II.D). The size of the ( He)jy clusters employed in the experiments of Toennies and co-workers [242-246] and of Northby and coworkers [208, 209] (i.e., N lO -lO ) are considerably larger than Amin- In this large cluster size domain the X point temperature depression is small [199], that is, (Tx — 2 X 10 — 2 X 10 for V = lO -lO. Thus for the current... 

Electron tunneling dynamics from electron bubbles in helium clusters strongly depends on the transport dynamics of the electron bubble within the cluster. In normal fluid ( He) and ( He)jy clusters the electron bubble motion is damped, while in (" He)jy superfluid clusters this motion is nondissipative [99]. Accordingly, bubble transport dynamics in ( He) clusters dominates the time scale for electron tunneling from the bubble, providing a benchmark for superfluidity in finite boson systems [245, 251]. In this chapter we address (a) the dynamics of electron tunneling from bubbles in ( He) and ( He) clusters [99, 209, 242-245, 251] and (b) the role of intracluster bubble transport on the lifetime of the bubble states. Our analysis provides semiquantitative information on electron bubbles in (" He) clusters as microscopic nanoprobes for superfluidity in finite quantum systems, in accord with the ideas underlying the work of Toennies and co-workers [99, 242-245]. 

The motion of the electron bubble in the field of the image potential within the cluster. 

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