TY - JOUR

T1 - Electron bubbles in helium clusters. II. Probing superfluidity

AU - Rosenblit, Michael

AU - Jortner, Joshua

N1 - Funding Information:
We are grateful to Professor J. P. Toennies for stimulating discussions and correspondence. This research was supported by the German-Israeli James Franck Program on Laser-Matter Interaction.

PY - 2006/5/21

Y1 - 2006/5/21

N2 - In this paper we present calculations of electron tunneling times from the ground electronic state of excess electron bubbles in (He4) N clusters (N=6500- 107, cluster radius R=41.5-478 Å), where the equilibrium bubble radius varies in the range Rb =13.5-17.0 Å. For the bubble center located at a radial distance d from the cluster surface, the tunneling transition probability was expressed as A0 φ (d,R) exp (-Βd), where Β≃1 Å-1 is the exponential parameter, A0 is the preexponential factor for the bubble located at the cluster center, and φ (d,R) is a correction factor which accounts for cluster curvature effects. Electron tunneling dynamics is grossly affected by the distinct mode of motion of the electron bubble in the image potential within the cluster, which is dissipative (i.e., τD < τ0) in normal fluid (He4) N and (He3) N clusters, while it is undamped (i.e., τD ≫ τ0) in superfluid (He4) N clusters, where τD is the bubble motional damping time (τD ≃4× 10-12 s for normal fluid clusters and τD ≃10 s for superfluid clusters), while τ0 ≃ 10-9 - 10-10 s is the bubble oscillatory time. Exceedingly long tunneling lifetimes, which cannot be experimentally observed, are manifested from bubbles damped to the center of the normal fluid cluster, while for superfluid clusters electron tunneling occurs from bubbles located in the vicinity of the initial distance d near the cluster boundary. Model calculations of the cluster size dependence of the electron tunneling time (for a fixed value of d=38-39 Å), with lifetimes increasing in the range of 10-3 -0.3 s for N= 104 - 107, account well for the experimental data [M. Farnik and J. P. Toennies, J. Chem. Phys. 118, 4176 (2003)], manifesting cluster curvature effects on electron tunneling dynamics. The minimal cluster size for the dynamic stability of the bubble was estimated to be N=3800, which represents the threshold cluster size for which the excess electron bubble in (He4) N- clusters is amenable to experimental observation.

AB - In this paper we present calculations of electron tunneling times from the ground electronic state of excess electron bubbles in (He4) N clusters (N=6500- 107, cluster radius R=41.5-478 Å), where the equilibrium bubble radius varies in the range Rb =13.5-17.0 Å. For the bubble center located at a radial distance d from the cluster surface, the tunneling transition probability was expressed as A0 φ (d,R) exp (-Βd), where Β≃1 Å-1 is the exponential parameter, A0 is the preexponential factor for the bubble located at the cluster center, and φ (d,R) is a correction factor which accounts for cluster curvature effects. Electron tunneling dynamics is grossly affected by the distinct mode of motion of the electron bubble in the image potential within the cluster, which is dissipative (i.e., τD < τ0) in normal fluid (He4) N and (He3) N clusters, while it is undamped (i.e., τD ≫ τ0) in superfluid (He4) N clusters, where τD is the bubble motional damping time (τD ≃4× 10-12 s for normal fluid clusters and τD ≃10 s for superfluid clusters), while τ0 ≃ 10-9 - 10-10 s is the bubble oscillatory time. Exceedingly long tunneling lifetimes, which cannot be experimentally observed, are manifested from bubbles damped to the center of the normal fluid cluster, while for superfluid clusters electron tunneling occurs from bubbles located in the vicinity of the initial distance d near the cluster boundary. Model calculations of the cluster size dependence of the electron tunneling time (for a fixed value of d=38-39 Å), with lifetimes increasing in the range of 10-3 -0.3 s for N= 104 - 107, account well for the experimental data [M. Farnik and J. P. Toennies, J. Chem. Phys. 118, 4176 (2003)], manifesting cluster curvature effects on electron tunneling dynamics. The minimal cluster size for the dynamic stability of the bubble was estimated to be N=3800, which represents the threshold cluster size for which the excess electron bubble in (He4) N- clusters is amenable to experimental observation.

UR - http://www.scopus.com/inward/record.url?scp=34547555107&partnerID=8YFLogxK

U2 - 10.1063/1.2192782

DO - 10.1063/1.2192782

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AN - SCOPUS:34547555107

SN - 0021-9606

VL - 124

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 19

M1 - 194506

ER -