Z. Phys. B 98, 323 329 (1995) ZEITSCHRIFT FORPHYSIK B 9 Springer-Verlag 1995 The binding of alkali atoms to the surfaces of liquid helium and hydrogen F. AncilottoZ, E. Cheng 2'*, M.W. Cole 2, F. Toigo 1 1Dipartimento di Fisica "Galileo Galilei", via Marzolo 8, UniversitS. di Padova, 1-35131 Padova, Italy 2Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, PA 16802, USA (e-mail: mwc@psuvm psu.edu, Fax: (814)-865-3604,Tel.: (814)-863-0165) Abstract. Alkali atoms have been shown previously to have only unstable binding states inside liquid 4He. We calculate the equilibrium configurations and binding ener- gies of single alkali atoms near the liquid-vapor interface of 4He and 3He. A simple interface model is used to predict the surface deformation due to the presence of the atoms. A more realistic density functional model yields somewhat higher energies in the case of 4He. For all alkali atoms, we find the surface binding energies to be around 10 to 20 K. A similar analysis with atom-Hz interactions finds that alkali atoms tend to submerge into liquid H2, with the exception of Li. PACS: 36.40.Mr; 67.40.Yu; 67.55.Lf I. Introduction Impurities on or in helium bulk or clusters have attracted much interest recently. It is expected inter alia that such impurities will help to reveal the structural and superfluid properties of a finite neutral cluster. Candidates for such attachment include electrons, alkali atoms, inert gas atoms, and molecules such as H2 and SF6. [1 5] Ne and SF6 have been shown experimentally to be captured by 4He clusters, although it is unclear whether they are at- tached to the surface or submerge inside the cluster. [2] Numerical simulations have found that molecules such as H2 and SF6, when settled into a state of small angular momentum, should stay inside the helium cluster. [-3,4] Calculations by Dalfovo indicate that, while most impu- rities have stable states at the center of a spherical 4He cluster at temperature T = 0, the alkali atoms do not. This is a consequence of the fact that alkalis are the weakest-binding materials to closed-shell atoms. [6-8] There is, however, the distinct possibility of attaching * Present address: Department of Chemistry, University of Califor- nia, Berkeley, CA 94720, USA alkali atoms to the surface of such a duster. In this paper, we present calculations of such surface states at the bulk liquid-vapor interface. We find stable states with binding energies Eb ~ 15 K for alkali atoms on helium surfaces. In Sect. II we describe the alkali-atom interaction po- tentials and use overly simple models to roughly estimate the energies of surface and "bubble" states. In Sect. III, a density functional theory is used to calculate more accurately the surface binding of alkali atoms on 4He. In Sect. IV, a somewhat less accurate "interface model" is used to treat surface states on 3He and liquid H2. Section V summarizes our results. II. Simple estimates of surface and "bubble" energies The weakness of the alkali-helium interaction plays an essential role in this problem. Theoretical and experi- mental information concerning these two-body interac- tion potentials is available. [8] Here, we adopt the Len- nard-Jones (LJ) form for simplicity: C12 C6 u(R) = R12 R6 , (1) where R is the interatomic distance. The van der Waals coefficient C6 is taken from Ref. [8] and the value of the coefficient C12 is chosen such that u(R) has the same well depth as given in Ref. [8]. The numerical values are listed in Table 1, along with those of the well depth e = C2/4Clz and equilibrium distance rm = (2C12/C6) 1/6. Figure 1 com- pares our He-Cs LJ potential with the potential of Patil [8]. The LJ potential has a slightly smaller core radius. Our use of approximate model potentials in this Section is justified by the facts that (a) these potentials are not extremely well known, and (b) our estimates employ fur- ther approximations. An alkali atom outside of the liquid experiences a physisorption potential V which is well approximated by an addition of two-body interactions. A zero order estimate of V can be obtained by assuming that the liquid density p(z) falls discontinuously from its bulk value Po to