CALCULATED PROPERTIES OF TWO-DIMENSIONAL SPIN-POLARIZED ATOMIC HYDROGEN

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CALCULATED PROPERTIES OF

TWO-DIMENSIONAL SPIN-POLARIZED ATOMIC

HYDROGEN

L. Lantto, R. Nieminen

To cite this version:

L. Lantto, R. Nieminen.

CALCULATED PROPERTIES OF TWO-DIMENSIONAL

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ&mc-:t c::: ? O 7 , Tome 41, j u i t Z e t 1980, page C 7 - 4 9

CALCULATED PROPERTIES OF TWO-DIMENSIONAL SPIN-POLARIZED ATOMIC HYDROGEN

L.J.

antt to*

**

*

**

Resum.5.- Des calculs variationnels HNC-Jastrow ont 6t6 effectues pour l1hydrog6ne polarise 2 deux dimensions. I1 en r6sulte des valeurs pr6cises pour l'snergie Ju

niveau fondamental, la Eonction de distribution radiale, 1'Bnergie d16change moyen- ne et la distribution d'impulsions 3 faibles densitgs atomiques

Abstract.- Optimal HNC-Jastrow calculations have been carried out for gaseous spin- polarized hydrogen in two space dimensions. Accurate values for the ground state energy, radial distribution function, average exchange energy and momentum distri- bution are obtained at low atomic densities.

We have recently reported /1/ accurate much as % 1 K. Then the possibility arises

ground state calculations for spin-polarized that in quasi-equilibrium the 3D H4 gas is atomic hydrogen (H4) prepared as a low- surrounded by essentially 2D gas of Ht phy- density three-dimensional quantum gas. The siorbed on the " ~ e coating.

calculations were based on the optimal We have extended our calculations /1/ to boson-HNC method /2/ and the Kolos-Wolnie- ideally 2D Ht systems. The optimal HNC- wicz /3/ potential ; results were quoted Jastrow method we use is presumably very

for the structure and thermodynamics of H4, accurate at the densities of interest and as well as for the minimal stabilizing produces reliable solutions for the gair fields against recombination to Hz, and for distribution function without any varia- the zero-momentum condensate fraction at tional parameters or imposed constraints.

T = O K . For details we refer to earlier published

Efforts to ccndense Ht on surfaces have work /1,6/ : the extension to 2D is strai- recently been reported / 4 / . Ideally, a beam ghtforward.

of hydrogen atoms in the two lowest hyper- The results for 2D H4 are summarized in fine states is prepared in a magnetic field figs. 1-2 and Table 1. Figures 1 and 2

and deposited on a cold inert substrate, show the pair distribution and static such as Ar or H2. If the impinging atoms structure function, respectively, at three stick and avoid depolarization and recom- different densities. The calculated ener- bination, a quasi two-dimensional (2D) Ht gies are listed in Table 1. The energy per can be formed. particle rises rapidly, and if the Mantz- In recent 3D experiments /5/ the walls of Edwards /6/ value of 0.6 K is adapted for the container have been coated with a film the binding energy of hydrogen on 4 ~ e , the of superfluid 4 ~ e to prevent spin flips at maximum density for this system is a 0.75 surfaces. 4 ~ e has probably the lowest ad- x l0l4 atoms/cm2. \Ye note that for 2D sorption potential for hydrogen ; however, hard disk Bose system the energy per par- recent calculations / 6 , 7 / suggest that the ticle can be shown to approach zero loga- surface of "He could bind hydrogen by as rithmically in the low density limit /9,

lo/, This behavior is linked to the fact

*

Permanent address : Department o f Theoretical

Physics, University of Oulu, Finland. that the zero energy scattering cross

**

Department of Physics, University of Jyvdskyla,

trast to 3D systems the scattering lencth

Finland.

JOURNAL DE PHYSIQUE

Fig. 1 : Pair distribution function g(r) for two- dimensional H4 at three densities.

of an arbitrary potential cannot be used to map the problem to a hard-disk one. In Table 1 we have also collected the mean exchange energy J(0) and the corresponding minimum stabilizing field H . for diffe-

mln

rent densities. As in 3D, recombination via finite wavelength "magnons" are suppressed well before overall stability is obtained

Fig. 2 : Structure function S(k) for two-dimensional

H4 at three densities.

in the long wavelength limit. The momentum distribution can be obtained using diagram- matic summation techniques /1/ similar to

HNC treatment of the pair distribution function, and the zero-momentum "conden- sate" fractions are listed in Table 1.

Table 1 : The energy per particle, the mean exchange energy, the minimal stabilizing field and the zero-momentum fraction for H4 in two dimensions.

References

/1/ Lantto, L.J. and Nieminen, R.M., J. Low Temp. /6/ Mantz, I.B. and Edwards, D.O., (to be published). Phys.

31,

/7/ Guyer, R.A. and Miller, M.D., Phys. Rev. Lett. /2/ Lantto, L.J. and Siemens, P.J., Phys. Lett.

-

68B (1977), 308.

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/3/ Kolos, W. and Wolniewicz, L., Chem. Phys. Lett. L.J., Nucl. Phys. (1979) 70 and references 24 (1974)

,

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/4/ Walraven, J.T.M., Eliel, E.R. and Silvera, I.F., /9/ Bruch, L.W., Physica

93A

/lo/ Miller, M.D. and Nosanow, L.H., J. Low Temp. /5/ Silvera, I.F. and Walraven, J.T.M., Phys. Rev. phys.

32,