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r0 (Bohrs)

Figure 48. Polarizability (a) for H as a function confining radius r0, for different barrier heights. In units of 10-24 cm2. Reprinted with permission from [205], J. L. Marín et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

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Figure 49. Pressure (P) for H as a function of confining radius r0, for different barrier heights. In units of 106 atm. Reprinted with permission from [205], J. L. Marín et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

ro (Bohrs)

Figure 49. Pressure (P) for H as a function of confining radius r0, for different barrier heights. In units of 106 atm. Reprinted with permission from [205], J. L. Marín et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

Considering each electron in a 1s state the interior wave-function is chosen as

Xi(r1, r2) = A(r0 - ar1 )(r0 - ar2)exp[-a(r1 + r2^ (243)

and the exterior function as

r r2

with A and B normalizing constants. Note that in this case we are using only two variational parameters. This choice will certainly make the trial wavefunction too rigid. However, as will be seen, even with this crude approximation fair results may be obtained.

Following the procedure outlined by Eqs. (232)-(235) the energy values for H—, He, Li+, and Be2+ are obtained as a function of r0 and V0. Table 4 displays the results of this exercise for some selected barrier heights. We note first the cases of He, Li+, and Be2+ for which the qualitative and quantitative behavior of the energies tend to the correct values [107] as the barrier height approaches infinity. Note, however, that for relatively large box sizes the energy values obtained for the penetrable case lie slightly lower than those for the impenetrable case. This effect is attributed to the rigidity imposed on the input wavefunction through the assignment of a single variational parameter for the interior as well as the exterior regions.

Interestingly enough, the H— system shows a particular sensitivity to the confining effect as may be verified from the overall trend of the energy values. Unfortunately, there are no other calculations to compare with for this confined system. The energies obtained in this work for large values of r0 correspond to the value of s = —0.473 Hartree reported by Wu and Falicov [128] in their variational treatment of free H— with a single exponential parameter. Furthermore, these authors have shown that using two exponential parameters in their trial wavefunction, the ground state energy ro (Bohrs)

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