Boson droplets (i.e., dense assemblies of bosons at low temperature) are shown to mask a significant amount of single-particle behavior and to manifest collective, droplet-wide excitations. To investigate the balance between single-particle and collective behavior, solutions to the wave equation for a finite size Bose system are constructed in the limit where the ratio! of the average nearest-neighbor boson distance to the size of the droplet or the wavelength of density disturbances is small. In this limit, the lowest order wave function varies smoothly across the system, i.e., is devoid of structure on the scale of the average nearest-neighbor distance. The amplitude of short range structure in the wave function is shown to vanish as a power of ! when the interatomic forces are relatively weak. However, there is residual short range structure that increases with the strength of interatomic forces. While the multiscale approach is applied to boson droplets, the methodology is applicable to any finite size bose system and is shown to be more direct than field theoretic methods. Conclusions for 4 He nanodroplets are drawn.

The minimum energy at which intrinsic defects resulting from electron bombardment have been detected in n-type Ge at 78°K is 360 keV. Defects referred to as subthreshold defects are produced at lower energies, but only in crystals grown in hydrogen. Heat treatment of such a crystal in either vacuum or hydrogen atmosphere at 450-500°C for 24 h renders the crystal immune to subthreshold damage. This treatment does not change the electrical conductivity. Subthreshold defects have hole-trapping properties which render the measured carrier concentration highly sensitive to the intensity of the electron beam used for irradiation. The traps can be emptied completely by heating the samples at 140-280°K without modifying the defects. They can be refilled by a short irradiation. There is no dependence of the subthresholddamage production rate on crystal orientation. The defects have different electrical properties and annealing behavior from those of defects produced by higher-energy electrons, suggesting that they may not involve the vacancy or interstitial. The production of subthreshold damage appears to be zero below about 40 keV. Damage rates at 78°K are larger than those at 273°K. Crystals grown in deuterium exhibit little or no damage. It is concluded that subthreshold damage is caused by a relocation of hydrogen impurity in the lattice. The surprising isotopic effect is suggestive of an ionization mechanism for relocation. The dependence of damage production rate on bombardment energy is consistent with an ionization-induced process, except that it should have a "zero-energy" threshold. Possible explanations are given to account for the apparent 40-keV threshold. 746Y. CHEN AND J. W.

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