Targets consisting of 3,4 He implanted into thin aluminum foils (approximately 100, 200 or 600 µg/cm 2 ) were prepared using intense (a few µA ) helium beams at low energy (approximately 20, 40 or 100 keV). Uniformity of the implantation was achieved by a beam raster across a 12 mm diameter tantalum collimator at the rates of 0.1 Hz in the vertical direction and 1 Hz in the horizontal direction. Helium implantation into the very thin (approximately 80-100 µg/cm 2 ) aluminum foils failed to produce useful targets (with only approximately 10% of the helium retained) due to an under estimation of the range by the code SRIM. The range of low energy helium in aluminum predicted by Northcliffe and Shilling and the NIST online tabulation are observed on the other hand to over estimate the range of low energy helium ions in aluminum. An attempt to increase the amount of helium by implanting a second deeper layer was also carried out, but it did not significantly increase the helium content beyond the blistering limit ( 6 × 10 17 atoms/cm 2 ).The implanted targets were bombarded with moderately intense 4 He and 16 O beams of 50-100 particle nA . Rutherford Back Scattering of 1.0 and 2.5 MeV proton beams and recoil helium from 15.0 MeV oxygen beams were used to study the helium content and profile before, during and after bombardments. We observed the helium content and profile to be very stable even after a prolonged bombardment (up to two days) with moderately intense beams of 16 O or 4 He. Helium implanted into thin (aluminum) foils is a good choice for thin helium targets needed, for example, for a measurement of the 3 He(α, γ) 7 Be reaction and the associated S 34 astrophysical cross section factor (S-factor).
In many physical relationships involving the Laplacian of a function, it proves useful to interpret the Laplacian as a measure of the local anomaly of that function. This little used, but often very illuminating interpretation, due originally to Maxwell, is illustrated with a number of examples drawn from mathematical physics.
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