Lewis Effect in Resonance Yield Curves

Abstract

Lewis 1 has recently pointed out that a thicktarget yield curve taken at a narrow resonance with a charged particle beam of high-energy resolution should have a maximum just above the resonance energy followed by a shallow minimum, before it assumes a constant value. The qualitative explanation for this phenomenon, which the authors have chosen to call "the Lewis effect, " is as follows: In passing through target material a charged particle loses energy in discrete steps Q. If some of these steps are larger than the natural width of a narrow resonance, some of the particles incident on a target at an energy well above the resonance energy, E^, will jump over the resonance. If particles are incident at E^ then all will have for a finite time the correct energy to interact. The yield curve should therefore exhibit a peak near E^.Gamma-ray yield curves from the Al 27 (p,y)Si 28 resonance reaction at 992 kev were studied with a proton beam having an energy spread at half maximum of about 125 ev. The natural width of this resonance is 80 ±40 ev. 2 Yield curves were initially taken from aluminum films formed in the target chamber by evaporation of aluminum from a tungsten filament. A peak in the yield curves appeared but could not be reproduced. This was interpreted as being due to the accumulation of surface deposits on the target. A new method of target preparation was developed 3 in which aluminum is slowly and continuously deposited on the target backing while taking data. Figure 1 shows several yield curves exhibiting the Lewis effect. Curve A is a yield curve calculated as outlined below. The data labelled B and C were taken during continuous evaporation of aluminum. Curves D and E were initial runs from two different targets prepared by filament evaporation; subsequent runs in both cases failed to reveal the Lewis peak.The yield per proton at a mean beam energy E^ from an infinitely thick homogeneous target is given by ..<>*<***}where n^ is the number of aluminum atoms per unit volume, g(E b ,E i )dE i is the probability that a proton in the beam of mean energy E b has an incident energy between E^ and Ej +dE^ <?(£#, E) is the cross section for the resonance, and r](E, Ej)dE represents the probability that a proton incident at an energy Ef has an energy between E and E +dE somewhere inside the target. The probability p(Q, E)dQ that a proton at an energy E will suffer a collision in which it losesFIG. 1. Thick-target yield curves showing the Lewis effect from the Al 27 (£,y)Si 28 resonance at 992 kev. Mean beam energy, Efr t is plotted relative to the resonance energy, E#. The position of ER is determined by the calculated yield curve. Plateau yields are normalized for easy comparison of peak amplitudes. 284

Monte Carlo simulations of the Lewis effect

“…This effect is a manifestation of the quantum nature of the energy transfers as the projectile slows down during its passage through the target. Several experiments were performed in the 1960's to investigate in detail the Lewis effect [2][3][4][5][6][7][8]. The size of the Lewis peak was observed to depend strongly on such factors as the purity of the target (especially on layers of surface contamination), the beam energy spread, and the beam energy stability.…”

“…In subsequent work [2][3][4][5][6][7][8] the collision spectrum co(Q) was assumed to arise predominantly from collisions with electrons in the target medium and to follow a 1/Q 2 law; however, this law is only valid for free electrons. To correct somewhat for this fact, the spectrum co(Q) was cut at a minimum energy transfer Qmin, where the value of Qmin was obtained from a fit to the data.…”