Práctica de laboratorio número 6: Non-Rutherford scattering near the 1.734 MeV 12 C(p,p) 12 C resonance 1) Scope In this experiment, the yield of protons backscattered from a thin gold foil deposited over a thick graphite substrate (~ 5 µm) is measured as a function of the proton energy in the energy range from 16 182 kev. From the yield of the Au and C (surface) signals, the energy dependence of both cross-sections will be determined and compared to the corresponding Rutherford cross section. 2) Theoretical background At ion energies above the Coulomb barrier, cross-sections for elastic backscattering are strongly dependent on ion energy, and deviate significantly from the classical Rutherford formula. For the elastic scattering reaction 12 C(p,p) 12 C there is a resonance in the cross-section with peak maximum positioned at 1734 kev and FWHM of ~ 4 kev. As non-rutherford cross-sections can be much higher (in some cases up to 1 times) than Rutherford ones, this can be utilized in practical applications to increase the analytical sensitivity of the backscattering technique. The intense resonance for 12 C or 16 O with helium ion beam is a commonly-used tool for depthprofiling carbon and oxygen in various substrates [1,2]. The differential cross-section for backscattered protons at a scattering angle θ is given by Eq. 1: dω ) S (E p, θ) = A S QΩ(θ)N S (1) Where Ep is the incident proton energy, A S is the area under the gold or carbon signals (yield), Q is the number of incident protons, Ω(θ) is the detector solid angle and N S is the number of gold or carbon atoms per unit area (atoms/cm 2 ). In the case of carbon, the area A S will be taken in an interval corresponding to the first 7 nm from the surface (about 2 channels). 3) Materials: 1. 3 MV Tandem accelerator 2. Target: thin Au layer on C substrate 3. PIPS detector 4. Electronic chain (preamplifier+amplifier+adc) 5. PC with Genies MCA software for spectra data acquisition 6. Current integrator 1
4) Methodology Master Interuniversitario en Física Nuclear (216/17) Figure 1 shows the experimental geometry. The measurements must be carried out in a vacuum chamber. The chamber should be light tight as the charged particle detector is sensitive to light (when bias is applied). A collimated proton beam with energy varied from 16 to 182 kev is incident on a thin gold foil (54 µg/cm 2 ) deposited over a thick graphite substrate (~ 5 µm). A particle detector is placed at a backward angle (165 ) to detect the backscattered protons. The proton beam charge is collected by the sample holder that is electrically connected to the current integrator. The secondary electrons emitted from the sample are recollected biasing the sample holder at +2 V using a battery. The backscattering yield for the 12 C(p,p) 12 C reaction is measured between 16 kev and 182 kev in steps of 1 kev. Fig.- 1. Experimental setup for backscattering of protons from the thin gold layer (54 µg/cm 2 ) deposited over a thick graphite substrate (~ 5 µm). All spectra are collected to the same number of incident particles i.e. to the same collected charge in the current integrator (Q = 4 μc in this case). The spectra of protons backscattered from the sample for several proton energies are shown in Figure 2. The peak that appears at higher energy corresponds to the protons backscattered from the Au atoms, while the continuous signal at lower energy comes from collisions with the carbon atoms. As observed, the C yield is very sensitive to the incident proton energy. 2
1 1 162 kev 1 1 1 175 kev 1 1 1 182 kev 1 5 1 15 2 E p (kev) Fig.- 2. Backscattering spectra of protons from Au/C target for several incident energies: a) 162 kev, b) 175 kev, and c) 182 kev. All spectra are recorded with the same number of incident protons (Q = 4 μc). Experimental procedure 1) For each spectrum, integrate the number of counts for the C and the Au signals. For C, the region of interest (ROI) will include only 2 channels starting from the highest carbon signal to integrate only the first 7 nm. 2) From equation 1 and using the answer to questions (2-5), calculate the differential cross sections for C and Au at the several proton energies. 3) Calculate the corresponding Rutherford cross sections for C and Au and compare with your experimental results. Are they similar? Why? 4) Use the SigmaCalc program [3] to calculate the differential 12 C(p,p) 12 C cross section and compare with your experimental results. Explain the differences. 5) Fill Table 1 and represent the data. 3
Ep (KeV) AAu (counts ) dω ) Au,exp dω ) Au,Ruth AC (counts ) dω ) C,exp dω ) C,Sigmacal dω ) C,Ruth 16 161 162 163 164 165 166 167 168 169 17 171 172 173 174 175 176 177 178 179 18 181 182 Additional questions: Question 1: Explain why the secondary electrons ejected from the sample must be collected during the experiment. Question 2: Knowing that the mass density of Au is ρ = 19.31 g/cm 3, calculate the atomic density (in units of 1 15 at/cm 2 ) and the physical thickness of the 54 µg /cm 2 Au layer. Question 3: Knowing that the mass density of C is ρ = 2.267 g/cm 3, calculate the atomic density (in units of 1 15 at/cm 2 ) corresponding to the thickness of 7 nm. 4
Question 4: Calculate the solid angle of the detector knowing that the distance sample-detector is 5 cm and the detector area is 1 mm 2. Question 5: Calculate the number of incident protons corresponding to an integrated charge of Q = 4 μc References [1] M. Berti.et al, 12 C(α,α) 12 C Resonant Elastic Scattering at 5.7 MeV as a Tool for Carbon Quantification in Silicon-based Heterostructures, Nucl. Instr. Meth. B 143 (1998) 357. [2] Y. Miyagawa et al, Oxygen depth profiling in TiO xsio 2 prepared by sol-gel method using 16 O(α,α) 16 O resonant backscattering, Nucl. Instr. Meth. B 136-138 (1998) 557. [3] SigmaCalc: http://sigmacalc.iate.obninsk.ru/ Appendix: Rutherford cross section The Rutherford cross section for backscattering in the laboratory system is given by: where is the scattering angle, E is the energy of the projectile, Z 1 and M 1 are the nuclear charge and the mass of the projectile, respectively, and Z 2 and M 2 are the nuclear charge and the mass of the target atom, respectively. 5