Institute of Physics & Power Engineering Current Status of the Problem of Cross Section Data for Ion Beam Analysis

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1 Institute of Physics & Power Engineering Current Status of the Problem of Cross Section Data for Ion Beam Analysis A.F. Gurbich

2 IBA Methods Acronym PIXE PIGE RBS NRA NRP or r-nra ERDA or FRS Particle-Induced X-ray Emission Particle-Induced Gamma Emission Rutherford Backscattering Spectrometry Nuclear Reaction Analysis Nuclear Resonance Profiling, resonant Nuclear Reaction Analysis Elastic Recoil Detection Analysis, Forward Recoil Spectroscopy Interaction Characteristic X-ray emission following ionization by the primary beam. Prompt gamma emission during ion beam irradiation Elastic scattering at backward angles Nuclear reaction between incident beam and nuclei in the target, producing a light charged particle. Exploitation of narrow nuclear resonances via scanning of the incident beam energy. Elastic recoil at forward angles, not necessarily Rutherford

3 Depth Profiling : Principle c(x) σ(x) δx x θ E inc A channel of width δe at energy E in the spectrum corresponds to a slice of width dx at depth x in the sample, with E and δe being inversely related to x and δx through a linear combination of the stopping powers for the incident and outgoing particle Y(E) δε E The number of particles accumulated into that histogram bin is proportional to c(x), δx, and σ(e x ), where E x is the energy of the incident beam when it gets to depth x. Y i ( E) = 2 Nc( x) σ ( ϕ, E1) δω 1 ( E' E) exp( ) de' ks( E ) 1.6Γ( x).36γ ( x) 1 S( E') + cos( ) cos( ) S( ke1 ) ϕ + θ θ

4 What nuclear data are needed for IBA? Differential cross sections dσ(e)/dω for: elastic scattering of light ions (p, d, 4 He, 7 Li, ) nuclear reactions induced by p, d, 4 He, 3 He in the energy range of.5 1 MeV

5 Distinctive feature of the nuclear data for IBA (as compared with other applications) IBA uses differential cross sections rather than total ones data for different angles are needed IBA employs data mainly for elements of natural abundance rather than for separated isotopes data acquired in nuclear physics studies are often not sufficient

6 The difference between cross sections for separate isotopes and for an element of natural abundance 8 dσ/dω, mb/sr Mg 25 Mg 26 Mg natural Mg Experiment (natural magnesium) Energy, kev

7 Evaluation Data Compilation Critical Analysis Theoretical Calculations Analysis of Discrepancies Cross Section Measurements Benchmark Experiments Data Dissemination

8 Compilation

9 How accurate is digitizing? Deviation, % σ/σ R Mean deviation: +.19% Mean square deviation: 1.44% Tabulated Digitized 16 O(α,α) 16 O Leavitt et al. θ=17 o Energy, kev

10 THE REASONS WHY EVALUATION IS NEEDED Reason 1: because of discrepancies between results of different measurements dσ/dσ R C(α,α ) 12 C Feng o Gosset o Bittner o Cheng o Davies o Leavitt o Somatri o Energy, MeV

11 THE REASONS WHY EVALUATION IS NEEDED Reason 2: because cross section may has a fine structure missed in some measurements Al(p,p ) 27 Al dσ/dω c.m. (mb/sr) Ra89 Chi1 θ=17 o Energy (kev)

12 2 WHY IS A FINE STRUCTURE ESSENTIAL? Suppose "true" cross section is as shown by a solid line and two measurements with 12 kev step are made, the measured points in the two sets being shifted by 6 kev dσ/dω, arb. units Step E=12 kev Simulated EBS spectra Black line simulation with "true" cross section, blue and magenta simulation with sparse point cross section measurements 3 dσ/dω, arb. units Step E=12 kev Counts/Channel Energy, kev Channel Number

13 THE REASONS WHY EVALUATION IS NEEDED Reason 3: because cross section may have a strong dependence on angle. σ/σ R E = 4.5 MeV 12 C( 4 He, 4 He) 12 C θ (º)

14 Evaluation of the proton elastic scattering from oxygen O(p,p ) 16 O 1 5 θ lab =17 o dσ/dω lab (mb/sr) θ lab =15 o Amirikas 93 Luomajarvi 85 Guohua 91 Chow 75 Eppling 57 Braun 83 Gomes θ lab =11 o Energy (MeV)

15 Evaluation of the proton elastic scattering from carbon C(p,p o ) 12 C Am93 17 o o Ra85 17 Li93 17 o o Sa93 17 Ya91 17o o Ja o Theory 17 4 dσ/dω lab (mb/sr) o Am93 15 o Li o Sa93 15 o Me o Theory 15 o Theory 155 o Theory Am93 11o Me76 144o Theory 11 o o Theory Energy (kev)

16 Evaluation of the proton elastic scattering from silicon

17 Evaluation of the proton elastic scattering from sulfur 4 Ol 168 o dσ/dω c.m., mb/sr Ra 17 o Evaluation 32 S(p,p ) Energy, MeV

18 Evaluation of the 4 He+ 1 H recoil cross section 14 dσ/dω, mb/sr Wa Bo Ya83 Na85 Evaluation 1 H( 4 He,p) Recoil angle 4 o Energy, MeV

19 Evaluation of the alpha elastic scattering from carbon 12 C( 4 He, 4 He) 12 C

20 Evaluation of the alpha elastic scattering from carbon a) θ = 135º energy (kev) 6 σ/σ R b) θ = 15º 3 σ/σ R energy (kev)

21 Differential cross section of the 12 C(d,p) 13 C reaction 12 dσ/dω c.m. (mb/sr) C(d,p o ) 13 C θ lab =165 o Energy (MeV)

22 Differential cross section of the 12 C(d,p) 13 C reaction 12 1 Kokkoris et al., 25 Balin et al., 1982 Kashy et al., 196 dσ/dω, mb/sr C(d,p ) 13 C θ=165 o Energy, kev

23 Differential cross section of the 16 O(d,p) 17 O reaction Si(d,p ).75 dσ/dω lab (mb/sr) Si(d,p 1 ) Energy (kev)

24 Differential cross section of the 28 Si(d,p) 29 Si reaction O(d,p ) dσ/dω lab (mb/sr) O(d,p 1 ) Energy (kev)

25 The differential cross section for alpha elastic scattering from silicon 3 25 dσ/dω c.m., mb/sr Energy, MeV

26 SigmaCalc CROSS SECTION CALCULATOR

27 Calculations are based on S- and R-matrix theories. As far as the optimal set of parameters has been found excitation functions for analytical purposes can be calculated for any scattering angle with reliability exceeding that for any individual measurement.

28 Results are presented both in tabular and graphical forms.

29 When the cross section has been evaluated it can be calculated for any scattering angle C(α,α ) C(p,p ) dσ/dω, mb/sr θ, deg 18 dσ/dω, mb/sr θ, deg Energy, kev Energy, kev

31 SUMMING UP PRESENT STATUS OF THE PROBLEM: RAW MEASURED DATA HAVE BEEN COMPILED IN ION BEAM ANALYSIS NUCLEAR DATA LIBRARY IBANDL SOME OF THE DATA HAVE BEEN EVALUTED AND ARE PROVIDED BY SigmaCalc CALCULATOR NEEDS OF THE IBA COMMUNITY: RECOMMENDED DIFFERENTIAL CROSS SECTIONS FOR ALL REACTIONS OF INTEREST TO ION BEAM ANALYSIS AVAILABLE IN ELECTRONIC FORM

32 CONCLUSIONS The compilation of the IBA related cross sections is in a good condition. New cross section measurements are needed in many cases. The work to evaluate the IBA cross sections should be continued. Further progress in resolving the problem of the nuclear data for IBA is expected due to establishing of a Coordinated Research Project (CRP) by the IAEA NDS.

Leverhulme Lecture III Similarities between Nuclear Data for IBA and Astrophysics

Nuclear Cross Sections Analysis and R-matrix Tools - Minischool Surrey Ion Beam Centre and Department of Physics University of Surrey, Thursday May 9th Friday May 10th 2013 Leverhulme Lecture III Similarities