A Study on The Stopping Power of Z=2-54 Elements for Protons Using Effective-Charge Approximation

Öz

The stopping power is the average energy loss per unit length of charged particles due to the interaction with the Coulomb field of electrons in target and nucleus. Stopping power has important applications in many areas such as atomic physics, nuclear physics and applications, radiation dosimetry. The aim of this study is to calculate the collision stopping power of Z=2-54 atomic elements by using the effective charge approach based on Bethe-Bloch theory for the 1 keV-1 GeV energy protons. For this purpose, the effective charge, effective mean excitation energies and potential energy functions of the target elements were firstly determined. For the electronic charge density, Roothaan-Hartree-Fock atomic wavefunctions were selected and the change of the effective charge of the target atoms with the energy of the protons was examined. Then, the collision stopping power values were calculated by using the obtained effective charges of the target atoms. It was seen that as the atomic number and the energy of the incoming protons increased, effective charge values ascended. It was determined that the stopping power values decreased as the number of atoms increased and the maximum points of stopping power shifted towards high energies. The calculated stopping power values for the carbon atom from the target elements were compared with the data of the ICRU 49, SRIM, CasP and Janni available in the literature. It was observed that the results were quite appropriate with the literature data at certain error rates. In addition, it is understood that the effective charge approach used in this study can be used in energies less than 1 MeV

Anahtar Kelimeler

• Stopping power,Effective charge,,Bethe-Bloch

Etkin Yük Yaklaşımı Kullanarak Protonlar için Z=2-54 Elementlerin Durdurma Gücü Üzerine Bir Çalışma

Öz

Durdurma gücü, hedef içerisindeki elektronlar ve çekirdeğin Coulomb alanı etkileşmesi nedeniyle yüklü parçacıkların birim uzunluk başına ortalama enerji kaybıdır. Durdurma gücünün atom fiziği, nükleer fizik ve uygulamaları, radyasyon dozimetrisi gibi birçok alanlarda önemli uygulamaları vardır. Bu çalışmanın amacı 1 keV-1 GeV enerjili protonlar için Z=2-54 atom numaralı elementlerin Bethe-Bloch teorisine dayalı etkin yük yaklaşımı yöntemi kullanılarak çarpışma durdurma gücünü hesaplamaktır. Bunun için öncelikle hedef elementlerin etkin yük, etkin ortalama uyarılma enerjileri ve potansiyel enerji fonksiyonları belirlendi. Elektronik yük yoğunluğu için Roothaan-Hartree-Fock atomik dalgafonksiyonları seçildi ve hedef atomların etkin yükünün protonların enerjisiyle değişimi incelendi. Ardından elde edilen hedef atomların etkin yükleri kullanılarak çarpışma durdurma gücü değerleri hesaplandı. Atom numarası ve gelen protonların enerjisi arttıkça etkin yük değerlerinin arttığı görüldü. Durdurma gücü değerlerinin ise atom sayısı arttıkça azaldığı ve durdurma gücüne ait maksimum noktalarının yüksek enerjilere doğru kaydığı belirlendi. Hedef elementlerden karbon atomu için hesaplanan durdurma gücü değerleri literatürde mevcut ICRU 49, SRIM, CasP ve Janni’nin verileriyle karşılaştırıldı. Sonuçların belirli hata oranlarında literatür verileriyle oldukça uygun oldukları gözlendi. Ayrıca bu çalışmada kullanılan etkin yük yaklaşımının 1 MeV’den düşük enerjilerde de kullanılabileceği anlaşıldı. 

Anahtar Kelimeler

• Durdurma gücü,Etkin yük,Bethe-Bloch,Proton

Kaynakça

1. Bohr, N. (1940). Scattering and Stopping of Fission Fragments. Phys. Rev., 58(7), 654-655.
2. Bohr, N. (1941). Velocity-Range Relation for Fission Fragments. Phys. Rev., 59(3), 270-275.
3. Bunge, C. F., Barrientos, J. A., & Bunge, A. V. (1993). Roothaan-Hartree-Fock Ground-State Atomic Wave Functions: Slater-Type Orbital Expansions and Expectation Values for Z = 2-54. Atomic Data and Nuclear Data Tables, 53(1), 113-162.
4. Cabrera-Trujillo, R., Cruz, S. A., Oddershede, J., & Sabin, J. R. (1997). Bethe theory of stopping incorporating electronic excitations of partially stripped projectiles. Physical Review A, 55(4), 2864-2872.
5. Damache, S., Ouichaoui, S., Belhout, A., Medouni, A., & Toumert, I. (2004). Stopping of 236 keV – 3.019 MeV protons in mylar and polypropylene films. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 225(4), 449-463.
6. Dib, A., Ammi, H., Hedibel, M., Guesmia, A., Mammeri, S., Msimanga, M., & Pineda-Vargas, C. A. (2015). Electronic stopping power data of heavy ions in polymeric foils in the ion energy domain of LSS theory. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 362, 172-181.
7. Garcia-Molina, R., Abril, I., de Vera, P., & Paul, H. (2013). Comments on recent measurements of the stopping power of liquid water. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 299(0), 51-53.
8. Grande, P. L., & Schiwietz, G. (2009). Convolution approximation for the energy loss, ionization probability and straggling of fast ions. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 267(6), 859-865.

9. ICRU. (1993). Stopping Powers and Ranges for Protons and Alpha Particles ICRU Report 49.
10. Janni, J. F. (1982). Energy loss, range, path length, time-of-flight, straggling, multiple scattering, and nuclear interaction probability: In two parts. Part 1. For 63 compounds Part 2. For elements 1 ⩽ Z ⩽ 92. Atomic Data and Nuclear Data Tables, 27(2–3), 147-339.
11. Pierce, T. E., Bowman, W. W., & Blann, M. (1968). Stopping Powers of S32, Cl35, Br79, and I127 Ions in Mylar. Physical Review, 172(2), 287-290.
12. Porter, L. E. (1980). Mean excitation energy of polystyrene extracted from proton-stopping-power measurements. Physical Review B, 22(5), 2221-2225.
13. Reynolds, H. K., Dunbar, D. N. F., Wenzel, W. A., & Whaling, W. (1953). The Stopping Cross Section of Gases for Protons, 30-600 kev. Physical Review, 92(3), 742-748.
14. Sugiyama, H. (1981). Electronic stopping power formula for intermediate energies. Radiation Effects, 56(3-4), 205-211.
15. Usta, M., & Tufan, M. Ç. (2017). Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions. Radiation Physics and Chemistry, 140(Supplement C), 43-50.
16. Usta, M., Tufan, M. Ç., Aydın, G., & Bozkurt, A. (2018). Stopping power and dose calculations with analytical and Monte Carlo methods for protons and prompt gamma range verification. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 897, 106-113.
17. Ziegler, J. F., Biersack, J. P., & Ziegler, M. D. (2013). SRIM, the Stopping and Range of Ions in Matter: SRIM Company.
18. Ziegler, J. F., & Manoyan, J. M. (1988). The stopping of ions in compounds. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 35(3–4), 215-228.