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

Year 2019, Volume: 12 Issue: 3, 1307 - 1314, 31.12.2019

Metin Usta

https://doi.org/10.18185/erzifbed.480745

Abstract

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

Keywords

Stopping power, Effective charge, , Bethe-Bloch

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

Abstract

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. 

Keywords

Durdurma gücü, Etkin yük, Bethe-Bloch, Proton

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