The study of the straggling energy loss

Straggling is the broadening of energy distribution of a beam charge particle penetrating through a material medium .The calculationsrepresenta problem of considerable complexity.The theoretical literature on straggling is rather limitedcomparedto the one on stopping cross section. In the present work, the energyloss of straggling has been studied theoretically for interaction of A l and C l N e O C , , , ions in N i target . The present work is a part of a thesis submitted for the PhD Degree in physics, in 2012 [1]. A program f o r Sana r V r n s . has been written inFORTRAN-90 using Compaq Visual FORTRAN V6.6 for compiling, linking and executing.A copy of the program is Available in [1]. Theagreementis achieved with previous works.


Introduction
Energy-loss straggling denotes the development of the width and shape of the energy spectrum of an initially monochromatic beam as a function of time or path length [2]. Straggling is an inherent feature of stopping measurements which cannot be reduced indefinitely by making more measurements. In many applications, information on the scatter of data is just as important as mean values [3]. Assuming that all the target electrons contribute to the energy loss, Bohr (1915) provided a simple expression for the value of the energy-loss straggling in the case of an elemental target [4]. Bohr straggling equation and it's frequently used to estimate the corresponding energy-loss straggling value for the case of high projectile velocities [5]. Quantum mechanics causes the energy loss to fluctuate from one collision event to another, even at one and the same impact parameter. For composite projectiles such as heavy ionscarrying electrons, the charge and the excitation state may vary over a trajectory,and since the energy loss typically depends on the projectile state, additionalfluctuations arise [6]. Energy-loss straggling has atomistic and statistical aspects which will be discussed atpresent work.

952
The dielectric formalism provides simple expressions for describing the energy loss and energy loss straggling of a fast projectile moving through matter with certain kinetic energy. The dependence on target properties account through its energy loss function [7].

Basic Theory
Bohr showed that unlike the mean energy loss, straggling is rather insensitive to the binding of target electrons. He predicted that the fluctuation of the energy loss E  of a beam of charged particles penetrating matter is characterized by the variance parameter W given by [8]: ( 1) In classical theory, the energy loss at a given impact parameter is uniquely defined if the electron is at rest initially. In semi-classical theory, the energy loss is a fluctuating quantity even at a given impact parameter.
A fundamental aspect of the Bohr theory is the splitting into two regimes for small and large impact parameter: close interaction is taking to follow Rutherford's law [9].
For distant interaction the energy transfer versus impact parameter p is described as excitation of harmonic oscillators by a time varying electric field in the dipole approximation [10,11].
Where is the oscillator frequency and K 0 and K 1 are modified Bessel function in standard notion [12].
According to close and distant, collision energy transfer given in p is critical distance where close and distant, collision are equal. and the definition of relative variance in energy [2], pdpT W  (7) Where T is the energy transfer for close and distant collision, Using a dimension parameters, Therefore, equation (7) becomes, Eq. (12) represents the variance in the energy lossof heavy ions taking in the consideration close and distant collisions,  (11) in to (12) and conveniently evaluated numerically,

Results and Discussion
Newton-Raphsonmethod [12] has been used in a program to evaluate 0 p which is the intercept point between close and distant collision of energy transfer T , and has been written in FORTRAN -90 using Compaq Visual Fortran V6.6 for compiling, linking and executing.