Molecular stopping

Development of the OLPA/FSGO treatment of molecular stopping 341... 

Equations (l)-(6) constitute a remarkable contribution by Oddershede-Sabin to the improvement of the KT in the analysis of atomic and molecular stopping. The partitioning in the stopping contributions from different atomic/molecular orbitals requires the fundamental assumption implied by equation (5) whereby... 

Using equation (14) and assuming isotropic orbital velocity distributions / (vi — v ) the corresponding expression to equation (2) for the orbital contribution to the molecular stopping was obtained as... 

So far we have given evidence for the flexibility and adequacy of the orbital implementation of the KT by Oddershede and Sabin to study atomic and molecular stopping through different approaches. A major breakthrough based on this theory is the OLPA put forward by Meltzer et al., since it incorporates the simplicity - yet physically sound basis - of the LPA for the calculation of mean excitation energies. 

Methods of Calculating the Molecular Stopping Power and Its Properties... 

The ratio SJn = se characterizes the stopping power corresponding to one molecule and is called the molecular stopping power (it is measured in eVcm2 per molecule). For electrons, the expression for Se is usually presented in the form5... 

The principal parameter characterizing the molecular stopping power in Bethe s theory is the average ionization potential Im, which depends only on the properties of the molecule. There are different ways of... 

In formulas (5.2) and (5.4) the quantity lM enters the logarithmic term, which changes only slightly when we vary the value of IM if lmv2l - f 2) > IM. Thus, in the case of the fast particles, the chemical bond has a weak effect on molecular stopping power, and Bragg s rule works well. 

If the charged particle is a nucleus with no electron shells around it, the molecular stopping power depends on the velocity of the particle in the following way. At relativistic velocities v = c, the dependence of Se on v is determined by the logarithmic term in the brackets, because at v- c the factor preceding the brackets tends to some finite limit. So the molecular stopping power experiences the so-called relativistic rise. As for Se, its relativistic rise in real dense media is slowed down by the density effect (see Section V.B.2). 

Fig. 11. Molecular stopping power of water for protons (curve 1, data of Ref. 159) and electrons (curve 2 -----, data of Ref. 161 ----, data of Ref. 160).

For a given constituent, the stopping power is proportional to the product of molecular stopping power and molecular concentration ... 

The molecular stopping power is equal to the sum of atomic stopping powers. These in turn are commonly considered to be proportional to the atomic numbers. 

Molecular stopping cross section Bragg s rule... 

The previous examples were concerned with atomic targets, however, one of the advantages of the END formulation is the ability to deal with many-atom systems. In this section we present a review of molecular stopping cross sections a la END. 

The many-body character of the molecular interaction introduces additional channels in the description of the molecular stopping cross... 

Equation (32), known as the Bragg s rule, neglects rotational, vibrational and chemical effects which should be considered in a sophisticated treatment for the molecular stopping cross section, particularly for the low projectile energy where these effects are predominant. 

Fig. 13. Molecular stopping cross section for H colliding with C2H6 as a function of the projectile energy. For completeness we compare with the theoretical results of Oddershede and Sabin [60] and of the FSGO model [61], as well as the Bragg s rule results when atomic values from END are used for C and H targets (see text).

E.K. Dalskov, J. Oddershede, J.R. Sabin, Generalized Oscillator Strengths for Calculation of Molecular Stopping Properties, Some Preliminary Results CO, AlP Conf. Proc. CP392 (1997) 1373. 

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