Nuclear Instruments and Methods in Physics Research B 83 (1993) 5-14 North-Holland NOM zyxwvutsrqp B Beam Interact9ons w ith Materials& Atoms Firsov approach to chemical bond stopping power of heavy ions * effects on the low-energy electronic S.A. Cruz, J. Soullard 1 and R. Cabrera-Trujillo zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK Departamento de Fisica, Universidad Autdnoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340, M&co, DF, Mexico Received 4 September 1992 and in revised form 14 May 1993 A recently derived modified version of the Firsov model to account for the low-energy electronic stopping cross section of protons due to molecular targets is extended here for the case of heavy projectiles. The method is free of adjustable parameters and is applied to projectiles with 2 I Z I 18 incident on a wide class of hydrocarbon materials and other simpler molecules. A fair overall agreement is observed with available experimental data for He and Li projectiles. The use of chara~eristic molecular groups as well as the core and bond (CAB) formalism for stopping power studies of heavy ions in compound materials is strongly supported by the results of this work. 1. Introduction Chemical binding effects on the electronic stopping cross section of heavy ions (S,) have received increas- ing attention in the last few years due to the impor- tance of ion-bombardment processes on composite tar- get materials, where the molecular characteristics of the structure can have strong influence on S,. Thwaites [l] has recently reported a ~mprehensive survey of experimental evidence for chemical binding and physi- cal state (phase) effects on S, for this kind of targets. The conclusion drawn by this author is that Bragg’s additivity rule is not adequate to account for the exper- imental observation, particularly for projectile veloci- ties around and below the maximum of the stopping curve. In addition to the bonding characteristics of the target material, it is now well established [2,3] that the phase conditions are also of paramount importance in order to account for the experimental measurements. For He and Li projectiles, a considerable amount of experimental info~ation on the electronic stopping cross section of molecular targets has been collected mainly by the Baylor [41, Koln [5] and Giessen [61 groups. However, from the theoretical point of view, only some isolated efforts have been aimed to consider the role of bond effects on S,. Although previous work Correspondence to: S. Cruz-Jimenez, Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340, Mexico, DF, Mexico. ’ Permanent address: Instituto de Fisica, UNAM, Apdo. Postal ZO-364,01000, M&&o, DF, Mexico. * Work partially supported by CONACYT under contracts 0494E and FOOS8. has been done on small molecules either by using the local plasma approximation [7] or modified versions of the Firsov theory [8,91, only until recently Oddershede and Sabin (OS) [lo] have applied successfully Sigmund’s kinetic theory of stopping [ll] to evaluate the contribu- tion to S, due to bonds and cores for hydrocarbons bombarded with protons. This constitutes the first fun- damental theoretical study to account for the role of the different bond types on the proton stopping, giving support to previous ideas on the pa~itioning of core and bond contributions (CAB) to S, 112j. Furthermore, Ziegler and Manoyan (ZMI 1131 have shown that the CAB expansion allows to describe experimental data for a wide set of compound target materials bom- barded by protons and heavier ions. More recently, the present authors have proposed a CAB method [14] based on the modified Firsov model 181using floating spherical Gaussian orbitals (FSGO) and the concept of molecular fragments to study the low-energy electronic stopping of protons due to molecular targets. It was shown there that this method yields fair agreement with calculations derived from OS and ZM for a wide variety of systems. So far the theoretical efforts have been centered on the energy loss of protons due to molecular targets to account for bond effects. To our knowledge, there is still no such a theory for heavy ion stopping. The task in dealing with such a complicated problem is enor- mous. Apart from the bonding characteristics of a given molecular target and the state of aggregation of the medium where it is immersed, the many-body na- ture of the problem imposes serious limitations on its tractability. In general, even in more simplified, yet realistic, approaches, the dynamical properties of both Old-S83X/93/$06.~ 0 1993 - Elsevier Science Publishers B.V. All rights reserved