Relaxation-time effects are included in the transverse dielectric function of a metallic system by analyzing the magnetic susceptibility of the medium. Our results extend the Mermin longitudinal dielectric function to a transverse case. %e use this model to analyze the infrared absorption of small spheres.The electromagnetic properties of condensed-matter surfaces and small particles can be described by using the appropriate dielectric response functions. For an homogeneous metallic system and infinite relaxation time, those functions are the well-known longitudinal, el, and transverse, eT, dielectric functions proposed by Lindhard. ' Sur-faces and small spheres can be analyzed to a good approximation by embedding the medium in an infinite homogeneous system, their properties being defined by er andFor a finite relaxation time, r, Mermin proposed the following longitudinal dielectric function:The main argument used to deduce this equation was based on the conservation of local electronic charge. The transverse dielectric function, er, was proposed by laiewer and Fuchs to be extended for a finite relaxation time as follows: eT 1 [cop jco(c---a+i j~)] && I 1 -~" /[(co+i /~) co ]},where f"are typical oscillator strengths for the transverse response.We believe that eT, as given by Eq. (2) is not an appropriate extension of eT. The main reason is afforded by the equations establishing the equivalence' between the response functions, (er, eT) and (e,p, ), E'= EL 1 -1/p=(co/ck( (eL, -eT ) .
3(a)
3(b)Indeed, from (3b) and (2) we find that @~1 for co~0. This precludes the appearance of any magnetic effect in the static limit.In this report, we propose an alternative way of obtaining eT (or equivalently p). Our main point is that it is convenient to discuss the electromagnetic properties of a metallic system using the (e,p) response functions, and assuming that the particles of the system can have electric and/or magnetic charges. This point of view puts in the same footing e and p, and allows us to use for p the same argument that Mermin did for e. In other words, if we assume that magnetic charges are responding to the electromagnetic field, magnetic charge conservation allows us to introduce the following equation:where p ls given by (p -1 ) jp = (co jck ) (eL -eT ) and el, eT are the Lindhard dielectric functions.Notice that Eq. (5) only includes those effects associated with the electronic currents. Spin magnetism can be easily added by redefining eT as (cojcq) (eT 1)=4m(X, +Xd), -7, and g~being the spin and the orbital susceptibility, respectively, Xd= -(e /mc q ) X IN+(2h /m)~"j[(co+ijr) co ]}, -