Quantum theory of static shielding II: Intermediate magnetic field strength

Abstract

A theoretical analysis of magnetic field effects on the Friedel-Kohn “wiggle” contribution to shielding by a quantum plasma is carried out here for conditions of intermediate magnetic field strength ( E F > ω c > kT). In this case, magnetic field quantum corrections to the Friedel-Kohn “wiggl” may be expected to be of two types: (1) monotonic magnetic field corrections associated with an expansion in powers of ω c E F and (2) DHVA-type oscillatory magnetic field corrections associated with oscillatory terms involving the DHVA oscillation frequency E F ω c . The analysis of the monotonic magnetic field corrections is carried out with an expansion in powers of ω c E F , and we find that the actual expansion parameter involved is not ω c E F which is small; but rather it is [ ω c E F ) · p Fr] which may be either small or large since p F r is large. For distances from the shielded impurity such that [( ω c E F ) · p Fr] ⪡ 1 , the power expansion is valid and the zero-field Friedel-Kohn “wiggle” is the dominant high-wavenumber shielding phenomenon, with monotonic and anisotropic magnetic field corrections given by the power series. However, for distances from the impurity such that [( ω c E F ) · p Fr] ⪢ 1 the power expansion is invalid, and we estimate the monotonic magnetic field corrections from a nonperturbative integral representation. The resulting estimate obtained shows that when [( ω c E F ) · p Fr ⪢ 1 the Friedel-Kohn “wiggle” no longer retains its zero-field form, but instead it takes on the properties of its counter-part in the quantum strong field limit, which has a rather different character in that the long range of the “wiggle” is destroyed by a decaying exponential envelope factor exp(−2p F| r|) , while the “wiggle” is still discernable through an anisotropic oscillatory factor cos(2 p F r z ). This is not very surprising since the effective magnetic field “mixed” parameter [( ω c E F ) · p Fr] ⪢ 1 is large enough to be associated with the quantum strong field limit, in spite of the fact that ω c E F ⪡ 1 is small in the intermediate field case under consideration. The analysis of DHVA-type oscillatory magnetic field corrections is of special physical interest, since the occurrence of such terms in conjunction with the Friedel-Kohn “wiggle” would suggest the observation of two of the most interesting specifically quantum phenomena of the quantum plasma in a single experiment. However, our investigation of the only mechanisms which could give rise to such DHVA terms shows that the Friedel-Kohn “wiggle” is in fact devoid of DHVA oscillatory effects at large distances from the shielded impurity [ p F r ⪢ 1 and ( ω c E F )p Fr ⪢ 1 ]. This analysis should serve to provide some insight into questions arising in connection with the recent work of M.E. Rensink [5] and M. L. Glasser [6].