Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupling of conduction electrons to two-level systems formed by
  hydrogen: A scattering approach   An effective Hamiltonian which could model the interaction between a
tunneling proton and the conduction electrons of a metal is investigated. A
remarkably simple correlation between the motion of the $TLS$-atom and an
angular-momentum change of scattering electron is deduced, at the first-order
Born level, by using a momentum-space representation with plane waves for
initial and final states. It is shown that the angular average of the
scattering amplitude-change at the Fermi surface depends solely on the
difference of the first two phase shifts, for small-distance displacements of
the heavy particle. For such a limit of displacement, and within a
distorted-wave Born approximation for initial and final states, the change in
the scattering amplitude is expressed via trigonometric functions of scattering
phase shifts at the Fermi energy. The numerical value of this change is
analyzed in the framework of a self-consistent screening description for
impurity-embedding in a paramagnetic electron gas. In order to discuss the
so-called antiabatic limit on the same footing, a comparison with matrix
elements obtained by the potential-gradient of an unscreened Coulomb field is
given as well. The coupling of the tunneling proton to a free-electron-like
electron gas is in the typical range obtained, by ultrasound experiments for
different metallic glasses, from scattering rates for a Korringa-type
relaxation process. That coupling is too weak to be in the range required for
realization of the two-channel Kondo effect.

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc