Indirect exchange integral

IW Dehye-Waller factor s-f anisotropic indirect exchange integral... 

The dependence of the transition temperature from the paramagnetic to the magnetically ordered state and the indirect exchange integral on the uniaxial mechanical stress and on the lattice parameters in Gd, Tb, Dy and... 

In the lanthanide metals where the magnetic 4f-electrons are strongly localized the exchange interaction is indirectly mediated via conduction electrons and has an oscillatory character. The exchange integral of this interaction can be expressed as (Liu 1978, Ruderman and Kittel 1954)... 

The cold recovery device consists of an exhaust air humidifier with an integrated heat exchanger and the supply air heat exchanger, which are connected by a fluid circuit. The first can be described as an indirect evaporative cooler. The cold recovery device is able to transport 83% of the maximum possible enthalpy difference from the exhaust air to the supply air. 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

In high spin Fe + there are no unpaired s-electrons and there is no orbital angular momentum. The internal magnetic field arises indirectly — the unpaired 3d-electrons, through the exchange interaction, interact with s-electrons of one spin differently than with s-electrons of opposite spin. As a result, electrons with spin up acquire a somewhat different spatial distribution compared with that for electrons with spin "down". The contact term in Eq. (238) may then be written (after integration of the S-function)... 

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