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The renormalization constant for the tunneling matrix of a heavy particle in metals has been investigated theoretically, When the renormalization constant is written as ( k T / D ) K , the cut-off D turns out to be of the order of \(N ω₀\), where ω 0 is the frequency of the particle motion in each well and N ∼ k F a ( a : the distance between the two wells; k F : the Fermi wave number).
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Jun Kondo (1987) studied this question.
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