Contraction of higher order derivative susy algebras in quantum mechanics with large energy gap

Starting from a polynomial (higher-order derivative) quantum mechanical SUSY algebra we study its contraction to the standard SUSYQM in the limit of large energy shifts between the lowest states of the super-Hamiltonian (of Schrodinger type). By a quasi-linearization method we obtain the charges of the higher derivative SUSY algebra in the (singular) limit of infinite energy gap, and find the resulting Hamiltonian. The singular behavior of the potential generated by this construction reflects the existence of the very deep level. Our results can suggest constructions of toy models where large energy splittings between fermionic and bosonic partners do not affect SUSY for other states.