We consider a degenerate or a nearly degenerate dark matter sector where a
sizable magnetic moment of an almost Dirac type neutral dark matter candidate N
is anticipated. Then, due to soft photon exchange, the cross-section in direct
detection of N can be enhanced at low Q^2 region. We discuss the implication of
this type of models in view of the recent CDMS II report.Comment: 7 pages with 5 figures. The definition of old F2 is related to the
conventional F2 and two more nuclei are added in Table