There is a growing new class of young spin-down powered pulsars called GeV-quiet soft gamma-ray pulsar; (1) spectral turnover appears around~10MeV, (2) the X-ray spectra of below 20 keV can be described by power law with photon index around 1.2 and (3) the light curve in X-ray/soft gamma-ray bands shows single broad pulse. Their emission properties are distinct from the normal gamma-ray pulsars, for which the spectral peak in $ u F_{ u}$ appears in GeV energy bands and the X-ray/gamma-ray light curves show sharp and double (or more) peaks. In this paper, we discuss that X-ray/soft gamma-ray emissions of the GeV-quiet soft gamma-ray pulsars are caused bythe synchrotron radiation of the electron/positron pairs, which are created by the magnetic pair-creation process near the stellar surface. In our model, the viewing geometry is crucial factor to discriminate between the normal gamma-ray pulsars and soft gamma-ray pulsars. Our model suggests that the difference between the magnetic inclination angle ($alpha$) and the Earth viewing angle ($beta$) of the soft gamma-ray pulsars is small, so that the synchrotron emissions from the high magnetic field region around the polar cap region dominates in the observed emissions. Furthermore, the inclination angle of the soft gamma-ray pulsar is relatively small, $alphaleq 30$~degree, and our line of sight is out of the gamma-ray beam emitted via the curvature radiation process in the outer gap. We also analysis the six year $Fermi$ data for four soft gamma-ray pulsars to determine the upper limit of the GeV flux.
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