  We present results on the Soft Gamma Repeater (SGR) 0501+4516, discovered by
the SWIFT Burst Alert Telescope (BAT) on 2008 August 22. More than 50 bursts
were identified from this source, out of which 18 bursts had enough counts to
carry out spectral analysis. We performed time-averaged spectral analysis on
these 18 bursts using 8 models, among which the cut-off powerlaw and the
two-blackbody models provided the best fit in the 15-150 keV energy range. The
cut-off powerlaw model fit yields a mean photon index Gamma_{CPL} = 0.54+/-0.11
and a cut-off energy E_C = 19.1+/-1.8 keV for the bursts. The mean hard and
soft blackbody temperatures are found to be kT_{BB_h} = 12.8+/-0.7 keV and
kT_{BB_s} = 4.6+/-0.5 keV, respectively, and are anti-correlated with the
square of the radii of the hard and soft emitting regions (R_{BB_h} and
R_{BB_s}) as R_{BB_h}^2 $\propto$ kT^{-5.8} and R_{BB_s}^2 $\propto$ kT^{-2.7},
respectively. The soft and hard component temperatures with different indices
support the idea of two distinct emitting regions with the hard component
corresponding to a smaller radius and the soft component corresponding to a
larger radius, which further corroborate the idea of the propagation of
extraordinary (E) and ordinary (O) mode photons across the photosphere, as
predicted in the magnetar model. We notice strong burst fluence-duration
correlation as well as hardness ratio-duration and hardness ratio-fluence
anti-correlations for the SGR 0501+4516 bursts. The burst fluences range from ~
4.4\times10^{-9} ergs/cm^-2 to ~ 2.7\times10^{-6} ergs/cm^{-2}, consistent with
those observed for typical short SGR bursts.
