the GQR TD state caused by the coupling to the whole 2p2h states.

![ Strength function of the GQR TD state evaluated by considering only surface vibration plus 1p1h (s.v.+1p1h) states based on Eq. (\[doorwaystr\]). $\gamma_{22}=0.75$ MeV is used. []{data-label="fig_doorwaystr"}](fig13.eps){width="6cm"}

From the estimate by the Fermi golden rule, we can give more detailed comparison between the width for the case of s.v.+1p1h states and that for the whole 2p2h states. It is noted in Table \[table1\] that the spreading width $\Gamma_2^{\rm (s.v.)}=0.074$ MeV and $\Gamma_2=0.41$ MeV are well accounted for by the estimate. In the Fermi golden rule the spreading width is governed by two factors; 1) the average value of squared coupling matrix elements $\overline{ V_{c\alpha}^2}$ between the GQR TD state and the states that couple to it, and 2) the level density of the coupling states. From Table \[table1\], we see that the large difference between the two widths simply reflects the difference between the number of s.v.+1p1h states 909 and 2p2h states 3142 whereas the coupling strength of s.v.+1p1h states $\overline{ V_{c\alpha}^2}=0.65\times10^{-4}$ MeV$^2$ is comparable to the coupling strength $\overline{V_{c\alpha}^2}=0.72\times10^{-4}$ MeV$^2$ for the whole 2p2h states.

Table \[table1\] and Fig. \[fig\_doorwaystr\] suggest that our model does not 