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\@writefile{lof}{\contentsline {figure}{\numberline {B.2}{\ignorespaces The potential penetrability obtained with several methods. The dotted line is obtained without channel coupling, while the dashed line takes into account only the collective vibrational excitation. The solid line shows the result with both the collective and the noncollective excitations.}}{93}{figure.B.2}}
\newlabel{fig:penet}{{B.2}{93}{The potential penetrability obtained with several methods. The dotted line is obtained without channel coupling, while the dashed line takes into account only the collective vibrational excitation. The solid line shows the result with both the collective and the noncollective excitations}{figure.B.2}{}}
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\newlabel{fig:qdist}{{B.4}{94}{The $Q$-value distribution for the reflected flux at four energies as indicated in the figure. It is obtained by smearing the discrete distribution with a Lorentzian function with the width of 0.2 MeV. The peaks at $E^{*}$=0 MeV and 1 MeV correspond to the elastic and the collective excitation channels, respectively}{figure.B.4}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {D.1}{\ignorespaces The upper panel: Fusion barrier distributions for a rotational coupling associated with a prolate deformation. The rotational states are included up to the 2$^+$ state. The red line includes only the collective excitations while the blue one includes also the noncollective excitations. The pink and the cyan spectra represent the position of the eigenbarriers corresponding to the red and the blue lines, respectively. The lower panel: The overlap of the perturbed and the unperturbed eigenvectors for a prolate rotational coupling. The orange and the purple lines represent the overlap with the eigenvector belonging to the lowest and the second lowest unperturbed eigenvalues, respectively.}}{98}{figure.D.1}}
\newlabel{fig7.23}{{D.1}{98}{The upper panel: Fusion barrier distributions for a rotational coupling associated with a prolate deformation. The rotational states are included up to the 2$^+$ state. The red line includes only the collective excitations while the blue one includes also the noncollective excitations. The pink and the cyan spectra represent the position of the eigenbarriers corresponding to the red and the blue lines, respectively. The lower panel: The overlap of the perturbed and the unperturbed eigenvectors for a prolate rotational coupling. The orange and the purple lines represent the overlap with the eigenvector belonging to the lowest and the second lowest unperturbed eigenvalues, respectively}{figure.D.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {D.2}{\ignorespaces Same as Fig. \ref  {fig7.23}, but with the $4^{+}$ state in the rotational coupling. The green lines in the lower panel represent the overlap with the eigenvector belonging to the third lowest unperturbed eigenvalues.}}{98}{figure.D.2}}
\newlabel{fig7.24}{{D.2}{98}{Same as Fig. \ref {fig7.23}, but with the $4^{+}$ state in the rotational coupling. The green lines in the lower panel represent the overlap with the eigenvector belonging to the third lowest unperturbed eigenvalues}{figure.D.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {D.3}{\ignorespaces Same as Fig.\ref  {fig7.23}, but for an oblate deformation.}}{99}{figure.D.3}}
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\bibcite{CL81}{1}
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\bibcite{dasgupta}{3}
\bibcite{L95}{4}
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\bibcite{BT98}{11}
\bibcite{LRL93}{12}
\bibcite{TCS97}{13}
\bibcite{MHD07}{14}
\bibcite{N04}{15}
\bibcite{J02}{16}
\bibcite{JRJ04}{17}
\bibcite{DHD07}{18}
\bibcite{S08}{19}
\bibcite{piasecki}{20}
\bibcite{T98}{21}
\bibcite{bnl}{22}
\bibcite{T96}{23}
\bibcite{T97}{24}
\bibcite{evers}{25}
\bibcite{lin}{26}
\bibcite{evers2}{27}
\bibcite{MBD99}{28}
\bibcite{EM07}{29}
\bibcite{LR84}{30}
\bibcite{NRL86}{31}
\bibcite{NBT86}{32}
\bibcite{ELP87}{33}
\bibcite{T87}{34}
\bibcite{TMBR91}{35}
\bibcite{TAB92}{36}
\bibcite{AA94}{37}
\bibcite{GAN94}{38}
\bibcite{HTBB95}{39}
\bibcite{THAB94}{40}
\bibcite{ccfull}{41}
\bibcite{WCHM75}{42}
\bibcite{LBF73}{43}
\bibcite{KPW76}{44}
\bibcite{AKW78}{45}
\bibcite{BSW78}{46}
\bibcite{akw1}{47}
\bibcite{akw2}{48}
\bibcite{akw3}{49}
\bibcite{akw4}{50}
\bibcite{YHR12}{51}
\bibcite{JBF77}{52}
\bibcite{BH83}{53}
\bibcite{FT90}{54}
\bibcite{RS}{55}
\bibcite{BM1}{56}
\bibcite{BM2}{57}
\bibcite{YGMY96}{58}
\bibcite{VMA97}{59}
\bibcite{YKG98}{60}
\bibcite{VMC98}{61}
\bibcite{VPE01}{62}
\bibcite{Rose}{63}
\bibcite{Wong}{64}
\bibcite{HTB97}{65}
\bibcite{KRNR93}{66}
\bibcite{RS81}{67}
\bibcite{HTDHL97}{68}
\bibcite{rmtrev1}{69}
\bibcite{rmtrev2}{70}
\bibcite{fermi1934}{71}
\bibcite{fermi1935}{72}
\bibcite{bohr}{73}
\bibcite{porter}{74}
\bibcite{rmtapp}{75}
\bibcite{MA97}{76}
\bibcite{BGS84}{77}
\bibcite{HW95}{78}
\bibcite{goe}{79}
\bibcite{leveldensity}{80}
\bibcite{goeuniv}{81}
\bibcite{ergod}{82}
\bibcite{delta3}{83}
\bibcite{NDE1}{84}
\bibcite{NDE2}{85}
\bibcite{BDK96}{86}
\bibcite{fresco}{87}
\bibcite{DMH96}{88}
\bibcite{IHI09}{89}
\bibcite{YHR10}{90}
\bibcite{Akyuz-Winther}{91}
\bibcite{RNT01}{92}
\bibcite{BB82}{93}
\bibcite{H73}{94}
\bibcite{KMM10}{95}
\bibcite{NMD01}{96}
\bibcite{parabola}{97}
\bibcite{BDK95}{98}
\bibcite{numerical}{99}
\bibcite{piasecki-priv}{100}