Low-energy photon scattering experiments of151,153Eu,163Dy,and165Hoand the systematics of theM1scissors mode in odd-mass rare-earth nuclei

Nuclear resonance fluorescence experiments were performed on the rare-earth nuclei ${}^{151,153}\mathrm{Eu},$ and with considerably increased sensitivity on ${}^{163}\mathrm{Dy}$ and ${}^{165}\mathrm{Ho}$ to study the fragmentation of the $M1$ scissors mode in odd-mass nuclei, and to clarify the puzzle of the missing total $M1$ strength observed for odd-mass nuclei so far. Using the bremsstrahlung photon beam of the Stuttgart Dynamitron (end point energy 4.05 MeV) and high-resolution Ge $\ensuremath{\gamma}$-ray spectrometers, detailed information was obtained on excitation energies, decay widths, transition probabilities, and branching ratios. Whereas in ${}^{151}\mathrm{Eu}$ only 11 weak excitations were observed, 161 and 138 excitations could be detected in the heavier nuclei ${}^{163}\mathrm{Dy}$ and ${}^{165}\mathrm{Ho},$ respectively. The results are compared to those observed recently at the Stuttgart facility for the neighboring odd-mass nuclei ${}^{161}\mathrm{Dy},$ ${}^{155,157}\mathrm{Gd},$ and ${}^{159}\mathrm{Tb}.$ The measured total strengths increase with the mass number $A.$ Ascribing the same portion of the dipole strength to $M1$ excitations as measured in the neighboring even-even nuclei, the total $M1$ strength deduced from the most sensitive experiment on ${}^{163}\mathrm{Dy}$ is comparable to those found in the neighboring even-even nuclei. The results for ${}^{163}\mathrm{Dy}$ and ${}^{165}\mathrm{Ho}$ are compared with a fluctuation analysis of the photon scattering spectra to estimate the amount of still unresolved strength eventually hidden in the background due to the extreme fragmentation of the $M1$ scissors mode in odd-mass rare-earth nuclei. For ${}^{165}\mathrm{Ho},$ the total derived strength of $B(M1)\ensuremath{\uparrow}=2.9(5){\ensuremath{\mu}}_{N}^{2}$ agrees within error bars with an earlier analysis of a different measurement of the ${}^{165}\mathrm{Ho}(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ reaction. In ${}^{163}\mathrm{Dy}$ the method leads to an unphysical background shape, underlining the experimental observation of a significantly reduced fragmentation pattern of the dipole modes in this nucleus, which must be traced back to structure features of the Dy isotopes.