The photoneutron cross sections of $^{162,163}\mathrm{Dy}$ have been measured for the first time in an energy region from the neutron threshold (${S}_{n}$) up to $\ensuremath{\approx}13\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. The $(\ensuremath{\gamma},n)$ reaction was induced with quasimonochromatic laser Compton-scattered $\ensuremath{\gamma}$ rays, produced at the NewSUBARU laboratory. The corresponding $\ensuremath{\gamma}$-ray strength functions ($\ensuremath{\gamma}\mathrm{SF}$) have been calculated from the photoneutron cross sections. The data are compared to reanalyzed $\ensuremath{\gamma}\mathrm{SFs}$ of $^{160\text{--}164}\mathrm{Dy}$, which are measured below ${S}_{n}$. The excellent agreement with the photoneutron data at ${S}_{n}$ confirms the principle of detailed balance. Thus, a complete $\ensuremath{\gamma}\mathrm{SF}$ is established covering in total the energy region of $1\ensuremath{\le}{E}_{\ensuremath{\gamma}}\ensuremath{\le}13$ MeV. These mid-shell well-deformed dysprosium isotopes all show scissors resonances with very similar structures. We find that our data predict the same integrated scissors strength as $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ data when integrated over the same energy range, which shows that the scissors mode very likely is consistent with the generalized Brink hypothesis. Finally, using the $\ensuremath{\gamma}\mathrm{SFs}$ as input in the reaction code talys, we have deduced radiative neutron-capture cross sections and compared them to direct measurements. We find a very good agreement within the uncertainties, which gives further support to the experimentally determined $\ensuremath{\gamma}\mathrm{SFs}$.

/pdf/verification-of-detailed-balance-for-g-absorption-and-4k61j0st9f.pdf

Verification of detailed balance for γ absorption and emission in Dy isotopes

The level densities and $\gamma$-strength functions of the weakly deformed $^{148}$Sm and $^{149}$Sm nuclei have been extracted. The temperature versus excitation energy curve, derived within the framework of the micro canonical ensemble, shows structures, which we associate with the break up of Cooper pairs. The nuclear heat capacity is deduced within the framework of both the micro canonical and the canonical ensemble. We observe negative heat capacity in the micro canonical ensemble whereas the canonical heat capacity exhibits an S-shape as function of temperature, both signals of a phase transition. The structures in the $\gamma$-strength functions are discussed in terms of the pygmy resonance and the scissors mode built on exited states. The samarium results are compared with data for the well deformed $^{161,162}$Dy, $^{166,167}$Er and $^{171,172}$Yb isotopes and with data from (n,$\gamma$)-experiments and giant dipole resonance studies.

https://arxiv.org/pdf/nucl-ex/0111012.pdf

Level densities and $γ$-strength functions in $^{148,149}$Sm

Using numerical and analytical methods implemented for different models, we conduct a systematic study of the thermodynamic properties of pairing correlations in mesoscopic nuclear systems. Various quantities are calculated and analyzed using the exact solution of pairing. An in-depth comparison of canonical, grand canonical, and microcanonical ensembles is conducted. The nature of the pairing phase transition in a small system is of a particular interest. We discuss the onset of discontinuity in the thermodynamic variables, fluctuations, and evolution of zeros of the canonical and grand canonical partition functions in the complex plane. The behavior of the invariant correlational entropy is also studied in the transitional region of interest. The change in the character of the phase transition due to the presence of a magnetic field is discussed along with studies of superconducting thermodynamics.

Thermodynamics of pairing in mesoscopic systems

Levels in ${}^{112}\mathrm{Cd}$ have been studied through the ${(n,n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction with monoenergetic neutrons. An extended set of experiments that included excitation functions, $\ensuremath{\gamma}$-ray angular distributions, and $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence measurements was performed. A total of 375 $\ensuremath{\gamma}$ rays were placed in a level scheme comprising 200 levels (of which 238 $\ensuremath{\gamma}$-ray assignments and 58 levels are newly established) up to 4 MeV in excitation. No evidence to support the existence of 47 levels as suggested in previous studies was found, and these have been removed from the level scheme. From the results, a comparison of the level density is made with the constant temperature and back-shifted Fermi gas models. The back-shifted Fermi gas model with the Gilbert-Cameron spin cutoff parameter provided the best overall fit. Without using the neutron resonance information and only fitting the cumulative number of low-lying levels, the level density parameters extracted are a sensitive function of the maximum energy used in the fit.

Properties of 112 Cd from the ( n , n ′ γ ) reaction: Levels and level densities

${}^{163,164}$Dy nuclei have been measured by use of the Oslo method on data from pick-up ${(}^{3}\mathrm{He},\ensuremath{\alpha})$ and inelastic scattering ${(}^{3}\mathrm{He}{,}^{3}\phantom{\rule{-0.16em}{0ex}}{\mathrm{He}}^{\ensuremath{'}})$ reactions, respectively. The level densities for these dysprosium isotopes together with previously measured ${}^{160--162}$Dy are extracted in the region below the neutron binding energy. Thermodynamic properties are deduced within both micro-canonical and canonical ensemble theories. A phase transition from the pair-correlated state at low energies to a less correlated or uncorrelated state is studied in both ensembles. It is investigated whether the temperature of the nucleus is constant or a varying function of excitation energy. It is found that above an excitation energy of 3 MeV the temperature of all five dysprosium nuclei have a constant value within the experimental uncertainties. The impact of a constant-temperature level density versus a Fermi gas level density is discussed with respect to the canonical heat capacity.

Level density and thermodynamic properties of dysprosium isotopes

The density of accessible levels at low spin in the ${(}^{3}\mathrm{He},\ensuremath{\alpha}\ensuremath{\gamma})$ reaction has been extracted for the ${}^{161,162}\mathrm{Dy}$ and ${}^{171,172}\mathrm{Yb}$ nuclei The entropy of the even-odd and even-even nuclei has been deduced as a function of excitation energy The entropy of one quasiparticle outside an even-even core is found to be 170(15) ${k}_{B}$ This quasiparticle picture of hot nuclei is well accounted for within a simple pairing model The onset of two, four, and six quasiparticle excitations in the ${}^{162}\mathrm{Dy}$ and ${}^{172}\mathrm{Yb}$ nuclei is discussed and compared to theory The number of quasiparticles excited per excitation energy is a measure for the ratio of the level energy spacing and the pairing strength

Entropy in hot161,162Dyand171,172Ybnuclei

Entropy in hot ^161,162Dy and ^171,172Yb nuclei

The density of accessible levels at low spin in the ${(}^{3}\mathrm{He},\ensuremath{\alpha}\ensuremath{\gamma})$ reaction has been extracted for the ${}^{161,162}\mathrm{Dy}$ and ${}^{171,172}\mathrm{Yb}$ nuclei. The entropy of the even-odd and even-even nuclei has been deduced as a function of excitation energy. The entropy of one quasiparticle outside an even-even core is found to be 1.70(15) ${k}_{B}.$ This quasiparticle picture of hot nuclei is well accounted for within a simple pairing model. The onset of two, four, and six quasiparticle excitations in the ${}^{162}\mathrm{Dy}$ and ${}^{172}\mathrm{Yb}$ nuclei is discussed and compared to theory. The number of quasiparticles excited per excitation energy is a measure for the ratio of the level energy spacing and the pairing strength.

Entropy in hot 161,162 Dy and 171,172 Yb nuclei

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Entropy in hot161,162Dyand171,172Ybnuclei

Entropy in hot ^161,162Dy and ^171,172Yb nuclei

Entropy in hot 161,162 Dy and 171,172 Yb nuclei