Thermal properties and radiative strengths in ${}^{160,161,162}\mathrm{Dy}$

The level densities and radiative strength functions (RSFs) in ${}^{160,161}\mathrm{Dy}$ have been extracted using the $\left({}^3\mathrm{He},\alpha \gamma \right)$ and $({}^3\mathrm{He},{{}^3\mathrm{He}}^{\prime }\gamma )$ reactions, respectively. The data are compared to previous measurements on ${}^{161,162}\mathrm{Dy}$. The energy distribution in the canonical ensemble is discussed with respect to the nucleon Cooper pair breaking process. The gross properties of the RSF are described by the giant electric dipole resonance. The RSF at low $\gamma$-ray energies is discussed with respect to temperature dependency. Resonance parameters of a soft dipole resonance at $E_{\gamma }\sim 3\text{MeV}$ are deduced.

Figure 1

Average experimental spin distributions (data points with error bars) compared to Eq. (6). The data include 130 nuclei along the $\beta$-stability line in the $A=150–170$ mass region.

Figure 2

Level densities estimated from neutron resonance level spacings at $B_n$. The data are plotted as a function of intrinsic excitation energy $U_n=B_n-C_1-\left({\Delta }_p+{\Delta }_n\right)$. The unknown level density for ${}^{160}\mathrm{Dy}$ (open circle) is estimated from the line determined by a least ${\chi }^2$ fit to the data points.

Figure 3

Normalization procedure of the experimental level density (data points) of ${}^{160}\mathrm{Dy}$. The data points between the arrows are normalized to known levels at low excitation energy (histograms) and to the level density at the neutron-separation energy (open circle) using the Fermi-gas level density (line).

Figure 4

Normalized level densities for ${}^{160,161,162}\mathrm{Dy}$. The filled and open circles are measured with the $\left({}^3\mathrm{He},\alpha \right)$ and $\left({}^3\mathrm{He},{}^3\mathrm{He}^{\prime }\right)$ reactions, respectively.

Figure 5

Experimental entropy for ${}^{160,161}\mathrm{Dy}$.

Figure 6

Observed probability density functions for ${}^{160,161}\mathrm{Dy}$. The right panels show the case where the experimental data of ${}^{161}\mathrm{Dy}$ are replaced by a constant temperature level density, see text.

Figure 7

Experimental (left) and theoretical (right) excitation energy $⟨E⟩$, heat capacity $C_V$, and skewness $\gamma$ of the $p_T$ distribution as a function of temperature $T$. The model parameters [22] used are ${\epsilon }_p={\epsilon }_n=3a∕{\pi }^2=0.19\text{MeV}$, ${\Delta }_p={\Delta }_n=0.7\text{MeV}$, $r=0.56$, $A_{\text{rigid}}=7.6\text{keV}$, and $\hslash {\omega }_{\text{vib}}=0.9\text{MeV}$.

Figure 8

Unnormalized radiative transmission coefficient for ${}^{160}\mathrm{Dy}$. The lines are extrapolations needed to calculate the normalization integral of Eq. (19). The arrows indicate the fitting regions.

Figure 9

Normalized RSFs for ${}^{160,161,162}\mathrm{Dy}$. The filled and open circles are measured with the $\left({}^3\mathrm{He},\alpha \right)$ and $\left({}^3\mathrm{He},{}^3\mathrm{He}^{\prime }\right)$ reactions, respectively.

Figure 10

Radiative GEDR strength function of the KMF model calculated for various temperatures.

Figure 11

Average temperature $⟨T⟩$ of the final state (solid line) and standard deviation ${\sigma }_T$ (dashed line) for the temperature distribution as a function of $\gamma$ energy in ${}^{160}\mathrm{Dy}$, see text.

Figure 12

The experimental RSFs for ${}^{160,162}\mathrm{Dy}$ (data points) compared to model predictions using a temperature dependent GEDR (solid line). The GEDR and pygmy resonance (solid lines) are the most important contributions to the total RSF. The total RSFs using a fixed temperature of $T=0.30\text{MeV}$ (dashed line) and $T=0.55\text{MeV}$ (dash-dotted line) give lower strengths for $E_{\gamma }<1\text{MeV}$.