Scissors resonance in the quasicontinuum of Th, Pa, and U isotopes

The $\gamma$-ray strength function in the quasicontinuum has been measured for ${}^{231–233}$Th, ${}^{232,233}$Pa, and ${}^{237–239}$U using the Oslo method. All eight nuclei show a pronounced increase in $\gamma$ strength at ${\omega }_{\mathrm{SR}}\approx 2.4$ MeV, which is interpreted as the low-energy $M1$ scissors resonance (SR). The total strength is found to be $B_{\mathrm{SR}}=9–11{\mu }_N^2$ when integrated over the 1–4 MeV $\gamma$-energy region. The SR displays a double-hump structure that is theoretically not understood. Our results are compared with data from ($\gamma$, ${\gamma }^{\prime }$) experiments and theoretical sum-rule estimates for a nuclear rigid-body moment of inertia.

Figure 1

First generation (primary) $\gamma$-ray matrix in ${}^{239}$U. At each excitation energy bin, $\gamma$ spectra can be projected out, giving the energy distribution of the first $\gamma$'s from that excitation energy. The excitation energy ($E$) and $\gamma$ energy ($E_{\gamma }$) axis have dispersion 14.0 keV/ch and 32.4 keV/ch, respectively.

Figure 2

Level densities for ${}^{232,233}$Pa. The experimental data are normalized to the level density of known discrete levels at low excitation energy $E$ (solid lines) and the level density extracted from known neutron resonance spacings $D_0$ at the neutron separation energy $S_n$. The connection between $\rho \left(S_n\right)$ (the upper right data points) and our experimental data are made with a constant-temperature formula with $T_{\mathrm{CT}}=0.44$ and 0.46 MeV for ${}^{232,233}$Pa, respectively. Note the extreme high level density for the odd-odd ${}^{232}$Pa, which reads $\approx$ 68 million levels per MeV at $S_n=5.55$ MeV.

Figure 3

Estimation of the underlying $\gamma$SF in Th (a), Pa (b), and U (c) isotopes. The red solid curve represents the strength expected without the scissors strength. The ($\gamma$, $x$) data are taken from Caldwell et al. [29] and the ARC data from Refs. [25, 30]. The dashed curves are the $M1$ spin-flip resonance recommended by RIPL and an unknown pygmy resonance, which is introduced to take into account the increased strength at $E_{\gamma }\approx 7.3$ MeV.

Figure 4

Normalization of the $\gamma$-ray strength functions with respect to the red solid curves of Fig. 3, which are assigned to the Th, Pa, and U isotopes.

Figure 5

The extracted scissors resonance for ${}^{231–233}$Th. The various nuclei are produced with different reactions and different excitation energy regions of the primary $\gamma$ matrix are utilized.

Figure 6

Same as Fig. 5 for ${}^{232–233}$Pa.

Figure 7

Same as Fig. 5 for ${}^{237–239}$U.

Figure 8

Comparison between Oslo (a) and HI$\gamma$S (b) data for ${}^{232}$Th. The HI$\gamma$S data are discrete levels with measured $B\left(M1\right)$. The folded red curve of these data using Lorentzian shapes are shown in arbitrary units. The Oslo and HI$\gamma$S data show some resemblance, except that the HI$\gamma$S data are shifted $\approx$300 keV up in energy and are a factor of 2 lower in summed strength than the Oslo data (see text).

Figure 9

Comparison between observed SRs for ${}^{232}$Th from Oslo and $\mathrm{HI}\gamma \mathrm{S}$. The data are compared with sum-rule estimates using ${\Theta }_{\mathrm{rigid}}$ and ${\Theta }_{\mathrm{gs}}$ for the two experiments, respectively. The deformation dependence for SR built on the ground state is assumed to be constant for $\omega$ and follows a ${\delta }^2$ rule for $\sum B\left(M1\right)$.