Probing nuclear shapes close to the fission limit with the giant dipole resonance in ${}^{216}\mathrm{Rn}$

The gamma-ray decay of the giant dipole resonance (GDR) in the compound nucleus ${}^{216}\mathrm{Rn}$ formed with the reaction ${}^{18}\mathrm{O}{+}^{198}\mathrm{Pt}$ at the bombarding energy of 96 MeV was investigated. High-energy gamma-ray spectra in coincidence with both prompt and delayed low-energy transitions were measured. The obtained GDR width at the average temperature $⟨T⟩\approx 1\mathrm{MeV}$ was found to be larger than that at $T=0\mathrm{MeV}$ and to be approximately constant as a function of spin. The measured width value of 7 MeV is found to be consistent with the predictions based on calculations of the nuclear shape distribution using the newest approach for the treatment of the fission barrier within the liquid drop model. The present study is the first investigation of the giant dipole resonance width from the fusion-evaporation decay channel in this nuclear mass range.

Figure 1

Calculated cross sections for the population of evaporation residues in ${}^{212,211,210}\mathrm{Rn}$ as functions of spin: with no condition on $\mathrm{\gamma }$-ray energy (top) and with the gate on $\mathrm{\gamma }$-ray energy in the GDR region (bottom).

Figure 2

Top panel: Time-of-flight spectrum measured by the catcher detector around the catcher foil. Regions corresponding to various processes taking place during the measurement are indicated. The region corresponding to the emission from recoils at the catcher is shown in detail in the inset; this spectrum is background subtracted. It corresponds to detection of the $\mathrm{\gamma }$ rays from the isomeric states in ${}^{211}\mathrm{Rn}$ and ${}^{212}\mathrm{Rn}$. Bottom panel: The $\mathrm{\gamma }$-ray spectrum measured with the Ge detector as obtained without any gate on the time spectrum (gray histogram) compared to the spectrum gated with the isomer part of time of flight (black histogram). The gated spectrum shows an enhancement of the transitions above the isomeric states. The inset to this panel shows the parts of the level schemes of ${}^{211}\mathrm{Rn}$ and ${}^{212}\mathrm{Rn}$ with transitions above the isomeric states.

Figure 3

The spectra of high-energy $\mathrm{\gamma }$ rays for three different conditions: recoils and background corresponding to the gates shown in Fig. 2 and the difference of these two spectra shown with filled squares.

Figure 4

The experimental coincidence fold-distributions of the low-energy transitions. The data without any conditions on the time-of-flight spectrum of Fig. 2 are marked with the squares, while the triangles correspond to the isomer gated data. The difference of these two distributions (after normalization in the total counts in the fold interval 1–4) is shown with the circles. The lines show the calculated fold distributions, each corresponding to a value of $l_{\mathit{max}}$ in the interval 33 to $45\mathrm{\hslash }$. The best fit to the data is for $l_{\mathit{max}}=39\mathrm{\hslash }$ (solid line), while the distribution with the average $\mathrm{\gamma }$-multiplicity, $M_{\mathrm{\gamma }}=5$, corresponds to the isomer gated data.

Figure 5

Top panel: The experimental high-energy $\mathrm{\gamma }$-ray spectrum corresponding to the folds 5–30 represented with full dots. The line is the result of the best-fit statistical-model calculations. Bottom panel: The data in the linearized form described in the text and the best-fit GDR line shape (solid line) consisting of the sum of three Lorentzian functions. The one-Lorentzian function drawn with the dashed line is compared to the sum (full line) of three Lorentzian components.

Figure 6

The experimental spectra (points) corresponding to the selected low-and high-fold regions, and the best-fit Monte Carlo cascade calculations (lines) performed with a value of the GDR width of 7 MeV.

Figure 7

The experimental high-energy spectrum gated by the isomer decay is shown with the full circles. Four statistical model Monte Carlo calculations are shown with lines. The calculation using the fold interval 5-30 and GDR width of 7 MeV, which corresponds to the best-fit curve of Fig. 5, is displayed as the thin solid line. The calculations corresponding to GDR widths of 4 and 11 MeV are shown with the dashed and dash-dotted lines, respectively. The fit to the isomer gated spectrum obtained for $\mathrm{\Gamma }=7.3\pm 1\mathrm{MeV}$ and assuming only the high-spin region $(⟨I⟩=35\mathrm{\hslash })$ is presented with thick solid line. The shaded area indicates the possible deviations of the calculated GDR spectrum from the best-fit curve within the 1 MeV error bars of the GDR width.

Figure 8

(Color online) The ${}^{216}\mathrm{Rn}$ potential energy maps calculated using the LSD model. As one can see, this approach predicts for the ${}^{216}\mathrm{Rn}$ nucleus an equilibrium shape (cf. the minima of the potential energy) which is approximately spherical up to the spins around $I=40\mathrm{\hslash }$. At $I=40\mathrm{\hslash }$, the fission barrier is about 3 MeV high, so that for $I⩾40\mathrm{\hslash }$ the fission decay mode is expected to dominate. Note that the only evolution with spin is the decreasing in the barrier height and no Jacobi transition is expected in this nucleus according to the calculations.

Figure 9

The probability distributions calculated using the model Boltzmann factors as discussed in the text. Observe the stability of the position of the maximum of the displayed distributions. However, the distributions spread out as a function of spin, their maxima get lower, and, at $I\sim 40\mathrm{\hslash }$, the traces of the fission path become visible.

Figure 10

Top panel: The GDR width as a function of spin obtained for experimental GDR strength functions is shown with points in the top panel in comparison with theoretical predictions (the horizontal error bars correspond to the half-width of the spin distribution selected by the gating conditions). The dotted line corresponds to results of calculations performed according to the Kusnezov formula. The GDR width calculated using thermal shape fluctuations based on potential energies obtained with LSD model is drawn with the dashed line. Bottom panel: The LSD model predictions for equilibrium deformation ${\beta }_{\mathit{eq}}$ are presented in the bottom panel with the dash-dotted line. The dashed line $⟨\mathrm{\Delta }\beta ⟩$ (square root of the variance of the $\beta$ distribution) indicates the extent of the possible deformations and $⟨\beta ⟩$ (solid line) is the average deformation.