Measurement of the Damping of the Nuclear Shell Effect in the Doubly Magic ${}^{208}\mathrm{Pb}$ Region

The damping of the nuclear shell effect with excitation energy has been measured through an analysis of the neutron spectra following the triton transfer in the ${}^7\mathrm{Li}$ induced reaction on ${}^{205}\mathrm{Tl}$. The measured neutron spectra demonstrate the expected large shell correction energy for the nuclei in the vicinity of doubly magic ${}^{208}\mathrm{Pb}$ and a small value around ${}^{184}\mathrm{W}$. A quantitative extraction of the allowed values of the damping parameter $\gamma$, along with those for the asymptotic nuclear level density parameter $\tilde{a}$, has been made for the first time.

Figure 1

Two-dimensional plot of ZCT versus energy deposited in one of the CsI(Tl) detectors in ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ reaction. The inset shows the projected spectrum of the alpha particles defined by the dotted two-dimensional gate. The vertical lines define three alpha energy bins (see text).

Figure 2

Time of flight spectrum in ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ reaction for the central energy bin of alpha particles. The arrows indicate the positions for two representative neutron energies.

Figure 3

(a) Measured neutron spectra from ${}^{205}\mathrm{Tl}$ target for three alpha bins I, II, III (see Fig. 1). (b), (c) Measured neutron spectra from ${}^{205}\mathrm{Tl}$ and ${}^{181}\mathrm{Ta}$ targets and SM calculations for the central alpha energy bin which corresponds to an excitation energy $\sim 21\mathrm{MeV}$.

Figure 4

(a) Comparison of data with SM calculation using ${\Delta }_S=13.1\mathrm{MeV}$ (for ${}^{207}\mathrm{Pb}$) and 11.7 MeV (for ${}^{206}\mathrm{Pb}$) for three values of $\gamma$ and (b) ratio plot of data to fits for these $\gamma$ values.

Figure 5

Exclusion plot of $\delta a\mathrm{\text{−}}\gamma$, where $\delta a=A/\tilde{a}$, for the shell correction energies quoted in Fig. 4. The acceptable values are within the contour.