Speaker
Description
The doubly magic nucleus $^{208}$Pb is the archetypal heavy ion system. Yet, there are unresolved questions about its structure. One of these puzzles pertains to the anomalous inelastic scattering populating the 4.086-MeV $2_1^+$
level. The measured differential cross-sections for the population of this level in 98-MeV $^{12}$C + $^{208}$Pb and 270-MeV $^{3}$He + $^{208}$Pb inelastic scatterings are underpredicted by the distorted wave Born approximation (DWBA) estimates by about a factor of two [1,2].
This difference between the theory and experiment has been unsolved for about half a century and cannot be attributed to errors in data normalization or the uncertainty in the adopted values of the coupling strengths for the excitation of the concerned $2_1^+$ level.
Nevertheless, the relatively large level density of $^{208}$Pb in the vicinity of 4\,MeV presents the possibility that the experimental resolution in the measurements mentioned above was insufficient to distinguish between several closely spaced energy levels, some of which might contribute to the measured angular distributions. Thus, assuming an experimental energy resolution of about 200-250\,keV, we calculated differential cross-sections for 98-MeV $^{12}$C + $^{208}$Pb and 270-MeV $^{3}$He + $^{208}$Pb inelastic scattering to the $2_1^+$ level, including also eight possibly unresolved levels, viz., the 3.961-MeV $5_3^-$,
4.051-MeV $3_2^-$, 4.125-MeV $5_4^-$, 4.144-MeV ($2_2^+$), 4.180-MeV $5_5^-$, 4.254-MeV $3_3^-$, 4.297-MeV $5_6^-$, and 4.324-MeV $4_1^+$, in addition to the 4.086-MeV $2_1^+$. A consistent picture was obtained using coupling strengths for these eight levels that were obtained by fitting the $^{208}$Pb(p,p') data at 35\,MeV [3]. The validation of the resulting values for the Coulomb and nuclear coupling strengths was tested against (p,p'), (d,d') and ($\alpha,\alpha'$) data [3,4].
The summmed DWBA calculations for these levels were in good agreement with the 98-MeV $^{12}$C + $^{208}$Pb and 270-MeV $^3$He + $^{208}$Pb inelastic scattering data, thus providing a plausible explanation of the anomalously large $0_1^+ \rightarrow 2_1^+$ cross section in these data sets. The most important contribution was from the $4_1^+$ level; however, although individually weakly populated, the other levels together account for about 20\% of the total cross section.
References:
[1] G. R. Satchler et al., Phys. Lett. B 60, 43 (1975).
[2] P. P. Singh et al., Pramana - J. Phys. 27, 747 (1986).
[3] W. T. Wagner et al., Phys. Rev. C 12, 757 (1975).
[4] H. P. Morsch et al., Phys. Rev. C 22, 489 (1980).
[5] J. Bojowald et al., Phys. Rev. C 38, 1153 (1988).