Identification of the $0^{+}$ proton pairing vibration state in the doubly magic nucleus ${}^{208}\mathrm{Pb}$ by particle spectroscopy

Among about 150 levels below $E_x=5.86\text{MeV}$ in ${}^{208}\mathrm{Pb}$ listed by the Nuclear Data Sheets as of 2007, most levels were recently identified as particle-hole states. All natural parity states excited by the ${}^{208}\mathrm{Pb}(\alpha ,{\alpha }^{\prime })$ reaction are identified, two of them are newly identified. The state at $E_x=5667\text{keV}$ is identified as the $0^{+}$ proton pairing vibration state. Based on the analysis of data from the ${}^{206,207,208}\mathrm{Pb}(d,p),{}^{208}\mathrm{Pb}(d,d^{\prime })$, and ${}^{208}\mathrm{Pb}(p,p^{\prime })$ reactions obtained with the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at Garching (Germany) at scattering angles ${15}^{\circ }\le \mathrm{\Theta }\le {138}^{\circ }$ and bombarding energies $E_d=22,24\text{MeV}$ and $14.8<E_p<18.2\text{MeV}$, the excitation energy is determined as $E_x=5666.7\pm 0.3\text{keV}$; the mean cross section in the nonresonant ${}^{208}\mathrm{Pb}(p,p^{\prime })$ and the ${}^{208}\mathrm{Pb}(d,d^{\prime })$ reactions is about $1 \mu \text{b/sr}$. A new state at $E_x=5042\pm 3\text{keV}$ is suggested to have the spin of $2^{+}$. The $0^{+}$ neutron pairing vibration state at $E_x=4868\text{keV}$ and the $0^{+}$ member of the double-octupole multiplet at $E_x=5241\text{keV}$ are verified by the nonresonant ${}^{208}\mathrm{Pb}(p,p^{\prime })$ and ${}^{208}\mathrm{Pb}(d,d^{\prime })$ reactions with cross sections of around $3\mu \mathrm{b}/\mathrm{sr}$.

Figure 1

Spectra for $5.63<E_x<5.70\text{MeV}$ taken on the $g_{9/2},i_{11/2}$, and near the $g_{7/2}$ and $d_{3/2}$ IARs and (at bottom) for ${}^{208}\mathrm{Pb}(d,d^{\prime })$; the range of proton bombarding energies is given in Table 2, the deuteron bombarding energy for $\left(d,d^{\prime }\right)$ was 22 MeV. The mean distance between two peaks is 5 keV. The spectra are obtained by summing up several runs (Sec. 3b). The fit by gaspan was performed with a Gaussian followed by an exponential tail [8, 39]; the dotted lines represent the center of the Gaussian. Spin and parity of all states are shown at bottom; the spins are from [8, 12]. The peak from the $5667 0^{+}$ state is marked magenta. $L$ satellites are observed in the spectrum taken near the $j_{15/2}$ and $d_{5/2}$ IARs (marked blue). For more details see Sec. 3b.

Figure 2

For the $5658 5^{-},5667 0^{+}$, and $5675 4^{-}$ states, angular distributions of cross sections at ${20}^{\circ }<\mathrm{\Theta }<{138}^{\circ }$ near seven IARs (Table 2) or excitation functions from $E_p=14.8$ to 17.6  MeV for four ranges of scattering angles shown in the first and third frame. For details see Sec. 4b2.