Positive parity states in ${}^{208}\mathrm{Pb}$ excited by the proton decay of the isobaric analog intruder resonance $j_{15/2}$ in ${}^{209}\mathrm{Bi}$

With the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at München at a resolution of about 3 keV, angular distributions and excitation functions of the reaction ${}^{208}\mathrm{Pb}$($p,p^{\prime }$) were measured at some scattering angles ${20}^{°}$–${138}^{°}$ for several proton energies $14.8$–$18.1$ MeV. All seven known isobaric analog resonances in ${}^{209}\mathrm{Bi}$ are covered. By the excitation near the $j{}_{15/2}$ intruder resonance in ${}^{209}\mathrm{Bi}$, several new positive parity states in ${}^{208}\mathrm{Pb}$ with excitation energies $4.6$–$6.2$ MeV are identified by comparison of the mean cross section to the known single particle widths. The dominant configuration for 27 positive parity states is determined and compared to the schematic shell model.

Figure 1

Excitation energies in ${}^{208}\mathrm{Pb}$, ${}^{207}\mathrm{Pb}$, ${}^{209}\mathrm{Bi}$, ${}^{207}\mathrm{Tl}$ determined from experiment [15] and gaps $\Delta Q$ derived from mass differences [Eq. (2)]. The magic gaps at 50, 82, 126, 184 nucleons, and the intruder levels (dotted, italic) are indicated. The $h{}_{9/2}$ orbits for protons and neutrons are matched to each other.

Figure 2

Action of the isospin lowering operator $T_{-}$ on the excess neutrons in ${}^{209}\mathrm{Pb}$ [Eqs. (6), (7)] where $T_0=\frac{44}{2}$ creates 45 components of the IAR. In each component one neutron ($\nu$) is converted into a proton ($\pi$). However only six out of the 164 core nucleons ($N,Z⩽82$), three out of the 44 excess neutrons ($82<N,Z⩽126$), and one orbit above $N,Z=126$ are shown. The depicted Coulomb barrier explains the change of the penetrability with the proton energy [7].

Figure 3

The proton decay of an IAR. The left frame reflects the elastic proton scattering, the right frame the inelastic proton scattering creating neutron particle-hole configurations in the parent nucleus.

Figure 4

Spectrum taken at scattering angle $\Theta ={88}^{°}$ for $5.3<E_x<5.7$ MeV and proton energy $E_p=16.630$ MeV (top: off resonance) and $E_p=16.405$ MeV (bottom: on $j{}_{15/2}$ IAR). Some positive parity states are identified (dotted lines), see Tables , . In the region $5.3<E_x<5.6$, $5.6<E_x<6.0$ the major fragments of the $j{}_{15/2}$$f{}_{5/2}$, $j{}_{15/2}$$p{}_{3/2}$ multiplet are located, respectively. The structure of other strongly excited states is not discussed.

Figure 5

Continuation of Fig. 4. Spectra taken for $5.7<E_x<6.1$ MeV.

Figure 6

Spectra taken for $4.835<E_x<4.935$ MeV and fitted by GASPAN. Satellites from $L$ electrons are fitted to the 4842, 4868 peaks (Appendix ).

Figure 7

Spectra taken for $4.920<E_x<5.105$ MeV and fitted by GASPAN. The ratio of the 4929, 5010 peaks to the 4974 peak is about $4:100$, $1:100$, respectively. The cross sections for the 4974 and 5037 states are nearly equal and increase by a factor 2 from $E_p=16.260$ to $16.460$ MeV. Satellites from $L$ electrons are fitted to the 4974 and 5037 peaks (Appendix ). In the lowest spectrum the proton energy is $E_p=16.310$ MeV (not $E_p=16.260$ MeV as indicated).

Figure 8

Spectra taken for $5.610<E_x<5.710$ MeV and fitted by GASPAN.

Figure 9

Spectra taken for $5.880<E_x<6.005$ MeV and fitted by GASPAN. Satellites from $L$ electrons are fitted to the 5886, 5924, 5969 peaks (Appendix ).

Figure 10

For proton energies $14.5<E_p<18.0$ MeV, normalized excitation functions for states with energy label $E$ given at left (Table ). Lorentzian curves are calculated for the $j{}_{15/2}$ (drawn) and the $d{}_{5/2}$ (dashed) IAR [Eq. (8) with parameters from Table ]. All known IAR in ${}^{209}\mathrm{Bi}$ are shown at bottom. Different regions of scattering angles are denoted by a triangle for $\Theta ={138}^{°}$, a square for $\Theta ={88}^{°}$, a diamond for ${72}^{°}<\Theta <{115}^{°}$. They correspond to data from different beam times (see Sec. 3f).

Figure 11

Expanded view of Fig. 10 for proton energies $16.2<E_p<16.7$ MeV covering the $j{}_{15/2}$ and $d{}_{5/2}$ IAR. Positive and negative parity states are best discriminated by comparing the ratio of the cross sections at $E_p\approx 16.35,16.60$ MeV.

Figure 12

Excerpt of a ${}^{207}\mathrm{Pb}$(d,p) spectrum taken at $\Theta ={30}^{°}$ and $E_d=22$ MeV. The exponential tail [Eq. (A3), linear in this logarithmic plot] is followed along almost the full peak-to-valley ratio of 2000. The 4997, 5020 levels belong to ${}^{206}\mathrm{Pb}$(d,p); the 4974, 5038, 5075, 5080 levels belong to ${}^{207}\mathrm{Pb}$(d,p). The broader $4994,5056$ levels are the result of the pragmatic fit of the $L_I,L_{\mathit{II}},L_{\mathit{III}}$ lines from the electron knockout (Appendix ). At bottom the residual spectrum $\Delta (j)$ is shown [Eq. (A5)]; the dashed lines show the values $\Delta (j)=\pm 2\sigma$. The systematic variation of the residuum spectrum at the low energy side may be improved by including another tail $A_T$ [Eqs. (A1), (A3)].