Complete Spectroscopy of negative parity states in 208 Pb with E x < 6 . 3 MeV

Using the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium, Garching, experiments with the 208Pb(p, p) reaction via isobaric analog resonances and using the207Pb(d, p) reaction have been performed with a HWHM of 1.5 keV on the low energy side. All 70 particle-hole states with negative parity predicted by the schematic shell model without residual interaction below Ex = 6.3 MeV are identified. Except for the states with spins 1 − and 2, more than 80% of the strength in each state can be described by at most four configurations; for spins 0 , 4, 6, 7, and 8 two configurations or even one configuration describe more than 95% of the strength. Natural parity configurations are more strongly mixed than unnatural parity configurations. 1 Experiments with the Q3D magnetic spectrograph at Garching The study of the doubly magic nucleus 208Pb is of key interest as more and more doubly magic nuclei come into the reach of modern experiments. The schematic shell model without residual interaction (SSM [1]) predicts 70 particle-hole states with negative parity below Ex = 6.3 MeV. The excitation energy in the SSM is derived from the masses of the nuclei 207Tl, 209Bi, 208Pb and207Pb,209Pb,208Pb, the excitation energies of the particle states in 209Bi, 209Pb, and the hole states in 207Tl, 207Pb, for proton and neutron particle-hole configurations, respectively. Particle spectroscopy o ffers t ols to determine some particle-hole components [1–5]. We have performed experiments since 2003 with the Q3D magnetic spectrograph at the MaierLeibnitz-Laboratorium, Garching, employing the 207Pb(d, p) reaction and the208Pb(p, p) reaction via isobaric analog resonances (IAR) [1]. We have especially studied the 208Pb(p, p) reaction; it is equivalent to the neutron pickup reaction on a target of 209Pb in an excited state. By adjusting the proton beam to a certain IAR, the neutron particle is selected. The analysis of the angular distribution allows the determination of the mixture of the neutron holes. Thus below Ex = 6.3 MeV, admixtures from 52 neutron particle-hole configurations of negative parity can be determined in more than 100 states (and 12 for positive parity). In contrast, the 207Pb(d, p) reaction allows the determination of only fourteen components of neutron particle-hole configurations where the hole is the p 1/2 n utron. However, the sensitivity is very high, strengths down to 0.1% can be reliably measured. ae-mail: A.Heusler@mpi-hd.mpg.de DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2014 , / 02049 (2014) 201 66 epjconf EPJ Web of Conferences 46602049 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20146602049 Figure 1. Spectra for the208Pb(p, p) reaction at 5.58 < Ex < 5.80 MeV. Seventeen states are identified. Four states with the dominant configuration j 15/2p3/2 are marked in cyan, five states with the dominant configuration g9/2f7/2 in red, and two states with the dominant configuration d 5/2f5/2 in magenta. The state at Ex = 5675 keV contains about 90% of the strength of the proton particle-hole configuration h 9/2d5/2. The 207Pb(d, p) and208Pb(p, p) reactions yield a mean resolution of 3 keV. Yet the line shape is asymmetric and only on the low energy side a half-width at half-maximum (HWHM) of 1.5 keV is achieved (see figure 1 at Ex = 5778keV). Depending on the scattering angle (20 ◦ ≤ Θ ≤ 140) a long tail may be evident. Atomic electrons limit the resolution since M-electrons in lead have a binding energy of 3 keV. Excitation energies can be determined with an uncertainty of 100 eV (if the statistics are sufficiently high) because of the high linearity of the Q3D magnetic spectrograph. 2 Predictions by the Schematic Shell Model and Experimental Results Figure 1 shows the selective excitation of states at 5 .57 < Ex < 5.80 MeV on the g9/2, j15/2, d5/2 IARs. The states with dominant configuration j 15/2p3/2 and spins 6, 7, 8, 9 (marked in cyan) are excited on the j 15/2 IAR but they are invisible on the g 9/2 IAR. (Near the d5/2 IAR, the cross section has decreased to one half from the top of the j 15/2 IAR since the distance between the two IARs is less than the width of the j 15/2 IAR.) EPJ Web of Conferences


Experiments with the Q3D magnetic spectrograph at Garching
The study of the doubly magic nucleus 208 Pb is of key interest as more and more doubly magic nuclei come into the reach of modern experiments.The schematic shell model without residual interaction (SSM [1]) predicts 70 particle-hole states with negative parity below E x = 6.3 MeV.The excitation energy in the SSM is derived from the masses of the nuclei 207 Tl, 209 Bi, 208 Pb and 207 Pb, 209 Pb, 208 Pb, the excitation energies of the particle states in 209 Bi, 209 Pb, and the hole states in 207 Tl, 207 Pb, for proton and neutron particle-hole configurations, respectively.Particle spectroscopy offers tools to determine some particle-hole components [1][2][3][4][5].
We have performed experiments since 2003 with the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium, Garching, employing the 207 Pb(d, p) reaction and the 208 Pb(p, p ′ ) reaction via isobaric analog resonances (IAR) [1].We have especially studied the 208 Pb(p, p ′ ) reaction; it is equivalent to the neutron pickup reaction on a target of 209 Pb in an excited state.By adjusting the proton beam to a certain IAR, the neutron particle is selected.The analysis of the angular distribution allows the determination of the mixture of the neutron holes.Thus below E x = 6.3 MeV, admixtures from 52 neutron particle-hole configurations of negative parity can be determined in more than 100 states (and 12 for positive parity).In contrast, the 207 Pb(d, p) reaction allows the determination of only fourteen components of neutron particle-hole configurations where the hole is the p 1/2 neutron.However, the sensitivity is very high, strengths down to 0.1% can be reliably measured.The 207 Pb(d, p) and 208 Pb(p, p ′ ) reactions yield a mean resolution of 3 keV.Yet the line shape is asymmetric and only on the low energy side a half-width at half-maximum (HWHM) of 1.5 keV is achieved (see figure 1 at E x = 5778 keV).Depending on the scattering angle (20 • ≤ Θ ≤ 140 • ) a long tail may be evident.Atomic electrons limit the resolution since M-electrons in lead have a binding energy of 3 keV.Excitation energies can be determined with an uncertainty of 100 eV (if the statistics are sufficiently high) because of the high linearity of the Q3D magnetic spectrograph.

Predictions by the Schematic Shell Model and Experimental Results
Figure 1 shows the selective excitation of states at 5.57 < E x < 5.80 MeV on the g 9/2 , j 15/2 , d 5/2 IARs.The states with dominant configuration j 15/2 p 3/2 and spins 6 + , 7 + , 8 + , 9 + (marked in cyan) are excited on the j 15/2 IAR but they are invisible on the g 9/2 IAR.(Near the d 5/2 IAR, the cross section has decreased to one half from the top of the j 15/2 IAR since the distance between the two IARs is less than the width of the j 15/2 IAR.)The ensemble of five states within 10 keV at 5.39 < E x < 5.50 MeV is disentangled.Namely, the 5640 1 − state is excited on the g 9/2 IAR only, the 5643 2 − state on the d 5/2 IAR only, the 5648 3 − state both on the g 9/2 and the d 5/2 IARs, the 5649 9 + state on the j 15/2 IAR only.Finally, the 5642 2 + state is excited by the direct-(p, p ′ ) reaction; it has a smooth excitation function.The distance between the 5642 2 + and 5643 2 − states and between the 5648 3 − and 5649 9 + states is about 500 eV.
The SSM predicts 70 particle-hole states with negative parity below E x = 6.3 MeV, two states with spins of 0 − and 8 − and up to fourteen states for spins 1 − -7 − (top of figure 2).For spins 1 − and 2 − the next configuration is s 1/2 p 3/2 at E x = 6361 keV, for spins 3 − -8 − j 15/2 i 13/2 at E S S M x = 6487 keV, and for the spin of 0 − g 9/2 h 9/2 at E S S M x =6844 keV.We have identified all 70 negative parity states predicted by the SSM below E x = 6.3 MeV (bottom of figure 2).At 6.02 < E x < 6.35 MeV (above the 6012 4 − state) only three states with the spin of 1 − and one state with a spin of 2 − are known.The gap corresponds to the predicted gap in the SSM space at 6033 ≤ E S S M x ≤ 6487 keV.The sum rules for 64 out of 70 particle-hole configurations with spins 0 − -8 − are found to be complete within about 10%.A one-to-one correspondence between the 70 SSM configurations and 70 experimentally observed states can be established.By this means complete spectroscopy of negative parity states in 208 Pb with E x < 6.3 keV is obtained.
The left side of figure 3 shows the distribution of the strengths for the lowest fourteen 4 − configurations in the lowest fourteen 4 − states.More than 80% of the strength of any state is described by two configurations, in the case of the 3475, 3947, 3995, and 4911 keV states even one configuration contains more than 90% strength.The proton configurations f 7/2 s 1/2 and f 7/2 d 3/2 are not detectable.Yet since all other twelve configurations predicted below E x = 6.3 MeV are almost completely identified, and the large gap predicted towards the fifteenth configuration j 15/2 i 13/2 at E S S M x = 6487 keV is verified (there is no 4 − state between E x = 6012 keV and 6243 keV), the transformation matrix between the configurations and states for a spin of 4 − may be assumed to be orthogonal [7].Thus the strength of the undetectable proton configurations can be also determined (marked by open rectangles).
The configuration mixing in the 5 − states is much larger (right side of figure 3).Except for the 4710 and 5075 keV states, no state contains more than 80% of a single configuration.The yrare state is the most strongly mixed state; five configurations contribute 10% -30% each.Similarly, as for the lowest twenty states [7], the determination of more amplitudes in the transformation matrices will allow us to deduce matrix elements of the residual interaction among particlehole configurations in 208 Pb from the wave functions of the states below E x = 6.3 MeV where the configuration space may be considered to be complete.The transformation matrices for spins 0 − , 4 − , 5 − , 6 − , 7 − , 8 − are indeed complete; for the spins of 1 − and 2 − the completeness is less evident.

Figure 1 .
Figure 1.Spectra for the 208 Pb(p, p ′ ) reaction at 5.58 < E x < 5.80 MeV.Seventeen states are identified.Four states with the dominant configuration j 15/2 p 3/2 are marked in cyan, five states with the dominant configuration g 9/2 f 7/2 in red, and two states with the dominant configuration d 5/2 f 5/2 in magenta.The state at E x = 5675 keV contains about 90% of the strength of the proton particle-hole configuration h 9/2 d 5/2 .

Figure 2 .
Figure 2. States with negative parity below E x =6.3 MeV.(top) Prediction by the SSM; neutron and proton configurations are marked by solid and dotted lines, respectively.(bottom) Experimentally identified states.At E x = 6243, 6251, 6256 keV states with major strength from the configurations g 7/2 f 5/2 and d 3/2 f 5/2 but unknown spins in the range 3 − -6 − are identified (dotted line).

Figure 3 .
Figure 3. Strengths of SSM configurations in states below E x = 6.3 MeV, (left) for the fourteen configurations and fourteen states with the spin of 4 − , and (right) for the twelve configurations and twelve states with the spin of 5 − .Strengths of the configurations with a p 1/2 hole are determined to 0.1% by the 207 Pb(d, p) reaction.The configuration with the dominant strength is determined by the indicated reaction.