Study of the low spin states of 208Bi through γ–γ spectroscopy

Study of the low spin states of 208Bi through γ–γ spectroscopy

Nuclear Physics A 768 (2006) 22–42 Study of the low spin states of 208Bi through γ –γ spectroscopy P. Boutachkov ∗ , K.H. Maier 1 , A. Aprahamian, G...

278KB Sizes 0 Downloads 1 Views

Nuclear Physics A 768 (2006) 22–42

Study of the low spin states of 208Bi through γ –γ spectroscopy P. Boutachkov ∗ , K.H. Maier 1 , A. Aprahamian, G.V. Rogachev 2 , L.O. Lamm, M. Quinn, B.B. Skorodumov, A. Wöhr Physics Department, University of Notre Dame, Notre Dame, IN 46556, USA Received 13 October 2005; received in revised form 13 December 2005; accepted 6 January 2006 Available online 26 January 2006

Abstract We studied the low spin structure of 208 Bi via γ –γ coincidence measurements using a sub-Coulomb 208 Pb(p, n)208 Bi reaction. This nucleus has one neutron hole and one proton particle relative to the doubly magic 208 Pb and therefore its spectrum directly depends on the particle–hole interaction. The available data on 208 Bi is re-evaluated using the data obtained in this measurement. Comparison of the measured energy levels with a shell model calculation with a realistic interaction is presented.  2006 Elsevier B.V. All rights reserved. PACS: 23.20.Lv; 21.60.Cs; 21.30.-x

1. Introduction One of the challenges facing nuclear structure physics today is the description of observed spectra in nuclei using an effective nucleon–nucleon interaction. Nuclei near 208 Pb are of interest since comparison of the experimental data with calculations based on few particles outside a doubly closed shell allow determination of the residual interaction. New codes and more powerful computers allow shell model calculations with more active particles and larger model spaces. An example is the calculation of 216 Th with 8 protons that agrees well with experiment [1,2]. * Corresponding author.

E-mail address: [email protected] (P. Boutachkov). 1 Current affiliation: Henryk Niewdoniczanski Institute of Nuclear Physics, Krakow, Poland. 2 Current affiliation: Physics Department, Florida State University, Tallahassee, FL 32306, USA.

0375-9474/$ – see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2006.01.004

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

23

The development of new facilities and techniques allow the study of exotic nuclei, but often without fixing the spins of the observed levels. Examples around 208 Pb are 211 Pb and 215 Bi [3,4]. In these cases, one has to rely on calculations to interpret the data. In order to perform these calculations one needs to know the residual interaction. Since the pioneering work of Kuo and Brown [5], the matrix elements of the residual interaction of the shell model can be calculated from the measured scattering of free nucleons. These calculations [6] have also become more refined and are remarkably successful in reproducing experimental data. Nuclei with just two active particles or holes offer the most direct test of these calculations and might give hints for further improvements. 208 Bi has one neutron hole and one proton particle relative to doubly magic 208 Pb. It therefore shows most directly this particle–hole interaction, which is the motivation for the present study. The previous experimental data on this nucleus have been evaluated by Martin [7]. Alford, Schiffer and Schwartz [8] measured the 207 Pb(3 He, d)208 Bi and the analogous (α, t) reaction, that populates levels with a 3p1/2 neutron hole. They also measured 209 Bi(d, t)208 Bi and 209 Bi(3 He, α)208 Bi, which is selective for states with the proton in the 1h 9/2 orbital. Crawley et al. [9] measured the analogous 209 Bi(p, d)208 Bi reaction. Ellegaard, Barnes and Canada [10] have measured the γ -decay of a few levels in 208 Bi using the 209 Bi(d, t)208 Bi reaction. Extensive inbeam γ -measurements have been performed by Proetel et al. [11] with the 208 Pb(p, n)208 Bi reaction. Some two particle two hole (2p–2h) states have been established with the 206 Pb(α, d)208 Bireaction [12]. All the above measurements have been performed 30 years ago. While the transfer reactions cannot be measured with notable improvement with today’s detectors, the technology for γ -spectroscopy has improved significantly over the early experiments. The study of the low spin states of 208 Bi in this paper is based on the above works and the new γ -spectroscopy measurement presented here. We found 204 new γ transitions and 56 new levels. About 15 states from Ref. [7] were dismissed as wrongly claimed, because they were not observed. The 208 Pb(p, n)208 Bi compound nucleus reaction populates all levels independent of their structure. A 9 MeV proton beam was used in order to favor population of low spin states in 208 Bi, but levels up to the 10− isomer have been seen. We have therefore measured γ –γ coincidences following the above reaction, in order to get a rather complete low-spin level scheme. Also, the spins and main configurations of the levels can be assigned from their γ -decay in combination with the information from the previously measured spectroscopic factors. One other recent γ -spectroscopy study of 208 Bi [13] with deep inelastic reactions found high spin yrast states. This work is complementary to our low-spin study. 2. Experiment and results 2.1. Reaction mechanism and experiment The 208 Pb(p, n)208 Bi reaction at 9 MeV is a statistical compound nucleus reaction; all low-spin states in 208 Bi will be populated independent of their structure. The population depends only on spin and energy. At this sub-Coulomb energy, protons form the compound nucleus preferentially with vanishing or very low orbital angular momentum, the angular momentum of the evaporated neutron and the emitted γ -rays is comparable or exceeds that for the captured protons. Therefore, states of low spin are preferentially populated and little if any alignment of the levels undergoing γ -decay is expected. The experiment was conducted at the FN Van de Graph accelerator at the Institute for Structure and Nuclear Astrophysics of the University of Notre Dame. A continuous 9 MeV proton

24

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

beam of about 0.6 nA was directed on a 98.5% enriched 208 Pb target. The target thickness was 300 mg/cm2 and it was placed at 45◦ relative to the beam direction. This target was thick enough to stop the proton beam. Two Hyper-pure Germanium (HPGe) detectors of 55% efficiency with BGO anti Compton shields were used. The detectors were positioned at 0◦ and 90◦ relative to the beam direction, reducing the background from 511 keV γ -ray coincidences and cross-scattering between the detectors. As the reaction occurs predominantly close to the surface of the target the γ -spectrum as seen in the 0◦ detector has been subject to absorption in the target, while there is little absorption at 90◦ . γ –γ coincidences and singles data were collected. The time difference between the two HPGe detectors was recorded with a TAC. In sorting the data, a time window was set on the prompt peak. The background from random coincidences was negligible. A total of 7 × 106 coincidence and 1 × 108 singles γ -rays were recorded. The energy and relative detector efficiency was calibrated with sources of 152 Eu and 56 Co placed at the target position. In addition, the low energy efficiency calibration was done with 133 Ba and the target in place to account for the absorption in the target. The cross section for the 208 Pb(p, n)208 Bi reaction has been measured [14,15] and found to be 91 ± 13 mb at 9 MeV and 51 ± 8 mb at 8.1 MeV. The Q-value for the 208 Pb(p, n)208 Bi reaction is Q(p, n) = −3.66 MeV. At the chosen beam energy, the (p, 2n) channel is closed because its Q-value is Q(p, 2n) = −11.73 MeV. In addition, any reactions on 208 Pb with a charged particle in the exit channel are strongly subdued by the Coulomb barrier. The 3− state in 208 Pb was weakly populated through Coulomb excitation, but it does not yield any γ –γ coincidences. Weak impurity lines in the coincidence spectra were found from 206 Pb and 207 Bi which originate from the admixture of 207,206 Pb in the target material. Also the usual transitions in 19 F and Ge due to neutron scattering on the detectors were observed, however no lines from Al or Fe were seen. The thick target avoids background from interactions of the beam behind the target. There is no background from 12 C and 16 O contaminations of the target as all reaction thresholds for these nuclei are above the 9 MeV proton energy. Because of this low background it is nearly certain that all the observed lines belong to 208 Bi, except those discussed above. Angular distributions of the γ -rays have also been measured. They were however isotropic in accordance with the reaction properties as mentioned above. Therefore only the selection rules for γ transitions could be used to assign spins and parities. M1 transitions dominate strongly in a shell model nucleus, such as 208 Bi. Both M1 and E2 transitions proceed with about 1 single particle unit or less in the absence of any collectivity. E1 transitions cannot occur within one major shell, they are hindered by roughly 105 or more. Single particle transition rates for a 500 keV γ -transition are: M1: 4 × 1012 s−1 , E2: 3 × 109 s−1 , E1: 5 × 1014 s−1 . Therefore we assume for spin assignments, that transitions below 1 MeV are M1 or E1 and M1, E1 or E2 for transitions above 1 MeV. If it was clear that a transition changes parity, as from the l-values measured in transfer reactions, only E1 was considered. 2.2. Data evaluation and results Coincidence data were sorted into a symmetric matrix and analyzed using the Radware package [16]. A level scheme was built where as a starting point the strongest adopted γ -rays [7] decaying to the ground and the first exited state at 63 keV were used. We checked that these γ -rays are present in the singles data and cross-checked that they are coincident with appropriate γ -transitions positioned higher in the obtained level scheme. In this way we excluded γ -rays like the suggested 628 keV [7] from the 628 keV level to the ground state or the 1032 keV γ -ray

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

25

Fig. 1. Spectrum coincident with the 1075 keV line of 208 Bi. Table 1 The energies of the single particle proton orbitals (p) and the single hole neutron orbitals (h) relative to 208 Pb taken from the levels in 209 Bi and 207 Pb, Refs. [24,25]. The energy of the p1/2 neutron hole is set to 0 MeV Esp [MeV]

p/h

Configuration

4.214 5.111 5.822 7.036 7.332 7.847 0.000 0.570 0.898 1.633 2.340 3.413

p p p p p p h h h h h h

h9/2 f7/2 i13/2 f5/2 p3/2 p1/2 p1/2 f5/2 p3/2 i13/2 f7/2 h9/2

from the 1094 keV level to the first excited state as they were not observed in coincidence with γ -rays feeding into the states from which they should have been emitted. Coincidences with the 1075 keV line that populate the 628 keV state are shown in Fig. 1. There is no indication of a 628.3 keV transition to the ground state (a 628 keV γ -ray occurs elsewhere in the level scheme). However one sees the 510 keV line that follows the very weak 118 keV transition and the 538 and 601 keV lines from the level at 621 keV following another highly converted 26.9 keV transition. A simultaneous least square fit [16] of all level energies was performed based on the γ -ray energies determined from the coincidence data (see Table 3). Then we checked for possible tran-

26

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Fig. 2. A partial singles spectrum around 2.6 MeV. Lines assigned as transitions to the ground and first excited state from otherwise established levels are marked. For these high lying states no coincidences with populating transitions could be found.

sitions to the ground state and first excited state at 63 keV in the singles spectrum, if there were no transitions above to gate on. An example of a γ -ray which was assigned by this procedure is the 2818.5 keV line from the 2881.3 keV state. The relevant part of the singles spectrum for these transitions is shown in Fig. 2. The γ -rays which were assigned from the singles data based only on their fitting energy difference are marked in Fig. 2. The branching ratios for these γ -rays are determined using the singles data. For two levels, that have been found in the 207 Pb(3 He, d) reaction, only one singles-γ line is observed from each; this fits however the expectation as explained in Section 3.2. Fig. 2 shows these 2 transitions and another one at 2869.6 keV. The 2869.6 keV line is so strong and in addition a 2806.5 keV line, the appropriate energy to the 63 keV state, has been observed, that we give a new level at 2869.6 keV. Besides these 3 exceptions all levels are based on γ –γ coincidences. Multipolarities were determined experimentally for the low energy transitions based on the difference of the total electron conversion coefficients between E1 and M1 transitions. A graph from a gate on of the ratio Is /I0 is shown in Fig. 3. I0 is the measured γ intensity obtained 1  I (1 + αi ), where a transition just above the γ -ray of interest. Is is determined as: 1+α i i 0 Ii are the γ -ray intensities for the transitions right after that of interest determined from the same gate. αi are the corresponding internal conversion coefficients. α0 is the internal conversion coefficient for the considered transition. If the correct multipolarity and consequently conversion coefficient α0 is assumed the ratio Is /I0 will be 1. In the above calculations theoretical conversion coefficients from the Radware package version rw01.1.3 were used [23]. E2-transitions have not been considered as they would show a measurable lifetime in this energy range. The spectrum used to determine the 275 keV γ -ray multipolarity is given in Fig. 4. This spectrum was obtained by gating on the 125 keV line just above the 275 keV line in the level scheme. It shows clearly that the 275 keV line is stronger than the main succeeding 263 keV transition. This is because the 275 keV transition in question is E1 and less converted. This is

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

27

Fig. 3. Determination of γ -ray multipolarities using the difference of electron conversion for M1 and E1 transitions. The ratio Is /I0 of the expected (Is ) over the observed (I0 ) γ -ray intensity is plotted. The squares are calculated assuming E1 transition while the circles show the results for M1 transitions. If the assumption is correct then, Is /I0 = 1. The assigned multipolarities are shown on the x-axis under the data points. See also text.

still true, when the lines in parallel to the 263 keV line (Fig. 4) and the fact, that the 275 keV transition is a doublet is considered. The fraction of the second 275 keV transition is evaluated by comparing the γ -intensity ratio of the 263 keV line to the 275 keV line determined from the 125 keV and 338 keV gate. The corresponding ratios are 0.49(2) and 0.51(2). These ratios are equal within the error showing that the contribution of the second 275 keV line in the 125 keV gate is less than the measurement error. Therefore the parity of the 2077.5 keV level is negative and it is the lowest observed 2p–2h state in 208 Bi. A partial level scheme of 208 Bi is shown in Fig. 5. In many cases, we were able to determine the branching ratios by gating directly above the level of interest. If this was not possible, we gated below the γ -rays of interest using a common γ -ray observed in both gates as normalization for the intensities of the two branches. The information about the γ transitions and levels is presented in Tables 2 and 3. We compare with the adopted γ -rays and the levels from the latest 208 Bi compilation [7] up to 3 MeV. Above 3 MeV a reasonable correspondence with previously found levels cannot be established. To obtain the full list of spectroscopic data on 208 Bi one should combine the information we provided in Tables 2 and 3, the high spin γ –γ data published in [13] and the states at energies higher than 3.5 MeV from Ref. [7]. A level seen in this experiment is taken as identical to a previously established, if the information on spin and parity and the energy agrees. Energies measured in charged particle spectroscopy have often to be shifted systematically by a few keV due to calibration errors (Refs. [8,9]). Using the information from Table 2 we determined the 208 Bi level energies by a χ 2 fit using all γ energies. In addition by comparison to the transfer data from [8,9] and using the multipolarities obtained as described above we set limits on the spins of the observed levels. This information is summarized in Table 3. The level scheme is critically reviewed in the next section.

28

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Fig. 4. Spectrum obtained by gating on the 125 keV line of 208 Bi. The 275 keV line which follows the 125 keV transition is marked. The γ -rays emitted from the level to which the 275 keV transition decays are also marked. These transitions were used to calculate Is (275 keV). The insert shows a partial level scheme of 208 Bi. A gate on the 338 keV line was used to exclude contributions from the higher member of the 275 keV doublet.

Fig. 5. Partial level scheme of 208 Bi. The levels with energy less than 2 MeV and the γ transitions initiated from these levels are shown. The arrows are proportional to the corresponding branching ratios. The level energies are shown under each level.

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

29

Table 2 The observed γ -ray transitions in 208 Bi. The present data are compared with the adopted γ -transitions for 208 Bi [7]. Elev gives the approximate level energies rounded to the first digit after the decimal point. Eγ gives the γ -energies of the transitions originating from the stated levels. Iγ is the branching ratio normalized to 10 for the strongest. The errors on the energies and intensities include fit and calibration uncertainties. EγA and IγA are the γ -ray energy and branching ratios published in the latest compilation [7]. Levels that have not been seen in the present experiment are not included and previously assigned γ decays from levels above 3 MeV are not presented in the table because none of them were confirmed Elev [keV] 63.1 510.2 510.2 601.4 601.4 628.3 628.3 628.3 633.1 633.1 633.1 650.5 650.5 886.4 886.4 886.4 924.8 924.8 936.2 936.2 936.2 959.0 959.0 959.0 959.0 1033.2 1033.2 1033.2 1033.2 1033.2 1069.1 1069.1 1069.1 1069.1 1069.1 1095.1 1469.4 1469.4 1469.4 1469.4 1469.4 1469.4 1529.4 1529.4 1529.4

Eγ [keV] 63.1(2) 447.1(2) 510.15(15) 538.2(2) 601.35(15) 26.91(11) 118.2(2)d 565.07(15) 31.5(2) 569.89(15) 633.0(2) 140.03(15)d 650.5(2)

0.72(18) 10.0(9) 5.4(5) 10.0(9) 0.004(6) 0.42(12) 10.0(7) 0.24(6) 10.0(6) 0.13(2) 5.1(13) 10(2)

823.2(2) 886.4(2) 291.56(15)d 861.8(2) 302.9(2) 873.3(3) 936.3(2) 325.62(15) 330.4(2) 896.0(2) 959.0(2) 146.6(2)d 399.8(2) 431.4(2) 970.24(15) 1033.31(15) 110.0(2)d 435.7(2) 467.37(15) 1006.23(15) 1069.3(2) 1095.0(2) 435.9(2)

7.8(17) 10(2) 10.0(10) 3.2(6) 0.13(2) 10.0(6) 0.16(4) 0.91(15) 0.29(10) 10.0(10) 4.0(5) 0.10(2) 0.23(3) 0.12(3) 4.5(3) 10.0(6) 0.06(2) 0.24(3) 0.90(7) 10.0(6) 0.28(4) 10.0(10) 1.8(4)

841.0(3) 959.0(2) 495.9(2) 592.8(2) 896.2(2)



0.9(6) 10.0(14) 10.0(12) 1.7(6) 4.4(8)

EγA [keV] 63.50(10) 447.3(2) 510.6(2) 538.5(2) 601.6(2)

IγA 10 0.31(8) 10.0(7) 4.6(5) 10.0(5)

565.30(10)

10

570.4(3) 632.9(3) 140.1(2) 650.7(2) 375.7(3) 823.4(2) 886.6(4) 291.70(10) 861.9(2) 303.20(10) 873.1(2) 936.6(7) 325.80(10) 330.8(2) 895.9(2) 959.0(3)

10 0.130(10) 5.8(9) 10.0(13) 0.41(14) 10.0(4) 10.0(4) 10.0(3) 3.00(10) 0.100(10) 10.0(3) 0.18(6) 0.96(5) 0.38(5) 10.0(4) 3.4(4)

970.3(3) 1033.5(2)

4.13(13) 10.0(2)

467.70(10) 1006.6(3) 1069.1(4)

0.86(4) 10.0(3) 0.23(2)

532.9(5) 583.1(3) 836.0(3) 841.2(3) 959.3(2) 496.20(10) 593.1(3)

0.65(13) 1.7(3) 5.6(5) 4.3(3) 10 10.0(4) 1.1(2)

(continued on next page)

30

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Table 2 (continued) Elev [keV] 1529.4 1529.4 1529.4 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1563.5 1570.8 1624.7 1624.7 1624.7 1624.7 1657.4 1666.5 1666.5 1666.5 1703.3 1703.3 1703.3 1703.3 1703.3 1703.3 1703.3 1703.3 1703.3 1715.5 1715.5 1716.2 1802.2 1802.2 1802.2 1802.2 1824.3 1824.3 1838.9 1838.9

Eγ [keV] 927.97(15) 1466.1(2) 1529.4(3) 470.06(15) 602.88(15) 614.22(15) 906.32(15) 937.8(2) 1476.5(2)

Iγ 10.5(11) 4.9(7) 1.9(5) 0.30(2) 2.03(12) 0.74(5) 10.0(6) 0.30(2) 1.20(8)

494.1(3) 529.9(2)

0.17(10) 2.5(8)

627.09(15)

10(2)

677.2(2)

3.8(10)

935.2(2)

6.7(14)

920.3(3) 530.4(4) 738.1(2) 974.0(2) 996.3(2) 1006.9(2) 1015.9(2)

10.0(5) 0.45(8) 1.2(3) 5.9(12) 10(2) 10 7(4)

1156.4(2)

10(4)

EγA [keV] 928.0(3) 1466.50(10) 1529.8(2) 470.50(10) 603.3(2) 614.4(2) 906.2(2) 938.1(5) 469 494 530.5(2) 605 627.2(2) 639 676.9(3) 913 930 934.7(3) 961.5(4) 1053 1501 1563 920.4(3)

1064.4(4)

233.7(3) 669.9(2) 744.2(2) 1075.0(2) 1640.4(2) 1703.1(2) 1064.9(2) 1205.8(3) 621.1(2) 262.50(15) 865.84(15) 877.2(2) 1169.07(15) 354.9(2) 1761.5(2) 135.6(2)d 805.6(2)

0.030(10) 0.6(4) 2.5(4) 1.4(3) 10.0(11) 3.6(5) 10(5) 8(4) 10 10.0(5) 1.63(10) 1.73(10) 0.68(4) 10.0(8) 8.7(8) 5.1(13) 1.3(8)

IγA 9.8(4) 6.2(4) 3.4(4) 0.220(10) 1.67(10) 0.58(2) 10.0(2) 0.29(8)

6.7(3) 4.9(2) 0.88(11)

10.0(6) 2.2

10

10

140.2(2)

3.2(8)

669.6(2)

2.8(2)

817.4(5) 1074.6(4) 1101.3(3) 1640.50(10) 1703.3(2) 1065.1(4) 1206.0(2)

0.37(19) 0.93(10) 4.5(2) 10.0(4) 2.9(3) 2.4(3) 10.0(5)

262.70(10) 865.9(2)

10.0(2) 1.17(6)

1169.0(2)

0.54(3)

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

31

Table 2 (continued) Elev [keV] 1838.9 1838.9 1838.9 1838.9 1838.9 1838.9 1870.7 1870.7 1870.7 1870.7 1870.7 1870.7 1882.1 1882.1 1882.1 1882.1 1882.1 1919.9 1919.9 1919.9 1919.9 1919.9 1919.9 1919.9 1919.9 2077.6 2077.6 2077.6 2077.6 2126.8 2126.8 2126.8 2126.8 2126.8 2126.8 2126.8 2126.8 2179.4 2179.4 2180.0 2180.0 2202.9 2202.9 2307.9 2307.9 2307.9 2340.0 2358.6 2358.6 2383.8 2383.8 2383.8

Eγ [keV] 879.9(2) 902.7(2) 952.5(3) 1205.9(2) 1210.8(2) 1775.7(3) 307.0(2) 331.0(2) 837.7(2)

Iγ 3.3(11) 5.0(15) 2.0(9) 5.8(15) 1.0(8) 10(2) 0.75(18) 0.55(17) 10.0(10)

934.7(2) 946.0(2) 412.5(2) 812.9(2) 849.0(2) 923.3(3) 946.0(2) 80.7(2)d 390.2(2) 886.7(2) 960.8(2) 983.7(2) 995.1(2) 1287.0(3) 1318.6(2) 275.26(15)d

7(3) 1.5(3) 2.5(4) 1.82(11) 0.36(18) 0.6(2) 10(1) 0.5(2) 0.73(10) 0.3(5) 0.87(14) 4.9(4) 10.0(7) 0.50(12) 2.8(3) 10.0(6)

1141.4(2) 1152.84(10) 255.7(2)

0.10(2) 0.08(2) 1.37(11)

597.2(2) 1057.5(3) 1093.4(8) 1190.81(15) 1202.2(2) 1493.8(2) 1083.8(4) 1293.2(2) 1084.9(2) 2180.3(4)a 125.3(2)d 663.3(2) 387.9(2) 838.1(3) 1239.09(15) 1829.8(4) 1725.4(2) 1758.1(6) 1750(1) 1754.8(6) 1782.6(3)

1.3(2) 0.35(7) 0.44(8) 10.0(7) 1.39(11) 1.63(13)

EγA [keV]

307.50(10)

911.1(5)

10.0(11) 10.0(11) 31(6) 10.0(15) 5.1(9) 0.50(9) 0.42(12) 10.0(8) 10 10.0(11) 1.6(8) 10.0(6) 3.1(13) 19(9)

IγA

10.0(9)

4.5(9)

275.40(10) 1044.0(4) 1141.4(4) 1153.0(5) 255.70(10) 586.8(4)

10.0(2) 0.084(11) 0.053(11) 0.042(11) 2.1(2) 0.7(2)

1190.7(2) 1202.0(3) 1493.7(2)

10.0(3) 1.20(10) 1.30(10)

388.20(10) 1239.1(2)

1755.9(2) 1782.5(2)

0.67(5) 10.0(3)

8.2(6) 10.0(6) (continued on next page)

32

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Table 2 (continued) Elev [keV] 2386.0 2386.0 2386.0 2386.0 2404.2 2409.0 2409.0 2409.0 2415.7 2436.9 2457.3 2457.3 2457.3 2457.3 2457.3 2478.4 2478.4 2478.4 2495.5 2495.5 2495.5 2495.5 2495.5 2495.5 2495.5 2501.6 2501.6 2501.6 2513.4 2513.4 2513.4 2513.4 2513.4 2513.4 2544.8 2556.4 2556.4 2556.4 2556.4 2564.9 2564.9 2564.9 2570.2 2570.2 2570.2 2586.6 2586.6 2586.6 2586.6 2586.6 2612.6 2612.6

Eγ [keV] 856.7(3) 1753.0(3) 1757.6(2) 1784.1(4) 1771.1(5) 1780.4(3) 1807.5(3) 1899.3(3) 337.9(2) 873.3(2) 918.0(2) 1532.6(2) 1824.13(14) 1856.0(2) 275.3(2) 558.5(2) 1845.5(2) 293.5(5) 656.2(4) 792.1(2) 1559.2(2) 1609.1(4) 1862.5(2) 1894.0(3) 1432.3(2) 1576.8(2) 1868.4(2) 1444.2(2) 1480.0(2) 1554.4(2) 1577.5(2) 1880.5(4) 1912.2(2) 467.21(12) 636.1(2) 1487.4(2) 1620.3(2) 1923.3(2) 149.4(4) 1936.6(2) 1963.4(3) 154.6(2) 492.5(2) 1645.6(2) 1627.4(2) 1700.5(2) 1953.4(2) 1984.9(3) 2523.5(3)a 1653.6(2) 1676.4(3)

Iγ 1.5(5) 5(5) 10.0(9) 0.02(3) 10 10.0(6)

EγA [keV]

IγA

10.0(6) 10 2.7(2) 5.0(4) 10.0(8) 7.3(6) 10.0(7) 2.05(17) 2.5(2) 6.2(5) 6.0(5) 4.8(4) 3.5(12) 10.0(8) 6.6(6) 2.0(6) 10(2) 9(2) 10.0(8) 3.9(3) 19(3) 2.9(5) 8.6(7) 8.9(7) 10.0(11) 4.6(4) 10.0(7) 2.33(19) 8.6(6) 0.39(15) 10.0(11) 0.7(10) 0.8(7) 10(2) 14(4) 5.9(6) 7.1(6) 6.4(6) 2.1(4) 10.0(8) 4.5(3) 1.3(3)

1388.0(4) 1532.7(3) 1824.1(2)

1.8(4) 4.6(7) 10.0(7)

1576.6(2) 1868.8(2)

9.4(4) 10.0(4)

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

33

Table 2 (continued) Elev [keV] 2612.6 2612.6 2612.6 2631.0 2631.0 2631.0 2636.3 2636.3 2636.3 2657.3 2660.6 2679.4 2679.4 2679.4 2679.4 2693.8 2693.8 2693.8 2693.8 2693.8 2693.8 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2718.5 2733.0 2733.0 2733.0 2739.5 2739.5 2739.5 2739.5 2838.9 2838.9 2838.9 2838.9 2838.9 2843.3 2869.6c 2869.6c 2879.6 2879.6 2881.3

Eγ [keV] 1979(1) 2011.3(3) 2102.3(3) 928.1(3) 1006.3(2) 1535.8(2) 1677.3(2) 2003.2(3) 2034.9(2) 454.4(2) 2010.1(3) 601.3(2) 1610.4(2) 1754.8(2) 2046.4(2) 149.4(4) 1624.8(2) 1660.9(4) 1757.4(3) 2060.3(3) 2630.6(2)a

798.42(15) 848.7(4)

Iγ 1(2) 10.0(8) 3.7(3) 6(2)

IγA

10.0(11) 7.8(9) 9.2(8) 10.0(8) 10.0(5) 10 10.0(5) 3.9(9)

4.2(3) 0.46(7) 0.029(3) 4.5(3) 10.0(8)

10.0(7) 4.2(3)

1189.7(3)

0.35(9)

1649.2(3)

1.10(9)

1782.2(2) 254.4(2) 530.2(2) 1808.3(2) 1114.6(2) 1780.4(3) 1814.9(2) 1853.2(2) 268.8(3) 282.2(2) 423.0(2) 761.3(2) 1914.4(2) 765.7(2) 2806.50(16) 2869.57(15) 1340.1(2) 1846.6(2) 294.6(3)

EγA [keV]

0.012(2) 10.0(6)

262.70(10) 593.1(3) 798.5(2) 849.0(3) 879.9(4) 1004.3(8) 1016.8(6) 1115.3(3) 1156.6(3) 1190.7(2) 1336.7(4) 1686.7(9) 1782.5(2)

10.0(3) 0.14(3) 0.95(3) 0.53(5) 0.16(3) 0.35(9) 1.4(3) 0.090(15) 0.180(15) 1.5(5) 0.075(15) 0.030(15) 0.77(5)

6.4(7) 4.6(10) 10.0(12) 8.2(9) 1.57(14) 1.32(12) 4.5(3) 10.0(8) 2.0(2) 10 2.80(15) 10.0(5) 5.9(6) 10.0(13) (continued on next page)

34

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Table 2 (continued) Elev [keV] 2881.3 2881.3 2881.3 2884.0 2884.0 2884.0 2886.6 2886.6 2886.6 2888.5b 2893.7 2893.7 2893.7 2893.7 2893.7 2893.7 2893.7 2903.7 2903.7 2932.9 2932.9 2932.9 2942.9b 2950.9 2950.9 2950.9 2950.9 2950.9 3069.4 3069.4 3069.4 3069.4 3069.4 3069.4 3154.9 3165.9 3165.9 3165.9 3165.9 3286.3 3286.3 3286.3 3286.3 3286.3 3286.3 3286.3 3351.3 3351.3 3351.3 3390.9 3390.9 3390.9

Eγ [keV] 1812.1(5) 1994.6(6) 2818.5(3)a 382.5(2) 1815.1(3) 1959.1(3) 330.5(2) 578.7(2) 2285.0(2) 2888.45(16)

Iγ 10.0(14)

973.8(2) 1091.6(2)

10(6) 0.8(7)

1364.1(4)

0.8(7)

1957.6(2) 1101.6(2) 1978.9(4) 1996.4(2) 2046.4(2) 2331.6(2) 2879.84(15) 873.3(2) 1411.3(3) 1992.3(2) 2026.1(2) 2317.6(2) 632.2(3) 1267.6(2) 1529.9(2) 1539.7(3) 2036.2(3) 2132.7(3) 846.9(2) 262.5(2) 601.4(2) 664.0(2) 1626.4(3) 1159.35(12) 1757.2(2) 2217.2(3) 2253.1(2) 2361.5(2) 2652.8(4) 2685.2(2) 738.8(4) 935.7(3) 1821.8(3) 440.2(6) 496(2) 2454.6(4)

5.1(7) 10 0.5(10) 2.5(3)

EγA [keV]

382.90(10)

IγA

1.90(17)

1959.4(4)

10.0(5)

765.9(3) 973.8(3) 1091.5(5) 1354.6(4)

2.19(16) 10.0(3) 1.09(16) 0.63(16)

1824.1(2)

4.4(3)

9.9(8) 10.0(8) 10

1.3(13) 10 2.1(4) 3.6(2) 10.0(7) 1.97(16) 10 3.2(2) 2.2(2) 10.0(8) 2.6(8) 10.0(6) 8.1(11) 2.2(8) 2.9(7) 0.039(7) 10.0(11) 10.0(11)

7.7(6) 4.1(7) 1.4(2) 6.4(6) 9.1(11) 6.4(11) 10.0(8)

10.0(5) 2.40(10) 0.0(10) 10.0(6)

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

35

Table 2 (continued) Elev [keV] Eγ [keV] Iγ EγA [keV] IγA 3425.0 538.2(2) 3425.0 545.6(4) 3425.0 1117.2(3) 2.2(2) 3425.0 2488.9(2) 5.1(4) 3425.0 2791.8(2) 10.0(8) 3427.3 862.4(3) 10.0(11) a γ -ray assigned only from singles data. b Level is based on only one γ -ray seen in singles and on data from transfer. c Level only based on single γ -rays to ground and 63 keV levels. d γ -ray multipolarities were determined using the difference of electron conversion for M1 and E1 transitions.

3. Discussion of the presented data Based on the previous data and those from this experiment, the level scheme is critically reviewed in the following section. At first the states below 2 MeV are discussed, as the scheme should be complete in this region and the shell model predicts clearly, which states are to be expected here. At higher energies 2p–2h levels also occur, at first only states with negative parity and around 3.5 MeV and higher positive parity states. This adds so many possible states, that a complete interpretation of the scheme is no longer possible. But the one-particle one-hole (1p– 1h) levels that have been established in the selective transfer experiments can in general still be assigned to levels seen here too. In a third subsection 2p–2h states are shortly discussed. 3.1. Levels below 2 MeV The experimentally known 1p–1h excitation energies are compared with shell model calculations in Fig. 6. These calculations use experimental single particle energies from 207 Pb [24] and 209 Bi [25] for the neutron-holes and proton-particles as shown in Table 1. A realistic residual interaction calculated from the H7B [19] parametrization of the interaction between free nucleons has been used [17,18]. The calculated states are grouped by their main configuration, that exceeds 80% for nearly all of the lowest 4 levels of a given spin and parity. These calculations are taken as a guide to determine which levels are expected. Below 2 MeV, a one to one correspondence with experiment is anticipated. The states are ordered by their dominant configuration. The spin assignments are definitive for the first 14 levels belonging to the: πh9/2 νp−1 1/2 , −1 −1 −1 πh9/2 νf5/2 , πh9/2 νp3/2 and πf7/2 νp1/2 configurations. Their γ -decay agrees with spectroscopic factors measured in the transfer reactions [8,9]. Two of the previously adopted levels [7] at 1384.3 and 1435.7 keV, that were only based on observed γ -rays in 209 Bi(n, 2nγ ) [20], are disregarded in this work. In this work a 14 MeV neutron beam was used to produce 208 Bi using the 209 Bi(n, 2n)208 Bi. Some wrong assignments are not surprising considering the sizeable neutron related background and that only γ -rays in singles were measured. The level at 1534 keV from 209 Bi(p, d) and 209 Bi(d, t) is taken as identical to the 1529.8 keV state, as also the energies of other states close by are too high by similar amounts. Next come the 6 states of the πf7/2 νf−1 5/2 configuration. For the parity assignment, we rely here upon the shell model, because all levels of negative parity around this energy have been identified (see below). The 1+ level is pushed up to 1802 keV by the residual interaction, its main decay is to the 2+ level of the same configuration at 1539 keV. This and its other decays to 2+ and 3+ levels confirm the spin assignment of 1+ . The 1539 keV level is populated from the 1+

36

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Table 3 Level energies and spin-parities for 208 Bi. Elev is the level energy determined from a χ 2 fit of all γ -ray energies from A and J π are Table 2. Jmin –Jmax is the range of possible level spins. π is 1 for positive parity and −1 for negative. Elev A 208 Bi Nuclear Data Sheets compilation [7]. Below the level energies and spin-parity assignments adopted in the latest 2 MeV the adopted levels are critically reviewed. Between 2 and 3 MeV the adopted levels are shown as given in [7], above 3 MeV the previously found levels are not given Elev [keV] 0.0(0) 63.08(7) 510.21(9) 601.43(7) 628.34(9) 633.11(7) 650.49(12) 886.37(9) 924.76(8) 936.25(8) 958.98(8) 1033.23(8) 1069.07(8) 1095.1(2)

Jmin –Jmax 5−5 4−4 6−6 4−4 5−5 3−3 7−7 5−5 2−2 3−3 4−4 4−4 3−3 6−6

π 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1469.38(12) 1529.39(7)

5−5 3−3

1 1

1539.38(8) 1563.50(10) 1570.8(4)

2−2 4−4 10−10

1 1 −1

1624.69(11)

6−6

−1

1657.4(2) 1666.5(2)

8−8 7−7

−1 −1

1703.26(9) 1715.5(2) 1716.2(2)

5−5 6−7 6−7

−1 −1 −1

1802.15(8)

1−1

1

1824.3(2)

4−6

1838.94(10)

4−4

−1

1870.74(10) 1882.12(12) 1919.94(8)

3−3 4−4 3−3

1 1 −1

2077.65(10) 2126.79(11)

2−2 2−2

−1 1

A [keV] Elev 0.0(0) 63.30(10) 510.60(10) 601.80(10) 628.60(10) 633.50(10) 650.7(2) 886.7(2) 925.20(10) 936.60(10) 959.30(10) 1033.60(10) 1069.50(10) 1094.5(2) 1384.3(6)a 1435.7(3)a 1469.8(2) 1529.80(10) 1534(2)b 1539.80(10) 1563.7(2) 1571.1(4) 1605.2(5)a 1625.5(6) 1636.9(8)a 1660(2) 1666.2(4) 1677.7(7)c 1703.60(10) 1716(2)d 1716(2)d 1738.4(6)a 1787(2) 1802.5(2) 1805.0(4)a

1837.1(2)a 1844.2(4)e 1845.1(5)a 1870.9(4) 1885(4) 1920.50(10) 1925.0(4)a 1938.0(5)a 2077.9(2) 2126.8(3) 2137(7)

JAπ (5)+ (4)+ (6)+ (4)+ (5)+ (3)+ (7)+ (5)+ (2)+ (3)+ (4)+ (4)+ (3)+ (6)+ (5+ ) (3+ ) (2+ ) (4+ ) (10)− (4+ ) (7)− (8)− (6)− (5)− (6+ ) 9− (1+ ) (5+ ) (4)− (3+ ) (3)−

(2+ )

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

37

Table 3 (continued) Elev [keV]

Jmin –Jmax

2179.4(2) 2180.0(2) 2202.88(12)

4−7 4−7 1−3

2307.94(12) 2340.0(4) 2358.6(2) 2383.8(3) 2386.0(2)

4−4 7−7 2−5 3−5 3−5

2404.2(6) 2409.0(2)

1−5 6−6

2415.66(14)

1−3

2436.9(2) 2457.33(12)

3−5 3−3

2478.43(13) 2495.49(14) 2501.46(13) 2513.43(11) 2544.8(2) 2556.37(11) 2564.9(2) 2570.19(13) 2586.61(12) 2612.59(14) 2631.0(2) 2636.33(14) 2657.3(2) 2660.6(4) 2679.38(12) 2693.75(12)

2−3 4−5 2−2 3−5 1−4 2−4 3−6 1−3 3−5 4−5 5−6 2−5 1−4 8−8 1−3 2−5

2718.53(13) 2733.0(2) 2739.49(12)

2−4 2−3 3−4

π

A [keV] Elev 2165(7)

JAπ

−1

1

2250(5) 2308.7(2) 2339(3)

(7)+

2384.1(4) 2401.6(2) 2408(3) 2413(5)

(6)+ 9−

2427(3)

(11)−

1

2457.5(4) 2475(4)

(3)+ 9−

1

2501.4(3) 2514(5)

(2)+

1

2560(5)

2609(6) 2641(6) 1

2661(3) 2688(5) 2716(5) 2720(3)

2808(6) 2830(6) 2838.85(13) 2843.3(2) 2869.57(12) 2879.62(14) 2881.3(2) 2884.0(2) 2886.63(12) 2888.45(16) 2893.74(14) 2903.7(2)

1−3 1−3 3−6 2−4 2−5 1−1 3−4 3−7 2−2 0−3

2932.88(13)

1−5

(8)+

(10− )

2850(7)

1

−1 1

2884.2(5)

(1)+

2891(4) 2893.9(5)

(3)+ (2− )

2915(5) (continued on next page)

38

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Table 3 (continued) Elev [keV] Jmin –Jmax π 2942.9(2) 2−6 2950.88(12) 2−4 3069.42(13) 2−3 3154.9(3) 2−6 3165.9(2) 3−3 1 3286.3(2) 2−4 3351.3(2) 2−4 3390.9(4) 3−3 3424.96(12) 3−5 3427.3(4) 1−8 a Level discarded see text. b To be shifted by −4.2 keV, identified with preceding level. c Misprint, identical with preceding level. d Unresolved doublet. e Misprinted energy.

A [keV] Elev 2945(5)

JAπ (2)+

Fig. 6. Comparison of the experimental data from this work with 1p–1h shell model calculation for 208 Bi using the H7B [19] interaction. The graphs show level energy vs. level spin. The open symbols are the calculated values while the experimental data are represented with closed symbols. The calculated states are grouped by the main configuration as indicated with first the proton- and then the neutron-hole orbital. The graph is split into two parts making it easy to read. The thick line at 2.1 MeV shows the energy from where 2p–2h excitations are possible.

state and decays to (2, 3, 4)+ levels. The 4+ assignment to the 1564 keV level is firm due to many transitions to (3, 4, 5)+ levels. Then it is also clear, that 3+ and 5+ have to be assigned to the 1529 and 1469 keV states. The 6+ state of this configuration might correspond to the measured 1824 keV level, but this could as likely be the 5+ state of the πf7/2 νp−1 3/2 configuration. Again the lowest spin state 2+ of the πf7/2 νp−1 configuration is pushed up. The low energy transition to 3/2

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

39

the 3+ level of the same structure is characteristic. This 3+ state at 1871 keV decays to (2, 3, 4)+ levels, the 4+ to (3, 4, 5)+ , and the 5+ to (4, 5, 6)+ . Therefore these spin assignments are firm. Our data give no evidence for a (4+ ) level at 1605 keV in the compilation [7]. Most lines from the γ -decay of the 1605 keV level are multiplets. Proetel et al. [11] did not state themselves a level at 1605 keV, it must have been deduced from their table of γ -transitions by others. Therefore this level is discarded; so is the level at 1738.4 keV for the same reasons. Only one γ -line in 209 Bi(n, 2nγ ) supports the level at 1636.9 keV [20]. We do not see it and conclude, that the level in question does not exist. The same holds for the 1805.0, 1925.0, and 1938.0 keV levels. −1 The π i13/2 νp−1 1/2 and π h9/2 νi13/2 configurations give multiplets of negative parity below 2 MeV excitation energy. There is a misprint (1677.7) of the energy of the 1667.7 keV level in the Nuclear Data Sheets. This level and the 1625.5 keV state are the two levels of the πi13/2 νp−1 1/2 configuration from the strong l = 6 transfer found in the 207 Pb(3 He, d)208 Bi reaction [8]. Two γ -transitions to 5+ levels give spin 6 for the lower level; from 7− these lines would be M2. The 206 Pb(α, d)-reaction agrees giving l = 5 for the lower and l = 7 for the higher lying level [12]. Next come the ten negative parity levels of the πh9/2 νi−1 13/2 configuration with spins from 2 209 to 11. All have been found in the Bi(p, d)-reaction [9], and the γ -decay of the 11− level was observed in Ref. [13]. As pointed out in the previous section the (p, n) sub-Coulomb reaction populates states with low spin in 208 Bi. The angular momentum carried away from the subsequent γ -decays allows population of states with higher spin than the one directly populated from the (p, n) reaction. The well-known 10− isomer has been seen in the present study. The 9− level might preferentially decay to the long lived 10− isomer preventing the observation of coincidences. A 214.5 keV line seen in the singles γ -spectrum would fit. This state is very weakly excited and therefore a hypothetical low energy (130 keV) alternative decay to 8− might have escaped detection. Other decays to lower lying positive parity states can be ruled out, as they would require M2-multipolarity. The 1657 keV level decays only to the 7+ state at 650 keV; any other decay would have to be M2 for the adopted spin 8− . The 1716 keV level is taken to be a 6− , 7− doublet, as proposed by Martin [7] based on the high strength in l = 6 neutron pickup from 209 Bi [8,9]. We could resolve this doublet, and the γ -decay of both states strongly supports either 6− or 7− for both levels however without deciding which is which. Alford et al. [8] and Crawley et al. [9] give reversed 4− and 5− assignments to the 1703 and 1839 keV levels. The parity changing γ -decays of the 1839 keV level to two 3+ states have to be E1 and decide that it is the 4− . Spin 3− is firm for the 1920 keV state from E1 transitions to 2+ , 3+ , and 4+ states. The allowed M1 transitions between the states of the same configuration have been observed and further strengthen these assignments. They are: 80.7 keV 3− → 4− proven as M1, and 135.6 keV 4− → 5− . The analogous 2− → 3− transition with the much larger energy of 973.8 keV has also been observed. It confirms together with E1 decays to 1+ and 3+ levels the previously tentative configuration and spin assignment [9] for the 2894 keV state. Below 2 MeV excitation energy the scheme as just discussed is free from erroneous levels and considered to be complete, except that there is only one candidate for the 5+ (πf7/2 νp−1 3/2 ) and 6+ (πf7/2 νf−1 ) levels. 5/2 3.2. Higher lying 1p–1h states Above 2.1 MeV 2p–2h levels occur, and the scheme becomes complicated. But most of the 1p–1h states that have been found with the selective transfer reactions can still be identified with levels seen here by their γ -decay. The transfer studies, particularly those of Ref. [9] give the

40

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

Fig. 7. Part of the spectrum measured in singles zoomed around 2.8 MeV.

level energies with 1 keV precision (except for a calibration shift of 6 keV) facilitating their identification with levels established here. All these states have also positive parity, while 2p–2h states with π = +1 occur only above 3.5 MeV. The 209 Bi(p, d) or (d, t) reaction populates the configuration πh9/2 νf−1 7/2 and all 8 states belonging to it have been identified with spectroscopic factors close to the (2I + 1) rule [9]. One expects the neutron spin flip M1 γ -decays to the πh9/2 νf−1 5/2 levels around 600 keV to prevail. Indeed the 6+ , 7+ , and 8+ levels decay exclusively to their 5+ , 6+ , and 7+ spin flip partners. The 2383.8 and 2386.0 keV states are an unresolved doublet in the transfer reactions and assigned 4+ , 5+ there. This agrees with the γ -transitions. But both levels show 3 decays to the 3+ , 4+ , and 5+ states, which does not allow a spin assignment to the individual levels. An additional 856.7 keV transition to the 3+ state at 1529 keV prefers to assign (4+ ) to the 2386 keV level. The 3+ and 2+ levels show the expected γ -transitions. Again the lowest spin level 1+ is pushed up by the residual interaction and decays characteristically to the 2+ state of the same configura+ tion; unfavorable angular momentum coupling slows the competing decay to the πh9/2 νf−1 5/2 2 state. Alford et al. [8] give the 3+ and 2+ states of the πf5/2 νp−1 1/2 configuration at 2890 and 2945 keV. One expects strong high energy E2 transitions from the f5/2 to the h9/2 proton orbital with I = 2 to the two lowest states at 0 and 63.1 keV. The singles spectrum shows two lines at 2888.5 and 2879.8 keV, that give level energies of 2888.5 and 2942.9 keV. This spectrum is clean and very well fitted as shown in Fig. 7. These transitions cannot be verified by coincidences, but as the singles spectrum is so clean, these assignments are probable. M1-transitions to the lev+ els of the πf7/2 νp−1 1/2 (1 ) configuration have not been observed. They are calculated for pure configurations to be 1/3 of the E2 transitions. The energy difference between our 3286.3 keV + level to the πp3/2 νp−1 1/2 (1 ) level [8] is 1.7 keV identical to that of the two previously mentioned levels. But 2 γ -transitions to 4+ levels mean that it is 2+ . The spectroscopic factor measured by Alford et al. is somewhat too large for 1+ , and as they find 7 levels with p3/2 transfer, instead of 2 for pure configurations, 2+ is actually also preferable for their result. For completeness it + + might be mentioned, that the πi13/2 νi−1 13/2 12 and 13 states have also been found [13,21].

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

41

3.3. Two particle two hole states The 275 keV E1 transition to the 1802 keV 1+ level signals the onset of 2p–2h states at 2077 keV. Levels of the structure 210 Bi × 206 Pb g.s. should lie lowest. The pairing interaction in the ground state of 206 Pb and the attraction between the h9/2 proton and g9/2 neutron in 210 Bi for the 1− , 0− , 2− , and 9− levels brings the energy of these states down. Calculations with empirical interactions, taken from the appropriate two particle (hole) states in neighboring nuclei, for a pure configuration give the 1− state at 2065 keV and the 9− at 2336 keV. The whole multiplet from 0− to 9− is lowered by a constant amount, in other words the relative energies are unchanged from 210 Bi. The 210 Bim (p, t)-reaction gives the 9− level at 2.47 MeV [22] in agreement with 206 Pb(α, d) [12]. Both reactions are specific for 2p–2h states of this structure. Adjusting the energy of the whole multiplet, that experiment and calculation agree for the 9− level, gives 2.20 MeV, 2.25 MeV and 2.52 MeV for the 1− , 0− , and 2− levels in 208 Bi. These energies have to be lowered by 0.13 MeV for the unadjusted calculations. The 0− and 1− states of the structure 206 Tl × 210 Po g.s. are likewise calculated to be very low at 2140 and 2445 keV. These levels have the proton hole in the s1/2 orbital. The d3/2 hole is little (∼ 50 keV) above the s1/2 hole due to the interaction with the h9/2 protons, suggesting another low 2− state in 208 Bi at about 2.2 MeV. If we allow only E1-decays from the 2077 keV level, the first 2p–2h state found here, then its spin is 2− . But the 1% 1141 keV branch to 3+ could also be M2, allowing 1− , the expected spin for the lowest 2p–2h level. The states at 2203 keV, 2416 keV, and 2478 keV, that decay to the 2077 keV level with low energy transitions belong to the discussed structures. But any detailed assignments are not possible, the experiment might have missed low energy transitions and the calculations give only estimates. An alternative classification of the states by the different intermediate coupling as 208 Pb × 208 Bi is more convenient for counting. This gives 14 levels around 2.6 MeV from coupling the 4+ and 5+ levels to the 208 Pb octupole state at 2.6 MeV and already 60 levels around an unperturbed energy of 3.2 MeV. The residual interaction can however change energies by 1 MeV, for instance the level at 2077 keV belongs to an unperturbed energy of 3.2 MeV. 2p–2h levels of positive parity are not expected below 3.5 MeV. The first positive parity level of 208 Pb is 2+ at 4.08 MeV. Alternatively it requires around 1.5 MeV to excite any proton or neutron hole or particle to the intruder orbital with opposite parity. It is this energy, that is also needed to go from negative to positive parity 2p–2h states in 208 Bi. 4. Conclusions The main goal of the present measurement has been to provide rather complete data of the one particle one hole states in 208 Bi in order to experimentally determine the shell model residual interaction. The 208 Pb(p, n)208 Bi reaction populates all levels independent of their structure. The cross section for populating individual levels depends only on the level spin and excitation energy. At the chosen proton energy of 9 MeV, spin 1 to 3 are roughly equally and most strongly populated. The population drops off at higher spins, the population of spin 6 and 7 is around a factor 10 to 30 weaker, nevertheless we observed a state with spin 10. Therefore nearly all levels below 2 MeV have been seen. We found 204 new γ -transitions and 56 new levels, some (about 15) previously [7] wrongly claimed states could be discarded, because they were not observed. On the other hand, nearly all states seen by the selective transfer reactions [8,9] could be confirmed including the spin assignments. We have also found additional levels that were not

42

P. Boutachkov et al. / Nuclear Physics A 768 (2006) 22–42

populated in transfer due to their configurations. This reaction offers very clean experimental conditions. Except for weak inelastic scattering, no other reactions can occur on 208 Pb or the usual target impurities 12 C and 16 O. Therefore we were able to detect weakly populated states and weak γ -branches. As evident in Fig. 6, the predictions of the shell model for the level energies are in very good agreement with the present extensively revised experimental scheme. All particle hole configurations with 4 or more possible spins show very clearly the same pattern: The lowest spin is pushed up, the state with the highest but one spin is lowest. The highest spin level moves up appreciably only when j = l + 1/2 for one and j = l − 1/2 for the other component. The measured γ -branching ratios give a wealth of information on the detailed wave functions of the states, that is not yet used in this article. 208 Bi is now the best studied case of a particle–hole nucleus and can be used to thoroughly test calculations of the residual interaction. Acknowledgements This work was supported by the NSF under Grant No. 02-030099. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

K. Hauschild, et al., Phys. Rev. Lett. 87 (2001) 072501. E. Caurier, M. Rejmund, H. Grawe, Phys. Rev. C 67 (2003) 054310. G.J. Lane, Phys. Lett. B 606 (2005) 34. J. Kurpeta, et al., Eur. Phys. J. A 7 (2000) 49. T.T.S. Kuo, G.E. Brown, Nucl. Phys. 85 (1966) 40. S. Bogner, T.T.S. Kuo, L. Coraggio, A. Covello, N. Itaco, Phys. Rev. C 65 (2002) 051301(R). M.J. Martin, Nucl. Data Sheets 47 (1986) 797. W.P. Alford, J.P. Schiffer, J.J. Schwartz, Phys. Rev. C 3 (1971) 860. G.M. Crawley, E. Kashy, W. Lanford, H.G. Blosser, Phys. Rev. C 8 (1973) 2477. C. Ellegaard, P.D. Barnes, T.R. Canada, Phys. Rev. C 7 (1973) 742. D. Proetel, M. Dost, E. Grosse, H.J. Koerner, P. von Brentano, Nucl. Phys. A 161 (1971) 565. M.J. Spisak, W.W. Daehnick, Phys. Rev. C 29 (1984) 2088. B. Fornal, et al., Phys. Rev. C 67 (2003) 034318. G. Chodil, et al., Nucl. Phys. A 93 (1967) 648. R.G. Thomas, W. Bartolini, Phys. Rev. 159 (1967) 1022. D.C. Radford, Nucl. Instrum. Methods A 361 (1995) 297. M. Rejmund, PhD thesis, Institute of Experimental Physics, Warsaw University, 1998. K.H. Maier, M. Rejmund, Eur. Phys. J. A 14 (2002) 349. A. Hosaka, K.I. Kubo, H. Toki, Nucl. Phys. A 444 (1985) 76. E.J. Feicht, H. Gobel, Z. Phys. 245 (1971) 13. B.D. Anderson, C. Lebo, A.R. Baldwin, T. Chittrakarn, R. Madey, J.W.W. Watson, C.C. Foster, Phys. Rev. Lett. 52 (1984) 1872. K.A. Erb, W.D. Callender, R.K. Sheline, Phys. Rev. C 20 (1979) 2031. http://radware.phy.ornl.gov. M.J. Martin, Nucl. Data Sheets 70 (1993) 315. M.J. Martin, Nucl. Data Sheets 63 (1991) 723.