Study of 121Te with the (d,t) reaction

Nuclear Physics A 672 (2000) 21–53 www.elsevier.nl/locate/npe

E t) reaction Study of 121Te with the (d, D. Bucurescu a , T. von Egidy b , H.-F. Wirth b , N. M˘arginean a , U. Köster b , W. Schauer b , I. Tomandl c , G. Graw d , A. Metz d , R. Hertenberger d , Y. Eisermann d a Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania b Physik-Department, Technische Universität München, D-85748 Garching, Germany c Nuclear Physics Institute, 250 68 Rež, ˇ Czech Republic d Sektion Physik, Universität München, D-85748 Garching, Germany

Received 15 October 1999; revised 20 December 1999; accepted 11 January 2000

Abstract E t) reaction at Ed = The structure of the 121 Te nucleus has been studied with the 122 Te(d, 24.0 MeV. About 100 excited states have been observed up to an excitation energy of 2.65 MeV, and for most of them spin and parity values are proposed. A theoretical analysis based on the Interacting Boson–Fermion Model-1 is presented for the whole isotopic chain from 119 Te to 129 Te. The evolution of both positive and negative parity low-lying levels in these nuclei is reasonably well described with an essentially constant boson–fermion interaction. A detailed comparison of the calculations with experimental data is presented for 121 Te. The level scheme up to about 1.5 MeV excitation is reasonably well accounted for. Possible indications of states with “intruder” character are discussed.  2000 Elsevier Science B.V. All rights reserved. PACS: 21.10.-k; 21.10.Jx; 21.60.Ev; 27.60.+j E t); E = 24.0 MeV; Measured particle spectra, σ (θ ), asymmetry; Enriched Keywords: Nuclear reactions 122 Te(d, targets; Magnetic spectrograph; 121 Te deduced levels, J, π ; Spectroscopic factors; Interacting boson–fermion model calculations and comparison for the odd-A Te isotopes 119 to 129

1. Introduction The structure of the tellurium isotopes, which are only recently reasonably well investigated especially in the upper half of the N = 50–82 shell, is still somewhat controversial, even concerning the low-lying states. Since these nuclei have only two protons above the closed shell Z = 50, one expects that the even–even isotopes are rather close to good vibrators. However, a more rigorous search for the fingerprints of a U(5) dynamical symmetry [1] has left only 122 Te as a potentially interesting candidate and points out the need of new, more precise experimental data. Taking another example, the recent study of 124 Te [2] illustrates the difficulty of describing within a single model such 0375-9474/00/$ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 0 ) 0 0 0 5 9 - 2

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D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

nuclei which are probably rather soft to triaxial deformations. One of the most challenging questions related to the low-energy structure of the Te isotopes remains the occurence of the “intruder” states, which are expected to arise in such nuclei due to two particle– two hole excitations across the closed-shell gap [3]. A systematic investigation of this phenomenon was considered by Rikovska et al. [4] on the basis of mixed configuration IBM-2 calculations, and it suggests that such intruder states are the lowest (around 1 MeV excitation) in the middle of the shell (N = 66–68), but may be still important below 2 MeV excitation even in 124 Te (N = 72). Again for 124 Te, recent lifetime investigations [5] show that, apart from several states representing a deformed intruder configuration, the lowlying states are successfully described in the frame of the Interacting Boson Model [6] by a transitional U(5)/O(6) structure. In the odd-mass Te nuclei we expect a large number of states at low excitation energies, arising from the coupling of a neutron in the valence shell orbitals 1g7/2 , 2d5/2 , 2d3/2 , 3s1/2 and 1h11/2 to the states of the even–even core nuclei briefly discussed above. The recognition of such structures may greatly help to assess the validity of different nuclear structure models. It requires, however, good experimental data in which an almost complete characterisation of the level scheme containing all levels at low energies with spins and parities is needed, both for low and higher spins. The present work is part of a series in which detailed and systematic investigations of the odd-mass Te isotopes have been carried out by using light particle induced transfer and (n, γ ) reactions. Two of these studies have been already presented, for 125 Te [7] and 123 Te [8]. 121 Te was investigated before by several approaches. Transfer reaction studies such as (3 He, α) [9], (p, d) [10] and (d, p) [11] provided information on many excited states up to about 2.6 MeV but left many ambiguities in the spin assignments for most of these levels. Hagemann et al. [12] have investigated the higher spin states through the (α, 2nγ ) reaction, establishing several weakly deformed band structures. Finally, the beta decay study of Mantica et al. [13] provided new information on low spin states up to about 2 MeV excitation. In this article we present the results of a high resolution investigation of 121 Te using E t) one neutron transfer reaction, which brings important new information on excited the (d, states up to about 2.5 MeV excitation. In the previous works on 125 Te and 123 Te [7,8], we have used the Interacting Boson– Fermion Model (IBFM-1) [14] to describe the observed states and their experimentally known properties. We have by now implemented this model, in a systematic manner, to describe the evolution of both the positive and negative parity states along the Te isotopic chain from 119 Te to 129 Te, with a very small number of parameters. Therefore, we include in this paper, first, a description of these calculations, and a presentation of the main results for the whole chain. Then, the detailed results of these calculations for 121 Te will be compared with all existing experimental data for 121 Te. In these IBFM-1 calculations we do not take into account the possibility of intruder excitations in the core nuclei. On the other hand, there is no systematic study how such states can be recognized in odd-mass nuclei, in a one nucleon transfer reaction.

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

23

Therefore, a detailed and systematic comparison between these calculations and the experimental data can eventually point out some states lying beyond the framework of our model.

2. Experimental procedure and results 2.1. The experiment The experiment was performed with a 24 MeV polarised deuteron beam (polarisation 55–60%) delivered by the MP tandem accelerator of the University and Technical University of Munich. The target consisted of 122 µg/cm2 122 Te evaporated on a 4.2 µg/cm2 carbon foil, and had an isotopic enrichment of 91.2%, the contaminants being other stable Te isotopes with masses between 123 and 130, none of them exceeding 1.91%. The reaction products were analysed with the Munich Q3D spectrograph [15], at eleven angles between 7.5◦ and 40◦ . The acceptance opening of the spectrograph was 10.89 msr. The analysed products were detected with a 1.8 m long focal plane detector [16] which made 1E − Erest particle identification and determined the position with good resolution. For each angle two runs were measured, with spin “up” and “down”, respectively. The different runs were normalized to the beam current integrated into the Faraday cup after passing through the target. As the tritons are very well separated from other reaction products, the resulting spectra are virtually free of other contaminants. The energy range covered by the focal plane detector for one magnetic setting of the spectrograph was up to about 2.7 MeV excitation energy. The energy resolution of the spectra was in the range of 5 to 7 keV FWHM. An absolute energy calibration was made at the angle of 17.5◦ with the reaction 144 Sm(d,t)143Sm [17], measured at the same spectrograph setting with a 50 µg/cm2 target. Fig. 1 shows as an example the 121 Te spectrum measured at 17.5◦ . 2.2. Experimental results Table 1 contains all the levels observed in the present experiment. For most of them, both angular distribution and analysing power could be obtained. Transferred angular momentum ` values, as well as spin values (J ) have been determined by comparing the experimental data with calculations made with the code CHUCK in the DWBA approximation. In these calculations we have employed standard optical model parameters for the deuteron [18] and triton [19] channels, respectively. Examples of these analyses are shown in Figs. 2 and 3, for all observed `, J transfers, for levels whose J π values could be unambiguously assigned in this work. It is seen from Fig. 3 that measuring E t) reaction is extremely helpful in distinguishing between J = asymmetries with the (d, ` − 1/2 and J = ` + 1/2; thus, for the stronger peaks unambiguous spin assignments could be made. In general, we find good agreement with previously known levels [20], both in excitation energy and ` or J π assignments (see Table 1). There are a few exceptions, when we make a different assignment: the levels at Ex = 1400.2, 1487.0, 1517.2, 1680.6,

24 D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

E t)121 Te reaction at 24.0 MeV and laboratory angle of 17.5◦ . The peaks labeled with the level Fig. 1. Example of the spectrum measured in the 122 Te(d, 121 energy (in keV) belong to Te.

Table 1 E t)121 Te experiment Results of the 122 Te(d, Ex (keV)

dσ ◦ dΩ c.m. (15.3 )

L

Jπ

C2S

ENSDF [20] Ex

(µb/sr) 239.1 215.0 17.5 < 1.7 32.6 302.2 49.2 16.6 261.0

0 2 5 5 4 2 2 3 2

1.08 0.54 2.22 0.084 1.92 0.59 0.11 0.28, 0.21 0.54

678.2(6) 684.2(6)

20.4 3.4

0 4

1/2+ (7/2)+

0.078 0.19

756.1(6) 806.2(5)

1.6 42.7

2 2

(5/2)+ 3/2+

0.0033 0.11

887(1) 912.2(3) 925.7(7) 941.0(8)

0.45 75.0 17.3 0.91

2 3 2

5/2+ (5/2)− 3/2+ , 5/2+

0.15 0.26 0.0023, 0.0019

994.0(5) 1018.4(6) 1043.0(5) 1050.7(6)

3.5 1.4 1.7 0.60

2 (5) 2 3

3/2+ , 5/2+

0.009, 0.007 ≈ 0.05 0.0036 0.011

5/2+ (5/2)−

0.0 212.19(3) 293.98(3) 438.49(7) 443.12(3) 475.253(23) 532.060(24) 538.67(6) 594.50(3) 660(20) 681.30(6) 683.06(3) 698(10) 757.97(6) 806.69(5) 810.93(3) 830.53(11) 887.64(6) 912.24(4) 923(6) 937(5) 970(20) 994.03(4) 1018.41(17)

C2Sa

1/2+ 3/2+ 11/2− (9/2)− (7/2)+ 5/2+ + 3/2 , 5/2+ (7/2)− 3/2+ , 5/2+

0.67 1.24 2.68 2.40 1.44

1.10

1/2+ (7/2)+ 3/2+ , 5/2+ (7/2− ) (9/2)+ 3/2+ , 5/2+

0.34

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

1/2+ 3/2+ 11/2− (9/2)− 7/2+ 5/2+ 3/2+ − 5/2 , 7/2− 5/2+

0.0 212.4(2) 293.4(5) 438.9(5) 443.3(4) 475.4(3) 532.5(5) 539.5(6) 594.0(3)

Jπ

3/2+ , 5/2+ (9/2)+

25

26

Table 1 — continued Ex (keV)

dσ ◦ dΩ c.m. (15.3 )

L

Jπ

C2S Ex

(µb/sr) 0.30 0.98 5.8 14.8 < 1.2

1171.2(6)

1226.6(10) 1251.5(7) 1281.5(6) 1305.7(6) 1340.0(5) 1364.0(5) 1388.6(6) 1400.2(7) 1410.6(9)

1080.26(16)

0 4 2 (4)

1/2+ 7/2+ 5/2+ + (7/2 , 9/2+ )

0.0037 0.38 0.29 0.036, 0.022

3.7

2 +5

3/2+ , 5/2+ +(11/2)−

0.009, 0.007 0.079

15.4 40.8 1.9 6.0 77.1 4.3 6 0.30 1.2 0.68

2 0 1 2 2 2

5/2+ 1/2+ 1/2− 3/2+ 5/2+ 3/2+ , 5/2+

0.031 0.20 0.048 0.016 0.16 0.011, 0.009

3 (3)

5/2−

0.017 0.011

Jπ (11/2)+

1148.66(4)

3/2+ , 5/2+

1170.21(6) 1171.0(4) 1172.88(6) 1185.59(10) 1226.89(3) 1254(6) 1283(6) 1306.35(4) 1340.64(5) 1363.97(5)

3/2+ , 5/2+ 1/2+ 1/2− , 3/2− 3/2+ , 5/2+ (3/2+ , 5/2+ ) (3/2+ , 5/2+ )

1404(6)

1/2− , 3/2−

1437.20(6) ∼ 0.11

1449(2)(D) (1447 + 1451) 1487.0(6) 1505.0(6) 1517.2(5)

1.5

5(+?)

3.6 0.31 4.2

2

(3/2)+

0.010

1486.63(4)

3

5/2−

0.063

1551.2(6)

0.47

1

1/2−

1516(6) 1540.20(13)

0.0064

C2Sa

(7/2)+ 3/2+ , 5/2+

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

1079.0(6) 1108.2(10) 1119.4(6) 1148.3(6) 1161.6(5)

ENSDF [20]

Table 1 — continued Ex (keV)

dσ ◦ dΩ c.m. (15.3 )

L

Jπ

C2S Ex

(µb/sr) 2.9 0.43 2.0 1.8 5.6

2 3 3 (5) (3)

3/2+ , 5/2+ 5/2− 7/2−

1/2+ 5/2+ 7/2+ , 9/2+

(5/2− )

1680.6(5) 1693.4(5) 1703.0(6)

1.7 9.4 0.54

0 2 4

1739.6(6) 1754.5(5) 1769.4(6)

0.43 8.9 < 0.5

0 5

1/2+ (11/2)−

1 5 5 2 0 1 2 1 2

1/2− (9/2)−

1806.0(7) 1824.2(7) 1832.0(5) 1841.6(6) 1854.9(5) 1869.6(5) 1879.5(6) 1886.8(6) 1900.0(7)

0.47 6 0.3 1.1 5.1 12.6 2.2 1.9 ∼ 0.8 3.7

3/2+ 1/2+ 1/2− 3/2+ 1/2− + 3/2 , 5/2+

0.0071, 0.0058 0.0064 0.020 ≈ 0.1011/2 0.11

0.0084 0.019 0.046, 0.028

0.036 0.019 0.017 0.029 ∼ 0.0811/2 0.012 0.055 0.044 0.0047 0.0095 0.009, 0.007

1579(6)

Jπ

C2Sa

(7/2+ , 9/2+ )

1626.40(6)

1669(10) 1681.04(5)

7/2+ , 9/2+ 3/2+ , 5/2+

1707(10) 1730.72(5)

3/2+ , 5/2+

1750(6) 1771(10) 1804(6)

3/2+ , 5/2+ 1/2− , 3/2−

1835(6) 1851.48(19) 1869(6)

3/2+ , 5/2+

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

1575.8(5) 1591.0(5) 1627.2(5) 1641.6(6) 1657.2(8)(D?) (1655 + 1660)

ENSDF [20]

1913.24(12) 27

28

Table 1 — continued Ex (keV)

dσ ◦ dΩ c.m. (15.3 )

L

Jπ

C2S Ex

(µb/sr) 1920.1(5)

3.2 8.2 2.8 1.2 0.97 0.96 1.4 0.74 0.90 (< 0.4) 0.58 1.8 0.51 6 0.4

2149.1(6) 2169.5(6) 2187.8(6) 2215.9(6) 2236.1(5) 2247.8(5) 2284.3(6) 2292.5(6) 2317.5(15) 2339.3(8)

3.9 0.41 2.6 2.0 1.4 0.7 1.6 1.4 0.23 1.2

2 0 2 2 (3) 2 3 (5) (2) 1 5 5 0 2 2 2 1 2 2 5 2

3/2+ 1/2+ 3/2+ + 3/2 , 5/2+ (5/2− ) (3/2)+ (5/2)− (3/2+ , 5/2+ ) 3/2− (11/2)− (9/2)− 1/2+ (3/2)+ + 3/2 , 5/2+ 3/2+ , 5/2+ 1/2− 5/2+ + 3/2 , 5/2+ 11/2− 3/2+ , 5/2+

0.0078 0.037 0.0064 0.0042, 0.0034 0.016 0.0036 0.012

0.0017, 0.0014 0.020 0.054 0.071 0.019 0.006 0.0044, 0.0036 0.0036, 0.0029 0.012 0.0036 0.004, 0.003 0.026 0.0032, 0.0026

Jπ

C2Sa

1917(15) 1943(6)

1993(6)

2049(6)

1/2− , 3/2−

2111(6)

1/2− , 3/2−

2143(10) 2146(6)

7/2+ , 9/2+ (3/2+ , 5/2, 7/2− )

2182(6)

2252(6) 2280(6) 2310(10) 2343(6)

3/2+ , 5/2+

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

1953.1(5) 1973.2(5) 1989.5(6) 1995.4(6) 2005.9(7) 2026.0(6) 2046.2(15) 2059.3(6) 2077.1(7) 2106.4(7) 2112.3(6) 2129.1(6) 2136.4(9)

ENSDF [20]

Table 1 — continued Ex (keV)

dσ ◦ dΩ c.m. (15.3 )

L

Jπ

C2S

2.6 4.0 < 0.6 1.0 0.78

2 2 5 (4) 1

3/2+ , 5/2+ 3/2+ 11/2− (7/2+ , 9/2+ ) 1/2−

2456.9(5)

6.4

2

3/2+ , 5/2+

2516.2(5) 2536.8(7) 2549.9(6) 2568.8(8)

2.6 0.43 3.1 1.3

1 (1) 2 0

1/2− − (1/2 , 3/2− ) 3/2+ 1/2+

2600.2(7) 2611.7(7) 2630.2(9) 2641.5(7)

< 1.5 1.7 0.67 2.2

Jπ

0.0060, 0.0049 0.009 0.027 0.040, 0.024 0.018

2376(6)

3/2+ , 5/2+

2406(10)

7/2+ , 9/2+ (5/2− , 7/2− )

0.016, 0.013

2441(6) 2463(10) 2486(6)

0.048 0.007, 0.006 0.0078 0.006

2

(3/2)+

0.0045

2

(5/2)+

0.0040

2548(10) 2568(6) 2591.1(4)? 2604(6)

(5/2− , 7/2− )

C2Sa

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Ex

(µb/sr) 2360.1(6) 2389.4(7) 2406.8(8) 2414.7(6) 2426.5(7)

ENSDF [20]

a From the (3 He, α) reaction (Ref. [9]).

29

30

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Fig. 2. Typical examples of the DWBA analysis for angular distributions measured in the present reaction. The continuous curves are DWBA calculations normalized to the experimental data. For all the levels shown in this figure, unambiguous J π assignment could be made in the present work, on the basis of the asymmetry data (see Fig. 3).

2046.2, 2149.1 and 2406.8 keV; it is not clear whether in all these cases we see exactly the same level as previously reported. One more level deserves a special discussion, since it is at low excitation energy, where the density of levels is very low. We observe a level at Ex = 756.1(6) keV, which coincides in position with a known level, at Ex = 757.97(6) keV and adopted in ENSDF as (7/2− ) [20]. This level has been observed in

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

31

Fig. 3. Asymmetry data for the same levels shown in Fig. 3. The continuous curves represent DWBA predictions.

the beta decay work [13], where, due to its decay to the 438.5 keV, 9/2− and 538.7 keV, (7/2)− levels, it is proposed to have J π = 7/2− . The same level has been observed also in the (α, 2n) work [12] and assigned as 9/2− ; it appears, however, that there is some inconsistency between the reported feeding of this level (from a presumably (11/2− ) level) and its decay intensity (towards the 9/2− level). For the level that we populate at the same excitation energy we assign a clear ` = 2 transfer, therefore J = 3/2+ , 5/2+ (the

32

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

asymmetry indication on J is not sufficiently clear due to weak statistics). We checked whether this peak might be contaminated by an ` = 2 transfer belonging to one of the other Te impurities from the target. It coincides, indeed, with the position of a level in 129 Te assigned as (3/2, 5/2)+ , at Ex = 2.183 MeV, but this assignment is very unlikely since we do not observe other levels of 129 Te which should be populated much more strongly. The possibility that we see a different level is, of course, not excluded, although the level density at this excitation energy is quite low. When comparing with the calculations, one should keep in mind that the present experimental data indicate a negative parity level at 758 keV, and a possible positive parity one at about the same energy. From Table 1 one can observe that the present data could resolve many of the existing spin ambiguities and also provided many new J π values for levels up to Ex ≈ 2.6 MeV. Thus, the present results, which characterize unambiguously many low-spin levels, some of them rather weakly populated with our reaction, constitute a quite challenging basis for comparison with model calculations.

3. IBFM interpretation and discussion Like in the previous works [7,8], we use the IBFM-1 version of the Interacting Boson– Fermion Model [14] (which does not distinguish between neutrons and protons) to analyse our experimental data. Since the model parameters have been determined not by calculating only the 121 Te nucleus, but rather by looking at the whole chain from mass 119 to 129, we present this general approach first. The odd-mass Te isotopes are described as a fermion (neutron hole in our case) coupled to the even–even Te cores (120 to 130). The calculations were performed with the existing codes ODDA (for levels), PBEM (for electromagnetic transitions) and SPEC (for one-nucleon transfer spectroscopic factors) [21]. 3.1. The even–even cores The first step in the IBFM-1 approach is to describe the even–even Te cores within the IBM-1 model [6]. In this description, the total number of bosons varies from 8 (for 120 Te), to 3 (for 130 Te). We have been working with the usual non-multipole form parameterisation of the IBM-1 Hamiltonian [22]: X 0 ˜ (L) ˜ (0) + 1 cL (d † d † )(L) (d˜ d) HIBM = ε0 (d † d) 2 L=0,2,4
 v2  † † (2) ˜ v0 2 (d d ) ds + H.c. + √ d † s 2 + H.c. +√ (1) 10 2 5 and have determined the six parameters with the following procedure. We start from a pure anharmonic vibrator picture, in which v0 = v2 = 0, ε0 (the energy of the d-boson) 0 is approximately equal to the E(2+ 1 ) energy and the cL (L = 0, 2, 4) are determined + + + by the anharmonicities of the 02 , 22 and 41 levels. However, with this picture one cannot, usually, reproduce experimental B(E2) ratios (or branching ratios) for many

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Table 2 Parameters used for the IBM-1 calculations of the isotopes 120 Te to 130 Te. The columns 3 to 8 give the parameters of the IBM-1 Hamiltonian in its standard non-multipole form (Eq. (1.35) of Ref. [22]), the ninth column gives the χ value used in the transition quadrupole operator (see text), and the last column gives the effective boson g-factor used in the M1 transition operator A

NB

ε0

c0 (0)

c0 (2)

120 122 124 126 128 130

8 7 6 5 4 3

0.64 0.61 0.64 0.68 0.75 0.84

−0.08 0.35 0.60 0.80 0.65 0.35

−0.05 0.0 0.02 0.03 0.0 −0.1

c0 (4) 0.045 0.045 0.0 0.0 0.0 0.0

v2

v0

χ

gb

0.147 0.147 0.127 0.113 0.071 0.071

−0.08 −0.08 −0.08 −0.08 −0.08 −0.08

−1.33 −1.33 −1.12 −1.01 −0.63 −0.63

0.02 0.02 0.04 0.08 0.08 0.08

levels, therefore one needs to introduce the terms with v0 and v2 and readjust the other parameters. In doing this, we have tried to reproduce as many experimental observables as possible, such as level positions, experimental branching ratios, B(E2) ratios, and, when available, static moments, absolute B(E2) values and δ(E2/M1) values. For the transition operators we have chosen parameters in the following way. The quadrupole ˜ (2) + b = (d † s + s † d) transition operator was taken proportional to the quadrupole operator Q ˜ (2) which results from performing the transformation of the Hamiltonian (1) into its χ(d † d) b equivalent multipole form [22,23]. The boson effective charge eB , which normalizes the Q operator, has been chosen equal to 0.12 eB , as determined from the known experimental + B(E2; 2+ 1 →01 ) values of the cores. For the M1 transition operator we have used the general second order operator of Ref. [24]: b1 L) b2 b b (1) + B2 (Q L + B1 (Q nd b L)(1) + C b L T (M1) = (gb + AN)b

(2)

in order to reproduce some measured M1 transitions and E2/M1 mixing ratios (the more common choice T (M1) ∼ b L does not produce M1 transitions). While, in general, one cannot have a proportionality between the sum of the two middle terms in (1) and the E2 transition operator, we have used this restriction since there were too little data available to determine freely all three parameters B1 , B2 , C. We thus kept A = C = 0 and determined the rest of the parameters such as to describe well the magnetic moments of the 2+ 1 states, + + + + known branching ratios (usually for the 22 , 02 , 42 , 31 states) and mixing ratios (usually + + + for the 2+ 2 → 21 and 42 → 41 transitions, sometimes others too). The value B1 we used was 0.069, and the values of gb are given in Table 2. In Fig. 4 we show the comparison of these IBM-1 calculations with the experimental energy levels. As discussed above, the assignment of calculated levels to experimental ones is not made only on the basis of their energies, but also with other observables. This figure is meant only to show which levels could be reasonably well described by the present IBM-1 calculations, and which ones could not be described, or were more poorly described. The experimental levels drawn at the right side of each panel, without theoretical counterpart, represent the later category. In some cases they coincide with those proposed to have large contents of intruder configuration [4]. Thus, in 120 Te, the rather low

34 D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Fig. 4. Comparison between experimental levels and results of the IBM-1 calculations for the even–even core nuclei 120 Te to 130 Te. The experimental levels shown without theoretical counterpart in the right side of each panel, could not be accounted for by the calculations, or were not so adequately described (see the discussion in the text). The model parameters are given in Table 2 and are also discussed in the text. The experimental data are from Ref. [33].

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35

+ 0+ 2 and 23 levels at 1.103 and 1.535 MeV, could not be accounted for by the calculations. 122 Te, this is the case with the deformed intruder band 0+ , 2+ , 4+ , . . . , based on the In 1.747 MeV level [29]. The 1.941 MeV, 0+ level, also drawn in this category of levels in the figure, might correspond to a 0+ calculated level at 2.160 MeV, but its γ -decay could not be well accounted for. In 124 Te, the 1.882 MeV, 0+ and 2.092 MeV, 2+ levels, which may have, according to Ref. [4], large contents of intruder configuration, were also not well accounted for by the present calculations. The 2.153 MeV, 0+ level might correspond

Fig. 5. A particular representation of the IBM-1 symmetry triangle [25]. The dynamical symmetry limits are as indicated. IBM-1 calculations here were made with the simplified Hamiltonian bQ b [26]. The same quadrupole operator Q b (depending on the parameter χ , see text) is used εnd + k Q both in the Hamiltonian and for the transitions. The grey (background) symbols are the results of about 3000 IBM-1 calculations with this Hamiltonian, with randomly chosen values of the model parameters which were √ varied in the √ following ranges: N between 4 and 16; ε between 0 and 2.5 MeV; χ between − 7/2 and 7/2; k was kept constant, equal to 0.03 MeV [27]. As it can be seen, these calculations fill in (and define) the area of the “symmetry triangle”. Positive (negative) √ parity values of Q/ B(E2) correspond to positive (negative) χ -values and oblate (prolate) nuclei, respectively. Transitions between the dynamical symmetry limits are shown as lines which were calculated as follows. O(6) to SU(3) (line (a)): ε = 0, N varied from 4 to 16 and χ varied linearly with √ N , from 0 to ± 7/2. √ This line does not practically depend on N . U(5) to SU(3) √ (lines (b) and (c)): line (b) with χ = ± 7/2 and line (c) with χ varied from 0 to maximum (± 7/2), in both cases N varied from 4 to 16 and ε/k varied linearly with N from 0.0 to about 80. The Te isotopes 122 to 128 are represented by filled circles (with 128 Te closest to the U(5) limit), and the open circles belong to + + all other nuclei for which both Q(2+ 1 ) and B(E2; 21 → 01 ) are known experimentally [28].

36

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

to the theoretical 0+ 3 level, but we could not reproduce its decay with the largest branch state. We also show in this figure (by dotted line) the first negative parity towards the 2+ 2 level in these nuclei. We do not take into account these levels either (e.g., by considering an f -boson in the Hamiltonian). When comparing IBFM results with the experiment one should therefore bear in mind that around approximately 2.0 MeV excitation one can meet negative parity levels resulting from coupling a positive-parity quasiparticle orbital to these 3− or 5− states. It is interesting to estimate the “position” of the considered Te nuclei with respect to the dynamical symmetry limits of the IBA-1 model [22]. A practical way to achieve this is to consider observables which have typical values for these limits and thus can define particular representations of the symmetry triangle of Casten [25]. Fig. 5 shows such an example, which highlights the position occupied by the light Teqisotopes discussed above. + + For this we use the correlation between the quantity Q(2+ 1 )/ B(E2; 21 → 01 ), where

+ + + Q(2+ 1 ) is the quadrupole moment of the 21 state, and the ratio R4/2 = E(41 )/E(21 ). Both these quantities have well defined values in the dynamical √ symmetry limits. Thus, the former ratio has the values 0.91, 0.0 and between 0 and χ/ N in the SU(3), O(6) and U(5) limits, respectively, whereas the latter has the well-known values 3.33, 2.5 and 2.0, respectively; thus, in a correlation plot between these two variables, the dynamical symmetry limits are well separated. From this figure one can see that the experimental values of the Te isotopes 122 Te to 128 Te are situated within the symmetry “triangle”, close to the U(5) “vortex”. From Fig. 4 one can see that, with the exception of the 120 Te isotope, which has rather low intruder states, one could describe reasonably well the level schemes up to almost 1.6 MeV excitation. Thus, mixing of the low-lying levels which are well described by IBM-1 with levels of other possible nature might be relatively small. In this case, one would expect also a good description of the level schemes in odd-mass nuclei with the IBFM-1 up to about 1.6 MeV, whereafter the influence of the other core excitations to which we couple the quasi-particle orbitals may give rise to a more complicated situation.

3.2. The odd-A Te chain We first give a short description of the model used. We have employed the IBFM-1 Hamiltonian [14] X Ej aj† aj + VBF , (3) HIBFM = HIBM + j

where HIBM is the IBM-1 Hamiltonian of the core (described above), the second term is the single quasiparticle energy and VBF is the interaction of the odd particle (fermion) with the bosons of the core. The main contributions to VBF are [14]: a monopole– monopole, a quadrupole–quadrupole and an exchange interaction, for which we used a semi-microscopic parameterisation [30]: Xp 5(2j + 1) b nd b nj , (4) Vmm = −A0 j

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Vqq =

X jj 0

Vexch =

  b † a˜ j 0 )(2) (0), Γjj 0 Q(a j

X jj 0 j 00

37

(5)

 j 00  ˜ (j 00 ) (d † a˜ j 0 )(j 00 ) (0) , Λjj 0 : (aj† d)

(6)

where

√ (7) Γjj 0 = Γ0 5 (uj uj 0 − vj vj 0 )Qjj 0 , √   − 5 j 00 Λ0 Qj 0 j 00 βj 00 j (uj 0 vj 00 + vj 0 uj 00 ) + Qj 00 j βj 0 j 00 (uj 00 vj + vj 00 uj ) ,(8) Λjj 0 = p 00 2j + 1

βjj 0 =

(uj vj 0 + vj uj 0 )Qjj 0 , Ej + Ej 0 − hω ¯

Qjj 0 = hj kY2 kj 0 i.

(9)

For given quasiparticle energies Ej and occupancies u2j , the VBF term is determined by the three strengths A0 , Γ0 and Λ0 , respectively. The odd neutron was allowed to occupy the shell model orbitals between the magic numbers 50 and 82: 2d5/2 , 1g7/2 , 2d3/2 , 3s1/2 and 1h11/2 . These orbitals account for the large wave function components of both positive and negative parity levels at low excitation energies. However, in the one-neutron pickup and stripping reactions we observe states which are excited through small wavefunction components due to the negative-parity distant orbitals below N = 50, and above N = 82, respectively. Since the code ODDA [21] allows the use of only 5 orbitals, we have performed, for the negative parity states, two separate calculations: one which includes the orbitals 1h11/2 , 2f7/2 , 1h9/2 , 3p3/2 and 3p1/2 , which is suitable for calculating spectroscopic factors for the (d, p) reaction, and one with the orbitals 1h11/2 , 2f7/2 , 1f5/2 , 2p3/2 and 2p1/2 which is suitable for calculating spectroscopic factors for the (p, d) reaction. The two calculations provide slightly different level energies, but the influence of the distant orbitals is small and all states we calculate at low energies (below 3–4 MeV) have as main configuration that of 1h11/2 coupled to the core states. Thus, we will describe the main properties of these states (excitation energy, static moments, electromagnetic decay) and obtain also a qualitative image of the fragmentation of the single particle strength distribution of the distant orbitals over the lowest energy states. The quantities Ej , u2j have been determined by a BCS calculation (with a standard pairing gap of ∆ = 12A−1/2 MeV), by using, for the valence shell orbitals, the spherical shell model single-particle energies of Reehal and Sorensen [31]. The distant shell model orbitals have been added at relative energies with respect to the 2d5/2 orbital, according to the singleparticle energies calculated with the universal Woods–Saxon potential of Nazarewicz et al. [32]. The one-nucleon transfer spectroscopic factors were calculated with the code SPEC [21] using the transfer operators as defined in Ref. [33]. The parameters A0 , Γ0 , Λ0 were then determined by performing calculations for all Te isotopes 119 to 129, and trying to describe their properties with a set of smoothly varying, or even constant, parameter values. For each isotope we have considered the available experimental information, including level energies and J π values, static moments, electromagnetic decay modes (absolute B-values, branching ratios, mixing

38

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

ratios), as well as one-neutron transfer spectroscopic factors. The search for the optimum parameters has been carried out especially for the positive parity levels, which are sensitive to the mixing between the different four orbitals employed. In general, for each isotope, we were able to make a one-to-one correspondence between experimental and calculated levels, at least for the first few levels of each of the spins 1/2, 3/2, 5/2, 7/2; when available, higher spin structures (quasibands) have been also considered. We were finally able to describe all five isotopes 119 Te to 129 Te with the same values of the quadrupole and exchange interaction strength parameters: Γ0 = 0.2 MeV and Λ0 = 0.95 MeV2 , whereas the strength of the monopole interaction was varied almost linearly, from A0 = −0.1 MeV for 119 Te to A0 = −0.28 MeV for 129 Te. Although the monopole interaction has some effect on the mixing between the different orbitals, its main effect is an overall scaling of the energy spectrum. Another gratifying result of these calculations is that we were able to describe reasonably well, with the parameter values deduced for the positive parity states, also the negative parity levels. Therefore, with the single particle spherical shell model energy levels of Ref. [31] and with an essentially constant boson–fermion interaction, we have been able to describe in reasonable detail a large number of levels of both parities in six isotopes, thus following the evolution of the structure in these Te isotopes from N = 67 to N = 77. For the electromagnetic transition operators, besides the parameter values determined for the cores we have used an effective fermion charge eF = eB and standard gyromagnetic ratios gl = 0 and gs = −2.68 µN (70% quenching of the free nucleon value). For the calculation of the spectroscopic factors no additional parameters were needed, only the odd-A nucleus wave functions and that of the 0+ (g.s.) of the even–even A − 1 nucleus (for neutron stripping) and of the A + 1 nucleus (for neutron pickup) were necessary. The detailed description of the properties of two isotopes, 125 Te and 123 Te are given in Refs. [7,8] (only slightly different parameters have been used then for 125 Te), and the discussion of 121 Te will be made in the forthcoming chapter. Here we present just the main conclusions concerning the description of the level scheme evolution along the considered Te chain. Fig. 6 shows a comparison of the experimental level schemes (low spin values) with the calculated ones. The overall agreement can be considered to be fairly good up to about 1.5 MeV excitation, even if not all nuclei are known in the same detail. Above this energy, it becomes increasingly difficult to make one-to-one correspondences between the calculated and experimental values, but one can appreciate that the calculated number and distribution of levels is generally correct. The lines connecting some levels serve firstly to show the correspondence between the experimental and calculated figures. Also, in the case of the calculated levels they usually join levels with similar configuration. These dominant configurations are as follows. For the 1/2+ levels: first level, s1/2 ; second level, d3/2 ; third level, in general, d3/2 . For the 3/2+ levels: first level, d3/2 , second and third levels, admixtures of s1/2 and d3/2 ; fourth level, also s1/2 and d3/2 , sometimes with sizeable g7/2 contribution. For the 5/2+ levels: the curve going up, levels dominated by s1/2 ; the “belllike” curve: d5/2 for the first two isotopes, d3/2 in the others. For the 7/2+ levels: the curve that is going steadily up follows the dominating g7/2 configuration; the three lower levels

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53 39

Fig. 6. Experimental and IBFM-1 calculated positive parity level schemes of the odd-A Te isotopes 119 to 129. Only the low spin levels are shown here. Levels for which the spin is not certain are drawn with dashed line if there is some preference for the spin value shown, or with dotted line if none of the two possible spin values, as resulting from transfer reactions, is preferred. All known experimental levels and all calculated levels up to an excitation energy of 2.0 MeV are shown. Experimental data are from the ENSDF data files [36] and our data (Refs. [7,8], present data, Ref. [37] for 119 Te, and Ref. [38] for 129 Te).

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D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Fig. 7. Same as Fig. 6, for negative parity levels.

on the right: d3/2 ; the middle curve, generally d3/2 except for the two nuclei in the middle where it is dominated by g7/2 . Fig. 7 presents the same type of comparison for the negative parity levels. All these low-lying levels result mainly from coupling of the h11/2 unique parity orbital to the core states (in general, h11/2 contributes more than 98% in their wavefunctions). The evolution of these “antialigned” states is described rather well, as well as their γ -decay properties. As argued in a recent article [34] these low-spin negative-parity states are essential for the special properties of the lowest 11/2− (isomeric) states in these nuclei. In conclusion, we have now an IBFM-1 description of the Te isotopes 119 to 129 with a set of parameters implying an essentially constant boson–fermion interaction. This global description reproduces reasonably well the evolution with N of the lower states, as well as that of known yrast quasi-bands. Consequently, this gives some confidence in using it to look in more detail at individual isotopes.

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

41

3.3. The 121 Te nucleus 3.3.1. Positive parity states Here we shall compare in more detail the results of the above calculations for 121 Te with the existing experimental data. Fig. 8 shows a comparison of the experimental and theoretical level schemes, and Tables 3 and 4 give the electromagnetic decay schemes.

Fig. 8. Comparison between experiment and IBFM-1 calculations, for the positive parity states in 121 Te. The upper panel displays all low-spin levels and (tentative) correspondences are indicated by dashed lines (see also Tables 3, 4 and discussion in the text). The lower panel shows a different arrangement of the levels, according to bandlike structures observed in the (α, 2n) work [12] (double spin values are given here). For the calculated structures, the orbital with the largest contribution in the wavefunctions is indicated above the band. The two numbers indicated for some of the low spin states represent spectroscopic factors for the (d, t) reaction (this work, the number above) and (d, p) reaction (Ref. [11], the number below).

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D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Fig. 9. Experimental and calculated spectroscopic factors for positive parity states, for the (d, t) and (d, p) reactions. Note that most of the levels with spin 3/2 or 5/2 (Table 1) are shown (with dotted lines) as 5/2 states.

Fig. 9 shows a comparison of the experimental and calculated (d, p) [11] and (d, t) (this work) spectroscopic factors for the 3s1/2 , 2d3/2 , 2d5/2 and 1g7/2 transfers. In Fig. 8, assignments of calculated levels to experimental ones are indicated in the upper part (for lower spin levels) by dashed lines. In the lower part of the figure, the levels are arranged into quasiband structures, as observed in Ref. [12]; the theoretical quasibands are labeled by the dominant single particle component of the wavefunctions. The associations between calculated and experimental levels are made on the basis of the decay properties (see Table 3) and the neutron transfer spectroscopic factors. From Fig. 9 it appears that only the states with the strongest population have been observed in the (d, p) reaction study [11]. The 1/2+ states. The first two such states can be readily assigned to the calculated ones, especially by comparing their spectroscopic strengths in both reactions (Fig. 9). Only one state is calculated around 1.2 MeV, while two states, at 1.108 and 1.252 MeV, are observed (the first one rather weakly seen only in the (d, t) reaction). Then, there is a group of states not so strongly excited in (d, t), between 1.68 and 2.60 MeV, whose distribution is well reproduced theoretically (although with a more reduced strength). On the whole, there are 10 states of this spin observed up to 2.6 MeV, and the same number of states are calculated within the same energy interval, with a rather similar energy distribution (see for example the small gap from about 1.2 to about 1.5 MeV, Fig. 8), so it would appear that the concordance with the theory is rather good. On the other hand, the state at 1.108 keV, with small (d, t) spectroscopic factor, might rise some suspicion concerning its

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

43

understanding within the frame of the IBFM calculations. The theoretical sum rule for the (d, t) spectroscopic factors is 0.89, experimentally the sum of the observed states is 1.52, therefore it appears that the 3s1/2 strength has been exhausted. The 3/2+ and 5/2+ states. We discuss together these states since there are many cases of ` = 2 experimental states for which one could not decide in favour of one of the two possible spin values. From Table 3 and Fig. 9 one can see that the assignment of the lowest few levels of each of these spins to calculated ones, on the basis of their decay and spectroscopic factors, is rather straightforward. The first three calculated 3/2+ states correspond one-to-one to the experimental ones (Figs. 8, 9, Table 3). The first of them is a d3/2 state, while the other two are dominated by a mixture of the s1/2 and d3/2 orbitals. It appears also that the first six, or even seven states assigned as 5/2+ can be put into correspondence with the first seven calculated ones, especially if we consider the description of their decay (Table 3); only the 5/23 and 5/24 states have been swapped in order to account for the decay of the 0.912 MeV level (the decay of the 1.043 MeV one is not known). We then have to explain the remaining experimental 3/2+ , or 3/2+ , 5/2+ states above 800 keV, which should be candidates for the calculated states above 3/23 . This task could not be done completely without ambiguities, and to illustrate this situation Table 4 shows the experimental decay of these states in comparison with different calculated possibilities. The decay of the 941 keV, (3/2+ , 5/2+ ) state is not known. Its small spectroscopic factor fits that of any of the calculated 3/2 states above 3/23 , so this does not allow any precise assignment. The 994 keV, (3/2+ , 5/2+ ) state has a decay which compares reasonably with that of both 3/24 and 3/25 states, somewhat better with the latter one. The 1171 keV, (3/2+ , 5/2+ ) state is better described by the 3/25 state, while for the 1306 keV, 3/2+ state both 3/25 and 3/26 are possible assignments. The 1365 keV, (3/2+ , 5/2+ ) state is well described by the calculated 3/27 state. Thus, for the 3/24 , 3/25 and 3/26 calculated states there are no unambiguous assignments, although the states at 994, 1171 and 1306 keV (possibly also the state at 941 keV) are good candidates. The 3/24 to 3/27 states have rather mixed wave functions, with important contributions from at least three single particle orbitals, the wave function of the 3/27 state being completely mixed, with practically equal contributions of all four positive parity orbitals considered in the calculations. For the higher states, the correspondence between experimental and calculated states becomes rather difficult. Based on Fig. 9 one can make only the qualitative conclusion that the observed distribution of the 2d3/2 orbital is reasonably well described by the model (note that few other possible weakly excited 3/2+ states, drawn in Fig. 9 as 5/2+ , would not change this conclusion). The theoretical sum rule for the (d, t) strength is 0.78, whereas the firmly established 3/2+ states give 0.85, so also in this case we have observed practically the whole 2d3/2 strength. Although the 5/2+ states appear better described from the γ -ray decay point of view (Table 3), the calculated spectroscopic factors, as seen from Fig. 9, are not always well predicted quantitatively. For 5/21 , both the (d, p) and (d, t) strengths are very much underestimated. Only the sum of the (d, t) strengths for the first two states at 0.504 and 0.772 MeV, which is 1.13, fits reasonably well the calculated one of 1.54. This means

44

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Table 3 Experimental and theoretical electromagnetic properties of 121 Te states. Experimental branching ratios are from Ref. [21]. The second column indicates (as subscript) the order number of the calculated state assigned to the respective experimental one. The decay of the levels at 994, 1171, 1306 and 1365 keV states is shown separately in Table 4 Ex (MeV)

Eγ Ji

0.212 0.443 0.475

3/21 7/21 5/21

0.532

3/22

0.594

5/22

0.681

1/22

0.683

7/22

0.806

3/23

0.831

9/21

0.887

7/23

0.912

5/24

1.018

9/24

Jf

(keV)

Positive parity states 1/21 212.2 3/21 230.9 1/21 475.3 3/21 263.1 1/21 532.1 3/21 319.9 5/21 56.8 1/21 594.5 3/21 382.3 7/21 151.4 3/22 62.7 1/21 681.1 3/21 469.2 3/21 470.9 7/21 240.0 5/21 207.8 1/21 806.7 3/21 594.5 7/21 363.6 5/21 331.4 3/22 274.6 5/22 212.2 1/22 125.4 7/21 387.4 7/22 147.5 7/21 444.8 5/21 412.5 5/22 293.2 7/22 204.6 1/21 912.2 3/21 700.0 7/21 469.2 5/21 437.0 3/22 380.2 5/22 317.8 7/21 575.3 5/21 543.2 5/22 423.9 7/22 335.3 7/23 130.7

Branch Exper.

100 100 100(4) 6.8(4) 100(4) 1.5(1) 1.0(1) 73(4) 100(5) 2.3(4) 0.5(3) 27(3) 100(6) 100(6) 2.7(7) 17.6(10) 100(4) 9.2(23) – – – – – 100 – 51(7) 81(14) 100(5) – – 100(8) 27(2) 8.8(8) 8.5(8) 36(2) – 100 – – –

Theor.

100 100 100 73.6 100 18.0 3.1 29.1 100 0.1 1.6 100 6.0 100 1.0 3.0 100 97.0 0.6 69.6 1.2 14.8 0.8 100 1.1 61.5 100 77.3 5.9 2.1 100 0.2 7.3 2.0 12.8 7.8 100 1.2 72.5 3.5

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

45

Table 3 — continued Ex

Eγ

(MeV)

Ji

1.043

5/23

1.079

11/21

1.148

5/25

1.208

11/22

1.227

5/26

1.340

[5/27 ]

Jf 1/21 3/21 7/21 5/21 3/22 7/22 3/23 7/23 7/21 7/22 9/21 1/21 3/21 7/21 5/21 3/22 7/23 5/24 5/23 7/21 7/22 9/21 7/23 9/22 11/21 1/21 3/21 7/21 5/21 3/22 5/22 1/22 7/22 3/23 9/21 3/24 1/21 3/21 5/21 3/22 5/22 1/22 7/22

(keV) 1044.1 831.9 601.0 568.9 512.0 361.0 237.4 156.4 637.2 831.9 249.7 1148.7 936.5 705.6 673.4 616.6 261.0 236.5 104.6 764.9 525.0 377.5 320.3 189.6 127.7 1226.9 1014.7 783.8 751.6 694.8 632.4 545.6 543.8 420.2 396.4 232.9 1340.6 1128.0 865.4 808.5 746.1 659.3 657.5

Branch Exper. – – – – – – – – 100(5) – 4.7(12) 20.6(13) 100(3) 12.2(16) 34.7(19) – – – 10.9(13) – 100(4) – – 6(2) – 13(1) 100(3) 5(1) 18(1) 79(3) 12(1) – 7(1) 5(2) – – – 100(5) 56(4) 33(5) – – –

Theor. 24.6 63.0 16.8 100 47.4 3.4 0.9 3.5 100 0.6 6.4 11.4 100 2.7 28.9 10.9 2.2 1.4 0.2 6.2 78.0 9.6 27.9 100 5.3 37.0 100 46.2 6.8 5.3 15.0 3.3 4.4 8.2 1.1 10.4 7.6 70.6 69.2 61.8 100 18.5 3.4

46

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Table 3 — continued Ex (MeV)

Eγ Ji

1.419

13/21

1.712

15/21

1.807

15/22

2.070

17/21

0.439 0.539

9/21 [7/21 ]

0.926 0.975

15/21 13/21

1.600

17/21

1.654 2.016

19/21 21/21

2.332

23/21

Jf 3/23 7/23 5/24 3/24 5/25 9/21 11/21 11/21 11/22 13/21 11/22 13/21 13/21 15/21

(keV) 533.9 452.9 428.4 346.6 191.9 588.9 339.2 631.6 503.9 292.5 598.7 387.3 598.7 358.4

Negative parity states 11/21 144.5 11/21 244.7 9/21 100.2 11/21 631.6 11/21 681.3 9/21 536.8 15/21 674.0 13/21 536.8 15/21 674.0 17/21 416.4 19/21 361.7 19/21 677.8 21/21 316.1

Branch Exper.

Theor.

– – – – – 100(3) 22(2) 100(5) – 16(3) 100 – 100(7) 19(5)

4.2 2.6 1.7 2.3 2.1 100 21.8 100 0.9 7.5 100 1.1 100 10.8

100 100 – 100 100(3) 29(1) (<100) 62(4) 100 19(8) 100(1) 43(4) 100(3)

100 44.2 100 100 100 19.1 69.4 100 100 100 13.6 100 32.6

that the two experimental states are more mixed in reality, and namely, that we miss some d5/2 orbital contribution into the 5/21 state, which is a s1/2 -dominated state. As remarked above, up to the seventh 5/2 state there is a good correspondence between experimental and calculated states. Also, if we take into account the higher states assigned as 3/2, 5/2, we can see from Fig. 9 that the d5/2 strength distribution is qualitatively reproduced. On the other hand, one can see that much of its strength is missing. The theoretical sum rule gives 5.62 for the (d, t) strength, experimentally we observe only about 2.54 (the small contribution of the states with ambiguous spin does not essentially change this figure). One notes, in Table 1, that there is some difference between our spectroscopic factors and those deduced from the (3 He, α) reaction [9]; however, even if we consider the generally higher spectroscopic factors of this later reference, we get a d5/2 sum of about 3.9, still

Table 4 Experimental and theoretical electromagnetic branching ratios of several 3/2+ or 3/2+ , 5/2+ states. For each state, below the experimental branches (first row) are shown the calculated branches towards the states indicated in the head of the columns, for two possible theoretical assignments. Branches less than 0.5 are not given, unless the experimental counterpart exists

Ex (keV) 994

1171

Jiπ

1/2+ 1

3/2+ 1

7/2+ 1

exp.

100(5)

96(5)

18(3)

3/2+ 4

5.8

48.0

4.3

20.9

0.2

3/2+ 5

100

exp.

100(8)

100(6)

3/2+ 4

4.2

37.3

7.0

24.2

0.6

3/2+ 5 1306

1365

100

5/2+ 1

3/2+ 2

5/2+ 2

14.3

6.5

2.2

6.4

24.8

7.9

4.1

11.9

1/2+ 2

7/2+ 2

3/2+ 3

5/2+ 4

12(3) 100 64.0

10.5

3.8 29(4)

100 94.4 32(3)

25.1

0.9

10.8

0.7

16.9

0.9

2.0

exp.

93(5)

100(5)

3/2+ 5

86.4

22.9

32.9

1.5

27.2

3/2+ 6

8.1

17.0

26.2

25.1

100

12.4

6.1

3.3

exp. 3/2+ 6 3/2+ 7

78(4) 7.5 73.7

100(5) 15.8 100

25.6 15.1

83(5) 24.7 55.3

100 15.2

13.5 34.0

25(3) 7.4 0.7

4.3 5.0

0.9

10.8

100

41(3) 5.1

14.1

D. Bucurescu et al. / Nuclear Physics A 672 (2000) 21–53

Branch to the state

47

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small compared to the theoretical prediction. We have no simple explanation for this lack of d5/2 strength. Since the d5/2 shell is practically full it is difficult to imagine how one can get theoretically lower strengths at low excitation energy. The 7/2+ states. Only three states are strongly excited in our reaction and they can be assigned to the first three calculated states (see Tables 1, 2, and Figs. 8 and 9). The calculations predict at least one more state with large spectroscopic factor, which was not seen. It might be assumed that the rest of states could not be seen due to difficulties in observing ` = 4 transfer with relatively low spectroscopic factors. The theoretical sum rule is 7.20, the observed one is 2.54. If we sum up the observations we made until now in comparing the IBFM-1 predictions for the positive parity states with the experiments, one may state that up to about 1.5 MeV excitation the IBFM-1 calculations account reasonably well for the experimental properties. Some discrepancies deserve, nevertheless, a special discussion. We have noted a few low-spin, low-lying states which do not seem to fit into the IBFM-1 level scheme. One is the 1/2+ state at 1.108 MeV, then the 3/2+ , 5/2+ states at 0.941, 0.994 MeV and (possibly) at 0.756 MeV. Also, we have noticed some difficulties in describing the decay properties of the 3/2+ and 3/2+ , 5/2+ levels from the energy range 0.8 to about 1.4 MeV (see discussion above and Table 4). Both these facts may indicate the need of considering configurations which are outside the IBFM-1. First, the coupling of one quasiparticle to intruder core states may give rise to such additional states. Besides the above observations, we can also make global considerations, based on the number of levels and their distribution in energy, which, although very rough, lead to a similar conclusion. Thus, up to 2.0 MeV excitation we have (experimentally) ten 3/2+ levels, nine with 5/2+ and five (or six) levels with J π = 3/2, 5/2+ , in total 24 (or 25) such levels. The calculations predict, in the same range, ten 3/2+ levels and twelve 5/2+ . We find therefore an excess of two or three levels of spin 3/2+ or 5/2+ in this energy range. It is not surprising that at higher excitation energies there are levels not accounted for by the model, which therefore represent “intruders” with respect to the present IBFM1 calculations. However, from the discussion we made above for the IBM-1 calculations for the Te cores, we would expect such states at higher excitation energies, so that their possible presence around 1 MeV is somewhat surprising. On the other hand, the core of 121 Te could be intermediate between 122 Te and 120 Te, and this would offer an explanation for the lowering of the possible intruder states. Secondly, we have noticed the relatively worse description of the decay properties of some of the lower states (those around 1 MeV, discussed in connection with the predicted 3/24 to 3/26 states). One possible explanation would be that the wave functions of the respective levels are not good enough, and might be changed in the right direction by further tuning of the model parameters; some trials in this sense were not successful, especially as the agreement deteriorated for other states. Another possibility is that there is admixture of some “intruder” configuration into the structure of these states, which has not been taken into consideration.

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Anyway, the assignment of “intruder” character to particular states in this odd-A nucleus, based on the present experimental data, is not so straightforward. A special difficulty is due to the fact that, because of the large separation between the intruder state and the ground state (in the core nucleus), their mixing is rather small and therefore the corresponding intruder states in the odd-A nucleus should be very weakly populated in one nucleon transfer reactions. The states presently under discussion (see above) are indeed weakly populated, but in the absence of other firm spectroscopic information this cannot be taken as an unambiguous indication of their possible intruder character. Ref. [13] proposes the detection of important E0 strength in J → J transitions in the odd-A nuclei as a possible manifestation of the mixing between the almost spherical “normal” states and the intruder ones (assumed more deformed) [35]; such E0 contributions were not found in transitions of 121 Te [13]. 3.3.2. Negative parity states The information on the negative parity states is not so rich, especially in the low-spin region. Figure 10 shows a comparison between the experimental and calculated levels. The known experimental levels are mainly from the high-spin work of Ref. [12]. Taking into account the level at 756 keV discussed above, it seems that there are candidates for both calculated 7/21 and 5/21 levels. The decay of the levels shown in Fig. 10 is reasonably well described (Table 3). All the calculated levels belong practically to the h11/2 family, their wavefunctions having more than 97% contribution from this orbital. Figure 11 shows the situation with the spectroscopic factors. Most of the (d, t) and (d, p) h11/2 strength is concentrated in the 0.293 MeV parent state. The fragmentation observed in the (d, t) reaction for this orbital resembles very much the calculated one, being concentrated in a group of states between 1.0 and 2.2 MeV; the theory underestimates somewhat the h11/2 strength in this region. We have observed a number of 1/2− states in the region above 1.2 MeV, indicating pickup from the 2p1/2 orbital. The model predicts only about three states in the same energy region, but with negligibly small spectroscopic factors, which do not explain the observed strength. We then observe one 3/2− state at 2.112 MeV; the only calculated state with appreciable strength is at 1.04 MeV, the rest (indicated in Fig. 11) having negligible strengths. Other negative parity states observed in our reaction are those with ` = 3; most of them are 5/2− and one or two 7/2− (Table 1 and Fig. 11). While the energy distribution of the J π = 5/2− states is relatively well reproduced, the calculations predict again too small f5/2 spectroscopic factors (the calculated (d,p) spectroscopic factors are not relevant in this case – since we did not consider the 2f5/2 orbital – and are not shown since the experimental ones are also missing). The underestimation of the f7/2 (d, t) strength is understandable in this case since in the calculations we have employed the 2f7/2 (empty) orbital. Although the 5/2− 1 state has not been experimentally identified with certainty, the present theoretical calculations predict such a low-lying state, similarly to the other isotopes (see Figs. 7 and 10). Thus, this state might play the rather important role of

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Fig. 10. Experimental and calculated negative parity states in 121 Te.

“funnel” in the feeding of the isomeric state 11/2− 1 from higher state, as found in our previous investigation [34]. In summary, while the present IBFM-1 calculations describe reasonably well some of the low-lying negative parity states, there are points of qualitative disagreement with the experimental observations. One is the large number of observed 1/2− states which are not predicted. Secondly, the one-nucleon transfer strength for the distant negative parity orbitals in the low-lying states appears to be systematically underestimated. At least some of the states in the range above 2 MeV are expected as a result of coupling positive parity orbitals to the first negative parity states of the core. Ways to improve the calculated transfer strengths for the distant orbitals using the present model are not obvious. Just a lowering of the single particle energies is not enough. For example, with the present model parameters, most of the p1/2 pickup spectroscopic strength (about 94% of the sum rule) is concentrated in the 20th 1/2− state situated about 5.6 MeV above the 1/2− 1 state; by lowering the 1p1/2 orbital by as much as 3.0 MeV, this strength is lowered in the 10th 1/2− state at about

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Fig. 11. Experimental and calculated spectroscopic strengths for negative parity states. The slight difference in energy between the states shown for the (d, p) and the (d, t) cases, respectively, reflects the small difference between the two different calculations performed for the negative parity states, as described in the text. The states predicted with negligible spectroscopic factors are only indicated by a standard small bar (“square”).

2.7 MeV above the first one, and the theoretical fragmentation of this orbital remains poor, as the first several 1/2− states (which experimentally accumulate a summed spectroscopic strength of about 0.20 – see Table 1) still have negligible calculated strengths. It might be possible that a completely different set of parameters, maybe combined with a different set of single particle energies, is able to provide more appreciable admixtures of the distant orbitals in the wavefunctions of the lowest states, as found experimentally. In the present work we have not performed, however, such extensive searches.

4. Conclusions As part of our program of detailed spectroscopy of the Te isotopes, we have investigated E t) reaction. The high energy resolution of this the 121 Te nucleus by means of the 122 Te(d, experiment, as well as the use of a polarised beam allowed the observation of almost 100 levels up to 2.6 MeV excitation and unambiguous J π assignments for many of them.

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To explain the observed large number of levels with low and medium spins, we have extended the previous calculations [7,8] based on the Interacting Boson–Fermion Model (IBFM-1). The experimental data known for all isotopes from 119 Te up to 129 Te have been exploited to deduce a set of model parameters; thus, with an essentially constant boson– fermion interaction, we were able to describe rather satisfactorily the evolution of the lowenergy nuclear structure along this chain of isotopes for both the positive and the negative parity levels. The calculations with this general parameter set are checked in detail for 121 Te, by comparing the model predictions with the presently known information on level excitation energies, J π values, γ -decay branching ratios and one neutron transfer spectroscopic factors. The model gives a generally good description of the low- and higher-spin states of both parities at low excitation energies. However, looking in greater detail, the problem arises whether this comparison with the IBFM-1 predictions can evidence some lowenergy, low spin states with an “intruder” character. One must be cautiuos in answering this question. Firstly, it is the problem of the degree of accuracy we require in the description of the experimental data, since this type of detailed comparison implies a certain extrapolation of the calculations, from some well-known low-lying levels (used to fix the model parameters) to virtually all levels. Secondly, although the present experimental study has brought much new information on the low-spin states, there are still many weakly populated levels whose spin remained ambiguously defined (given as J = ` ± 1/2), and, in addition, their γ -decay is not known. In such conditions, the comparison with the IBFM-1 remains semi-qualitative, and both more realistic calculations and more complete experimental data are desirable.

Acknowledgments The support of the Deutsche Forschungsgemeinschaft, Bonn, is appreciated and especially D.B. wishes to thank them for generous financial help during working stages at the Technical University of Munich. The work was supported by the Beschleunigerlaboratorium der Universität und der Technischen Universität München. We are indepted to Th. Faestermann for the Q3D maintenance and to P. Maier-Komor and K. Nacke for target preparation.

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