Lifetime measurement in 124Te

Nuclear Physics A 672 (2000) 3–20 www.elsevier.nl/locate/npe

Lifetime measurement in 124Te C. Doll a,b,1 , H. Lehmann b , H.G. Börner b,∗ , T. von Egidy a a Physik-Department, Technische Universität München, D-85748 Garching, Germany b Institut Laue-Langevin, F-38042 Grenoble, France

Received 1 December 1999; revised 16 December 1999; accepted 17 December 1999

Abstract Lifetimes of nuclear levels in 124 Te have been measured by the γ -ray induced Doppler broadening (GRID) technique using the GAMS4 crystal spectrometer at the Institut Laue Langevin, Grenoble. The new experimental data allow the determination of absolute transition rates. The results show that the structure of 124 Te is best described by a configuration mixing calculation in the framework of the IBM-2. Precise γ -ray measurements confirm a 2+ –3+ level doublet at 2039 keV with a spacing of 129 eV.  2000 Elsevier Science B.V. All rights reserved.

1. Introduction In spite of the important efforts which have been made to improve the knowledge on the nuclear level schemes [1–10], the structure of the even–even tellurium isotopes remains enigmatic. On one hand there seems to be evidence that 124 Te exhibits a vibrational behaviour: The ratio of the 4+ 1 level excitation energy to the excitation energy of the first 2+ level E4+ /E2+ is nearly two. The first excited 0+ state, however, which in this picture 1 1 should belong to the two phonon triplet, is about 400 keV too high in excitation energy. Therefore, this interpretation can only hold, if one considers very large anharmonicities [4]. On the other hand also an interpretation as γ -soft nucleus is proposed [2]: The high excitation energy of the second 0+ state as well as the level sequence seem to indicate that this isotope might be successfully described as an O(6) nucleus even if the E4+ /E2+ ratio 1 1 is far from the expected value of 2.5. These isotopes have been discussed thoroughly in the framework of the Interacting Boson Model (IBM) [11]. In addition to the dynamical limits of the IBM — corresponding to the above mentioned limiting cases of the collective model — shape coexistence is proposed within this model [12]. Due to the fact that a possible intruder configuration in the Te isotopes would be built up by a higher number of nucleons it should be more deformed ∗ Corresponding author. 1 Present address: TUM-Tech GmbH, D-81925 München.

0375-9474/00/$ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 9 9 ) 0 0 8 4 8 - 9

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C. Doll et al. / Nuclear Physics A 672 (2000) 3–20

(more SU(3)-like) as the one observed in the neighbouring Cd and Sn isotopes where the deformed configuration is described by the O(6) limit of the IBM (see for instance [13]). Thus the properties of a shape-coexisting system in the Te isotopes might be quite different from the well understood U(5)–O(6) configuration mixing examples in the Cd nuclei. Finally, one might argue that strong quasi-particle contributions for some low lying excitations are the cause for the troubles in describing the excitation spectrum of the Te isotopes. Based on systematics on the N = 72 isotones Lee et al. [6] propose large quasi+ particle contributions for the 6+ 1 and 41 states. It might thus be instructive to reconsider the Quasiparticle Phonon Model (QPM) [14]. As the excitation energy spectrum alone is clearly not sufficient to answer these open questions, wave function sensitive information is needed to clarify the structure of 124 Te. Since only few known experimental absolute transition probabilities are known, it is the purpose of the present study to extract absolute transition probabilities from lifetime measurements by applying the GRID (Gamma Ray Induced Doppler broadening) technique [15]. In Section 2 the experimental details and the analysis of the data are described, whereas section three gives the results of the lifetime measurements, the deduced transition rates as well as the energies of the resolved doublet at 2039 keV. The comparison of the experimental results with the theories is done in Section 4. Finally, in the last section we present our conclusions.

2. Experimental method The lifetimes of the levels of interest have been determined via the GRID technique [15], using the two-axis flat-crystal spectrometer GAMS4 [16] installed at the high-flux reactor of the Institut Laue-Langevin in Grenoble. The technique is based on the Doppler broadening of γ rays. After thermal neutron capture, the target nucleus finds itself in an excited state which will decay by γ -ray emission. The induced recoil causes the atom to move in the bulk of the target where it is gradually slowed down by collisions with the neighbouring atoms. All γ rays — emitted whilst the nucleus is still in flight — will thus show a Doppler broadened lineshape. The Doppler broadening of the measured lineshapes depends on four effects: the initial recoil velocity distribution, the slowing-down process in matter, the temperature of the target and the lifetime of the excited nuclear state which decays through the measured γ -ray transition. Provided that the first three processes are understood the observation of the Doppler broadening allows the determination of lifetimes in femtosecond to picosecond range. The determination of the broadening, which is of the order of some eV for γ -ray energies in the MeV region, requires an instrument with a resolution in the 1E/E = 10−6 region. This can be achieved with the two-axis flat crystal spectrometer GAMS4 [16] at the Institut Laue-Langevin (ILL) in Grenoble. In the present experiment, a target of highly enriched 123 TeO2 was used. A total of 760 mg of TeO2 , canned in a carbon container was exposed to a neutron flux of 5 × 1014

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Fig. 1. Line-profile of the 602 keV groundstate transition, measured in second order of reflection in dispersive and non-dispersive mode. The inner grey shaded region shows the line profile coming from dynamical diffraction theory. The dashed line represents the folding of dynamical diffraction theory with instrumental response. The solid line shows the fit for the thermal broadening, corresponding to the folding of dynamical diffraction theory, instrumental response and thermal Doppler-broadening.

cm−2 s−1 . Due to the high cross section of 420 b we have been able to determine the lifetimes of 8 levels with sufficiently good statistics. The instrumental response was determined using scans of the 602 keV transition in non-dispersive geometry [15] resulting in a FWHM of ∼ 1.3 eV. The contribution of the temperature of the target material to the broadening of the lines was deduced from scans of the same transition in dispersive geometry taking into account the known lifetime of 6.2 ps [17]. A thermal broadening corresponding to a thermal velocity of 382 ± 30 ms−1 was obtained. The measured line profile including the thermal broadening and the instrumental response is shown in Fig. 1. The inner grey shaded region shows the lineprofile resulting from the dynamical diffraction theory whereas the dashed line represents the folding of the instrumental response function with the dynamical diffraction theory. This line profile is then folded with the thermal Doppler broadening and is shown by the solid line in Fig. 1. Each transition of interest was measured several times (see Table 1). The slowing-down process is described in the mean free path approximation (MFPA) which is commonly used in GRID experiments (see [15] for more details). The initial recoil distribution is determined from the feeding pattern of the level of interest. In Table 1 the measured lines are shown together with information about the known part of the feeding. Since the feeding in most nuclei is only partly known, we have to make different assumptions for the remaining part of the feeding. The known part of the feeding ranges from 0% to 83% for the different levels of interest.

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Table 1 Levels of interest in 124 Te which have been measured. In column 2 the spin and parity of the level is displayed, the energy of the measured transition is given in column 3. The fourth column indicates the number of individual scans of a given transition, the next column the diffraction order for both crystals. The last column (feeding) represents the part of known incoming intensity compared to the outgoing intensity Ex [keV]

Iπ

Eγ [keV]

Number of scans

Order

Feeding

1324 2039 2039 1657 1248 2091 1883 3101

2+ 2 2+ 3 3+ 1 0+ 2 4+ 1 2+ 4 0+ 3 2−

722.8 713.8 1436.7 1054.5 645.9 1488.9 557.5 353.9

9 8 6 6 2 4 8 9

3 3 2 3 3 2 2 3

50% 1% 1% 0% 66% 26% 0% 83%

The unknown part of the feeding originating from multi-step cascades has been treated by different assumptions using extreme feeding scenarios and two-step cascades. To obtain a lower limit for the lifetime the minimal possible recoil has to be considered. This can be done by assuming that the remaining unknown feeding originates from a hypothetical 500 keV transition from a hypothetical intermediate level with an infinite lifetime τ → ∞. To find an upper limit the maximal possible recoil has to be considered. Strong primary transition — leading to this maximal recoil — are usually known. The next strongest scenario for maximal recoil can be simulated by a two step cascade where the lifetime of the intermediate level is supposed to be τ = 0. For this case the location of the hypothetical intermediate level has only minor influence as the two recoils caused by the two transitions (primary and secondary transitions) simply add up vectorially. The resulting lifetime limits are shown in Table 2. A more realistic approach is obtained by using a two-step cascade in which the lifetime and the energy of the intermediate level is varied. The resulting recoil distributions have then been used to deduce the lifetime. For more detail of this kind of analysis the reader is referred to a recent reference [18]. For a variation of the energy of the intermediate level and its lifetime τ a χ 2 -distribution is shown in Fig. 2. In this figure the χ 2 -distribution is shown for the example of the 557 keV-transition coming from the 0+ 3 -level at 1883 keV. A 3 clear minimum corresponding to a level lifetime of τ1883 = 1.12 ps is seen. The lifetime of the intermediate level was varied with τ = 0, 10, 100, 500 and 1000 fs and its energy was varied to be 2, 2.5, 3, 3.5, 5 and 6.5 MeV. The χ 2 -minimum corresponds to an intermediate level lifetime of τ = 500 fs and an intermediate level energy of 2.5 MeV. The so obtained lifetime value can be considered to be the most probable one of the level of interest but the results from the extreme assumptions have to be kept in mind.

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Table 2 Upper and lower limits for the lifetimes τ in 124 Te coming from extreme feeding scenarios and most probable lifetime-values τ in 124 Te as a result from the χ 2 -analysis Lifetime τ (ps)

Levels of interest Lower limit

τχ 2

Upper limit

min

2+ 2 2+ 3 3+ 1 0+ 2 4+ 1 2+ 4 0+ 3 2−

1324 keV 2039 keV 2039 keV 1657 keV 1248 keV 2091 keV 1883 keV 3101 keV

1.1 0.07 0.3 0.2 1.1 0.2 0.6 1.4

1.532 0.721 0.821 0.821 2.020 7 0.411 1.132 1.522

3.5 1.8 1.4 0.9 6.7 1.0 6.3 2.0

Fig. 2. χ 2 -distribution for different energies of the hypothetical intermediate level and its lifetime τ . Here the 557 keV-transition is shown.

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Fig. 3. The line shape of the 1054 keV transition measured in third diffraction order. The solid line is the fit to the measured γ ray, whereas the grey shaded line shows the instrumental response.

3. Results 3.1. Lifetimes and transition probabilities Following the above presented procedure we get for each level of interest a set of three values, the lower τmin and upper limit τmax of the lifetime and the most probable value τχ 2 from the χ 2 -analysis: min

τmin < τχ 2 < τmax . min

These values are shown in Table 2. In Fig. 3 the effect due to the lifetime compared to the contributions from thermal broadening and instrumental response is shown in a typical scan using GAMS4 for the example of the 1054 keV transition. The measured lifetime ranges and values allow the calculation of absolute B(E2) values for transitions decaying from a given state or at least a range of B(E2) values provided the branching ratios, conversion coefficients and mixing ratios are known. These transition probabilities in units of [e2 b2 ] are listed in Table 3. The values obtained with the extreme feeding assumptions — which are far from being realistic but provide limits based on the knowledge of the level scheme — yield lower or upper limits, respectively. Inbetween the most probable values for the transition probabilities are indicated. These values were obtained by using τχ 2 resulting from the χ 2 -analysis. At this place one has to note that min

+ the multipolarities of the γ rays decaying from the 2+ 3 and the 31 state are not known due to the doublet which is formed by these two levels. All angular correlation measurements will thus be obfuscated and the mixing ratios given in literature wrong. Due to this fact for

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Table 3 Transition probabilities for the levels 124 Te. The mixing ratio δ was taken from [9] and NDS [17]. For unknown δ a pure E2-transition was assumed. α are taken from [28]. The branching ratios B.R. are taken from [5] and from this experiment (see Fig. 6) Transition

Einitial

Efinal [keV]

2+ 1 → 01

603a

0

B(E2) [e2 b2 ]

Eγ (Upper limit) 603a

2+ 2 → 01 + 22 → 2+ 1

1324 1324

0 602

1324.51 722.78

+ 4+ 1 → 21 + 02 → 21

1248 1657

602 602

645.86 1054.51

03 → 2+ 2 2+ 3 → 01 + 2+ 3 → 21 + 2+ 3 → 41 + 23 → 2+ 2

1883 2039 2039 2039 2039

1325 0 602 1248 1324

557.46 2039.42 1436.68 790.8 713.9

+ 3+ 1 → 21 + 31 → 4+ 1

2039 2039

602 1248

1426.68 790.7

+ 3+ 1 → 22

2039

1325

713.8

+e 2+ 4 → 21

2091

602

1488.89

2 χmin

(Lower limit)

0.1136(1)a 0.002 0.3b 0.3c 0.6 0.3 2.5 0.01 0.078

0.0018 0.21b 0.2c 0.36 0.076 1.4 0.001 60.12d 0.008 60.13d

0.0008 0.09b 0.1c 0.1 0.07 0.2 0.0005 0.002

60.0008d 60.02d 60.6d 0.0006c

0.0002c

0.0001c

a NDS [17]. b δ from Warr et al. [9]. c δ from NDS [17]. d Pure E2-transition was supposed. e The B(E2) value for the transition down to the 2+ level given in several references [9,17] is 2

not given here, as the placement is not certain [9] and the mixing ratio not known at all.

transitions having the potential to be mixed we are only able to give upper limits for the B(E2) values decaying from this level doublet. 3.2. Discussion of the level doublet at 2039 keV The level at 2039 keV represented for a long time a puzzle, because many properties pointed to a 3+ assignment, while the groundstate transition required a 2+ assignment. From systematics and from Quasi-Particle-Model calculations for this energy a 3+ assignment is expected [10]. This is shown in Fig. 4 where the decay schemes of

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Fig. 4. Decay scheme of the 3+ level in 122 Te, 124 Te and 126 Te. The intensities are given in relative units [19].

Fig. 5. The γ -ray doublet at 1436 keV coming from the 2039 keV level doublet and populating the 2+ 1 level at 602 keV.

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Table 4 The measured γ -energies of transitions coming from the 2039 keV doublet in 124 Te Transition

γ -energy [keV]

+ Eγ (2+ 1 → 01 ) + Eγ (4+ 1 → 21 ) + Eγ (31 → 2+ 2) + Eγ (2+ → 2 3 2) + Eγ (22 → 2+ 1) + Eγ (3+ → 4 1 1) + Eγ (23 → 4+ 1) + Eγ (3+ → 2 1 1) + Eγ (23 → 2+ 1) + Eγ (2+ → 0 3 1)

602.729 (1) 645.853 (4) 713.776 (2) 713.906 (2) 722.783 (1) 790.711 (3) 790.837 (3) 1436.559 (5) 1436.689 (5) 2039.395 (20)

Table 5 Level energies for the level scheme shown in Fig. 6. The energies are relative to the 602.731(3) keV excitation energy of the 2+ 1 -level [17]. The brackets show statistical errors and errors taking into account the error of the NDS value [17], respectively

122 Te, 124 Te

Level

Level energy [keV]

2+ 1 4+ 1 2+ 2 3+ 1 2+ 3

602.731 (1) (3) 1248.584 (2) (4) 1325.517 (1) (3) 2039.296 (2) (4) 2039.425 (2) (4)

and 126 Te are compared. Since the γ -branching of this level depends on its population, Berendakov et al. [19] proposed already that there is a doublet with a 2+ level about 100 eV above the 3+ level. Warr et al. [9] found also experimental evidence for this doublet. With the extremely high energy resolution of the spectrometer GAMS4 the different transitions originating from the levels at 2039 keV can undoubtly be resolved. Fig. 5 shows the γ -ray doublet at 1436 keV coming from the 2039 keV level doublet and populating the 2+ 1 level at 602 keV. The difference in energy between the two peaks was found to be 129(5) eV. The energies have been determined from dispersive and non-dispersive scans of the respective transitions in several orders of reflections. From the angle distance between these orders the energy can be deduced. In Table 4 the resulting energies — corrected for recoil — are listed. One has to note that in the present work no effort was made to determine

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Fig. 6. γ -decay level scheme of the resolved doublet at 2039 keV. The energies are given relative to the 602.729(3) keV [17] ground state transition, only statistical errors are given (see also Table 5). The intensities of the transitions are based on the intensity of the 602 keV ground state transition and indicated behind the energy error.

absolute energy values. The energies are given relative to the 602.729(3) keV ground state transition as given in the Nuclear Data Sheets [17]. The γ -decay of the two levels at 2039 keV is shown in Fig. 6. The level energies were determined with a least squares fit of the level energies to the transition energies and given in Table 5. The resulting spacing of the level doublet at 2039 keV is 129(5) eV. Taking into account the reflectivities of the crystals given by the dynamical diffraction theory and the measured count rates an estimation of absolute intensities of the two transitions based on the intensity of the 602 keV ground state transition can be given.

4. Comparison of experiment and theory The values for the transition probabilities shown in Table 3 have been compared with results from different theoretical descriptions. First, we tried to reproduce the experimental data with the simple ansatz of a harmonic vibrator. Secondly, the values have been compared to calculations in the framework of IBM-1, where no distinction between neutron and proton bosons is made. Furthermore, the assumption of an intruder configuration is discussed in the IBM-1 as well as in the

C. Doll et al. / Nuclear Physics A 672 (2000) 3–20

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Table 6 Parameters for the U(5) and U(5)–O(6) model calculations Parameter for the IBM-1 model calculations ε

α

β

γ

η

pure U(5) [10] pure O(6) [9]

569.0 keV

43.3 keV

−25.6 keV 112.9 keV

−9.3 keV −10.5 keV

−59.1 keV

IBM-1 U(5)/O(6) + SU(3)-intruder configuration [9]

800.0 keV

IBM-1 U(5) [10] + SU(3)-intruder configuration

569.0 keV

Model

∆ 6 MeV 43.2 keV ∆ 5.75 MeV

−7.5 keV ζ −13 keV

−1.76 keV

−10 keV γ 26 keV

−25.6 keV ζ −13 keV

−9.3 keV γ 26 keV

IBM-2 model (allowing the distinction between neutron and proton bosons). Finally, a comparison with QPM calculations is also shown. We did not consider the particle–core coupling model (PCM) [20] as it was shown already by Warr et al. [9] that this model cannot describe the transition rates. The results from the different theoretical models are given in Table 7 where they are confronted to the experimental values for the transition probabilities. As the consideration of transition rates alone would be incomplete the theoretical models are also tested by means of the excitation energies. This comparison is shown in Table 8. The quality of the models can be characterised by a χ 2 -test between the experimental and theoretical B(E2) values. In Table 9 the standard deviations are shown for the different theoretical B(E2) values from the experiment in units of the B(E2) bandwidth given by the extreme feeding scenarios. The normalised standard deviation given by sP P x 2 − ( x)2 χ2 = n(n − 1) is related to the value of the deviations for the experimental B(E2) values from the theoretical B(E2) values in units of the bandwidth x=

B(E2)exp − B(E2)theo . B(E2)exp(max) − B(E2)exp(min)

For the energies the standard deviations are derived in the same way with the exception that the value of the deviation is given by x = Eexp − Etheo . They are shown in the lower part of Table 9. As almost all considered models have already been applied to the present isotope in publications, they are only briefly discussed below. The reader who is interested in details of the calculation is referred to the corresponding references.

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Table 7 Experimental and theoretical B(E2) values Transition

B(E2)exp [e2 b2 ]

B(E2)theo [e2 b2 ] H.V.a

U(5)b

O(6)c

U(5)+SU(3)d

U(5)/O(6)–SU(3)e

IBM-2f

IBM-2g

QPMh

0.1136 (1) )i 0.0008–0.002 0.09–0.3 0.1–0.6 0.07–0.3

0.1136 0.0 0.2272 0.2272 0.2272

0.1143 0.0 0.1877 0.1899 0.1688

0.1142 0.0044 0.1496 0.1496 0.0

0.1153 0.0 0.1919 0.1934 0.1978

0.1068 0.0005 0.1695 0.1728 0.0837

0.1136 0.0011 0.1527 0.1675 0.0897

0.1136 0.0010 0.1574 0.1689 0.0910

0.098 0.0095 0.1314 0.2815 0.4976

03 → 2+ 2 2+ 3 → 01 + 2+ 3 → 21 + 23 → 4+ 1 + 2+ 3 → 22

0.2–2.5 0.0005–0.01 60.12 0.0002–0.006 60.13

0.3408 0.0 0.0 0.1168 0.1947

)j )j )j )j )j

0.1525 0.0 0.0006 0.0 0.0

0.0032 0.000102 0.000102 0.0175 0.02074

0.0401 0.000036 0.0012 0.0010 0.0073

0.044 0.0 0.0002 0.0214 0.0015

0.0393 0.00009 0.000127 0.0257 0.0117

0.2423 0.00059 0.0224 0.0307 0.05063

+ 3+ 1 → 21 + 31 → 4+ 1 + 3+ 1 → 22

60.0008 0.004–0.02 60.6

0.0 0.0974 0.2434

0.0 0.0669 0.1599

0.0042 0.0435 0.1088

0.000002 0.0683 0.1638

0.0005 0.0536 0.1376

0.0017 0.0596 0.1477

0.00015 0.0581 0.1419

0.0764 0.2453 0.4104

+ 2+ 4 → 21

0.0001–0.0006

0.0

0.0

0.0

0.000007

0.0002

0.0025

0.000087

0.0003

a Harmonic vibrator. c O(6) [9]. e U(5) with O(6) admixture and SU(3) intruder configuration (see Warr et al. [9]). g Rikovska et al. [12] with increased Majorana force parameters, see text. i NDS [17].

b Pure U(5) see Schauer et al. [10]. d IBM-1, Schauer [10] et al. + SU(3) intruder configuration. f Rikovska et al. [12]. h M. Grinberg [29]. j Not in model-space.

C. Doll et al. / Nuclear Physics A 672 (2000) 3–20

2+ 1 → 01 2+ 2 → 01 + 2+ 2 → 21 + 41 → 2+ 1 02 → 2+ 1

C. Doll et al. / Nuclear Physics A 672 (2000) 3–20

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Table 8 Comparison of the experimental level-energies with theory Level Eexp [keV]

2+ 1 4+ 1 2+ 2 0+ 2 6+ 1 0+ 3 4+ 2 3+ 1 2+ 3 2+ 4 0+ 4 4+ 3

Etheo [keV] H.V.a

U(5)b

O(6)c

U(5)+ SU(3)d

IBM-2g

QPMh

603

626

389

627

662

611

610

599

1249

1206

1211

919

1206

1325

1206

1342

1066

1340

1311

1299

1290

1251

1338

1354

1368

1348

1657

1206

1656

1655

1629

1455

1617

1597

727

1747

1809

1757

1883

1809

)j

1591

1753

1958

1978

1973

2106

2032

1874

1610

2094

2072

2143

1958

1809

1962

1822

1951

1987

2102

2109

2210

2039 2039

1809

2063

1906

2031

2010

2074

2117

2068

1809

)j

2043

2008

1746

1937

2127

1700

2091

2412

)j

2721

2467

2296

2246

2263

2217

2153

2412

2148

2837

2161

2047

2255

2702

2505

2225

2412

)j

2574

2379

2256

2717

2366

2483

603)i

U(5)/O(6)– IBM-2f SU(3)e

a Harmonic vibrator. b Pure U(5) see Schauer et al. [10]. c O(6) [9]. d IBM-1, Schauer [10] et al. + SU(3) intruder configuration. e U(5) with O(6) admixture and SU(3)-intruder configuration (see Warr et al. [9]). f Rikovska et al. [12]. g Rikovska et al. [12] with increased Majorana force parameters, see text. h M. Grinberg [29]. i NDS [17]. j Not in model-space.

4.1. Harmonic vibrator

This model is characterised by the constant level-distance based on the difference of the first excited level energy to groundstate [21]. The anharmonicity in the level energies cannot be reproduced by these calculations. However, seen the simplicity of this approach, the relatively good agreement for the B(E2) values is quite astonishing. This fact shows that this nucleus has basically a vibrational character. Even the transitions which are in the framework of the harmonic vibrator model forbidden are experimentally clearly retarded.

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Table 9 Standard deviations of the experimental values from theory. The B(E2) values are expressed in units of the bandwidth of the B(E2) values resulting from the extreme feeding scenarios. For the + transition from the 2+ 3 state and the 31 state where the mixing ratios are not known due to the doublet structure formed by these two levels, pure E2 transitions have been assumed. For the energies absolute deviations are shown (see text) Standard deviations H.V.a U(5)b

of the experimental B(E2) values of the experimental energies

U(5)/O(6)– O(6)d SU(3)c

U(5)+ SU(3)e

IBM-2f

IBM-2g

QPMh

1.8

1.6

0.94

2.0

1.2

1.7

0.98

34.9

222

19

166

339

118

156

143

361

a Harmonic vibrator. b Pure U(5) see Schauer et al. [10], four levels are outside the model space. c U(5) with O(6) admixture and SU(3)-intruder configuration (see Warr et al. [9]). d O(6) taken from Warr et al. [9]. e IBM-1, Schauer [10] et al. + SU(3) intruder configuration. f Rikovska et al. [12]. g Rikovska et al. [12] with increased Majorana force parameters. h QPM calculation by M. Grinberg [29].

4.2. IBM-1 4.2.1. The pure U(5) limit The parameter for these calculations are taken from Schauer et al. [10] and are listed in Table 6. These calculations are dealing with a quadratic term in the U(5) Hamilton operator. For the numerical calculations a slightly changed version [22] of the computer code OCTUPOLE [23] has been used. The parameters for the E2 operator are derived from the 21 → 01 groundstate transition (e2 ) and the quadrupole moment (for the parameter χ ). Table 9 shows that the energies are well reproduced by Schauer et al. [10] but several states are not in the model space (see Table 6) rendering the description incomplete. For the B(E2) values the deviations are also small but one must keep in mind that several states are simply not described in this model. The decay of the 23 state, for instance, is not integrated at all and the problems are simply loaded on the intruder configuration. It is thus clear that an alternative solution has to be searched for. 4.2.2. The pure O(6) configuration This calculation takes the parameters from the work of Warr et al. [9]. Although the sequence for the low lying levels is better reproduced than in the U(5) case, the description of the energies is worse. Especially, the energy of the 2+ -level at 603 keV is poorly described (389 keV). Concerning the transition rates a crucial point is the fact that the 0+ (σ = N − 2) state in the O(6) description should exhibit in first order no decay to lower lying states. In the present case the 02 is assigned to be the (σ = N − 2) 0+ state and should

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thus not decay to the lower lying states at all. Experimentally, however, this transition has quite a large value. Assigning the third excited 0+ level to this σ = N − 2 state even makes the situation worse as the experimental transition is yet bigger. For this severe reasons we can exclude the pure O(6) configuration. 4.2.3. U(5) with O(6) admixture and SU(3)-intruder configuration One can now try to combine the advantages of both dynamical limits described above by deviating from the pure symmetry limits into intermediate regions. In this so called transitional regions the Hamiltonian consists of operators from the two different limits. Starting from a basis made by the U(5) limit a slight O(6)-admixture is added. Although this approach improves the level sequence for the two-phonon triplet, the problems in the three-phonon states remain and the number of 0+ and 2+ states predicted is still too low [9]. In the neighbouring Cd isotopes [24] the description of the nucleus was improved by the introduction of a γ -soft intruder configuration. Using the intruder analog formalism (see for instance [25]) the possible intruder configuration in the Te isotopes should be analog to the ground state configuration of the Ba isotone [13]. As the Ba isotopes exhibit more a deformed SU(3) structure, a SU(3) intruder configuration is considered for the Te isotopes. Also for this calculation we adopted the set of parameters given by Warr et al. [9] which are shown in Table 6. The small O(6) admixture is represented by the parameter η. The excitation energies show a fair agreement (see Table 9). The transition probabilities are close to the experimental values and the pattern of the data is well reproduced. It is important to note that nearly one-to-one mixing of the two first excited 0+ states occurs which makes it possible to distribute the two-phonon to one-phonon annihilation strength over the two states. 4.2.4. U(5) configuration with SU(3) intruder states Seen the fact that the U(5) description proposed by Schauer et al. [10] can describe very accurately the chosen vibrational states, the remaining states should belong to the intruder configuration. We thus tried to add a SU(3) configuration as described above. The energies of this coexisting structure are determined by the levels excluded by Schauer et al. [10]. The parameters for this calculation are also listed in Table 9. The description of the energies is now complete and yields an accurate picture of the experimental energies. The description of the transition probabilities, however, is worse than in the previous approach. The 0+ 3 -state in this model is supposed to be the bandhead of the intruder configuration but the transition probability down to the 2+ 2 differs clearly from the experimental value. This is the major drawback of this ansatz. Furthermore, the decay of the 2+ 3 state is not as good reproduced as in the previous approach. The reason for this lies probably in the fact that for the description of small transitions minor cancellation effects can play an prominent role. 4.3. IBM-2: U(5) configuration and intruder states Due to the high number of 2+ states in the 2 MeV region (there are four 2+ levels between 2 and 2.5 MeV), even the integration of an intruding configuration cannot describe

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Table 10 Experimental and theoretical B(M1) values Transition

+ 2+ 4 → 21

B(M1)exp [µ2N ]

0.012–0.058

B(M1)theo [µ2N ] IBM-2a

IBM-2b

0.008

0.022

a Rikovska et al. [12]. b Rikovska et al. [12] with increased Majorana force parameters, see text.

all observed states. The model space can be enlarged by the proton–neutron degree of freedom taken into account by the IBM-2 model. Herein, additional states, so called mixed symmetry (ms) states, appear. In a vibrational nucleus the lowest lying ms level should be a 2+ level. Only recently such states have been identified experimentally [26] in the neighbouring isotope 112 Cd at an excitation energy of about 2.2 MeV. Hence, these states are the ideal candidates to explain the high number of observed 2+ levels between 2 and 2.5 MeV. Calculations in the framework of the IBM-2 including a SU(3) intruder configuration for the Te isotopes have been made by Rikovska et al. [12]. The reproduction of the energies is fair and also the transition rates are described to a good extent (see Tables 8, 3 and 9). + In the calculation of Rikovska the 2+ 3 state is the ms state whereas the 24 level belongs to the intruder configuration. And it is especially the transition from the latter state which is not very well described within this approach. The 2+ ms state should show a large B(M1) value for the decay to the first excited 2+ level with a small branch to the ground state [27]. + Whereas the 2+ 3 state at 2039 keV shows a more complicated decay pattern, the 24 state at 2091 keV decays to the 21 state by a γ ray with a predominant M1 component (99%). The transition down to the second excited 2+ state decaying from this level is weak and the mixing ratio not known. Moreover the placement is uncertain [9]. This might suggests that the fourth and not the third 2+ level is the ms state. Moreover, the fifth 2+ state could have an important component of the ms 2+ level, as it decays also via a predominant M1 transition (96%) down to the 2+ 1 state. We increased thus the Majorana force parameters from Rikovskas calculation by a factor of two in order to increase the energy of the ms states (ξ1 = ξ3 = 2ξ2 = 0.36). This change improved not only the description of the B(E2) values but also slightly the overall excitation energy agreement (see Table 9). Furthermore, as can be seen in Table 10 the + description of the B(M1) value from the 2+ 4 state down to the first excited 2 state is + improved in this approach. Due to these facts we conclude that the fourth 2 should be described as ms state (having at least an important component of this excitation) whereas the 2+ 3 belongs mainly to the intruder configuration. 4.4. QPM In this section we consider the calculation presented by Schauer et al. [10]. Slight differences in the results of the calculation given by Schauer are due to an enlargement

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of the basis in the present calculation. One has to note that the parameters have not been individually adjusted to 124 Te but are resulting from a global adjustment for all tellurium isotopes and that no intruder states are included. Therefore, it is not astonishing that the energies differ quite a bit from the experimental values. Especially, the energy of the second excited 0+ level is not well described. Although the decays of the lower lying levels can be described to some extent problems appear in the description of the decay of the 2+ 3 + and the 3+ states. It is very interesting to note that this calculation describes the fourth 2 1 + level as the isovector 2 state corresponding to the ms level in the IBM-2 description. The B(E2) value being correctly described gives an additional hint to the correctness of the interpretation of this state being the ms level.

5. Conclusion The nucleus 124 Te was investigated with the GAMS4 spectrometer at the ILL in Grenoble. Due to the high energy resolution a long questioned γ -ray doublet could be resolved and lifetimes from levels in 124 Te have been determined by the GRID-method. The lifetime measurements and the resulting B(E2) values show a clear disagreement with respect to the assumption that 124 Te can be described as a γ -soft nucleus. The pure vibrational assumption is more successful. The general pattern of the absolute B(E2) values is reproduced what is astonishing regarding the simplicity of this model. The description, however, remains incomplete. The nucleus exhibits thus neither the pure U(5) nor the pure O(6) dynamical limit of the IBM corresponding to the limiting cases of the collective model. In the framework of the IBM-1 the description using a transitional U(5)/O(6) structure for the ground configuration combined with a SU(3) intruder configuration is clearly more successful. Spurred by the high number of 2+ states above 2 MeV excitation energy and the Ml + characteristics of the 2+ 4 → 21 transition the IBM-2 was considered. The here presented configuration mixing approach in the IBM-2 framework based on Rikovskas parameter set [12] but using an increased Majorana force is the most successful description for the nucleus 124 Te. Assuming that the 2+ 4 state has an important component of the ms state the present approach can not only describe the B(E2) values but also the above mentioned magnetic transition rate and the excitation energies.

Acknowledgements The work was supported by the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Bonn, Germany. The authors are grateful to Prof. M. Grinberg for the QPM calculations. Dr. J. Jolie is acknowledged for providing his adapted version of the code OCTUPOLE and for valuable discussions concerning the interpretation of the data.

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