Decay properties of low-lying collective states in 132Ba

Nuclear Physics A 697 (2002) 75–91 www.elsevier.com/locate/npe

Decay properties of low-lying collective states in 132Ba A. Gade ∗ , I. Wiedenhöver 1 , H. Meise, A. Gelberg, P. von Brentano Institut für Kernphysik der Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany Received 22 March 2001; revised 13 July 2001; accepted 24 July 2001

Abstract The decay properties of low-lying collective states in 132 Ba were studied by means of γ spectroscopy following the β-decay of the 2− ground state (T1/2 = 4.8 h) and a 6− isomer (T1/2 = 24.3 min) of 132 La. The lanthanum nuclei were produced at the Cologne FN TANDEM accelerator using the reaction 122 Sn(14 N, 4n)132 La. The γγ coincidences and singles spectra were measured with the OSIRIS-cube spectrometer. Beside ground and quasi-gamma band many other low-lying states were observed. The γγ angular correlations were analyzed to assign spins to the excited states, and to determine the multipolarities of the depopulating the γ transitions. We also confirmed the expected dominant E2 character of transitions in the quasi-gamma band and from the quasi-gamma + to the ground band but with a certain deviation: the decay 6+ 2 → 61 shows an unexpected large M1 fraction. Also the decays of the third, fourth and fifth 2+ states are dominated by M1 radiation. 132 Ba. The experimental data are compared A level at 1660 keV could be identified as the 0+ 3 state in with calculations using the proton–neutron interacting boson model (IBM-2). Good agreement is reached in the vicinity of the O(6) limit.  2002 Elsevier Science B.V. All rights reserved. PACS: 21.10.Re; 23.20.En; 23.20.Gq; 21.60.Fw; 27.60.+j Keywords: Radioactivity 132 La(β+ ) [from 122 Sn(14 N, 4n)]; Measured Eγ , Iγ , γγ-coin., γγ(Θ); 132 Ba deduced levels, J , π, δ; Comparison with IBM-2 calculations.

1. Introduction In the mass region A ≈ 130 the xenon, barium and cerium nuclei may start to form a transitional path between closed shell structure and strong deformation. The even–even nuclei of this region seem to be soft with regard to the γ-deformation at an almost maximum effective triaxiality with γ ≈ 30◦ [1,2]. The low-lying states show a rich * Corresponding author.

E-mail address: [email protected] (A. Gade). 1 Present address: NSCL, Michigan State University, East Lansing, MI 48824, USA.

0375-9474/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 2 4 7 - 7

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collective structure discussed in the framework of various nuclear models, such as the Rigid Triaxial Rotor [3–5], the triaxial Rot–Vib Model [6–9], the nucleon-pair shell model [10, 11], the algebraic Interacting Boson Model (IBM) [12,13] and its proton–neutron extension IBM-2 [14]. As shown in Ref. [15], the excitation spectra of the even–even nuclei in the Xe–Ba mass region can be well approximated by the O(6) dynamical symmetry limit of the IBM, which is the algebraic analogue to the geometric γ-unstable rotor model by Wilets and Jean [16]. At the top the aim of our experiment is to investigate the decay properties of the low-lying collective states in 132 Ba especially under the aspect of E2/M1 multipole mixing ratios. For the even-mass xenon nuclei, reactions of the nonselective (α, n) type at the Coulomb barrier served as a powerful method to populate these states [17–19]. The (α, n) reaction is not feasible for producing Ba nuclei due to the need of xenon targets. Therefore most knowledge of the low spin structure in the different barium isotopes is due to γ spectroscopy following β decay [20–22], investigations using (n, n ) reactions [23], (γ, γ ) measurements [24] and heavy-ion collisions [25]. In this work we present the detailed experimental data from the analysis of γγ angular correlations in 132 Ba populated by β decay which significantly improve our knowledge of this nucleus and we compare the excitation spectrum and the determined E2/M1 mixing ratios to a calculation in the framework of the proton–neutron Interacting Boson Model (IBM-2) near the dynamical O(6) symmetry.

2. Experiment For the study of 132 Ba we produced radioactive 132La in the center of the OSIRIS cube spectrometer at the Cologne FN TANDEM accelerator facility using the fusion–evaporation reaction 122 Sn(14N, 4n)132La at a beam energy of 62 MeV. We applied a cyclic procedure of activation with the beam on target for one second, followed by one second of measuring the γγ coincidences and γ-singles off-beam. The spectrometer was equipped with five anti-Compton high-purity germanium detectors at the faces and the EUROBALL CLUSTER detector positioned at top of the cubic target chamber. Two unshielded detectors at corners of the cube provided an additional angle of 54.7◦ for the γγ angular correlation analysis. The detectors were calibrated for energy and efficiency with a 226 Ra source. In a sorting process the energies of the coincidence events were sorted into 8k × 8k matrices. The information about the coincidence time was used to subtract random coincidences. One matrix comprising all coincidences between the six shielded detectors was used to compose the level scheme of 132Ba. In Fig. 1 a part of a spectrum gated on the 464 keV transition + (2+ 1 → 01 ) is displayed and in Fig. 2 we present a part of the level scheme, containing the prominent collective levels with positive parity, for example the ground band, the even and odd part of the quasi-gamma band and several states which are discussed later. Three additional matrices were sorted, according to the angles between the detector axes. These matrices contain coincidence events detected by pairs of detectors with relative angles of 90◦ , 180◦ and 54.7◦ , respectively.

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Fig. 1. Spectrum observed following the β-decay of 132 La: part of a spectrum obtained by gating + on the 2+ 1 → 01 transition. Due to measuring off-beam the γ spectrum is extremely clean with low background. The 2− and 6− isomers in 132 La have half-lives of 4.8 h and 24.3 min, respectively.

3. Angular correlations The analysis of angular correlations of photons emitted following the β decay provides a possibility of determining spin values and multipole mixing ratios. In the following we refer to a coincidence event of two successive γ transitions with multipole mixing ratios δ1 and δ2 connecting three levels with spins Ii , I and If : δ1

δ2

Ii → I → If . The angular correlation intensities were determined by fitting the peak areas in coincidence spectra obtained by gating in the three γγ matrices which were sorted according to the relative angles of detectors pairs in our setup (see previous section). The areas were corrected for the calibrated coincidence efficiency of the respective detector pairs and compared to theoretical correlation patterns for different spin and multipolarity hypotheses, calculated following [26,27]. In this experiment only the mixing of electric quadrupole (E2) and magnetic dipole (M1) radiation is important. The square of δ equals the ratio of the E2 and M1 transition probabilities. The sign of δ is determined by the relative phases of the E2 and M1 matrix elements. In literature there exist two conventions for defining the sign of the mixing ratio δ. Our analysis follows the convention of Ref. [27].

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Fig. 2. Part of the level scheme of 132 Ba. Presented are collective states with positive parity, containing the ground band, the quasi-gamma band the additional 0+ and 2+ states which are discussed in the text.

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It should be noted that the angular correlation pattern has much stronger variations caused by the P4 (cos θ ) term than the angular distributions of γ transitions observed inbeam with respect to the beam axis. In many cases this property enables the determination of unique multipole mixing ratios with only the three angles provided by our experimental setup. In fact, the concentration of the coincidence statistics on only three angles results in a very high sensitivity of this method. This technique proved its special usefulness already in the analysis of the nuclei 132 Ce [28] and 134 Ce [29] populated in β decay. If all spins in the two-photon cascade are known we compare the efficiency corrected experimental intensity ratios W (E1 , E2 ; θ )/W (E1 , E2 ; 90◦) to the theoretical values W (Ii , δ1 , I, δ2 , If ; θ )/W (Ii , δ1 , I, δ2 , If ; 90◦). In our analysis we took into account only coincidence cascades in which one transition is known to be a pure E2 or E1 decay. By this condition we were able to fix one multipole mixing ratio and derived the unknown δ by varying this parameter in a χ 2 fit. In order to demonstrate the power of this method, we give in Table 1 the results of the angular correlation analysis for negative-parity states in 132 Ba. For the parity-changing decays we were able to confirm the expected nearly pure E1 character of the emitted radiation. Table 1 Results of the γγ angular correlation analysis for negative-parity states in 132 Ba Ei [keV]

Eγ [keV]

Transition

δ

Dominant

2026.9 2068.6

899.2 940.9 1036.8 1604.0 175.2 187.6 991.9 1188.4 1909.8 305.8 645.0 1342.7 2102.8 623.0 569.1 498.9 859.3 2959.7 3171.2

+ 4− 1 → 41 − 31 → 4+ 1 + 3− 1 → 22 − 31 → 2+ 1 + 5− 1 → 43 − 51 → 6+ 1 + 5− 1 → 41 − 3 → 2+ 2 + 3− 3 → 21 − 33 → 3− 1 + 3− 3 → 42 + 3− 3 → 22 − 34 → 2+ 1 + 3− 4 → 43 − 34 → 2+ 4 − 3− 4 → 31 − 35 → 3− 1 3− → 2+ 1 1− → 2+ 1

−0.02 ± 0.03 −0.03 ± 0.04 −0.04 ± 0.16 0.02 ± 0.02 0.01 ± 0.03 0.01 ± 0.02 0.03 ± 0.01 −0.11 ± 0.08 −0.02 ± 0.01 −1.13
δ
−0.04 0.06 ± 0.05 0.15 ± 0.14 −0.02 ± 0.01 0.06 ± 0.03 −0.06 ± 0.04 −1.03
δ
−0.08 −1.84
δ
0.33 −0.02 ± 0.03 −0.01 ± 0.04

E1 E1 E1 E1 E1 E1 E1 E1 E1

2119.5

2220.1 2374.4

2567.3

2927.8 3423.8 3635.2

E1 E1 E1 E1 E1

E1 E1

The columns give the excitation energy, the transition energy of the analyzed decay and the determined multipole mixing ratio δ. For parity-changing decays, δ equals the ratio of M2 and E1 transition rates. We observed the expected dominant E1 decays for those transitions.

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Table 2 Experimental E2/M1 mixing ratios for decays of low-lying collective states Ei [keV]

Eγ [keV]

Transition

δ

1031.8 1511.2

2046.3 2240.5 2492.3

567.3 1046.6 479.5 383.3 654.0 1221.2 601.8 816.6 1533.7 966.5 1581.8 308.6 1364.6

+ 2+ 2 → 21 + 3+ 1 → 21 + 31 → 2+ 2 + 3+ 1 → 41 + 23 → 2+ 2 + 2+ 3 → 21 + 42 → 4+ 1 + 4+ 3 → 41 + 24 → 2+ 1 + 2+ 4 → 22 + 25 → 2+ 1 + 6+ 2 → 61 + 4(6) → 4+ 1

14+3 −2 2.19 ± 0.08  12 6±1 0.28 ± 0.08 −0.25 ± 0.02 −2.6 ± 0.2 0.03 ± 0.06 0.02 ± 0.02 0.11 ± 0.06 −0.02 ± 0.02 −0.2+0.3 −0.4 0.40 ± 0.05

2505.4

2040.7

1685.8 1729.4 1944.3 1998.2

(2) → 2+ 1

−0.11 ± 0.03

δ 2 [%] 1+δ 2

99.5 ± 0.2 83+1 −1  99 97+1 −1 7+4 −3 6+1 −1 88+2 −2
0.16
0.8 1.2+1.6 −1.0
0.16 4+22 −3 14 ± 3
+0.7  1.2−0.6

Dominant E2 E2 E2 E2 M1 M1 E2 M1 M1 M1 M1 M1 M1 M1

In the last column the deduced T (E2)-fractions δ 2 /(1 + δ 2 ) are additionally listed. We found the expected large E2-fractions for the decays in the quasi-gamma and from the quasi-gamma to the + + + ground band. But for the 6+ 2 → 61 transition and the decays of the 23 and 24 states we observed large M1-fractions.

Table 2 shows the experimental E2/M1 mixing ratios for several decays in the quasigamma band, from the quasi-gamma to the ground band and for the decays of other prominent collective states to the bands mentioned above. We confirmed the expected dominant E2 transitions in the quasi-gamma and from the quasi-gamma to the ground band, + but we additionally found certain deviations. The 6+ 2 decays to the 61 state dominantly by + + + M1 radiation and also the transitions of the 23 , 24 and 25 states are nearly pure M1 decays. In the next section we will discuss these M1 fractions in the framework of an IBM-2 calculation. In the case when the the spin of the three states belonging to a coincidence cascade is unknown, we compared the experimental ratios W (180◦ )/W (90◦ ), W (55◦ )/W (90◦ ) to the theoretical ones calculated for different spin hypotheses. In cases where one finds large differences in the χ 2 minima for the various spin assumptions an unique spin assignment is possible. Notice that it is often necessary to examine the angular correlations in several two photon cascades before the missing spin assignment can be determined unambiguously or at least restricted to two possibilities (Table 3). For example we analyzed the 1660 keV level, assigned as the 2+ 3 state in Ref. [21]. We were able to exclude this spin assignment by analyzing the angular correlations for + both transitions depopulating this level to the 2+ 1 and to the 22 state. Testing various spin + 132 hypotheses establishes this level as the third 0 state in Ba as suggested on the basis of

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Table 3 χ 2 -test of spin hypotheses for 132 Ba Elevel [keV]

Eγ [keV]

2505.4

2040.7

2876.7

2412.1 1845.0

3663.8

2632.2

Transition

δ

χ2

Conclusive spin assignment

2 → 2+ 1 3 → 2+ 1 1 → 2+ 1 2 → 2+ 1 1 → 2+ 2 2 → 2+ 2 1 → 2+ 2 2 → 2+ 2 3 → 2+ 2

−0.11 ± 0.06 0.81 ± 0.11 −0.05 ± 0.02 0.60 ± 0.06 0.02 ± 0.13 0.64 ± 0.27 −0.56 ± 0.08 −0.19 ± 0.15 1.05+0.60 −0.38

0.2 5.4 4.3 19.6 0.0 0.8 0.3 3.4 3.0

→ (2) → (1) → (1) → (2+ ) → (1+ )

Listed are the excitation energy Elevel , the transition energy of the investigated decay and the multipole mixing ratio and χ 2 value gained under different spin assumptions. In the last column we give the most probable spin assignment concluded by comparing the χ 2 values of the different spin hypotheses.

weak evidence in the framework of (p, t) cross sections [30]. If spin 2 h¯ would be allowed no accordance between experimental and calculated intensity ratios is obtained whereas the spin hypothesis 0+ led to an acceptable agreement. The angular correlation analysis of the 1660 keV level is summed up in Fig. 3.

4. IBM-2 calculations In order to describe the observed excitation energies and electromagnetic transitions, the experimental results have been compared to IBM-2 calculations in the vicinity of the dynamical O(6) symmetry. The following Hamiltonian was used [13]: π · Q ν + M πν + V ππ + V νν ,  = (nˆ dπ + nˆ dν ) + κ Q H     † (2) (2) ρ = d s + s † d˜ Q + χρ d † d˜ ρ , ρ = π, ν, ρ

where

(1) (2)

are the quadrupole operators,  † †  (2)  † (2) πν = 1 ξ2 sν dπ − dν† sπ · sν d˜π − d˜ν sπ M 2   (k)  (k) + ξk dν† dπ† · d˜π d˜ν

(3)

k=1,3

is the Majorana interaction and  1  (L)  (L) ρρ = cρL dρ† dρ† · d˜ρ d˜ρ , V 2 L=0,2,4

ρ = π, ν,

(4)

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Fig. 3. Angular correlation patterns for the analysis of the 1660 keV level. We compare the efficiency corrected intensities (90◦ -, 180◦ - and 55◦ -coincidences corresponding to groups 1, 2 and 3) of the two observed depopulating transitions to the calculated results for spin hypothesis 0+ on the left and for the assumption spin 2 on the right. For both decays the agreement between experimental values and hypothesis spin 0+ is acceptable whereas under the assumption of spin 2 no accordance is reached even in the χ 2 minimum, which is plotted here.

an interaction between identical bosons. The E2-transition strengths were calculated by using the operator π + eν Q ν , T(E2) = eπ Q

(5)

where eπ and eν are boson quadrupole effective charges. The M1 operator is given by   3
 ν ,  gπ Lπ + gν L (6) T (M1) = 4π √ ρ = 10 [dρ† d˜ρ ](1) is the angular momentum operator of either kind of bosons, where L and gπ and gν are the proton and neutron boson g-factors, respectively. For the description of M1 transitions in the interacting boson model, one needs to consider the proton–neutron degrees of freedom, through the concept of F-spin [13,14,31]. The F-spin is the analog of isospin for bosons. A boson has F = 1/2 and the projection 1/2 and −1/2 for a proton or neutron boson, respectively. A basis state is characterized by two quantum numbers: the F-spin F and the projection F0 = (Nπ − Nν )/2. Here, Nπ 2 operator has the and Nν are the proton and neutron boson numbers, respectively. The F eigenvalue F (F + 1). The values of F are

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83

|F0 |
F
(Nπ + Nν )/2 = Fmax .

(7)

The states with F = Fmax are totally symmetric and they have the lowest energy. States with F < Fmax are called mixed symmetry states (MSS) [31]. These states contain at least one antisymmetric pair of bosons. Besides, M1 transitions between totally symmetric states (F = Fmax ) are forbidden [32]. Therefore, if M1 transitions occur between low-lying collective states, these states can be described in the IBM-2 only through admixtures of components with mixed symmetry (F < Fmax ). This allows to interpret the occurrence of M1 transitions between low-lying collective states as an indicator of F-spin mixing. The dynamical O(6) symmetry can only be fulfilled by choosing χπ = χν = 0 or L = c L and  is the same for proton approximated with χs = 12 (χπ + χν ) ≈ 0. If we use cπ ν 1 and neutron bosons the size of χν = 2 (χπ −χν ) = 0 determines the F-spin breaking which is responsible for M1 transitions. The aim of our calculation is to reproduce the observed decay properties of the low-lying collective states. The numerical diagonalization has been carried out by using the NPBOS code [33]. The values of the main parameters of the Hamiltonian are given in Table 4. We choose κ, , cLπ = cLν and χs to describe the excitation spectra of 132 Ba and χν , ξ1 , ξ2 and ξ3 in order to reproduce M1 fractions and the presumed positions of mixed-symmetry states. Due to the lack of information on the 1+ scissors mode in 132 Ba, ξ1 was fitted to reproduce the position of the known 1+ states at about 2.9 MeV in the neighboring even barium isotopes. + ξ1 = ξ3 was assumed because 1+ sc and 3ms should belong to the same isovector multiplet. ξ2 was chosen to position the 2+ ms state at about 2 MeV because at this excitation energy + 2ms states in N = 84 nuclei [34,35], in 128 Xe [36], 126 Xe [19], 134 Ba [23] and 136 Ba [24] have been identified as (fragments of) the lowest mixed symmetry state predicted by the IBM-2. In Fig. 4 we show the the results for the fit of the energy levels. Good agreement is reached for the ground band, the lower part of the quasi-gamma band and the second and third 0+ states. The additional 2+ states are not equally well fitted. This may indicate a common feature in the IBM-2 because also in our calculations on 126Xe [19] we found a very similar deviation from the experimentally observed energies of these additional 2+ Table 4 IBM-2 parameters

132 Ba



κ

χπ

χν

cρ0

cρ2

cρ4

ξ1 = ξ3

ξ2

0.94

−0.297

−0.092

0.042

−0.980

−0.794

−0.500

0.280

0.060

All parameters in MeV with exception of χπ and χν . For the transition operators we choose eπ = 13.3 e fm2 , eν = 11.3 e fm2 , gπ = 0.9 µN and gν = 0.1 µN . The effective boson charges and + boson g-factors were fitted in order to reproduce the experimental B(E2; 2+ 1 → 01 ) strength [40] + and the M1 strength for the decays of possible mixed-symmetry states, B(M1; 1sc → 0+ 1 )IBM-2 = + + 2 2 0.21 µN and (B(M1; 2ms → 21 )IBM-2 = 0.18 µN , consistent with the experimentally known data for 134 Ba [23] and 136 Ba [24].

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Fig. 4. Comparison of the experimental and calculated excitation spectra. A satisfactory agreement is reached for the ground band, the lower part of the quasi-gamma band and the second and third 0+ state. The decreasing level spacing in the higher part of the quasi-gamma band is due to backbending effects which are outside of the IBM-2. The levels are arranged in τ multiplets as explained in the text. + excitations. The decreasing level spacing between the 4+ 2 and 62 state is probably due to backbending effects which are outside of the simple IBM-2. From the wave functions and the energy spectra we consider 132 Ba on a transitional path between the O(6) and U (5) limit but closer to the γ-soft description. Along the transition between these two limits the d-boson seniority τ (IBM-1) is a good quantum number [13]. The corresponding IBM-2 labels (τ1 , τ2 ) reduce to (τ, 0) for the totally symmetric states [13] and therefore τ is used in Fig. 4 to classify these states.

4.1. E2 transitions In Table 5 we compare the experimentally determined B(E2) ratios to the theoretical predictions. In the cases of unknown multipole mixing ratios, the experimental values only serve as upper limits. We reached a good agreement for the decays in the quasi-gamma band and especially every E2 transition suppressed by the selection rules in the IBM-2 is very weak indeed. The decay pattern of the 0+ 3 state disagrees with the calculation. This + discrepancy is of minor importance because the transition to the 2+ 1 and 22 state is heavily + suppressed in the IBM-2 calculation and predicted to be very weak B(E2; 0+ 3 → 21/2 )
4 2 50 e fm . Large values of δ and resulting dominant E2 fractions could be observed for the E2allowed transitions (+τ = ±1 in the O(6) limit of the IBM) in the quasi-gamma band and for decays from the quasi-gamma to the ground band. The experimental and theoretical E2

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Table 5 Experimental and theoretical B(E2) ratios for the decays in the ground and quasi-gamma band B(E2) ratio

Intensity ratio

+ 2+ 2 →01

2+ 1 + 31 →2+ 2 4+ 1 2+ 1 + 4+ →2 2 2 4+ 1 2+ 1 3+ 1 + 0+ 2 →22 2+ 1 + 03 →2+ 2 2+ 1 + 2+ 3 →31 0+ 2 2+ 2 2+ 1 0+ 1 + 4+ 4 (3) →31 4+ 2 4+ 1 2+ 1 2+ 2 + 5+ →3 1 1 4+ 2 4+ 1

exp

exp

IBM-2

54

2.7(4)

0.05

100

100

100

100

100

100

8

38(6)

31

60

2.6(4)

0.06

100

100

100

40

73(10)

89

35

1.8(3)

0

0.15a,b


50(11)

0.5

100

100

100


37


0.7(1)

0.2

24

100

32

100

17(4)

100

0.8a,b


86(12)

90

1.0a,b

100

100

30

1.2(9)

0.2

100

0.01(1)

0

100

2.8(4)

0.2

72.5b

100

100

80b


1516(210)

87

100b


9(1)

0

12.8b

0.08(1)

0

42.5b

2.4(3)

0

100

100

100

7.3(8)b


45(7)

45

19


2.2(3)

0

In the last two columns we compare the B(E2) ratios deduced from the experiment with the theoretical predictions of our IBM-2 calculation. Additionally in the first column the branching ratios (intensity ratios) for the decays of the prominent collective states are shown. The errors of the branching ratios are generally 10% unless particular values are given. When the multipole mixing ratio is unknown, the values listed serve as upper limits. We compare the 4+ 4 state to the calculated 4+ state. 3 a Transitions not observed in the present experiment. b Values taken from [21].

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Table 6 Comparison of experimental and calculated multipole mixing ratios and deduced E2-fractions δ 2 /(1 + δ 2 ) for transitions which are E2-allowed in the IBM-2 for 132 Ba Elevel [keV]

Eγ [keV]

Transition

δ

1031.8 1511.2

567.3 479.5 383.3 601.8

+ 2+ 2 → 21 + 31 → 2+ 2 + 3+ → 4 1 1 + 42 → 4+ 1

14+3 −2  12 6±1 −2.6±0.2

1729.4

δ 2 [%] 1+δ 2

99.2±0.2  99 97+1 −1 88+2 −2

2 δibm [%] 2 1+δibm

94 99.4 98 95

Our experiment confirms the expected large E2 fraction for these transitions between totally symmetric states.

fractions for these transitions with +I < 2 are compared in Table 6. The experimental data confirm the expected large E2 fractions. 4.2. M1 transitions The mechanism of generating M1 transitions for nuclei far from shell closure can involve either a quasiparticle part ∝ gqp Lqp and/or a proton–neutron collective term ∝ gπ Lπ + gν Lν . During our investigations of 132 Ba we found an example for a quasiparticle induced M1 transition and also M1 decays which may be interpreted as proton–neutron collective; both cases will be discussed in the following sections. + Following the selection rules of the IBM the transition 6+ 2 → 61 is expected to be dominated by E2 radiation. The experimental E2/M1 mixing ratio δ equals −0.2 (Table 2), that means the decay is nearly of pure M1 character (3.8% E2 fraction). This M1 dominance may be related to backbending. The wave function of the 10+ 1 state has a strong −2 + (νh11/2)10+ component mixed with a weak boson 10 one [37]. The noticeable lowering of the 10+ 1 state indicates that the mixing is due to a strong quasiparticle–core interaction. Therefore it is natural to expect two-quasiparticle admixtures in the 8+ and 6+ states, too, thus enhancing the M1 strengths. In 126 Xe [19] and 128Xe [38] the determined small multipole mixing ratios indicate a very similar situation. Recently calculations based on a model in which two quasiparticles are coupled to a boson core have been carried out for 132 Ba [39]. The calculated mixing ratio of the 6+ → 6+ transition is |δ| = 0.39, which is 2 1 at least in qualitative agreement with the experiment. We stress that we choose our IBM-2 parameters quite similar to the set of IBM-2 core parameters used in the calculations of Ref. [39], especially the same structural parameters were chosen. + + + The transitions 2+ 4 → 21 and 25 → 21 with their small mixing ratios δ are nearly + + pure M1 transitions; the 23 → 21 decay is dominated by M1. These transitions may have +τ > 1, so that the E2 strengths are strongly reduced. From the decay pattern the 2+ 4 state state (Table 5), because the strongest E2 decay in 132 Ba can be identified with the 2+ τ =4 state (τ = 3, see Section 4.3) and following the is observed for the transition to the 0+ 2

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selection rules the decay to the 2+ 1 state is E2-forbidden and M1-allowed. The remaining + 2+ and 2 states are candidates for the mixed symmetry 2+ state or at least for fragments 3 5 + of this isovector excitation. In the neighboring nucleus 134Ba the 2+ 3 and 24 states at about 2 MeV were found to have mixed symmetry character. Due to the lack of information on absolute transition strength the question remains open whether especially the 2+ 5 state at state may have a collective (possibly fragmented) mixed symmetry 2 MeV and/or the 2+ 3 structure as implied by the systematics of mixed symmetry states in this mass region [19, 23,24,34–36] or whether these 2+ states are based on quasiparticle excitations in spite of the low excitation energy, apparently the excitation energy of the 2+ 3 state does not agree with the IBM-2 prediction. In Fig. 5 we compare the decay properties of the possible 132 Ba with the known decay scheme in 134 Ba [23] where the 2+ state is 2+ ms states in ms fragmented over the third and fourth 2+ state. The IBM-2 calculation for 132 Ba predicts 2+ states with mixed symmetry character at about 2.2 MeV, the wave function of the calculated 2+ 3 state is clearly dominated by components with F = Fmax − 1 (Table 7). Experimentally mixed symmetry states can be identified by observation of large M1 transition matrix elements. Therefore, the knowledge of lifetimes, i.e. absolute E2 and M1 transition strengths, is very important for the unambiguous identification of mixed

Fig. 5. The characteristic decay pattern of the 2+ ms state predicted in the IBM-2 is a strong M1 state and in the case of eπ = eν a weakly collective E2 decay to transition to the symmetric 2+ 1 the ground state. In 134 Ba these decay properties could be observed [23] and are compared to the + 132 Ba. Due to the lack of information on absolute transition decay scheme of the 2+ 3 and 25 states in strength, the question remains open whether these states have also collective character.

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Table 7 Squared F-spin amplitudes in the calculated wave-functions of five 2+ states State

Fmax

Fmax − 1

Fmax − 2

2+ 1 2+ 2 2+ 3 2+ 4 2+ 5

0.983 0.967 0.025 0.741 0.260

0.000 0.001 0.958 0.222 0.708

0.016 0.032 0.016 0.029 0.008

The states of the ground and quasi-gamma band are dominated by components with F = Fmax . In + this calculation the mixed symmetry character is spread over the 2+ 3 and 25 states. F-spin mixing is the reason for M1 transitions between low-lying collective states.

symmetry states. In the literature mixed symmetry assignments are sometimes only based on the measurement of small E2/M1 multipole mixing ratios if lifetime information is absent. We stress, however, that small mixing ratios do not necessarily mean large M1 transition strength, because the corresponding E2 strength could also be very small. Therefore, the identification of short lifetimes τ  1 ps is desirable for a mixed symmetry assignment. 4.3. The 0+ 3 state An excitation spectrum with O(6) symmetry can be characterized by the (IBM-1) quantum numbers σ , τ and ν+ . For each value of the quantum number σ the same sequence of states appears with same spin values and level spacings but with an offset in energy. τ is the d-boson seniority [13]. States in a given σ subset are arranged in τ multiplets (see Fig. 4 for these multiplets). The decay pattern of the 0+ 2 state indicates that this state belongs to the τ = 3 multiplet, because the E2 decay to the 2+ 2 state (τ = state (τ = 1) is heavily suppressed in the 2) is strongest while the transition to the 2+ 1 experiment. Also the excitation energy is in agreement with the τ = 3 assignment. For the + 0+ 3 state we exclude first the assignment τ = 3 due to the rather strong E2 branch to the 21 state with τ = 1 and second the classification τ = 6 because the resulting high excitation energy (characteristic τ (τ + 3) energy dependence) would be inconsistent with the rather low experimentally observed excitation energy of 1660 keV. The remaining possibility is that the 0+ 3 state forms the “ground state” of the σ = Nπ + Nν − 2 subset. The wave function of a state in the IBM can be decomposed into components with even and odd numbers of d bosons, respectively. In the O(6) dynamical symmetry τ is a good quantum number and states with even τ only have the part with even d-boson numbers, whereas a state with odd τ is characterized by odd numbers of d bosons in the decomposition of the wave function. In Fig. 6 the three 0+ states are analyzed according to the d-boson decomposition. In this figure we compare our calculation to the pure O(6) and U (5) limit. The 0+ 1 state (τ = 0 in the O(6) limit) is clearly dominated by even numbers of d bosons. Obviously, our calculation is very near to the O(6) limit but also influenced

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Fig. 6. Decomposition of the wave functions of the first three 0+ states into parts with even and odd d-boson number. We compare the results of our calculation to the pure O(6) and U (5) limit. As explained in the text τ is approximately a good quantum number and our calculation shows a non-negligible U (5) contribution. Our calculation predicts the 0+ 3 state as the “ground state” of the σ = Nπ + Nν − 2 subset, though pure O(6) symmetry is slightly broken. Trivially nd = 1 has always a vanishing expectation value and is not listed.

by certain U (5) admixtures (we used d = 0) which is easy to see for the 0+ 1 state by the enhanced expectation value of nd = 0 compared to the pure O(6) limit. For the second and third 0+ state τ is still approximately a good quantum number and our calculation predicts + the 0+ 3 with a structure very close to the first 0 state, but with σ = Nπ + Nν − 2.

5. Conclusion Summing up, we have investigated the low-lying collective levels in 132Ba by coincidence γγ spectroscopy following the β decay of 132 La using the OSIRIS cube spectrometer. This reaction yielded extremely clean spectra. From the spectroscopic side, 132 Ba was identified for the first time. We were able to determine accurate the 0+ 3 state in E2/M1 multipole mixing ratios δ. Extremely large E2 fractions for transitions between low-lying collective states have been found corroborating assumptions made in previous analyses of the Xe–Ba region, but we also observed large M1 fractions in several decays. We found the E2-allowed transitions + 6+ 2 → 61 to be dominated by M1 radiation, which can be described in the IBM-2-plus-twoquasiparticles model by quasiparticle admixtures to the wave function. Also the decays of the third, fourth and fifth 2+ states contain dominant fractions of M1 radiation. These M1 fractions could be reproduced in the framework of an IBM-2 calculation indicating collective proton and neutron degrees of freedom. A tentative assignment as (fragments of) the 2+ ms state needs further investigation. A lifetime analysis for these states would be desirable, but seems not to be feasible with the presently available experimental techniques.

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We obtained good results in comparing our experimental energies and B(E2) ratios to IBM-2 calculations near the dynamical O(6) symmetry. From 14 mixed E2/M1 transitions we found 5 with dominant E2 and 9 with M1 character which we would not necessarily expect in a strongly collective nucleus. The occurrence of these M1 transitions may indicate that the nucleus 132 Ba with N = 76 approaches the shell closure N = 82 and starts to build up quasiparticle excitations (we discussed the possible 2qp admixtures to the 6+ 2 state) and looses collectivity. The study of the transition from collectivity to shell structure is clearly of great interest and detailed shell model calculations are needed. We note that this mass region is now feasible with the Monte Carlo Shell Model [41].

Acknowledgements We thank Prof. Dr. G. Cata-Danil, Prof. Dr. T. Otsuka, Dr. S. Kasemann, A. Fitzler and Dr. H. Tiesler for stimulating discussions. This work was partly supported by the Deutsche Forschungsgemeinschaft under contract Br 799/10-1.

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