E0 transitions in 70Ge and shape-coexistence interpretation of even-mass Ge isotopes

Nuclear Physics @ North-Holland

A441 (1985) 261-270 ‘Publishing Company

EO TRANSITIONS

IN “Ge

INTERPRETATION A. PASSOJA,

AND

SHAPE-COEXISTENCE

OF EVEN-MASS

R. JULIN,

J. KANTELE

and

Ge ISOTOPES M. LUONTAMA

Department of Physics, University of Jyviiskylii, 40100 Jyviiskylii, Finland and M. VERGNES Institut de Physique NuclsSaire, EPl, Received

6 February

91406 Orsay, France 1985

Abstract: The branching ratios of EO and E2 transitions depopulating the 0: and 0: states in “Ge have been studied using conversion-electron and -y-ray spectroscopy, as well as a new internal-pair measurement technique. A value of 3.7 (2) ns has been obtained in a remeasurement of the half-life of the 0: state. Two new EO transitions, 0: + 0: and 0: + O:, have been observed. A comparison of the measured X(EO/E2), p*(EO) and B(E2) values for the excited O+ states in “Ge with the corresponding “‘Sm data supports a recent shape-coexistence interpretation of the even-mass Ge isotopes.

E

NUCLEAR REACTION “‘Ge(p, p’v), E = production spectrum, yp’-coin, (ce)p( t). “Ge parameter p2. Ge(Li) detectors, magnetic spectrometers.

6.9 MeV; measured I,, E,, I(ce), deduced levels, J, T, B(EO)/B(E2), plus Si(Li) conversion-electron, Enriched targets.

internal pair EO strength internal-pair

1. Introduction

The even-mass Ge isotopes are especially interesting because of their anomalously low 0: state which becomes the first excited level in ‘*Ge. The striking discontinuity observed at N = 40 in the E(OT)/E(2:) ratios of even-mass Zn, Ge and Se isotopes, both for the excited 0: and 0: states, is shown in fig. 1. The nature of the abrupt change in the structures of the Ge isotopes has been attributed to pure neutron excitations or to pure proton excitations ‘). Systematic studies of the Ge isotopes using stripping and pickup reactions also appear to show some discontinuities around N = 40, suggesting both the existence of a shape transition (from spherical to weakly deformed) between N = 40 (72Ge) and N = 42 (74Ge) and the coexistence of different shapes I). In a nucleus having a spherical (deformed) ground state, the 0: state appears to have a more deformed (spherical) shape, while the 0: state has a shape more similar to that of the ground state+. + It should be understood (or permanent), feature.

that the term “shape”

is used here to mean a dynamic,

261

rather than a static

A. Passoja et al. / EO transitions

262

4 a

Se

3

+N z +a-2 W

1

L

I

1

I

1

I

I

34

36

30

40

42

44

NEUTRON Fig. 1. The ratio

E(Ot)/E(2:)

The 70Ge nucleus

for even-mass

i,6

NUMBER

Zn, Ge and number N

seems to be somewhat

I

46

Se isotopes

anomalous

as a function

within

of the neutron

this framework.

An

interpretation “) of the two-neutron transfer reaction data would indicate a similar nature for the 0: and 0: states in “Ge. On the other hand, recent Coulomb excitation measurements ‘) and analysis of transfer data on the Ge and Ga isotopes “) have also shown the presence of a structural change between 70Ge (N = 38) and 72Ge (N = 40). The apparently anomalous characteristics of 70Ge have been explained ‘) tentatively in views of oblate or prolate shapes attributed to the 0’ ground and excited states in the Ge nuclei. According to this interpretation, there is a gentle oblate-to-prolate shape transition between N = 38 and N = 40, and a spherical-todeformed shape transition between N = 40 and N = 42. The ground and first excited coexisting O+ states in 70Ge would be oblate and prolate spheroids, respectively, with a deformed 0: state. The suggested interpretation would also integrate harmoniously the existence of shape coexistence, a spherical-to-deformed and an oblate-to-prolate shape transitions in the even-mass Ge isotopes, which have emerged from the experimental and theoretical studies ‘).

A. Passoja et al. / EO transitions

If the above be very similar

263

description is valid, then the characteristics of the O+ states should in “Ge and in the transitional nucleus “‘Srn, where the 0: and 0:

states have been described as nearly spherical, coexisting with a deformed 0: state ‘). The experimental distribution of the relative (p, t) strengths to the O:, 0: and 0: states in the “*Sm(p, t)i5’Sm reaction is completely different 6-8) from the one observed 93’o) in the ‘*Ge(p, t)“Ge reaction. According to the above interpretation, the (p, t) reaction on the deformed ‘52Sm should populate strongly the deformed 0: state in 15’Srn, whereas the (p, t) reaction on the fairly spherical ‘*Ge should populate favourably the spherical 0: and 0: states in “Ge, as observed experimentally 6-1o). In this respect, neglecting other data, the relative (p, t) strengths to the different O+ states in the ‘*Ge(p, t)“Ge reaction would appear to be more similar to the strengths in the 15’Sm(p, t)14’Sm reaction than in the 152Sm(p, t)“‘Sm reaction. Several theoretical approaches of the even-mass Ge isotopes have been carried theory out during the past few years 13’2-14). However, only the boson expansion (BET), by coupling of collective quadrupole and monopole pairing vibrations 12), and the interacting boson model (IBM) plus configuration mixing 13), have been able to reproduce satisfactorily, both the energies and the transition rates at the same time for all the low-lying levels. Because the probabilities of the EO(Oi + Or) transitions are related to the change in the mean square radius between the initial and the final O+ levels, these transitions appear in principle as sensitive probes for the study of shape transitions or shape coexistence in nuclei. In a recent work, the EO-decay branches of the excited O2 and 0: states in the N = 88 and 90 nuclei, “‘Srn and “*Sm, have been determined “). A more extensive project has also been started in the Ge-Se region, with the goal of measuring the EO matrix elements of the excited 0: and 0: states in the even-mass Ge and Se isotopes,

and of obtaining

information

on the structures

of the Ot states

and their possible “Ge. A comparison interpretation

connection with deformation. Here we present our results for with the “‘Srn data is then used as a test for the above mentioned of the characteristics of the O+ states in “Ge.

2. Measurements

and results

In this work, branching ratios of EO and E2 transitions depopulating the 0: and 0: states in “Ge have been studied using various types of conversion-electron and y-ray spectroscopy, as well as a recently developed technique for internal-pair measurements 15*‘6).The Of states were excited in the (p, p’) reaction at E, = 6.9 MeV. Enriched (81.4% and 92.4%) metallic “Ge targets of about 1.0 mg/cm* thickness were employed. In the following, some of the details of the present measurements are described. The electromagnetic decay of the 0: state in “Ge at 1215.5 keV has been investigated in several studies I’). Parts of the present singles conversion-electron and anti-Compton y-ray spectra from the “Ge(p, p’) reaction are presented in fig. 2.

A. Passoja et al. / EO transitions

7DGe (p.p’) GAMMA-RAY

Ep= 6.9 MeV SPECTRUM

h

0’

* 800

900

1100

1000

CONV.

1200

ELECTRON

SPECTRUM

K 1267.5

1200

1400

CHANNEL Fig. 2. Partial

(a) anti-Compton

-

keV

1600

1800

NUMBER

y-ray and (b) singles conversion-electron reaction at 15, = 6.9 MeV.

spectra

from the “Ge(p,

p’)

decay branch of The observed value for the EO(O: + 0:) K-conversion-electron 9.1 (4) x lo-” is in agreement with the previous result of 12 (5) x lo-3 [ref. ‘“)I. The half-life of the ‘“Ge(0:) state was determined in a direct two-parameter lifetime

measurement

using a magnetic

lens plus Si( Li) electron

spectrometer

19) in

conjunction with the naturally pulsed beam of the Jyvaskyla 90 cm cyclotron. The half-life value of 3.7 (2) ns, derived from the slope of the delay distribution shown in fig. 3, is considerably shorter than a recent result obtained with Coulomb excitation techniques 3), 5.6?::; ns, and slightly longer than the value obtained with the slope method in connection with /3-e- coincidence experiments 18), 3.0 f 0.5 ns. In order to determine the decay branches of the 70Ge(0:) state identified “) at 2307.1 keV, anti-Compton y-ray, yp coincidence, singles conversion-electron and sum-coincidence pair-line measurements were carried out. In a y-ray spectrum in coincidence with protons popuIating the 0: state, the E2(0:+ 2:) and E2(0: 3 2:) lines were observed. The branching ratios for these transitions were then deduced from the anti-Compton y-ray measurements: 55 (4)% and 45 (4)%, respectively.

A. Passoja et al. / EO transitions

DECAY 0;

OF

STATE

1215.5 IN

265

keV

70Ge

PROMPT

SHAPE

I

I

I

I

I

50

60

70

80

90

CHANNEL

IT

1oc1

NUMBER

Fig. 3. Half-life measurement of the 1215.5 keV 0: states in “Ge.

The EO(O: + O:)/E2(0: + 2:) decay branching ratio was obtained from a singles conversion-electron spectrum shown in fig. 2. The resulting value for the ratio of the K-conversion-electron intensities is Z,(EO; 0: + O:)/Z,( E2; 0: + 2:) = 0.59 (8). The branching ratio Z,( EO; 0: + O:)/ ZK(E2; 0: + 2:) = 1.6 (5) was derived from a sum-coincidence pair-line measurement with a fixed momentum window centred at $E(O:) - 1022 keVj, shown in fig. 4, and from a conversion-electron measurement with a fixed momentum window at the K-conversion line of the E2 transition. The two runs were normalized with the aid of the integrated beam charge. When combined + 2:) y-ray branching ratio and the theoretical with the observed E2(0: + O:)/E2(0: E2 conversion coefficients 20), these results correspond to the EO(e,: O:+ 0:) and EO( r; 0: + 0:) branches of 6.2 (9) x 10e5 and 1.8 (5) x 10e4, respectively. An independent determination of the EO(Ol +O:) branch was obtained from a conversion-electron measurement. The observed ratio of Zk(O: + O:)/Z,(O: + 2:) = 0.35 (10) corresponds to an intensity ratio of ZK(EO)/Zy(E2) = 6.5 (18) X lo-‘. The adopted value of X,,,(EO/E2) = B(E0; O:+O:)/B(E2; 0:+2:), as a weighted average from internal-pair measurements [0.23 (6)] and conversion-electron measurements [0.20 (5)], is 0.21 (5). Since there were no previous measurements of the lifetime of “Ge(0:) state, we employed a centroid-shift time measurement method 2’) in an attempt to determine the half-life of the 0: state, the result being an upper limit of 40 ps. 3. Summary and discussion The absolute EO and E2 transition probabilities of the excited O+ states in “Ge as determined in this work are presented in fig. 5. The observed ratios of the reduced

A. Passoja et al. / EO transitions

266

70Ge ( p , p’ > E, =6.9 MeV INT. PAIR SPECTRUM

2275 fl2295

0

1

600

650

CHANNEL

700 NUMBER

Fig. 4. Partial internal-pair spectrum of ‘OGe in the energy range of 2.1 to 2.5 MeV obtained using the sum-coincidence technique with a fixed momentum window centered at &E(O:) - 1022 keVJ.

EO and E2 transition probabilities, X(EO/E2) values, are presented in table 1, together with the B(E2) and p’(E0) values as extracted from the present results. As mentioned earlier, the neutron-transfer cross sections and the Coulomb-excitation results suggest the coexistence of different types of deformation in the Ge isotopes. A large number of studies have been dedicated to the phase transition from the spherical to the deformed shape which occurs rather abruptly between rsoSm and 152Sm. Data from two-neutron transfer reactions 5-8) suggest that the 0: and 0: states in “‘Srn are nearly spherical, while the 0: state is deformed. This interpretation is very much similar to the shape coexistence picture of “Ge suggested in ref. “) on the basis of transfer-reaction data and Coulomb-excitation measurements. For that in table reason, a comparison between the “Ge and “‘Srn data is also represented 1. Of particular interest are the EO transitions between the different Of states, since they depend sensitively on the nuclear charge distribution and deformation. A

261

A. Passoja et al. / EO transitions

E2

EO TRANSITIONS

TRANSITIONS B(E2C) in W.U.

103x {(EO) 0’

2307.1

Fig. 5. Summary of the present results on the EO and E2 transition probabilities of the 0: and 0: states in “Ge. Recent Coulomb-excitation results 3, for 2: and 4: states are also shown. Since the half-lives of the 0: and 2: levels are not known, only relative transition probabilities of the EO and E2 transitions depopulating these states are given.

comparison of the “Ge and “‘Srn data given in table 1 shows clear similarities between these nuclei leading to the following comments: collective com(a) The 0: states in “Ge and “‘Srn have clearly an important ponent, leading to B(E2; 0: + 2:) values of 53 W.U. in each of these nuclei. However, TABLE 1 Electromagnetic

decay properties of excited ‘%m “Ge this work

B(E2Mw.=l”) lo3 x p*(EO)r, b, 1osxx*,, ‘) X 321 X 322 X 31, X3,, WE2),,lJ-W2),, P~(EO),,/P~(EO),, “) B(E2),, = B(E2; O;+ 2:). b, $(EO), = ~‘(0: + Of). ‘) X,j, = B(E0; O:+Of)/B(E2;

53 (3) 6.3 (4) 4.2 (3) 1.00 (15) 0.029 (6) 0.21 (5) 0.0060 (18) 35 (5) 4.8 (13)

O+ states in “Ge

and

“‘Sm ref. I’) 53 (5) 18 (3) 11.3 (8) 6.4 (6) 0.033 (5) 0.22 (2) 0.0012 (2) 195 (40) 29 (4)

O:+ 2:) = B(EO),j/B(E2),,.

268

A. Passoja et al. / EO transitions

the experimental

values of p*(EO; 0: + 0:) being 6.3 x low3 (“Ge) and 18 x 10m3 (isoSm) cannot be explained by a spherical vibrator 22723),PZibr= (O.l5lZ/l~~,,)‘. The vibrational predictions are larger than the experimental values by factors of 9.4 (“Ge) and 6.3 (“‘Sm). The experimental value of p’( EO) = 18 x 10m3for ‘soSm agrees well with the prediction (22 x 10e3) of a pairing-plus-quadrupole model modified and applied by Kumar 24) to the transitional nuclei ‘50,152Sm. In a recent work of Tamura et al. I*), the 0: states in the Ge isotopes have been described as the pairing vibration (described by RPA) coupled to the collective quadrupole oscillation (described by boson expansion). The calculated value of p*(EO) = 1.6 x 10e3 is smaller than the experimental value by a factor of 4. (b) The electromagnetic decay of the 0: state, suggested to be the deformed state coexisting in a nearly spherical nucleus, has two striking features in each of these nuclei: (i) The EO decay to the 0: level is favoured as compared to the one to the ground state; the ratio of p*(EO; 0: + O:)/p*(EO; 0: + 0:) has the values of 4.8 (13) and 29 (4) for “Ge and 15’Srn, respectively. (ii) The E2 decay to the 2: level is also strongly favoured as compared to the one to the 2: level, the ratio of B(E2; O:+ 2:)/B(E2; O:+ 2:) being 35 and 195 for “Ge and 15’Sm, respectively. (c) The ratios of the reduced EO and E2 transition probabilities, X,,(EO/E2) = B(E0; 0; + Of)/B(E2; 0: + 2:), have quite similar values for “Ge and “‘Sm, as shown in table 1. The X,,,(EO/EZ) values are smaller than the values for a spherical vibrator, Xvibr = p&,,, by factors of 12 (“Ge) and 3.3 (i5’Sm). A comparison of the experimental B( E2), p’( EO) and X,, values, presented above, strongly supports a similar character for the corresponding O+ states in “Ge and in 15’Sm. The experimental level schemes of even-mass Ge isotopes, including the behaviour of the 0: state energy, are reasonably well reproduced up to about 3 MeV by recent calculations performed employing both the boson expansion theory (BET) [ref. “)I and the interacting boson model plus configuration mixing (IBA) [ref. “)I. In table 2 we compare the experimental results with theoretical predictions on reduced E2 transition strengths between some low-lying states in “Ge. The large B(E2) values and the smallness of the cross-over of the 2:+0:, 2:+2: and 4: + 2: transitions 2:+ 0: transition are reproduced by both BET [ref. “)I and IBA [ref. “)I. The transitions in which the largest discrepancy is encountered between theory and experiment are those connected with the 0; state. The B( E2; 0: + 2:) value reveals a strong collectivity in it, and both of these models fail to predict the large experimentaLvalue. The calculated B(E2) strengths are smaller than the present experimental value by a factor of 35 and 13 for BET and IBA, respectively. The strongly enhanced E2 decay to the 2: state: B(E2; 0: + 2:)/B(E2; 2: + 0:) = 2.55 (15) may be connected with the intriguing question of the possible deformation of the excited O+ states. The large B(E2) value could be alternatively interpreted to imply a rotational structure, associated e.g. with mixed bands. In ref. *‘) the 0: state is associated with a band head in “Ge. Some support for this idea comes from the

269

A. Passoja et al. / EO transitions TABLE

2

Comparison of experimental and theoretical B(E2; Ii+ I,) values in Weisskopf units (1 Wu. = 17.1 e2 . fm*) for transitions between some low-lying states in “‘Ge

Transition

Exp. ref. 3,

2:-o:

20.8 (4)

o;-t2:

53 (3) “) 35 (9) 65 (11) b, 0.16 (12) 0.26 ‘) 29 (11) 2.1 (18) 3.6 ‘) 11.1 (23) 32 ‘)

2:+0: 2;+2: 2:-o: q-2:

BET ref. “)

IBA ref. IX)

21.1

13.9

1.5

4.1

0.13

0.12

29.7 0.26

20.8 0.12

30.5

20.6

“) This work. b, From ref. ‘*). ‘) From ref. I’).

observation 26) that the relative B(E2) decay of the 2157 keV 2: state to the 0: state is about 200 times that for the ground-state decay (fig. 5). However, the obsehed value 27) of the ratio of B(E2; 2: + O:)/B(E2; 2: + 0:) = 14 (2) indicates that the band structure of “Ge cannot be interpreted in a simple way. Unfortunately, the theoretical values in the framework of BET and IBA are available only for the 2: state: the experimental value of B(E2; 2:+0:)/B(E2; 2:+= 0:) is larger than the theoretical predictions by an order of magnitude (table 2). The band structure in “Ge is still a puzzle. In summary, the previous results of the (p, t) and (t, p) reactions and Coulomb excitation experiments, as well as the present results of the electric monopole strengths in 70Ge and ‘soSm indicate that in these nuclei, states with various deformations occur which, of course, mix. However, it would be very important to determine the half-lives of the 0: states. The absolute values of the monopole matrix elements ~~(0: + 0:) and p*(O: + 0:) would allow more definite conclusions on the structures of the excited Ot states in terms of deformation and configuration mixing as, for example, is the case for the Sn and Cd nuclei 28-32).

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Phys. Rev. C25 (1982) 2812, and

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1979, Inst. Phys.

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