Collective excitations in the117, 119, 121Te nuclei

M1 : 3.A

Nuclear Physics A329 (1979) 151-191 ; © North-Holland Pnbllshinp Co., Amuerdant

Notto be reproduoed by photoprint or microfilm without written permiation from the publisher

COLLECTIVE EXCITATIONS IN THE "', """Te NUCLEI U. HAGEMANN, H.4 . KELLER, Ch. PROTOCHRISTOW and F. STARY Zentralinstitutfür Kernforschung Rossendorf, GDR Received 21 February 1979 (Revised 19 June 1979) Abstrad: High-spin states in odd-mass Te nuclei were studied by means of the (a, 2n), ('He, 3n) and (d, 2n) reactions. Using in-beam spectroscopic methods y-ray energies, intensities, excitation functions, time and angular distributions and y-y coincidences were measured . Also, for " 1 Te, measurements of the linear polarization of y-rays and internal conversion electron spectra were performed. Level schemes of odd-mass Te nuclei (A = 117-121) were established up to spin values of J = Y. The predominantly excited level sequences, built on the Y- states, are compared with the ground state bands in doubly even Te nuclei . The systematics of decoupled ~L - bands in the Z = 50 region is given. Deviations of the level spacings for maximum aligned states of the h12 ® R multiplets from those of the g.s. bands in the neighbouring core nuclei can be observed . The energetically favoured coupling to J.-1 may be caused by the blocking effect due to the Pauli principle or by dynamical shape fluctuations. The h 1 ,,, level systems of the Te nuclei are furthermore compared with particle-core coupling calculations where different models for the core are tested, such as the rigid triaxíal rotor, the soft rotor including hexadocapole deformation, and the y-unstable potential. Each model assumption leads to a rather good agreement with the experimental level energies.

E

NUCLEAR REACTIONS 115 .117, ' 1 'Sn(a, 2ny), E = 19 .8-27.0 MeV ; 117 Sn('He, 3ny), E = 32 McV;'uSb(d, 2ny), E = 13 .5 MeV ; measured a(E E,, e), E,, I,, yy-com, a-7(t), E,., In, P,. 117 .119 , 1uTe deduced levels, J, x, T, 1=, ICC, y-multipolarity, ó. Enriched targets. Ge(Li) and SkLi) detectors, solenoidal electron spectrometer. Rigid triaxial rotor, soft rotor, 7-unstable potential calculations .

1. Introductiou Experimental investigations on odd-proton transitional nuclei just above the Z = 50 shellclosure (in particular Sb and I nuclei) have recently been published 1 - s). The analysis of the experimental data indicated the presence of a coupling between the motions of the odd quasiparticle and the collective field of the doubly even core . Different coupling types (strong coupling, aligned coupling, intermediate coupling) may be observed, which are mostly in coexistence in the same nuclide. Till now, almost no data on high-spin states in odd-neutron nuclei of this mass region have been published. A comparison of the band structures in odd-N nuclei with those observed in odd-Z nuclei having the same underlying doubly even core should provide a more complete and deeper . understanding of the particle-core phenomena. 157

158

U. HAGEMANN et al.

In this respect the unique-parity states are of special importance because in that case the state of the odd particle can be assumed to be a relatively pure single particle one. We therefore .tnvestigated the odd-mass Te nuclei with particular interest to the negative-parity states, which are based on the coupling of an h.,,, quasiparticle to the vibrating doubly even Te core. Together with the data of the odd-N nuclei 7-15) Pd, (d, Sn, Xe and Ba a systematics of the negative parity h,,, level system as a function ofthe neutron number is available and hence it is possible to see how level structures and nuclear properties change when the Fermi surface enters the h,, shell. In this paper we present the data of an experimental and theoretical study of the high-spin states in 117,119,1z1Te. Some results of the measurements concerning the positive-parity dJ = 1 band structure on weakly deformed low-lying isomeric states were published previously 16) . 2. Experimental procedure 2.1 . EXPERIMENTAL ARRANGEMENT AND SINGLES SPECTRA

High-spin states of the nuclei 117. 119 " "'Te were populated using the following 121Te. reactions : 115-119 Sn(a, 2n)117-121Te, 117Sn(3He, 3n)1 17Te and 121Sb(d, `' 2n) The beams were supplied by the Rossendorf cyclotron U-120 . The enriched Sn targets used in the experiments were self-supporting metallic foils of x 10 mg/cm2 thickness. The isotopic compositions of the Sn target material are givenin table 1 . For the Sb target a 10 mg/cm2 layer of metallic powder enriched to 95 % in 121Sb was deposited on a 0.5 mg/cm2 lavsan backing. In-beam y-ray measurements were performed with different coaxial Ge(Li) detectors of 20 to 30 cm 3 volumes and a high-resolution (0.7 keV at 100 kev) 1 cm 3 planar Ge(Li) detector in connection with standard electronics and data acquisition systems. For the off-line analysis of the spectra the peak-search and peak-fitting Isotopic composition of the used Sn targets Isotope 115 116 117 118 119 120 122 124

in target 1 15Sn

"'Sn

50.7 28 .1 3 .& 7.2 2.t) 6.4 0.7 b.8

0.6 2.4 85 .6 9.1 0.8 1 .1 0.2 0.2

119 Sn

0.2 0.4 0.5 3.4 86 .9 7.6 0.3 0.3

117,119,121Te

159

programmes PICOZEI, GAMMA and ASYVAR ") were mainly used . The spectra, particularly those from the 11 'Sn target, showed rather strong contributions of y-ray transitions from reactions induced on the even mass Sn admixtures . The energy calibration was performed by a simultaneous recording of y-rays from standard radioactive calibration sources "). 2.2 . EXCITATION FUNCTIONS

For isotopic identification and assignment of spin sequences in the level schemes, y-ray spectra were measured at the a-particle beam energies 19 .8, 22.2, 24 .2. and 27.0 MeV. The necessary beam energy degradation was produced by aluminium absorbers leading to an uncertainty in the particle energy of about 1 MeV. The y-ray intensities were normalized to the intensity of an appropriate reference line and plotted as function of the bombarding energy (cf. figs. 7, 11 and 14). 2.3 . COINCIDENCE EXPERIMENTS

Prompt y-y coincidences were measured using two coaxial Ge(Li) detectors placed at f90° with respect to the beam direction and 5 cm distant from the target . Lead shielding of the detectors strongly suppressed the y-ray scattering from one detector into the other. The coincidence time gate amounted to about 200 ns. The coincident energy signals were digitized and recorded event by event on magnetic tapes l9). Gamma-ray counting rates of x 15000 cps and total coincidence rates of ~-. 800 cps were employed. For off-line summation of coincidence spectra 2°) energy peak and background gates were set on the projected spectra. Examples of background corrected spectra obtained are shown in figs. 5, (3, 9 and 13. .

2.4 . LIFETIME MEASUREMENTS

To search for isomers with half-lives T* > 1 ns, spectra were recorded time related to the r.f. signal of the cyclotron. With a planar Ge(Li) detector two-dimensional time-energy spectra were measured between the natural beam bursts of 4 ns pulse width and 90 ns repetition period . The timing system 21) allowed a time resolution of less than 5 ns FWHM for energies E., > 100 keV. Time-differential y-ray spectra are displayed in fig. 1 . Three isomeric states at 274.4, 320.4 and 443.1 keV with half-lives of 19.1(9), 2.2 (2) and 86 (6) nswere identified in "'Te, 119Te and " 1Te, respectively. The time distributions of delayed y-rays have been published earlier 16) . 2.5 . ANGULAR DISTRIBUTIONS

Gamma-ray angular distributions were measured at 90°,105°,120°,135° and 150°,

160

U. HAGEMANN et al. 117TO

w

r Z

PF

r X

b

100 Fig. 1 . Time differential y-ray spectra following the reactions ' I sSn(a, 2n)' "Te, ' "Sn(a, 2n)"'Te and 119Sn(a 2n)"Te.

111 . 119. 121TC

and for t t'Te also at 160° with respect to the beam direction. The spectra were normalized to the beam intensity using a Ge(Li) monitor counter positioned at 125° to the beam axis at a distance of about 10 cm from the target. The normalization was checked by using the known Az"p values for stretched E2 ground state (g.s.) band transitions of the doubly even Te nuclei 22), which were always present in the spectra due to target impurities. The angular distributions were fitted by a leastsquares procedure to the Legendre polynomial expansion 4). In order to derive mixing ratios of mixed M1 +E2 transitions the angular distributions were further analysed to determine attenuation coefficients a2 which describe the degree of alignment ofthe initial state. Based on the level schemes presented in sect. 3 the 012 coefficients were extracted from stretched E2 transitions by comparing the experimentally obtained AZ= r = aA values to the theoretical A2 values to as 0.e 0.7 Ot2

06

as 04 0.s 02 (il 0

Fig. 2 . Attenuation coefficients az for stretched E2 transitions in "' - "'Te following (a, 2n) reactions at 27 MeV plotted as a function of the initial spm J, . The solid line is a parabolic fit through the data points . The dashed curves represent the standard deviation of the fit . Errors drawn at the experimental points are only statistical ones .

given by Yamazaki 23). In fig. 2 the obtained a2 values are displayed as a function of the spin J, of the initial state. The solid curve represents a parabolic fit through the experimental data. These interpolated values were used to evaluate the mixing ratios of mixed transitions. 2.6. CONVERSION ELECTRON MEASUREMENTS

Conversion coefficients of several transitions in t. . Te were determined by meas-

162

U. HAGEMANN et al .

uring the conversion electron spectra with the aid of a broad-range solenoid electron spectrometer 24) . A homogeneous magnetic field perpendicular to the beam axis was applied to transport the electrons to a cooled 50 mm2 Si(Li) detector 20 cm distant from the target . In the energy range 200-400 keV the transmission of the spectrometer amounts to a few percent. The efficiency calibration of the spectrometer was performed using 1s2Eu and 206Bi sources. The conversion electron spectrum obtained by a-particle bombardment of a rolled metallic 1 .5 mg/cm 2 thick " 9 Sn target is shown in fig. 3. The analysis of the 14 12

11 ~Sn+a

[E- 27MOV]

CONVERSION ELECTRONS

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200

400

800 600 CHANNEL NUMBER

1000

1200

1400

Fig . 3 . Conversion electron spectrum induced in the reaction " 9 Sn+a .

Fig . 4 . Intçrnal conversion coefficients for some transitions in "'Te . The solid curves represent the theoretical values of Hager and Seltzer 2s).

117, 1111, 12 'Te

163

1)

spectrum was performed with an asymmetric shape function for the conversion lines. The conversion coefficients were compared with theoretical values from Hager and Seltzer (fig . 4). The required normalization was obtained with the help of the K-conversion coefficients aK = 0.0768 (17) for the 212.2 keV + -+ + transition in "Te which is known from radioactive decay measurements Ze).

2°)

2.7 . LINEAR POLARIZATION

The linear polarization 2') of some y-ray transitions in 121Te was measured at a bombarding energy of 27 MeV by means of a planar Ge(Li) one-crystal polarimeter 28) with an active volume of 27 x 27 x 5 mm'. The resolution of this detector was 2.5 keV at 1.3 MeV. The polarization sensitivity of the polarimeter was determined from transitions with known multipolarity in "'Kr, ' Ag and 120,121 .122 Te. A relative normalization of the spectra was obtained by means of a monitor detector . Results of the linear polarization measurements of y-rays complement the angular distribution analysis and were used to remove ambiguities in some multipolarity assignments.

28)

05

3. Experimental results 3.1 . THE "'Te NUCLEUS

30)

The nucleus 121Te was investigated earlier by Sergolle 29); Föller and Langhoff and Spejewski et al. All these authors studied the decay of 1Z1í and identified some low-lying levels and concluded the spin assignment I to the first excited state at 212.2 keV. The compilation of these data is given in ref. 32). In the level schemes there are, however, some contradictions which will be discussed together with the experimental data given in this paper. From thedecay oftheisomeric ~ state the conversion coefficient a. = 0.0768 of the 212.2 keV transition was determined by Edvardson et al. 26) . Later this nucleus was studied in the reactions 120Te(d, p)121Te by Lien et al. and 122Te(3He,-u)121Te by Fernandes and. Rao sa). From DWBA analysis of the measured angular distributions they extracted transferred angular momenta and spectroscopic factors. The spin and parity assignment of J , J+ and for the ground and the first two excitedstates wereconfirmed. Furthervalues weretentatively given for other low-spin levels . The results of our experiments concerning the 121Te nucleus are summarized in table 2. Sample y-y coincidence spectra are shown in figs. 5 and 6. The rather complex level scheme of the 121Te nucleus based on these experimental data is shown in fig. 8. The level order is supported from the analysis o¬ the y-y

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165

B"ound corroded I-V coincidence spectra from the 11 "Sn(m, 2u)"'Te

coincidence

M AM cascade 631 .6 kéV, 729.7 kéV and 67-71.8 keV (see

Y. 5 and ym M either M go or M IA d isomeric~- state. From the excita-

functïans the latter alternative was considered to be mars likely . Further y-ray relatedtothis cascade werelocated on Wbasisofcomcidence and energy -ray transitions have large

166 TABU

Proptrtnes of y-ray transitions observed in the "'Sn(a, 2n)'x'Te and Er (key)

f,,(d)

1p)

A,-

A,rn

0.14(6)

0.00(8)

-0.03(3)

0.00(4)

7.6(4)

0.19(4) 0.04(5)

-0 .03(6) -0 .07(6)

7.7 (4) 4,3 (6)

10zaK ")

3 144.6(1) 189.6(2) b) 202 .1(2) 207.7(2) b) 212.2(1) 219.4(2) 230.9(1) 244.8(1) 249.8(2) b) 263-2(2) 265.5(1) 283.3(2) 292 .3(3) `) 293.3(3)') 316.1(1) 319.8(3)°) 319.8(3) °) 339.2(1) 358.7(2) 361 .7(1) 382.2(1) 387.4(1) 416.4(1) 419.6(3) 470.8(1) 475.2(1) 525.0(1) 532.3(3) 535 .6(2) 543-2(2) 588.8(2) 594.4(3) 598.7(2) 6243(3) b) 631.6(1)') 631 .6(1)°) 637 .2(1) 650-9(2) . 674.0(1) ". 674MI) °, b)

36.8(4) 1 .2(3) L1(3) 2.8(6) `) I00.0(7) °) 1.8(3) 57.3(5) 14.5(4) 1 .2(3) 1 .3(4) 7.0(4) 1 .7(4) 3.1(5) 4.4(5) 26.9(7)

41 .1(3) 0.2(1) b) 3.4(4) 100.0(i)
5.2(5) 1 .8(5) 71 .0(9) 6.1(6) 21 .6(7) 14 .0(6) 2.5(5) 23 .3(6) 19 .6(5) 19 .2(7) 9.5(6) 1110) 10.6(7) 23 .4(8) 13 .6(7) 20.7(8) 21 .9(14) 207.5(30)x)

1 .3(3)

681 .3(1) 724 .4(3) 728.7(1) 739.0(2) b) 936.8(3)',')

45 .0(13) 9.9(12) 131 .4(18) 13 .4(11)

b) 1.6(3)

6.2(3)

4.0(6)

19.5(10) x)

4.2(2) 11 .00) 15 .4(4) 2.1(3) 26 .0(5) 29 .4(5) 11 .9(4) 9.5(4) 6.0(4) IOA(4) 10.9(4) 9.2(6) b) 11 .8(6) 3.3(4) 45 .0(12)

25 .4(13) 9.6(7)

14 .2(6) 2.0(3)

11 .6(10)

3.9(3)

7.5(4)

b)

21 .4(6) 7.4(6) 16 .1(6) 4.0(3)

b)

-0.31(12)

0.00(15)

-0.47(10)

0.17(16)

17

(2)

-0 .38(5)

0.00(7)

-0,52(4)

-0 .01(5)

1 .9 (2)

-0 .27(5) 0,47(9)

0.14(7) -0 .02(13)

1 .4(4) 1 .3 (3)

0.24(7) 0,24(6) 0=6)

-0 .03(9) -0 .02(8)

0.74(11)

0.21(11) 0Z(12) 0.26(5) 0.24(12) 0.35(9) 0,43(8) 0.33(4)

0.04(15) --0.33(17) -0 .08(7) 0.23(17) 0.01(12) -0 .02(12) -0 .08(4)

0.33(7) 0,46(12)

0.03(11) -0,10(18)

-0.98(5)

~ 0.07(8)

0.52(12)

0.06(21)

0.31(3) 0 .08(12)

0.06(22)

-0M(4)

0.20(6)

0.37(4)

~ 0.39(9) 0.30(7) 0.23(3)

117,119,12 Te

167

2

"Sb(d~ 2n)' l'Te reactions at E. = 27 MeV and Fb = 13 .5 MeV, respectively P.A .

P.,

Multipolarity

7

8

9

-0.31(5)

-0.22(26)

M1+E2

0.56(3)

-0.24(3)

-0 .18(6)

Ml+E2

0.30(6)

0.30(8)

0.20(8)

E2 Ml +E2

0.37(8)')

-0 .31(9)

0.68(58)

(E1)

-0 .27(4)

-0 .14(16)

-0.20(3)

Initial state (kcV)

6..a . 11

12

-0.39 5 6 ;S -0 .19

437.8 1208 .0 1176 .8 683 .0 212.2 (464 .2) 443.1 (244 .8) 1080.3 475.2 2280.7 1171 .0 1711 .9 887.7 2331 .3 532.3 757.6 1419 .3 2070 .2 2015 .2 594A 830.5 2015 .2 r) 683.0 475.2 1208 .0 532.3 974.5 1018.4 1419.3 594A 1806.6 1598 .8 924.8 1711 .9 1080 .3 2070 .2 1598.8 (1850.8)

10

0.14 5 3 :S

0.27

0.94(4)

-0 .10 ;5 6 5

0.05

Ml +E2

0.94(4)

-0.10 ;S 6 :S

-0 .02

-0 .19(6)

MI +F-2

0.90(4)

-0 .19

0.19(2) 0.93(24)

-0.04(16) -0.16(32)

M1+E2 (E2

' 0.56(3) 1.15(22)

0 .39(15) 0.40(13) 0.32(13)

0.29(20) 0.26(22) 0.26(40)

(E2) (E2) (E2)

0A7(14) 0.42(10) 0.48(13)

0.37(22)

0.16(48)

0.40(11)

0.26(26)

(E2) (E2) (E2)

0.48(25) 0.55(26) 0.59(11)

0.81(20) 0.55(9)

0.05(29) 0.34(5)

(E2) (E2) E2

0 .81(21) . 1 .02(19) 0.77(9)

0.61(16)

0.09(24)

0.14(4)

0.02(14)

(E2) (112)

Ml+E2

0.73(15) 1 .1 (3) 0 .81(4)

(E2)

1 .3 (3)

0.04(4)

0.22(13)

Ml +E2

0.47(7)

0.34(15)

E2

0.76(7)

;s a ;5 -0 .11

-5 .2 ;5 6 -< -4.0

-1 .4 5 6 -043 or -2 .3

$

-0 .54

6 ;S -0.28 6 ;5 -1 .6

2331 .3

974.5 (1482.0) 1653 .5 1176.8 (2952.0) `)

168

U. HAGEMANN et al.

positive A?=° coefficients being characteristic of stretched E2 transitions, whereas other strong transitions connecting the two main cascades show large negative anisotropies being typical for mixed dipole-quadrupole transitions. In some cases the multipolarity is supported by conversion electron and linear polarization data. Taking into account excitation functions of the related states shown in fig. 7 the spin and parity assignments given in the level scheme of fig. 8 could be concluded. The spin assignments tentatively given to the low-spin negative parity states are based on the excitation functions. The anisotropy coefficient of the 416.4 keV transition from the (221- ) level at 2015.2 keV is rather big for a stretched E2 transition . However, another spin assignment to the 2015 .2 keV level is very unlikely because of the multipolarity of the exciting 316.1 keV transition and the branching to the Y - and (z -) levels. The 416.4 keV y-ray line might be superimposed in the spectrum by a second one. Levels at 1850.8 and 2592 .0 keV were tentatively introduced because of weak lines in the coincidence spectra. A positive parity of the (Y + ) level at 2280 .7 keV was concluded - - from the linear polarization measurements of the 265.5 keV transition leading to the assumption of El multipolarity for this transition . Most ofthe other y-ray transitions are connected with the 212 .2 keV g.s . transition known from radioactive decay 32). The strongest coincidence is seen with the 230.9 Footnotes to table 2.

Errors indicated in parenthesis are given in units of the last digit. Columns 2 and 3: The relative intensities h are measured at an angle of 125° with respect to theincident beam . Columns 4 and 5 : Angular distribution (a.d.) coefficients A"P according to the equation W(9) 1+A2"°P2(eos 9)+A ;`PP4(cos e), measured in the (a, 2n) reaction at 27 MeV a-particle energy. Column 6: Conversion coefficients were determined by measuring the conversion electron spectra with the aid of a broad-range electron spectrometer with Si(Li) detector. Columns 7 and 8 : From the measured ad . coefficients the linear polarization values P.A. were calculated for spin changes and mixing ratios given in the table assuming no parity change. The experimental polarization values PP were obtained according to the expression QPP = (N(9(r)N(0°))/(N(90°)+N(0°)) with the efficiency Q of the polarimeter. Column 9: The multipolarity assignments of the transitions are based on all available experimental data . Column 10 : The attenuation coefficients listed for E2 transitions have been calculated using the experimental and theoretical 2') a.d . coefficients . The values for mixed transitions have been determined from the functions a,(1,) fitted through the data of E2 transitions (cf. fig. 2) . Column 11 : The mixing ratios ó,,. are believeed to be good to one standard deviation. ') For the y-transitions 144.6, 212.2, 230.9 and 316.1 keV the conversion ratios 04 L/a, were determined providing the values 7.6(10), 7.8(8), 5.0(6) and 8(2), respectively . ") Influenced or obscured by y-rays not listed in the table. °) The intensity has been corrected for a content of a ""fe transition . °) Normalization. °) Doublet in the y-ray spectrum . r) Not placed in the level scheme. 2) The intensity has been corrected for a content of the second 631 .6 keV transition . ") Evidence from coincidence data . ') isomeric state with T, n = 156 ns .

117, 119,

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U. RAGEMANN et al.

117, "9 .

"'Te

keV transition jndicating a level at 443 .1 keV. In the literature, however, there are somecontradictionsconcerning this443.1 keV level. Fromdecaymeasurements, 29-31) of 1211 only Spejewski et al. 31) concluded the existence of such a level. In contrast to our measurements they reported on a 443 keV cross-over transition to the g.s. with 15 % branching ratio. From our singles y-ray and y-y coincidence spectra (cf. fig. 6) follows that the branching ratio limit is lower than 2 % for this hypothetical 443.1 keV transition . For the 230.9 keV transition our experiments suggest an E2 multipolarity which follows from the angular distribution coefficients, the conversion coefficients and the linear polarization . Taking into account the excitation function shown in fig. 7 the most probable spin and parity assignment for the 443 .1 keV level is 1` = -j * . Fernandes and Rao 34) found in pick-up reactions an unresolved dóublet at 0.45 MeV and assigned tentatively }+ and I + spin and parity values to appropriate levels . The cascade on top of the 443.1 keV level connects levels forming a positive-parity band . The deexcitation of this band is characterized by weak cascade and stronger E2 cross-over transitions. From angular distribution measurements and excitation functions (fig . 7) J', J+, (4+), ( +)~ (Al') and (A.+ ) may be assigned to the corresponding levels . The assignments for the higher-spin levels are uncertain because of the weak intensities of the deexcitatiog transitions. The 631 .6 keV line in the spectrum is a doublet of transitions from the 1711 .9 keV level and the 924.8 keV level with equal energy . The relative intensities of both transitions were evaluated from the coincidence spectra. A second level sequence with positive parity is established from its strong E2 cross-over transitions. The 475.2 keV transition is placed directly on the g.s. confirming the ordering given in refs. 30,31) in condratiction to that of Sergolle 29). Also the branching ratio to the I + state is in agreement with the data of decay measurements 30 .31). The spin-parity assignments (J+), (1.+), '(1+ ), (u+) and (-V+) to the levels are based on angular distribution data together with excitation functions. Data for the levels above 1 MeV are given only tentatively because the y-ray lines are obscured in the spectra by background lines. In particular, the 598 .7 keV transition is strongly distorted by the 601 .2 keV transition in 120Te . The 532.3 keV level, deexciting via 532 .3 keV and 319.8 keV y-rays is known from decay measurements 29-31). However, the observed branching ratio is different from that observed in our measurements (decay : h (532 keV) = 61Y (319 keV)) . A 319 .8 keV y-ray line appears also in coincidence spectra gated on the 144.6 keV line. Therefore we believe, that the 319.8 keV line is a doublet. Since we have no possibility to estimate its partial intensity, the 319 .8 keV transition from the 532.3 keV level is given only tentatively. Also the 594.4 keV level was known from decay measurements 29-31 ) . The weak cascade 283.3 keV and 293.3 keV is assumed to feed this level because these transitions are in coincidence with the 382.2 keV transition. The ordering is due to their relative intensities. Spin and parity assignments could not be determined definitely . A 244 .8 keV transition formerly 32) placed

172

Er (keV) 62 .9(1) 140.7(2) 170.6(1) 200.9(1) 207.0(1) 242.8(2) 257.5(1) 299.0(2) 305 .6(2) 320.4(1) 325.1(2)') 334.9(1)') 340.7(2)`) 3483(1) 353.4(2) 382.6(3)') 422 .6(2) 431 .1(3) 443.7(3) 482.9(1) 5032(1) 505.6(2) 512.0(3) 514.2(3) 518.3(3) 524.4(2) °} 577 .8(2) 592.9(3) 618.7(1) 625 .4(2) `) 640.3(1)') 640.5(2)h ,J) 653.5(2) 659.0(2) 672.2(2) 697.4(2) 717.7(2) b) 719 .0(2) b) 747.5(3) 908.2(5) 1010 .0(4)

TABLE

3

Properties of y-ray transitions observed in the'"Sn(a, 2n)"'fe reaction at 27 MeV Multipolarity

Initial state (keV)

Ir

A«p

A*C-'9

22 .8(13) 2.6(2) 8.8(3) 6.9(4) 61 .3(6) 4.8(4) 100.0(5) x) 3 .5(3) 4.4(4) 40 .0(6) 7.4(6) 7.5(8) f) 3.6(8) 11 .4(6) 14(5) 24 .6(10) r) 9.4(8) 2.9(6) 12(6) 263(7) 27 .8(18) 6.2(17) 30.3(16) 14.4(15) 8.1(17) 9,7(15) 17.2(7) 7.2(8) 36.2(8) 28.7(8) 188.8(ó0)') 20 .0(30)') 25.8(10) 11 .8(10) 110(7) 13 .8(12) 96 .0(57) 54 .9(50) 12 .0(7) 4.2(16) 12 .1(19)

-0 .06(8) 0.07(13) -0 .35(6) -0 .35(7) 0.10(2) -0 .44(24) -0 .05(2)

0.16(13) 0.02(17) -0.02(8) -0.10(12) -0.01(3) 0.27(28) -0.05(2)

-0 .99(24) 0.22(3) 0.30(12) -0 .53(11) 0.14(23) -0.35(14)

-0.11(33) (M1+E2) 0.70(3) -0 .07(4) E2 0.39(5) -0 .03(18) 0.13(14) (MI +E2) 0.63(3) -0.06(33) 0.17(16) (MI+E2) 0.48(4)

-1 .60 5 3 5

0.76(3) 0.07(5) (MI+E2) 0.48(4) -0 .13(11) -0 .29(16)

& --

-0 .80(4) 0.34(6)

0.00(6) -0 .17(7)

0.07(10) -0.27(16) 0.31(6) -0 .04(9) 0.32(7) 0.22(6) 0.32(4)

-0 .05(11) -0 .11(8) -0 .07(6)

a2

(M1+E2) 0.39(4) (Mi +E2) 0.94(4) 0.9«4) (M1+E2) 0.56(3) (M1+E2) 0.56(3) (MI+E2) 0.30(6)

0.00 5 - 3S -0 .09 -0 .09 -0 .27 -0 .80 0.11

5&5 S & 5S & 55_ & 5-65 5 -

-0.50 S & 5-0.52 S 6 5

0.23')

320.4 b) 0.00') 2011 .5+x9 0.00') 2041 .8+x `} -0 .20 207.0+x `) -0 .03') 945.8 0.23 257.5 (505 .6+x)°) 1586 .3 -0 .45 320 .4 994.2 -0.16 1280.7 598.2 -0.02') 669.1 1939.7 -0.8 0) 703.0 b)

b)

(MI +E2) 0.90(4) -0.42 5 & 5 -0.29 (E2) 0.83(15)

E2

0 .69(13)

E2 E2

0.76(171 0.46(12)

E2

0.74(10)

E2 1 .02(14) 0.41(6) -0.04(9) 0.12(18) (E2) 0.97(25) 0.42(11) 0.36(12) 0.18(16) 0.09(19) (MI +E2) 0.81(3) -1 .05(27) 0 .14(3) 0.05(5)

-0 .8 5)

1840.9+x °) 1840.9+x °} (505.6+x)°) 719.0+x °) 771 .7 b) 1256 .1 1280 .7 1899 .0 1337 .7+x') 945.8 640.3+x') 1586 .3 2011 .5+x `) 1939 .7 b\

1337 .7+x °) 1358 .0+x `) 719.0+x `) (945 .5 +x)°) (2749.1 +x)°) 11)

Columns 1-8 : Cf. corresponding footnotes to table 2. 4) Two solutions of & are possible. The one with the smallest absolute value is contradiction to the A4"p value. b) Not placed in the level scheme. '} The exact energy is unknown because of the undetermined energy x of the u_ state (cf: fig. 10); x 280 keV. x} Normalization . °) influenced or obscured by y-rays not listed in -the table. 7 The intensity has been corrected for a content of a "9Sb transition . ") The maximum value A2 = 1 .2 is reached at this mixing ratio. b) Doublet in the y-ray spectrum. ') The intensity has been corrected for the content of the 640.5 keV transition . f) Evidence from coincidence data.

! 17,E 29, 121 To

Fig. 9. Selected y-y coinc a-particles. Peaksdenoted by

ecorded during the bombardment of ..Sn with 27 is kcV are judged to be in coincidence with the gate transition .

173

17 4

U. HAGEMANN er al.

above the 443.1 keV level is proposed to feed the g.s. Besides the 219.4 keV transition no further coincidences with y-ray transitions already assigned to "Te were observed in the coincidence spectrum gated by the 244.8 keV line. 3.2 . THE "'Te NUCLEUS

Previous information on low-lying states in "9Te was obtained from 119I decay studies 31 .35, 36), giving spin and parity assignments of the g.s. and first excited 257.5 keV state as I + and J + , respectively . An isomeric - state with T} = 4.7 d was known 37) in " 9Te due to its fl-decay. Since no y-decay branch of this longlived isomer could hitherto be observed, its exact excitation energy is still unknown. Our experimental results are summarized in table 3. Examples of y-y coincidence spectra are displayed in fig. 9. The level scheme of "9Te resulting from these data is shown in fig. 10. It shows a band pattern quite similar to that observed in the level scheme of the neighbouring nucleus 121 Te. Thenegative-parity states are most strongly populated. The arguments for placing the levels are the same as in the case of 121Te (see subsect. 3.1). Since no

u

Fig. 10 . Level scheme of " 9Te proposed from present in-beam expenments. The location of the state is unknown. The width of the arrows reflects the y-ray intensities.

-

175

117, 1 19,121Te w a

0 q O ..7

Ls

b

H

lsiinn ~avaiieM AIISN31NI

d

19

21

4,

o> ó~ '$ c .:

176

U. HAGEMANN et al .

y-ray transition was observed connecting negative-parity levels of the h,,, family with positive-parity levels the absolute excitation energy of negative-parity states is unknown due to the unknown excitation energy x of the -u - isomeric state. The spin and parity assignments of these levels are mainly based on the excitation functions shown in fig. 1 l and angular distribution data indicating stretched E2 character for cascade transitions andinixedM1 + E2 transitionsbetween the twomain cascades . Somewhat ambiguously is the assignment ( 122- ) to the (719 .0+x) keV level. Both the 719.0 keV transition and the 512.0 keV transition are energetically unresolved from the superimposing 717.7 keV transition and the 511 .0 keV annihilation radiation, respectively. However, the consistency of the whole negative-parity family with the neighbouring odd-mass Te nuclei suggests the (V - ) assignment . The AJ = 1 level sequence built up on the 320.4 keV level is well pronounced . The excitation functions of these levels (see fig. 11) point to a sequence with increasing spin. The cascade transitions between these levels have negative anisotropy indicating mainly dipole character. They are corroborated by stretched E2 crossover transitions with angular distribution coefficients Azw = 0.2-0 .4. The 320.4 keV level which was already known from decay measurements 31) decays via a 62.9 keV transition cascading with the 157.5 keV g.s. transition or a 320.4 keV crossover transition . The multipolarity of the cross-over transition to the I + g.s. was determined as E2 whereas the cascade transitions are of mixed M 1 + E2 character. Therefore spin-parity assignments of I + up to (J~I + ) are proposed for this AJ = 1 band . The assignment J" _ + to the first excited state confirms the results of previous decay measurements 31). Another cascade composed of the 514.2, 524.4 and 592.9 keV y-ray transitions follows from coincidence data. However, we did not succeed in determining definite spin and parity assignments to the appropriate levels, because the respective lines in the y-ray spectra are considerably obscured by background lines. Further weak transitions are placed on the basis of coincidence data . The 348.7 keV transition confirms the 669.1 keV level already found 31) in the "9I decay data. 3.3 . THE ""Te NUCLEUS

First investigations of the "'I decay using Ge(Li) spectrometers were made by Ladenbauer-Bellis et al. 36) and Sergolle et al. 38). The proposed decay scheme 36) of 11 'Te shows a first excited state at 325 keV with spin-parity j + assigned on the basis of the log ft value. A 274 keV y-ray transition was observed in coincidence with. the 325 keV photopeak 36). In systematic investigations of nuclear isomerism in the Z = 50 mass region, Brinckmann et al. 39) found a delayed 274.4 keV transition which, contrary to the above findings, was placed on the "'Te g.s. The appropriate 274.4 keV level is populated from a 104, ms isomeric - state at about 300 keV via an unobserved low-energy transition . Themeasured 39) total conversion coefficient

u

117 . 119, 12'Te

177

and the K/(L+ M) ratio of the 274.4 keV y-ray transition determine its multipolarity as E2, suggesting the assignment J + of the 274.4 keV level, which was confirmed in a re-investigation ") of the ' "Te isomeric decay. Additionally a 2.96.0 keV J + level was introduced on the basis of the observation of a delayed M1 transition with 21.6 keV energy . However, the isomeric transition itself remained hitherto unobserved . The results of our in-beam experiments for t t'Te are summarized in table 4. For T~ 4

Proporties of y-ray transitions observed in the "'Sn(a, 2n)'l'Te reaction at 27 MeV E7 (keV)

17

21 ..6(1) 3.2(4) 37 .4(2) 0.7(2) 111.8(1) 0.9(1) 03(1) 139 .8(2) 248.2(1) 0.9(1) 274.4(1) 100.0(10) °) 294.6(1)9 3.6(2) 303.3(2) L0(2) 325.6(1) 3.4(2) 341 .0(1) 7.4(2) 365.7(2) 1 .5(2) 407.1(1) SA(2) %5 .4(2) 1 .7(3) 525.2(2)£) 53(4) 540.0(2) 3.7(4) 595.1(2) 1.7(2) 623.9(2) S.6(4) 631 .9(2) t) SA(3) 655.2(2) 4.0(4) 670.6(1) 253(15) 713.0(2) 11 .9(5) 717.2(3)') L0(5) 746.9(2) 6.2(5) 759.3(2) 2.7(3) 798.0(2) 5 .80)

Asv

AWV

Multipolarity

az

-0 .0901) -0.11(18) -0 .07(10) -0 .20(18) (MI+E2) 0.56(3) 0.10(2) 0.06(6) -022(16) 0.23(6) 025(7)

-0 .02(3) -0 .01(9) -0 .02(26) -0 .10(8) 0.01(12)

-0.60(5)

0.08(7)

E2 °) (Ml)

Initial state (keV)

6.A.

2% .0') 577.7 0.01 5 d S

0.19

-0 .28 5 ó :5

0.11

0.18(4)') 0.48(4)

(M 1 +E2) 0.48(4)

-1 .40 5 6 5 -0 .47

-0.58(4) 0.46(10) 0.17(6) 0.36(9) 0.43(15) 0.32(8) 0.37(3) 035(5)

0.12(8) (MI+E2) 0.56(3) -1 .90 5 6 S -0 .30 0.33(16) -0 .04(10) -0 .16(14) E2 0.90(23) 0.04(22) (E2) -0 .07(11) E2 0.67(16) 0.86(7) -0 .10(4) E2 -0 .11(6) Ez 0.85(10)

0.30(8) -024(8) 0.49(4)

-0 .14(11) (E2) 0.62(16) 026(12) (MI+E2) 0.81(4) 0.17(6) (MI+E2) 0.70(3)

-21 5 b 5 -6') 0.5 5 6 5 2.6

b)

8212 929.7 274.4 577.7 325.6 918 .7 1186 .9 681 .5 1186 .9 821 .2 540 .0 1416 .3 2007 .5+x9) 1429 .9+xs) 929.7 670.E+x') 1383 .E+xs) (1903.1) 1021 .3 1429 .9+x 8) 798.0+x7

Columns 1-8: Cf. corresponding footnotes to table 2. ') Evidence from delayed y-ray-measurements b) Not placed in the level scheme. `) Normalization . °) The multipolarity E2 of the 274.4 keV transition has been confirmed by delayed conversion-electron spectra 39 .40). . ') The attenuation coefficient has not been included in fig. 2 because of partial excitation of the 274.4 keV through the 104 ms J~ - isomer . ') Influenced or obscured by -t-rays not hated in the table. The exact energy of this level is unknown because of theundetermined energy x ofthe - state(cf. fig. 12). b) Evidence from the coincidence data. Because of the positive Ar value the mixing ratio with higher absolute value is given.

178

U. HAGEMANN et al.

a E ó W 0

a

0 .a

a U

t-fV

0 4 CL W O u

"1- "9 . 12'Te

179

a clearer isotopic identification of the observed y-lines to' I Te two reactions using a-particles and 'He particles were utilized . The level scheme of I "Te is shown. in fig. 12. It is mainly based on the coincidence data. Selected y-y coincidence spectra are displayed in fig. 13. In the y-ray spectra the statistics is worse compared to that in the "9Te and 'x'Te measurements, because of the smaller cross section of the (a, 2n) reaction and the only 501 target enrichment.

Fig. 13 . Selecxed y-y

ce spectra of 31'Te.

4

A cascade of stretched E2 transitions is populating the - isomeric level. For more detailed arguments see analogous considerations for "'Te (subsect . 3.1). Since no -t-ray transition was found connecting the 11- family with any other level of this nucleus the energies of the negative-parity levels are given only relative to the energy x of the Ij- state. The excitation functions shown in fig. 14 suggest

18 0

U. HAGEMANN et al.

Fig. 14 . Relative excitation functions of the negative-parity band in "'Te.

values ~- and Y - for the (798 .0+x) keV and (1429 .9+x) keV levels, respectively, compared to the - and-y- assignment of the (670 .6+x) keV and (1383 .6+x) keV levels. Coincidences with the 274.4 keV g.s. transition show the existence of the 274.4, 681 .5, 929.7, 1186 .9 and 1903 .4 keV level sequence grouped in analogy to 119Te and 12 1 Te. The life-time of the band head was measured as T.ß(274 .4 keV) = 19.1(9) ns. The annular distribution of the 274.4 keV transition is strongly attenuated because of the feeding via the 104 ms isomer . Due to the lack -of coincidence information concerning y-ray transitions below 50 keV the placement of further weak transitions is ambiguous. The location of the 821 .5 keV level results from the agreement of energy sums of the branching transition cascades . The same arguments holds for the level ordering 540.0, 577.7 and 918.7 keV. No coincidences were observed between the 274.4 keV transition and the 325.6 keV transition . Therefore, in contradiction to Ladenbauer-Hellis et al . ae) a 325.6 keV level was introduced, in agreement with the results of decay measurements of Sergolle et al. 3s). 4. Dlwmdon 4.1 . SINGLE-PARTICLE ASPECTS AND POSITIVE-PARITY STATES

The Te nuclei belong to the transitional region between the "new" deformed region ") of nuclides with N and Z between 50 and 82 and the spherical Z = 50 closed-shell nuclei .

117. 119. 121Te

The complex level schemes of the odd-mass Te nuclei show fairly separated sequences of positive-parity states as well as negative-parity states . These states are expected to result from the spherical configurations d.., 94, s.. and d} or from the unique-parity orbital h,,, . The doubly even Te nuclei are commonly considered to have vibration-like properties . However, deviating from the simple harmonic picture, anharmonicities have to be regarded 42). For heavier Te nuclei two-proton core coupling aspects were introduced 43) to describe the energetically close-lying 6 + and 4 + levels. Therefore, the excited states in the odd-mass Te nuclides are expected to contain besides of single-particle components strong collective modes. In this sense, oddmass Te nuclei with mass numbers A z 123 were the subject of several theoretical investigations . A first approach to describe low-lying levels was used by Glendenning 44) who calculated the energy spectra assuming that the unpaired neutron in the s., and dt states is coupled to the collective core surface vibrations. Another attempt was made by Kisslinger and Sorensen 4s) using the pairing-plusquadrupole force model. These calculations describe the low-lying positive-parity states quite well, especially the revised model of Kisslinger and Kumar 4e) including more complicated phonon states . More recently the properties of low-lying states in 123-127 lie nuclides were studied by Sen 47) in a particle-phonon coupling scheme

Fig. 15 . Systematics of low-lying states in odd-mans Te nuclides . The data are taken from the present I .4°) for 117Te~ ref. 31) 31 . 33 . 34) for 121 Te, ref. °°) work and refs . ".49) for 'Te, refs . l for I 'Te, refs. 39 for 12 Ire and refs . '° . 31) For 123Te . The 2* excitation energies of the doubly even Te cores °2) are marked in order to point at the possibility of the presence of low-lying collective modes.

182

U. HAGEMANN et al.

which incorporates both anharmonicity in the core vibrations ana pairing effects in the odd-neutron motion . A particle-phonon coupling scheme was also utilized by Fernandes and Rao ") to calculate the level scheme of ' 21 Te. Contrary to these collective approaches Kuriyama et al. aa) introduced the conception that fundamental excitation modes characterizing low-lying states in spherical odd-mass nuclei are complicated quasiparticle modes. Evidence for such an excitation mode is a low-lying j-1 intruder state from js configurations . The observed low-lying I - states in odd-mass Te nuclei are explained in this way as coming from so-called dressed three-quasiparticle modes. In fig. 15 the systematics of the low-lying experimentally determined levels in the odd-mass Te isotopes is shown. This picture is an extension of the systematics of positive-parity states given by Walthers and Meyer s°) to more neutron deficient Te nuclides. A remarkable systematic behaviour is to be seen . The low-energy level variation is very similar to that of the single-particle states in the odd-A Sri nuclei . However, the spacing of the relative excitation energies decreases from Sri nuclei to Te nuclei. The ,, d, and h,,, states in neutron deficient Te nuclei vary only slowly as neutron pairs are added. A stronger dependence on the neutron number can be observed for the first J + and I + states coming from g4 and d.. configurations, respectively . This could indicate a rapid change of the positions for the corresponding single-particle states with mass number A. However, collective phenomena may also affect the relative position of these low-lying levels . The observation of positive-parity AJ = 1 bands built on I + and -J + states in . . .. . . 9Te and 12 'Te, respectively (see figs. 8, 10 and 12), lead to the interpretation of the states as members of rotational bands built on j + [402] and j + [404] Nilsson orbitals, respectively, in a slightly deformed system . These orbitals show a very strong up-slope as function of the deformation. Therefore, the relative excitation energy can strongly be shifted if the underlying deformation is changed. The coexistence of such low-lying deformed and spherical states in odd-mass Te nuclei has been discussed in more detail in a previous paper 16). 4.2. NEGATIVE-PARITY STATES

The experimental levels of negative parity belonging to the h,, system are compared in fig. 16 to the corresponding levels of the neighbouring doubly even Te nuclei . The energies of the 15 - -" JL - , I? - -" ~- and ~- -+ -V - transitions in odd-mass nuclei (in particular in 1 'Te) are similar to the 2+ -. 0 + , 4+ -. 2+ and 6± -" 4 + transition energies in the core nuclei . This suggests that the ~L - , i -, and i- states form a "decoupled" sequence . The aligned coupling of particles in the unique-parity orbital hV is one of the most fundamental excitation modes found in many odd-proton and odd-neutron nuclei around Z = 50. A compilation of the negative-parity bands in this mass region mostly interpreted as decoupled bands aa) is given in fig. 17. The energy ratio

117, 119,

121Te

183

r = (E(J)-E((J-2))/(E(R)-E(R-2)) is plotted as function of the neutron number

of the underlying core for the P = zs- ,11 - and ~- states and the respective core states R = 2 +, 4+ and 6 + of the A-1 core nuclide. The "decoupled" limit of this energy ratio is r = 1 . The odd-neutron nuclei show a relatively smooth behaviour especially for the -y - state. The energy ratio r approaches unity for neutron numbers midway between the shell closures at N = 50 and N = 82. Some hints for deviations from complete alignment can be found in the detailed analysis of the negative-parity level sequence

1 ----,--_____-0__ ___ 1~ 1~ _ 2w) 1 __

jMM~ ,

1

.assn

----1Mä

~X

JIM IDA '~ \

.

fl9A

_

661.3

11r2-

.1

6M

vv

i

264& ' W2

0 0+ 11/1-

I*Te

1177e

0 -0

207A

144.E

0 +

. '*Te 11% '2 °Te

0t

' 2'Te

'22Te

2*

W2-

17U

94A, 0 ,~ 11r2-

0+

t23Te '24Te 125Te 'XT@

Fig . 16. Systematics of negative-parity states in odd-mass Te nuclei in comparison with the low-lying states of the corresponding doubly even Te nuclei. The 1sä .123Te data are taken from refs . " . ° 1 ), respectively .

184

U. HAGEMANN et al.

in the odd-mass Te nuclei with A > 118. With rising core spin values R the spacings between maximum aligned states (J = J.=) of the ham®R multiplets show an increasing deviation from the level spacings of the g.s. band of the even-mass core (see also fig. 16). This behaviour may be understood in terms of a blocking effect due to the Pauli principle in the h., neutron orbital. The blocking effect has to be taken into account, ifstates of the g.s. band in doubly even Te nuclei contain a considerable contribution of the v(h.,) 2 configuration. In this case a J.-1 coupling should be energetically favoured . In fact this coupling seems to be mostly pronounced for the XL- states in the heavy odd-mass Te nuclei (see fig. 16). The coupling ofan h,, proton would not be affected by such a v(h V) 2 configuration in the core nucleus . In odd-proton iodine nuclei for example, maximum alignment has been observed 4) indeed . In going from 5O Sn, s2Te to 54Xe, , 611a nuclei (fig . 17) the whole character of the negative-parity band is changed into a AJ = 1 structure. The type of band structure is determined by the sign of the product qQ of the quasiparticle quadrupole moment q and the core quadrupole moment s9) Q . For positive sign we should observe a a AJ = 2 decoupled band whereas a AJ = 1 band is formed if qQ < 0. For positiveparity I + bands in odd-mass Pd nuclei the change in the band structures from a AJ = 2 to a AJ = 1 behaviour was explained s9) by the change of the sign of the effective coupling strength for the d.. particle due to a change of the occupation factor (u.I- - v 2.) if the chemical potential A crosses the spherical single-particle energy of the d t level . Such an explanation does not hold for the above mentioned change of the band character for isotones with N > 66, the chemical potential of which is regarded to be constant . The change of the band character may therefore be caused by shape fluctuations leading to a change of the sign of the core quadrupole moment Q.

Isobars with e.g. Z = 54 and Z = 55 with the same underlying core show again a change from a AJ = 1 to a AJ = 2 behaviour. This gives evidence, that in oddmass nuclei the nuclear shape is strongly influenced by the odd valence particle . This so-called dynamical polarization has recently been investigated 6°). For 1231 it has been shown, that the nuclear shape is considerably changed if the unpaired particle occupies different orbitals . Therefore, it is suggested to conclude also a quite different polarizing action on the underlying soft core, if the unpaired particle is a proton or a neutron. Furthermore, it should be mentioned that for neutron deficient odd-proton iodine nuclei the significant deviation of the energy ratio r from the decoupled limit will be removed if a coupling of a hole to the A + 1 core is assumed to be dominant (fig . 17). This points to the treatment of transitional nuclei where quasiparticle coupling to A -1 and A + 1 cores is taken into account 6U " 61) . In conclusion of our qualitative discussion, in the mass region under investigation severe transitional nuclei are encountered. The interplay of different aspects such as the blocking effect, shape fluctuation, dynamic polarization, as well as generalized

117,119,121Te

185

NUMBER OF NEUTRONS OF THE CORE Fig. 17 . Energy separation of the hl In bands in odd-mass nuclei near to Z = 50 compared with those of the g .s . bands of the appropriate doubly even A-1 core nuclei. The energy ratio r = (E(!)-E(J-2))J (E(R)-E(R-2)) is plotted as function of the neutron number of the core. Black dots stand for odd-N nuclei, open circles for odd-Z nuclei, triangles are taken, if hole-(A +I)-core coupling is assumed. Data of odd-mass nuclei are taken from ref. '°) for Mo and Ru nuclei, refs.' , ') for Pd, refs . 9- ") for C(, ref. '_) for Sn, refs. 1 . 3 ) for Sb, refs. " " °') and this paper for Te, refs .' " s . ss) for 1, refs. 13,14 .73) for Xe, ref. °') for Cs, ref. for Ba and ref. es) for La. Data for the doubly even cores are taken from ref. 52) .

186

U . HAGEMANN et al.

quasiparticle-core coupling, has to be taken into account in order to understand such transitional nuclei in their whole complexity . In a next step we want to test in a more quantitative way different models for the negative-parity system in odd-mass Te nuclei and to compare the energetic behaviour with the experimental findings . Generally, the aligned band structures can be understood in the particle-core coupling model, in which the nuclear structure is described by the coupling of spherical quasiparticles to quadrupole vibration modes 62) . In this model the above-mentioned enefgy ratio r is expected to be smaller than unity as was observed for instance in the I'd and Cd nuclei . If, however, the chemical potential comes close to the unique-parity orbit, as in the case of the heavier Te nuclei, this particlecore coupling model may not be sufficient. Two approaches have been tried to overcome these difficulties : (i) D6nau and Frauendorf 6t) developed a generalized core-quasiparticle coupling formalism which correctly accounts for the particlehole structure in the odd-A transitional nuclei . (ii) In a microscopic study Suzuki et al. 6s) took three-quasiparticle correlations into account. The behaviour encountered in Te nuclei (including non-yrast states -, - and zz) may also be compared to a situation where one particle is coupled to a rotorlike core, where thecore is triaxially deformed 6t) or shows a significant hexadecapole deformation 6a). In order to test these different approaches for explaining the level structure explicit model calculations have been performed although, according to Strutinsky calculations for the even-mass Te nuclei, no hints ~to triaxial or hexadecapole deformations were found 65 .66) . We investigated three models for the core field : (i) The rigid triaxial-rotor model, (ii) the soft-rotor model including hexadecapole deformation and (iii) the y-unstable-potential model (Wilets-Jean model 6')). In the calculations t we followed the lines of (i) Meyer-ter-Vehn 6s), (ii) Winter et al. 64) and (iii) D6nau and Frauendorf 6t) . In fig. 18 energy values of negative-parity -states obtained in these calculations are compared to the experimental energies . For the first glance the agreement with the experiment is similar for the three models though the used core models are based on rather different assumptions about the potential energy surface. However, the calculated level schemes show some discrepancies in detail . From the three model calculations the following conclusions may be drawn : (i) The assumption of a rigid triaxial shape for the cores is not adequate, leading to too wide energy spacings . (Note, that in fig. 18 the respective energy scales differ by a factor of two.) The inclusion of core softness would improve the agreement with the experiment . For neutron deficient Te nuclei the chemical potential is located at the beginning r The authors are very much indebted to Drs . J. Meyer-ter-Vehn, G . Winter and F . D8nau for placing their computer codes at our disposal .

117, 119 .121 Te

187 b

.a 3

û Y

42 C

F-

5, 1 Q Ó ,~ w G .9 u

!9 1 ol : 1 ~.

U

Va RP 0. e si

u

Ó~ w

W .

ki

ï

Li

Là IL .

 ~S W Q

18 8

U . HAGEMANN et ai.

of the b y Nilsson multiplet (A x e2). In this situation a correct level order up to spin -y - is reached for the assymmetry y 30°. Only the low-lying 4 7. state cannot be reproduced in. this calculation as well. For heavier Te nuclei A lies midway in the multiplet (A ~ e3) . With this position of the chemical potential, low-lying I - and states as well as ~-, -u - and iz - , 12 - doublets will be obtained at more axially symmetric shape (y x 5°). Again the low-lying 2,' - state cannot be described at the same y-deformation . Also the second _Vz state appears too high in the calculated level scheme. (ii) In the theoretical approach of a soft rotor it is attempted to describe the negative-parity band by a Coriolis coupling calculation. In this calculation the moment of inertia parameter was assumed to vary with collective angular momentum in the same way as in the g.s. band of doubly even Te nuclei . Such a description was successful for the interpretation of the deformed J + [404] band in 121Te as discussed in ref. 16) . A detailed analysis of the calculated negative-parity bands gives evidence for the influence of hexadecapole deformations e4 in these nuclei. Indeed, its inclusion into the calculation improves the agreement with the experimental data. The inversion of the doublet structures for the yrast states, i .e. from thelevel order E(J..) > E(J.x -1) to the reverse order E(J,u -1) > E(J.), is well explained with a hexadecapole deformation e4 = -0 .025. However, some troubles appear with the incorrect order of the low-spin levels J - , J - . ., 15 %) bigger value for the effective moment of inertia would A somewhat ( ; bring the energy spacings into better absolute agreement with the experimental ones. The additional contribution to the effective moment of inertia may be caused by the unpaired particle . To test the reliability of hexadecapole deformation in these odd-mass transitional nuclei a systematic investigation would be desirable. In other regions of the nuclidic chart there are hints to the significance of hexadecapole deformation in odd-mass systems . So, for instance, in 193 Au evidence for an influence of hexadecapole deformation on positive parity states was found 69), and in 153Tb the nh,, system is well described"") with e4 = -0.02. (iii) A y-unstable potential for the core nuclei is the most favourable one in Te nuclei as the calculation of the potential energy surface pointed out 66) . The results of the core-particle calculation are in agreement with the experiment provided the set of collective states included in the computation is sufficiently large. In our approach core states up to spin R = 14 grouped into multiplets with energy 4 v(v+3) (where v is the seniority) were included . The peculiar lowering of the I level occurs as in the triaxial case. The order of the ~-, ~- doublet is, however, not in agreement with the experiment. Here the inclusion of the blocking effect could give a further improvement. Another reason could be the truncation of the single-particle basis. In the present calculation the single-particle space containes only the h,V shell, because higher dimensions were unmanageable for us. Shells energetically distant by several MeV can change the order of the doublet structure

117 . 119, 12 1Te

189

of the spectrum . The importance of a sufficient large configuration space for the description of transitional nuclei has also been emphasized by Leander'°) . In conclusion it seems hard to prefer one of the considered models for the oddmass Te nuclei. Only a rigid and axial shape of the core nucleus is certainly ruled out. However, there is no sharp cut-off between a static or dynamic y-deformation . Indeed, one possibility of explaining the difficulties mentioned above is the assumption of different deformations for different orbitals. This idea ofvariable quadrupole, hexadecapole or nonaxial deformations would be conformable to the starting point of an underlying soft core . From investigations in the region of transitional nuclei with Z z 82 the similar conclusion has been drawn 61, 71, 72), that the only systematics of level energies does not allow a definite decision between the above mentioned models. It surely will become necessary to look for more model sensitive expectation values and to compare them with the experiment . The authors are indebted to Drs. F. D6nau and G. Winter for many valuable discussions. References 1) W. D. Fromm, H.-F. Brinckmann, F. DSnau, C. Heiser, F. R. May, V. V. Pashkevich and H. Rotter, Nucl . Phys. A243 (1975) 9 2) A. K. Gaigalas, R. E. Shroy, G. Schatz and D. B. Fossan, Phys . Rev. Lett . 35 (1975) 555 3) J. Bron, W. H. A. Hesselink, H. Badet, H. Verheul and G. Vanden Berghe, Nucl. Phys. A279 (1977) 365 4) U. Hagemann, HA . Keller and H.-F. Brinckmann, Nucl . Phys. A289 (1977) 292 5) D. M. Gordon, M. Gai, A. K. Gaigalas, R. E. Shroy and D. B. Fossan, Phys . Lett. 67B (1977) 161 6) U. Garg, T. P. Sj(reen and D. B. Fossan, Phys. Rev. Lett . 40 (1978) 831 7) F. A. Rickey and D. C. Simms, Phys. Rev. Lett. 31 (1973) 404 8) W.'Klamm and J. Rekstad, Nucl . Phys . A258 (1976) 61 9) U. Hagemann, H.-F. Brinckmann, W. D. Fromm, C. Heiser and H. Rotter, Nucl . Phys. A229 (1974) 112 10) D. C. Stromswold, D. O. Elliott, Y. K. Lee, L. E. Samuelson, J. A. Grau, F. A. Rickey and D. C. Simms, Phys . Rev. C17 (1978) 143 11) S. Ohya, Y. Shida, N. Yoshikawa, O. Hashimoto and M. Ishii, Contributed papers to Int. Conf. on nuclear structure, Tokyo 1977, p. 347 12) O. Hashimoto. Y. Shida, S. Ohya, G. Ch . Madueme, N. Yoshikawa and M. Sakai, Proc . Int. Conf. . Soc. Japan 44 (1978) Suppl. p. 532 on nuclear structure._Tokao 1977, J. Phys 13) Ì. Rezanka, A. Kerek, A. Luukko and C. J. Herrlander, Nucl . Phys. A141(1970) 130 14) A. Kerek, A. Luukko, M. Grecescu and J. Sztarkier, Nucl. Phys . A172 (1971) 603 15) A. Ttzon, J. soon .and N. Yoshikwa, Contributed papers Int. Symp . on high-spin states and nuclear structure, Dresden 1977, ZfK-336 p. 17 16) U. Hagemann, HA . Keller, Ch . Protochristow and F. Stary, Z. Phys. A290 (1979) 399 17) G. Winter, ZfK-182 (1969) and private communication; E. Will, ZfK-283 (1974) 185 (annual report) 18) V. Zobel, J. Eberth, U. Eberth and E. Eube, Nucl . Instr. 141 (1977) 329 19) G. Lang and G. Winter, ZfK-295 (1975) 137 (annual report) 20) G. Winter, ZfK-315 (1976) 201 (annual report) ; H.-J. Keller, ZfK-350(1978) 245 (annual report) 21) P. Manfress, W. Andrejtschfi, F. Dubbers, K.-D. Schilling and W. Seidel, ZfK-255 (1973) ; P. Renner, J.-U. Berlin and L. KAubler, ZfK-315 (1976) 165 (annual report)

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"Te

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