Yrast spectroscopy of the N=48 nucleus 84Kr

Nuclear Physics A514 (1990) 401-433 North-Holland

YRAST S P E C T R O S C O P Y OF THE N = 4 8 N U C L E U S 84Kr H. ROTTER, J. D ( ) R I N G , L. FUNKE, L. K,~UBLER, H. PRADE, R. S C H W E N G N E R and G. WINTER

Zentralinstitut fiir Kernforsehung, Rossendorf DDR-8051 Dresden, GDR A.E. ZOBOV, A.P. G R I N B E R G , I.KH. LEMBERG, A.S. MISH1N, L.A. RASSADIN, I.N. C H U G U N O V , A.D. EF1MOV and K.1. E R O K H I N A

A.F. Joffe Physico-Technical Institute, SU-194021 Leningrad, USSR V.I. 1SAKOV

Leningrad Nuclear Physics Institute, SU-188350 Gatchina, USSR L.O. N O R L I N and U. R O S E N G A R D

Manne Siegbahn Institute of Physics, S-10405 Stockholm, Sweden Received 18 January 1990 (Revised 15 March 1990)

Abstract: More than 20 new levels of 84Kr populated via the 82Se(a, 2n 3') reaction have been established up to spin J - 14h at an excitation energy of E X= 7.65 MeV by in-beam 3,-ray and conversion-electron spectroscopy. For 31 excited states the mean lifetimes have been measured by applying Doppler-shift and pulsed-beam 3,-ray timing methods. The dominant structure of the J= = 12 + isomer at 5373 keV (T~/2 = 44:i-2 ns) has been inferred from the comparison of the experimental g-factor of g(12 +) +0.173-0.02 with estimates for different 4qp configurations to be the stretched 4qp configuration "rr(fs/12, p3/12)v(g9/2). This interpretation of the 12 + state has been confirmed by shell-model calculations with SSSr as the core. Some enhancement of the E2 strength observed for the 10~ ~ 8 + transition might point to the alignment of two g9/2 protons. Most of the negative-parity states could be grouped into two band-like sequences, built on top of the two lowest-lying 5 states, with zlJ = 2 and AJ = 1, respectively, and B(E2) values of about 10 W.u. Some arguments allow the two-neutron hole configuration v(gg/12, Pl/2)I to be ascribed to the 5~ state and the AJ = 2 level sequence, whereas for the 52 state and the AJ = 1 level pattern a two-proton configuration 7r(f5/12 or p3/12, g9/2) might be predominant. The highest-lying levels of S4Kr observed up to spin 14h at an excitation energy of 7.65 MeV were found to have odd parity and to be connected by fast M1 transitions. NUCLEAR REACTIONS 82Se(a, 2n), E - 1 2 - 2 7 M e V ; measured Ev, 1~,, l(ce), Iv(E) , Iv(0), 3`(0, H, t) 3,3,-, 3,3,(t)-coin, 3,(t), 3,-ray linear polarization, DSA, recoil distance. 84Kr deduced levels, J, rr, ICC, ~*, 6 ( E 2 / M I ) , B(A), g-factor, configurations. Enriched targets. Ge, Ge(Li), NaI(T1), p-Si detectors. Shell-model calculations.

1. Introduction The evidence for strong quadrupole ground-state

deformation

bands of the neutron-deficient

provided

i) b y t h e r o t a t i o n a l - l i k e

k r y p t o n n u c l i d e s 74'76Kr h a s s t i m u l a t e d

0375-9474/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

402

H. Rotter et aL / Yrast spectroscopy

the interest in studying the level structure also of the heavier-mass Kr nuclides, which are situated in the transitional region between strong deformation and spherical shape. In particular, the high-spin states of the transitional Kr nuclei have been the subject of recent spectroscopic investigations, to trace, especially, the interplay between collective and few-quasiparticle excitations in dependence on the number of neutrons. For the heavier Kr isotopes near the N = 50 closed-neutron-shell nucleus 86Kr, however, little information on the high-spin levels is available till now. In the present work on the N = 48 nucleus 84Kr special attention has been given to measurements of electromagnetic transition probabilities and magnetic moments of higher-lying yrast states. The paper continues our systematic study of yrast states in even-mass 2-4) and odd-mass 5-8) Kr nuclides. Preliminary results of this investigation, in particular the evidence for a four-quasiparticle (4qp) isomer, have been published previously 9,1o). So far, excited states of 84Kr have mainly been investigated in /3-decay studies of 84Br and 84Rb as well as by neutron capture work [see the latest A = 84 compilation 1~)]. Additional data have been obtained from two earlier (a, 2n) in-beam y-ray spectroscopic investigations 12.~3), from Coulomb excitation 14) and proton scattering 11) experiments.

2. Experimental methods and results Levels of 84Kr have been studied in the present work by in-beam y-ray and conversion-electron spectroscopy via the 82Se(ce, 2n) reaction with 27 MeV a-particle beams provided by the 120 cm cyclotrons of the FTI Leningrad and the Z f K Rossendorf. This c~-particle energy exceeds the energy for the m a x i m u m cross section of the 82Se(ce, 2n) reaction by about 5 MeV and was chosen in most of the experiments to enhance the population of high-spin states. As a consequence of the relatively low threshold of the 82Se(ce, 3n) reaction the analysis of the singles spectra, however, is complicated due to the considerable yield of 83Kr. Relative y-ray excitation functions, prompt yy-coincidences and angular distributions of the y-rays were measured and analyzed in Leningrad as well as in Rossendoff, whereas other experiments demanding some specific techniques or experimental conditions were performed at one of the laboratories only. That concerns internal-conversion-electron and plunger measurements carried out in Leningrad, while linear polarization, magnetic moment, pulsed-beam y-ray timing and delayed ),y-coincidence measurements were performed in Rossendorf. A complementary g-factor experiment was carried out at the former 225 cm cyclotron in Stockholm. The targets enriched to 92.2% in 82Se consisted of layers of a thickness of some m g . cm -2 except those for the plunger and conversion-electron measurements. In the experiments performed in Leningrad at E~ = 14-27 MeV a 6 mg• cm -2 layer of 82Se evaporated on a 0.3 mg • cm 2 plastic foil was used; for the measurements at E ~ = 1 2 - 1 6 M e V a 2 . 8 m g . c m 2 layer of 82Se was evaporated on a 2 . 8 m g . c m 2

403

H. Rotter et al. / Yrast spectroscopy

tantalum backing. For m o s t o f the e x p e r i m e n t s in R o s s e n d o r f a target prepared by depositing 20 mg • c m 2 p o w d e r o f S~Se on a 0.7 mg • c m - 2 plastic backing was used; the target for the angular distribution m e a s u r e m e n t consisted o f a self-supporting 8 mg • c m -~ foil of 8~Se.

2.1. SINGLES MEASUREMENTS The in-beam

T-ray spectrum

following the if-particle bombardment

o f a S2Se

t a r g e t w a s m e a s u r e d f r o m 50 k e V u p to 2.4 M e V w i t h v a r i o u s G e d e t e c t o r s o f u p t o 10% r e l a t i v e e f f i c i e n c y . T h e e n e r g y r e s o l u t i o n FWHM

w a s t y p i c a l l y b e t t e r t h a n 2.5 k e V

f o r 1.3 M e V y - r a y s . A s p e c t r u m m e a s u r e d

with a high-purity Ge detector

o f 1 0 % r e l a t i v e e f f i c i e n c y is d i s p l a y e d i n fig. 1. F o r e n e r g y c a l i b r a t i o n t h e y - r a y spectrum

was recorded

~

40

in a separate run simultaneously

m ~

o

with the radiation from

2 7 M e V o( PARTICLES ON 82Se SINGLES SPECTRUM ( 0 = 9 0 °}

° a3Kr

20

0j

-0~ -

10 0

~ -

~q

30

w

50

,~

70

10 o

z

~

c)

o

~

....

~ -

~

~

,'o

y~

, =_~?o

~

,o~

--

2 0 - 6

700

,q

14'00

- - ~

900

'

16'00

• ENERGY (keV)

1100

J

1800

1300

'

20~00

Fig. 1. Singles y-ray spectrum recorded with a high-purity Ge detector of 10% relative efficiency (FWHM 0.9 and 1.9 keV for 60 and 1300 keV y-rays, respectively) during the irradiation of a 8~Se target of 8 mg • cm 2 thickness with 27 MeV a-particles. Peaks marked by their energy in keV have been assigned to ~4Kr.

404

H. Rotter et al. / Yrast spectroscopy

several radioactive sources. Relative y-ray yields were measured as a function o f the c~-particle b e a m energy; some examples are shown in fig. 2. The angular distribution o f the y-rays was determined at E~ = 27 MeV by recording the radiation with a Ge detector positioned at angles o f 20 °, 35 °, 45 °, 55 °, 65 °, 90 ° and 115 ° with respect to the beam direction at a distance o f 20 cm from the target (Leningrad) as well as at 25 °, 90 °, 105 °, 120 °, 135 ° and 155 ° at a distance o f 12 cm (Rossendorf). In addition, the angular distribution o f the y-rays was measured in Leningrad also at b e a m energies o f 20 and 12 MeV, to enable some transitions proceeding from low-spin states to be studied without interference with transitions o f nearly the same energy deexciting high-spin states. For normalization the angular distribution o f the well-known 4+-.2~ - 1463.8 keV transition 11) o f S4Kr was used. Its anisotropy, in contrast to that o f the 4+-* 2 + yrast transition, is not reduced due to the missing feeding from the 8 + microsecond isomer. The feeding of the 4~- level from the f l - decay o f 84mBr [jTr = (5, 6 )] p r o d u c e d by the 82Se(c~, pn) reaction has been neglected. The angular distribution coefficients A2 and A 4 o f the 1463.8 keV stretched E2 transition have been adjusted to the theoretical values 15) taking into a c c o u n t the attenuation coefficients a 2 = 0 . 5 5 and t Y 4 = 0 . 1 5 , a s suggested by

i

J

i

I

E~ J~

~

1213.54~

500 1077.6 6÷

1463. 84* 63.5 8{

200

>,I.-[I.-J,.100 I Z 5o i

1968.0101

f

- J-

730.2 lO3

-> 2O I--....1 I..IA

wlO

¢6 50 2'3 J7 BOMBARDING E N E R G Y E~(MeV) Fig. 2. Examples of relative excitation functions, labelled by the transition energy in keV and spin and parity of the initial state.

H. Rotter et al. / Yrast spectroscopy

405

systematics 3,4,16) and statistical-model calculations 17). With this normalization consistent A~ and A4 values resulted for well-established stretched quadrupole and dipole transitions of s2"S3Krbeing present in the singles spectra. The angular distribution coefficients A2 and A4 deduced for the y-ray transitions of 84Kr are listed in table 1 together with the energies and intensities. The latter have been determined taking into account the Doppler shift of the y-ray energies (see subsect. 2.3). For the stronger y-ray transitions the linear polarization was measured with two different polarimeters at E~ = 27 MeV to cover the y-ray energies of 169 and 1968 keV arising from the decay of the 4qp isomer. For y-rays up to 1.5 MeV a plate-shaped Ge(Li) detector of 27 x 27 x 5 mm 3 active volume was applied and positioned 14 cm below the target with the detector plane being either parallel or perpendicular to the reaction plane. For y-ray energies up to 2 MeV a set-up of two Ge(Li) detectors of 5% and 7% relative efficiency was used at a distance of 17 cm from the target, both detectors acting as scatterer and absorber. Details of the polarimeters and of the specific data analysis have been described previously 3,1s,19). In order to normalize the spectra measured at the two orientations of the polarimeters the polarization value P~o calculated from the angular distribution coefficients of the 1463.8 keV E2 transition was used. The results of the polarization measurements are compiled in table 2, where the experimental polarization values Pexv are compared with the values Pa.d calculated from the experimental values A2, A4 and & Transitions with change of parity are characterized by opposite signs of Pexp and P~d. The agreement between the experimental polarization values obtained with the two polarimeters as well as that between experimental and calculated values is fairly good for most of the transitions considered. Furthermore, the multipolarity of several strong transitions up to 1.1 MeV could be determined from experimental internal-conversion coefficients. The conversionelectron spectrum was measured in-beam by means of a broad-range electron spectrometer of the mini-orange type described in refs. 17,2o). The target consisted of a 0.4 mg • cm 2 layer of ~2Se evaporated on a 0.3 mg • cm -2 plastic backing. The transversal magnetic field was produced by an arrangement of four plane SmCo5 plates of trapezoid-shaped contour, that enabled us to nearly double the transmission in the energy range of interest compared to the set-up with rectangular plates 21). The transmission of the spectrometer with four plates was determined to be T = 0.5-1.2% of 27r in the energy range of Ee = 150-800 keV with the maximum found at about 300 keV. For calibrating the transmission, conversion electrons emitted by several radioactive sources of known absolute strength were used and likewise the continuum /3-ray spectrum of a 137Cs standard source, recorded with and without the magnetic filter. The electrons were measured by a p-type Si surface-barrier detector (12 mm diameter, 2.3 keV F W H M at Ee = 975 keV), The detector together with the FET in the input stage of the preamplifier was cooled down near the liquid-nitrogen temperature and separated from the beam-pipe vacuum by an aluminized 0.3 mg • cm -2 plastic foil. In table 3, the experimental K-shell conversion

406

H. Rotter et al. / Yrast spectroscopy

TABLE 1 Gamma-ray transitions assigned to 84Kr from the (c~, 2n) reaction ~) E v (keY) 63.5 (1) 169.3 (1) 179.0 (5) 180.1 (2) 244.5 (1) 298.5 (1) 367.6 (1) 419,0 (3) 425.2 (1) 443.7 (2) 447.6 (3) 448.9 (1) 519 (1) 540.7 (2) 556.6 (2) 605.1 (4) 612.1 (2) 637.4 (3) 659.1 (2) 662.6(3) 670.4 (2) 694 (1) 711.6 (2) 730.2 (1) 763.0 (2) 767.3 (2) 801.1 (3) 802.4 (3) 816.6 (2) 881"0 (33 k) 881.6(13 886.9 (2) 943.2 (2) 947.6 (3) 950.0 (2) 1016.2 (3) 1049.4 (2) 1077.6 (1) 1097.3 (3) 1114(1) 1124.5 (2) 1141.5 (5) 1198.6 (2) 1200.7 (2) 1213.5 (1) 1228.6 (3) 1252.6 (2) 1268.1 (3) 1463.8 (1)

A2 ")

1.r b)

44 (7) ~) 100 (13) r) 4 (1) h) 20 (3) 33 (3) 9 (1) 77 (8) 3 (1) 240 (20) 25 (7) 12 (3) 55 (7) =3 h) 15 (5) 50 (6) 6 (3) 64 (9) 13 (4) 40 (6) = 1 0 h) 11 (4) =25 h) 9 (3) 38 (6) 11 (3) 19 (3) 23 (7) 15 (5) 8 (2) ~ll0h) 1000 ~) 20 (3) 30 (5) 9 (3) 21 (2) m) 15 (3) 24 (5) 450 (30) --20 h) --15h) 105 (15) --8 ") 24 (5) 43 (8) 645 (30) 10 (3) 11 (3) --7 h) 315 (20)

0.08 (1) g) 0.34 (1) 0.28 --0.11 --0.22 0,11

A4 ':) -0,05 (2) -0.08 (2)

(3) (2) (2) (1)

0.01 0,00 0,03 0.02

(4) (3) (3) (2)

--0.20 (1) -0.31 (2) 0.23 (4) 0.31 (2)

0.01 0.01 -0.09 0.03

(2) (3) (6) (4)

0.05 0.03 -0.17 0.35 -0.31 -0.24

-0.01 0.02 0.07 0.06

(2) (3) (6) ~) (4)

(2) (1) (5) ~) (3) (6) (2)

6 d)

--0.12 (8) 0.07 (3) 0.24 (6)

0.18 (5) 0.17 (4)

0.02 (3)

-0.10 (3)

~ J

0.33 ( I ) --0.34 (5) 0.37 (2)

0.09 (3) 0.04 (6) --0.06 (4)

0.16(2)

0.00(3)

-0.34 (8) / ~

0.22(1) g) 0.26 (123 0.27 (8) -0.01 0.25 0.37 0.11

(3) ~) (2) i) (3) (1) g)

--0.20 (2) 0.40 0.37 0.17 --0.58 0.36

(5) (2) (2) ~) (4) ,7) (8)

0.27 (1)J)

--0.02(2) --0.02 (9) 0.02 0.01 -0.07 0.01

(3) ~) (3) i) (5) (2)

0.01 (3) 0.04 (8) --0.08 (3) --0.03 (3) --0.24 (10) 0.05 (2)~)

0.4 (1)

0.16 (8)

E i (keY) e) 3236 5373 coin 444 3832 3832 3587 3587 3639 2771 7016 2345 3220 3220 4929 4388 2700 3832 7653 3832 3951 6572 6068 5641 5449 4350 4719 4388 2700 3587 3652 882 4719 3289 3043 1832 1898 5902 3173 4929 coin 244, 368, 557, 881/882 3220 6590 6572 4852 2095 3999 5641 6472 2345

407

H. Rotter et al. / Yrast spectroscopy TABLE 1--continued E~, (keV) 1543.7 (3) 1546.0 (2) 1605.7 (3) 1616.1 (2) 1636.8 (4) 1740 (1) 1741.3 (2) 1856.2 (3) 1897.8 (3) 1968.0 (2) 2160.8 (6)

I~,b) 3 (1) 20 (4) 7 (3) 18 (5) ~3 h) --70 h) 6.0 (3) ,n) 15 (4) 35 (4) 170 (20) 8 (3)

A2 c)

0.39 0.32 -0.23 --0.45 0.79 0.29 0.29 0.20 0.34

(3) (4) (3) (10)n) (7) (5)~) (2) (3) (1)

A4 c)

~ d)

-0.10 (6) -0.07 (5) 0.03 (5) 0.08 --0.23 --0.02 --0.10 --0.05

(8) (8)~) (3) (6) (3)

--1.5 (5/10)

e i (keV) °) 3639 4719 3951 4852 4407 4976 2623 3951 1898 5204 3043

") In the present paper the errors are given in parentheses in units of the last decimal; if asymmetric, the notation is upper/lower uncertainty. b) Relative intensities of the y-rays at E,~ = 27 MeV, normalized to the intensity (= 1000) of the 2~-+ 0~ transition. The values were derived either from the isotropic term of the angular distribution [see footnote ")], or, if not evaluated, from a spectrum recorded at an angle of 125 ° relative to the beam axis, or in case of a complex peak from a coincidence spectrum measured at 90 °. c) Angular distribution coefficients determined at E,~ = 27 MeV, except for some transitions, and normalized to the angular distribution of the 1463.8 keV y-ray transition. The values given for E,~ = 27 MeV are the averages of the values obtained in Leningrad and Rossendorf. a) Quadrupole-dipole mixing ratios as derived from the angular distribution taking into consideration the attenuation. °) Energy of the initial state according to the assignment in the level scheme. If the transition is not placed in the level scheme, its coincidence relation is given. ~) For internal conversion see table 3. g) Anisotropy reduced in addition due to feeding from the 8 ~ microsecond isomer. h) Intensity estimated from the coincidence measurement. ~) Angular distribution measured at E, ~ 12 MeV. k) Gamma-ray energy deduced from level spacing (see subsect. 3.2). t) Normalization. m) Intensity determined at E, - 12 MeV. ,1) Angular distribution measured at E,~ = 20 MeV.

coefficients determined in the present work including the total conversion coefficient of the 63.5 keV transition (see subsect. 2.2) are presented and compared with theoretical values 22) for transitions of pure multipolarity. 2.2. G A M M A - G A M M A C O I N C I D E N C E MEASUREMENTS

Extensive prompt yy-coincidence measurements up to 2 MeV y-ray energy were performed at c~-particle energies of 27, 23 and 12 MeV in Leningrad and at 27 MeV in Rossendorf with a time window of 50 ns selected in the fast coincidence circuit. Two Ge(Li) detectors of about 6% relative efficiency placed perpendicular to the beam axis were used. About 8 x 107 coincidences in each of the measurements were stored event by event in a two-parameter mode (E~, E~2) on magnetic tape. The coincidence events were sorted of Lline into a two-dimensional matrix of 2048 x 2048

408

H. Rotter et aL / Yrast spectroscopy

TABLE 2 Linear polarization data on y-ray transitions of ~4Kr measured at E~ = 27 MeV

Ez, (keY)

Pa.d. a)

169.3 180.1 244.5 298.5 367.6 425.2 443.7 448.9 556.6 612.1 659.1 730.2 801.1/802.4 881.0/881.6 886.9 943.2 1049.4 1077.6 1124.5 1198.6 1200.7 1213.5 1463.8 1897.8 1968.0

0.57 (5) 0.56(10) -0.34(15) -0.28 (3) -0.46 (30) -0.27 (3) -0.41 (6) 0.57 (7) -0.40 (35) 0.60 (7) -0.31 (3) 0.55 (3) 0.26 (4) 0.36 (4) -0.34 (20) -0.58 (30) 0.65 (8) 0.17 (2) -0.27 (3) 0.77 (12) 0.64 (5) 0.26 (4) 0.44 (5) 0.28 (7) 0.59 (6)

eexp ~) (plate-shaped detector) 0.42 (6) 0.3 (3) -0.5 (1) 0.25 (20) -0.38 (4) 0.20 (4) -0.05 (20) 0.57 (10) 0.33 (10) 0.23 (7) 0.20 (13) 0.10 (14) 0.55 (22) 0.24 (4) 1 (1) -0.32 (20) 1.2 (3) 0.16 (5) 0.17 (10) -0.8 (9) 0.03 (40) 0.22 (5) 0.45 (7)

eoxp h) (two detectors)

-0.45 (25) 0.20 (2) -0.32 (17) 0.41 (10) 0.33 (7) 0.41 (8) 0.34 (8) 0.41 (7) 0.28 (1) 0.35 (20) -0.44 (25) 0.07 (2) 0.19 (2) 0.32 (6) -0.4 (3) 0.32 (12) 0.23 (2) 0.48 (5) 1.0 (4) 0.56 (15)

Multipolarity c)

E2 M l + l % E2 M1 +0.5% E2 E1 M1 +6% E2 E1 M1 M1 M1 +3% E2 E2 E1 E2 E2/E1 E2/E2 El MI + 16% E2 E2 E2 E1 E1 E2 E2 E2 E2 E2

'~) Polarization value calculated from the experimental values of A2, A 4 and 6 (see table 1) according to eq. (2) in ref. 3) for a transition without parity change. b) Experimental polarization value derived according to the formula P e x p - Q ~[aN(90 °) N(O°)]/[(aN(90°)+N(O°)], where Q is the polarization sensitivity of the polarimeter and a is a normalization factor. The errors include statistics and uncertainties of a and Q. c) Multipolarity of the transitions as resulting from the linear polarization of the y-rays and the quadrupole-dipole mixing ratio (see table 1). c h a n n e l s a n d w e r e s u b s e q u e n t l y a n a l y z e d b y s e t t i n g g a t e s in t h e e n e r g y a x e s o f t h e matrix on photopeaks ground-corrected

and appropriate

coincidence

background

intervals. Examples

of back-

s p e c t r a f o r s e l e c t e d y - r a y s a r e s h o w n in fig. 3. T h e

c o i n c i d e n c e r e l a t i o n s o b t a i n e d will b e d i s c u s s e d in c o n n e c t i o n w i t h t h e level s c h e m e (sect. 3). S i n c e t h e 8 + y r a s t s t a t e o f S4Kr h a s a m i c r o s e c o n d

half-life, the higher-spin levels

decaying into this state could be established by ixs-delayed coincidences o r d e r to d e t e c t t h e t r a n s i t i o n s f e e d i n g t h e 8 + i s o m e r , a t i m e - t o - a m p l i t u d e (TAC)

o n l y . In converter

was started by the signals from a 9% efficiency Ge(Li) detector and was

s t o p p e d b y t h e p u l s e s o f a N a I ( T 1 ) s c i n t i l l a t i o n d e t e c t o r (7.5 c m d i a m e t e r x 7.5 c m

H. Rotter et al. / Yrast spectroscopy

409

TABLE 3 Experimental K-shell conversion coefficients for transitions of S4Kr in comparison with theoretical values

103× a~,oor~) E v (keV)

63.5 169.3 244.5 367.6 425.2 556.6 612.1 1077.6

103 × c~,Xp")

7 ( 2 ) x 1 0 ~°) 88 (30) 12 (2) 4.1 (4) 1.5 (2) 1.6 (2) 1.8 (2) 0.4 (1)

Multipolarity El

MI

E2

M2

350 a) 17 5,8 1,9 1,3 0.67 0,53 0.17

460 d) 28 I1 4.0 2.8 1.5 1.2 0.35

5000 d) 116 31 7.6 4.7 2.1 1.6 0.37

7300 d) 186 55 15 9.8 4.6 3.5 0.8

E2, M2 E2 MI M1 El MI(+E2) E2 (E2)

;') The 881.6 keV transition was assumed to be a pure E2 one and its K-shell conversion coefficient was used for normalization (a~"r(881.6 keV) = 5.9 x 10 4). h) Theoretical K-shell conversion coefficients 22). ~) Total conversion coefficient estimated from the intensity balance in the isomeric decay (see subsect. 2.2). d) Theoretical total conversion coefficient 2z).

length). In the NaI(T1) detector branch a y-ray energy interval from about 800 to 1300 keV was selected covering the main y-ray transitions of the cascade depopulating the isomer. Spectra of prompt and delayed y-rays were obtained by setting gates in the time distribution. Behind the prompt peak three successive time windows of 0.36 I~S width each were selected. Since the rate of random coincidences increases considerably during the beam bursts of few nanoseconds (time between them 90 ns), the spectra of delayed y-rays contain, apart from the y-rays feeding the 1.9 ~s isomer, also all strong y-ray transitions of S4Kr with relative intensities like those observed in the singles spectrum. In addition, the feeding y-rays could be distinguished by their decreasing intensity in the three spectra of delayed events from lines arising from random coincidences, which are of constant intensity in the delayed spectra. As shown in fig. 4a, the y-rays of 169.3,443.7, 694, 1198.6, 1268.1, 1616.1, 1740 and 1968.0 keV, and with less confidence that of 637.4 keV were found to be connected with the feeding of the 8 + isomer. In a second delayed-coincidence experiment the pulses from the NaI(TI) detector (lower threshold set on E ~ = 1300 keV) were used to start the TAC, whereas the stop signals for the TAC were supplied by a 1 cm 3 Ge low-energy photon detector. Gamma-rays arising from the decay of the 8' isomer were recorded up to about 900 keV in three successive time gates of 0.36 t~s width each, which were selected in the time distribution behind the prompt peak. The spectrum of delayed y-rays displayed in fig. 4b clearly revealed the isomeric 8 ~~ 6 + transition at E~= 63.5 (1)keV. Considering the intensity balance between the y-rays of 63.5 and 881.6 keV in the isomeric decay, the total conversion coefficient of the isomeric

410

H. Rotter et al. / Yrast spectroscopy I

i

i

i

[

r

i

i

-

I

~

27MeV 0(-PARTICLES ON a2Se COINCIDENCE SPECTRA

1 0.5

~

~ 0", ~

-4"

GATE 169keV ~ I

~

~

L

t

1

r~ -.tro

t---

..,.~

a:~co

~

I/ oo

o~

t--

~

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l

--

GATE 244 keV i,

0.5l

~

~--[ - - . c o

c',4

0.2

,.

~

~

.

co,~

~

~

~co ~o~

GATE 2 9 8 k e Y

~"

~

o

~_~

GATE 444 keY

t~

O.

.... ~

|

0.4

__

.~ ~

co

'

0.2

~

~- 0oo b

~,~~o

,,

~ ~

~

~

~-

co

~ o

/

T

~I~

~

GATE 4481449 keY _co

~

~

#

o

~

~

~

~AT ~ 7qni-e,,

1

..t

~Ln

~

u~o,-o~rq

0oh-co

co~

GATE 881/882 keY

~1-~

"i

~ ~ ~

0.4

~ ~,

co

o

~~

~

'

~

GATE 943 keY

o

~

~ GATE 1049 keV

~"

~

u~

0.2]

,~

O~

"~ -4-

on

0.1; u

~

,/

0.5, '

~

- ....

~

GATE 1199 keY

..J

0"05 ~ ~ . . ~ a . ~ . . ~ I

200

I

~-.

~0o ~o,:o "/

GATE 1201 keY

,,,_,.a~,, ......... h . . . . . . . I

I

600

i

GATE 1898 keV I

i

1000 ENERGY (keV)

.__

i

1400

I

I

I

1800

Fig. 3. Examples of background-corrected 1,3,-coincidence spectra recorded during the bombardment of S2Se with 27 MeV ~-particles. Peaks marked by their energy in keV are considered to be in coincidence with the gating y-ray transition.

411

H. Rotter el al. / Yrast spectroscopy

(a) 10

~.

27MeV a - P A R T I C L E S ON 82Se DELAYED COINCIDENCES

co z::m

~ t

o

i

+

g,

o~

m

,

I

J,A

I

,

I

400

1

800

I

co

co

~

I

i

]

I

I

1200

o

I

I

I

1600

r lO

s

~.

(b)

×5

o--

I

2000

200

6;0 ENERGY (keV)

Fig. 4. Spectra of delayed yy-coincidences recorded during the irradiation of a ~Se target with 27 MeV ~,-particles. Random coincidences have been subtracted. Spectrum (a) (delay 0.56 p.s, width of gate 1.1 ~s) exhibits the y-rays (labelled by their energy in keV) feeding the 8+ isomer ( T~/, = 1.9 p,s) o f g4~Zr 1,, , while spectrum (b) (delay 0.72 p,s, width of gate 0.72 b~s) displays the y-rays depopulating that isomer.

63.5 keV transition c o u l d be d e t e r m i n e d as Cqod63.5 keV) = 7 (2), which is c o m p a t i b l e with the m u l t i p o l a r i t y E2 or M2 (see subsect. 3.l).

2.3. LIFETIME MEASUREMENTS So far, lifetimes o f e x c it e d states in S4Kr were m e a s u r e d only for the 8 + and 2 + yrast levels 1_~,~4). In the p r e s e n t work the m e a n lifetimes o f 31 excited states in S4Kr h a v e b e e n d e t e r m i n e d by m e a n s o f the D S A , R D D S and p u l s e d - b e a m y-ray t i m i n g m e t h o d s c o v e r i n g a time region f r o m tenths o f p i c o s e c o n d s up to a few m i c r o s e c o n d s . T h e D S A m e t h o d was a p p l i e d to y - r a y spectra m e a s u r e d u n d e r different angles (see subsect. 2.1) at a - p a r t i c l e energies o f 27, 20, 14 an d 12 MeV. Th e b e a m energy was l o w e r e d to such an extent that lifetimes for low-spin levels in S4Kr co u l d be d e t e r m i n e d , In the D S A e x p e r i m e n t s at EL, = 27 M e V p e r f o r m e d in R o s s e n d o r f a h i g h - p u r i t y G e d e t e c t o r o f 10% relative efficiency was applied. Th e R D D S e x p e r i m e n t s were carried out m a i n l y at E , = 20 M e V using the p l u n g e r c h a m b e r d e s c r i b e d in ref. >). The target consisted o f a 0.22 mg • cm 2 layer o f SeSe e v a p o r a t e d on an a l u m i n i z e d 0.3 mg • cm 2 plastic backing. Such plastic foil was used also as p l u n g e r material. T h e y-ray spectra were r e c o r d e d at three o b s e r v a t i o n

412

H. Rotter et al. / Yrast spectroscopy

angles relative to the b e a m d i r e c t i o n : at 0 = 25 ° a n d d i s t a n c e s b e t w e e n target a n d p l u n g e r o f D = 12, 20, 50, 200 a n d 11 500 i~m, at 0 = 135 ° a n d D = 13, 40 a n d 200 Ixm a n d at 0 = 90 ° a n d D = 11 500 ~Lm. TO d e t e r m i n e lifetimes o f low-lying levels u p to J=4h, o n e R D D S m e a s u r e m e n t was c a r r i e d out at E~ = 12.5 M e V a n d 0 = 0 °. In this e x p e r i m e n t the 0.28 m g . c m 2 target o f 82Se e v a p o r a t e d on a 2.8 m g . c m 2 t a n t a l u m b a c k i n g was p o s i t i o n e d at d i s t a n c e s o f D = 7, 11 a n d 40 ixm with r e s p e c t to the 2.8 m g • cm 2 Ta plunger. Lifetimes were d e r i v e d f r o m b o t h kinds o f D o p p l e r - s h i f t e x p e r i m e n t s b y i i n e s h a p e analysis 24.25), a p p l y i n g the a d j u s t m e n t factors fe = 0.8, f , = 0.7 a n d ~ , = 0.7 [Lening r a d v)] o r f e = 0 . 9 a n d f n = 0 . 7 [Rossendorf3'4"6)] for the e l e c t r o n i c a n d n u c l e a r s t o p p i n g p o w e r s , respectively, o f K r ions in Se. F o r the h i g h e s t - l y i n g levels o b s e r v e d at a b o u t 7 M e V a s i d e - f e e d i n g time o f 0.15 ps i n c r e a s i n g b y 0.03 ps • M e V ~ with d e c r e a s i n g level energy has b e e n a s s u m e d as in p r e v i o u s p a p e r s 4,25). The results o f the p r e s e n t lifetime m e a s u r e m e n t s are c o m p i l e d in table 4. The lifetime values o b t a i n e d b y a n a l y z i n g i n d e p e n d e n t m e a s u r e m e n t s in L e n i n g r a d a n d R o s s e n d o r f by the D S A m e t h o d agree fairly well within the error bars. In a d d i t i o n to the statistical u n c e r t a i n t i e s , the lifetime errors q u o t e d in t a b l e 4 i n c l u d e an e r r o r o f 0.03 ps for the s i d e - f e e d i n g time a n d a c o n t r i b u t i o n o f 10% p r e s u m e d to arise f r o m the uncertainties o f the s t o p p i n g power. E x a m p l e s o f l i n e s h a p e a n a l y s e s for several y - r a y s are d i s p l a y e d in fig. 5. The lifetimes o f the 83 a n d 10 + levels c o u l d be d e t e r m i n e d with b o t h D o p p l e r - s h i f t m e t h o d s . Because o f t h e i r r e l e v a n c e to the i n t e r p r e t a t i o n o f the level structure (subsect. 4.2) the d e t e r m i n a t i o n o f these lifetimes will be d e s c r i b e d in s o m e detail here. The l i n e s h a p e o f the 730.2 keV y - r a y d e e x c i t i n g the 107 level at 5449 keV reveals a small, nevertheless u n a m b i g u o u s D o p p l e r effect as s h o w n in fig. 5. The D S A m e t h o d e n a b l e d us to estimate the lifetime values o f T = 7 (2) ps ( R o s s e n d o r f ) and r=4(3/1)ps ( L e n i n g r a d ) , while from the p l u n g e r e x p e r i m e n t the value o f ~- = 5 (2) ps was o b t a i n e d , w h i c h was a d o p t e d for the lifetime o f the 5449 keV level. The lifetime o f the 87 level at 4719 keV c o u l d be d e t e r m i n e d b y a n a l y z i n g the l i n e s h a p e s o f the 1546.0 keV y - r a y a c c o r d i n g to the D S A m e t h o d a n d o f the 767.3 keV y - r a y m e a s u r e d in the p l u n g e r e x p e r i m e n t . T h e 1546.0keV y - r a y forms t o g e t h e r with the 1543.7 keV y - r a y a d o u b l e t in the singles s p e c t r u m r e c o r d e d at E , = 27 MeV. The m a x i m u m D o p p l e r shift o f this d o u b l e t e x t e n d s from 1533 keV at 0 = 155 ° to 1554 keV at 0 = 25 ° a n d thus shows that the D o p p l e r shift arises m a i n l y from the 1543.7 keV y-ray. The l i n e s h a p e analysis o f this y - r a y r e c o r d e d u n d e r two observation angles at E , = 14 M e V w h e r e the 1546.0 keV c o m p o n e n t d i s a p p e a r s r e v e a l e d a lifetime o f r = 1.0 ( 4 / 3 ) ps for the 3639 keV level (see fig. 5). W i t h this lifetime v a l u e fixed, the analysis o f the 1543.7/1546.0keV d o u b l e t m e a s u r e d in L e n i n g r a d at E~ = 27 M e V u n d e r several angles b e t w e e n 20 ° a n d 65 ° r e s u l t e d in a l o w e r limit o f r > 2 ps for the 4719 keV level. This l o w e r limit has b e e n c o n f i r m e d b y the l i n e s h a p e analysis o f t h a t d o u b l e t r e c o r d e d in R o s s e n d o r f u n d e r 25 ° a n d 155 ° at E~ = 27 MeV. F r o m the l i n e s h a p e a n a l y s i s o f the 767.3 keV y - r a y m e a s u r e d in the R D D S experi-

H. Rotter et al. / Yrast spectroscopy

413

TABLE 4 Mean lifetimes of excited states in S4Kr Level

~ (ps)

E~ (keY)

Jy

E~ (keY) ~')

RDDS

882 1832 1898 2095 2345 2623 2700 2771 3173 3220 3236 3289 3587 3639 3832 3951 3999 4350 4388 4407 4719

21 0f 2+ 4+ 4+ 2~ 3/ 5~ 6+ 52 81 57 6~ (53) 7~ 6~+ (4t) (54) 8~ (62) 8,+

881.6 950.0 1897.8 1213.5 1463.8 1741.3 605.1 425.2 1077.6 1124.5 1077.6 943.2 367.6 1543.7 659.1 1856.2 1228.6 763.0 556.6 1636.8 767.3 1546.0 1200.7 1616.1 540.7 1968.0 169.3 730.2 1252.6 1049.4 1198.6 670.4 443.7 637.4

5 (2) 36 (15)

4852

9t

4929 5204 5373 5449 5641 5902 6572

(92) 10+ 12+ 102~ (101 ) 11 1 (12~)

7016 7653

(13i) (14 l)

DSA-L b)

DSA-R c)

0.43 110/5) 0.65 17/10) 34 (4) 0.4 (2) 2.5 120/16) 11 (3) 3.8 (10) 25 (5) 0.45 (15) >4

8 (2) 1.0 (4/3) 7 (3) 1.3 (7) 0.50 (15) 0.4 12/1) 9.7 (25) 0.45 (20) 8 (3) >2 1.3 110/5) 0.8 (3) 0.14110/5) 5(2)

4(3/1) 0.5 (2) 3.0 (7) 1.0 110/3) 0.25 (15) 0.25 125/15)

>2 1.4(3) 0.7 (3/2) 0.20 (6) 7 (2) 0.9 (2) 2.4 (8) 0.6(1) 0.25 (8) 0.40 (8)

adopted 6.1 (3) d) 36115) 0.43 (10/5) 0.65 17/10) 34(4) 0.4 (2) 2.5 120/16) II (3) 3.8110) 25 (5) 2.73 (6)x I0 6e} 0.45 (15) 8(21 1.0 (4/3) 7(3) 1.3 (7) 0.50 (15) 0.4 (2/1) 9.7 (25) I).45 (20) 8(3) 1.2 (5) 0.8(3) 0.20 (6) 63 (3) x 103 ~) 5 (2) 0.7 (3) 2.7 (9) 0.6 (2) 0.25 (10) 0.4 (1)

~) Gamma-ray transitions used for the determination of the mean lifetimes. .) Mean lifetime values deduced by the Leningrad group applying the DSA method at a-particle bombarding energies of 12 to 27 MeV. ") Mean lifetime values determined by the Rossendorf group by the DSA method at 27 MeV a-particle energy. d) This more precise value of ~- was derived from Coulomb excitation experiments 14). e) Value obtained by using an external beam pulsing. f) Value determined by the delayed r.f.-y coincidence method.

414

H. Rotter et al. / Yrast spectroscopy

J

45~ E~"= 443.TkeV

osA

/ °=25° ! Ea = 27MeV I ..............

t

i

[ / / 447.6 4489 Kr ,J

35, 8 =25°

'~ =(7.2±0.5Jps

"7 +~+,e r

~ 20 8

'-

~o 2.=

....

i

....'

1

'

j

I

0=155°

I

I1

[

3O

/

25 30t 25 ~Zo

I

35

p

0 =155° %_{o,25+o.O2}pso 83Kr J/ E~f 445.8 /

40

I 1

F?.77#:~v .; IETII'

/

8

r

DSA

.,jE~

_~0 ~5

i

4.50

7~5

E~IkeVl

7~o

E~ (keV)

7~s

Fig. 5. Examples of lineshape analyses for T-ray transitions in 84Kr investigated by the DSA and RDDS methods. The full lines correspond to the fit. The errors quoted for the lifetime values result from the fit only. The lineshape analysis for the 443.7 keV transition (Rossendorf data) had to be performed within a group of lines comprising in addition (1) a background peak at 441.8 keV as shown by the spectrum recorded at 25° with respect to the beam direction, (2) the 445.6 keV T-ray of 8SKr proceeding from a level with ~"- 1.5 (6/4) ps [refs. 7,8)], (3) the 447.6 keV and (4) the 448.9 keV y-rays of 84Kr deexciting the relatively long-lived 4~" and 52 levels, respectively (table 4).

m e n t a lifetime o f r - - 8 (3) ps was derived. In a c c o r d a n c e with the D S A estimates we a d o p t e d this v a l u e for the lifetime o f the 4719 keV level. M e a s u r e m e n t s o f the time distribution o f the T-rays relative to the r a d i o f r e q u e n c y signal f r o m the c y c l o t r o n ( f = 11.24 M H z ) r e v e a l e d that the e m i s s i o n o f the 169.3 a n d 1968.0 keV y-rays is c o n s i d e r a b l y delayed. F r o m the sl o p e o f the time distribution o f these transitions a half-life o f T]/2 = 45 (5) ns for the c o r r e s p o n d i n g i s o m e r i c level was d e t e r m i n e d 9), the relatively large e r r o r b ei n g m a i n l y d u e to the given rather short b e a m burst r e p e t i t i o n time o f 90 ns. Later on, time distributions o f the 169.3 an d 1968.0 keV y-rays were o b t a i n e d in the course o f a g - f a c t o r m e a s u r e m e n t at the S t o c k h o l m c y c l o t r o n (subsect. 2.4), using an external b e a m p u l si n g system 26), w h i c h e n a b l e d l o n g e r p u ls e repetition times to be e m p l o y e d . Th ese time spectra r e c o r d e d u n d e r f o r w a r d a n d b a c k w a r d angles were n o r m a l i z e d an d s u m m e d up, to cancel o u t the m o d u l a t i o n o f the time d i s t r i b u t i o n by the spin p r e c e s s i o n in the m a g n e t i c field, and a l l o w e d the u n c e r t a i n t y o f the d e t e r m i n a t i o n o f the half-life to

415

H. Rotter et al. / Yrast spectroscopy

16 14

i

i

DSA

E~I = 1198.6 keV E~2 = 1200"7 keY 8=25 °

FwHE~=21"77MkVv ~1 = (0"56-+O'03)ps ~2 = [1.37±O.07)ps 12

f\ / l E°II [ l ~ l '~ f g - ~ DSA

~

10

E~f = 1543.7keV 0 = 125 ° E~ = I&MeV (.09.0S, 03,PS

o0 }-

z 8 !

o

I

I

I

~16 O

S

14

6

Ee=l~Me¢

12

10 2

8 i

1195

12'00 E~, ( keV )

1205

1535

1540

1545 E~,(keV)

1550

Fig. 5 (cont.). The shapes of the 730.2 keV line (with background drawn in) and of the 1198.6-1200.7 keV double line (Rossendorf data) were analyzed in a common fit of both the energy spectra recorded at 25 ° and 155°, to extract the lifetimes of the respective levels by the DSA method. The lineshape of the 1543.7 keV transition (Leningrad data) is shown as recorded under two observation angles at E~ - 14 MeV, where the interfering 8 + ~ 6 + 1546.0 keV transition is absent.

be r e d u c e d , p r o v i d i n g t h e final r e s u l t o f T w 2 = 4 4 ( 2 ) n s . A l r e a d y in the first ~2Se(a, 2 n y ) i n - b e a m s t u d y by M c C a u l e y a n d D r a p e r ~2) d e l a y e d y - r a y s o f 168 a n d 1965 k e V w e r e r e p o r t e d , a n d t h e h a l f - l i f e o f t h e i s o m e r was e s t i m a t e d as T~/2 = 48 ( 2 0 6 / 3 0 ) ns, b u t t h e t r a n s i t i o n s c o u l d n o t s u r e l y a s s i g n e d to 84Kr. T h e h a l f - l i f e o f t h e 8 + yrast state at 3236 k e V d e t e r m i n e d in ref. 13) as T w 2 = 1.84 (4) ~s has b e e n r e m e a s u r e d in the p r e s e n t w o r k to be T~/2 = 1.93 (4) ~s. T h i s m e a s u r e m e n t has b e e n c a r r i e d o u t at t h e p u l s e d a - p a r t i c l e b e a m o f t h e i s o c h r o n o u s c y c l o t r o n at t h e T S L U p p s a l a [ p u l s e w i d t h 100 ns, p u l s e r e p e t i t i o n t i m e 16 ~s], u s i n g t h e e x t e r n a l p u l s i n g s y s t e m 26) w h i c h was f o r m e r l y i n s t a l l e d at t h e c y c l o t r o n in S t o c k h o l m .

F o r t h e h a l f - l i f e o f t h e 8 + i s o m e r at 3236 k e V t h e a v e r a g e v a l u e

T j / 2 = 1.89 (4) p~s o f b o t h e x p e r i m e n t a l results was a d o p t e d .

416

H. Rotter et aL / Yrast spectroscopy

Roos

E =1124.SkeV /

/

k & \

/

RDDS

E,= 2oMev ~=~° o =~0~ =

+

E~-=1463.8 keY E~ =20 MeV e =25 ° 0 = 20~Jm = 6_+5)ps

ps

2

Z 0

~0

r

I

I

03 FZ O ¢_)

r

~ /~

4

Eo~= 20 MeV 8 = 25 ° D = 50pro

E~ = 20 MeV

} p ~ +i _

0

i

I

1120

1125

E~,{keV)

1130

0

1460

1470 Ea,(keV )

Fig. 5 (cont.). The energy distributions of the 1124.5 keV and 1463.8 keV y-ray transitions measured in the R D D S experiment in Leningrad for different distances D between target and plunger were evaluated, to determine the lifetimes of the 52 and 4 + levels, respectively. The radius of the experimental dots of the 1463.8 keV line correspond to their statistical uncertainty.

2.4. g-FACTOR MEASUREMENTS

The g-factor o f the 44 ns i s o m e r has been determined in two i n d e p e n d e n t experiments using the T D P A D m e t h o d . The first m e a s u r e m e n t was performed in Rossendorf with 27 M e V c~-particles bombarding a 50 mg • cm z p o w d e r target of S2Se, which was m o u n t e d on a b e a m stopper o f 2 m m Pb. A t w o - d e t e c t o r arrangement was used with the G e ( L i ) detectors (5.3% and 7.4% relative efficiency) placed at 45 ° and 135 ° relative to the undeflected b e a m before entering the magnet. An external magnetic field of a strength o f Bex t = 2.456 (5) T was applied perpendicular to the b e a m - d e t e c t o r plane. Further details of the experimental set-up can be found in ref. ~s). T i m e spectra for gates set in the energy axis on p h o t o p e a k s and appropriate background intervals were stored to give background-corrected time distributions for selected y-rays. The 169.3 keV y-ray in the energy spectrum recorded at forward direction turned out to be suppressed by the b e a m stopper. Therefore, the n o r m a l i z e d a s y m m e t r y ratio R (t) f o r m e d from the two m o d u l a t e d time spectra m e a s u r e d at 45 ° and 135 ° could be derived only for the 1968.0 keV y-ray. From the Larmor frequency

H. Rotter et al. / Yrast spectroscopy

417

SPIN PRECESSION SPECTRA 82Se(o(,2n

) 84Kr

A2 > 0

3~=12 +

Ex=5373.SkeV E~. = 169.3 key

R(t)

Def. 1 - Def.3

TI/2 = 44(2}ns 9=0.178(8)

0.5

0.0

-0.5

460 E ~-= 169.3 key

i

i

I

300

200

100

Def.1

Det.2

g = 0.12"7 (12)

0.5

IlJl!,ll,~~l ,,h[.,.}

0.0

-0.5 I 300

400

2~o

~60 ( ~ ' , p n ) ~ S F E×=1119keV A2 >0 J~ = 5 ~ E~=184.1 key Det.1 -- Det.3

16o T1/2=153ns g=0.576(7)

0.5

0.0

-0.5

1~o

loo --

sb

o

TIME (ns)

Fig. 6. Spin p r e c e s s i o n s p e c t r a in the form of the a s y m m e t r y ratio R(t) o b t a i n e d for the 169.3 keV t r a n s i t i o n in SnKr and the 184.1 keV E2 y-ray from 18F. The full lines represent fitting results. The detectors were p o s i t i o n e d at 135 ° (det. 1), 225 ° (det. 2) a n d 45 ° (det. 3) with respect to the b e a m direction.

418

H. Rotter et aL / Yrast spectroscopy

obtained by fitting the analytical expression for R(t) to the experimental data, the g-factor of the new isomer was determined 9) to be g = +0.14 (3). The experimental error appears to be relatively large, since the Larmor frequency was rather low and only half an oscillation period could be observed within the fixed beam burst repetition time of 90 ns available at the Rossendorf cyclotron. The comparison with the R(t) function of the 197.1 keV E2 transition of 19F being present in the spectrum confirmed the positive sign of the g-factor obtained. In order to reduce the experimental uncertainty, a further g-factor measurement was carried out at the former 225 cm cyclotron in Stockholm using the external pulsing system 26). The 30 MeV a-particle beam was pulsed in the 1 : 9 mode giving a beam repetition time of 1.23 txs. The T D P A D measurement was performed with three detectors set in the horizontal plane: one Ge low-energy photon detector (det. 1) was positioned at 135 ° to the beam direction, and two Ge(Li) detectors were placed at 45 ° (det. 3) and 225 ° (det. 2). The strength of the external magnetic field applied amounted to Be×t = 2.170 (1)T. Prompt and delayed signals from the three detectors were stored event by event on magnetic tape and were sorted off-line into matrices (E~, t). The subsequent analysis was carried out by setting gates on photopeaks and appropriate background intervals in the energy axes of these matrices, providing the time distributions for selected y-rays. From the backgroundcorrected time spectra the asymmetry ratios R(t) were formed for the 169.3 keV transition in 84Kr and the 184.1 keV E2 y-radiation of ~SF, as displayed in fig. 6. The comparison of these R(t) functions confirmed again the positive sign of the g-factor discussed. Fits of the corresponding analytical expressions to the R(t) data and to the time curves of the 1968.0 keV y-ray as well provided four independent g-factor values, the weighted average of which amounts to g = +0.175 (15). Taking into consideration the results of both measurements we finally adopted the value g = +0.17 (2) for the g-factor of the 44 ns isomer. 3. Level scheme

The level scheme as deduced from the present experimental data is shown in fig. 7. All levels were established on the basis of yy-coincidence relations. The main arguments which led us to the spin and parity assignments given will be discussed in the following. As a result of previous investigations of 84Kr, spin and parity could definitely be + + + assigned to seven excited states ~1), namely the 0~-, 2 f , 2 2 , 2 3 , 3 ~ , 4~- and 42 levels. Some of the definite J ~ assignments made recently 27) seem to be questionable (see below). 3.1. POSITIVE-PARITY STATES

The yrast level sequence in 84Kr was known up to the isomeric (8 +) state ~1.~3). The measured g-factor 13) of g = -0.246 (2) for the (8 +) isomer strongly suggests

6590 ,- , 6/.,72.3

7653.2

(14-)

7015.8

["13-)

6572.1 ~

(12-) 59~ 111 10-)

5448.

10+

, ~ 4976

5640.9

169.31~ /~ 12+ 5/2=ta'(2)~ (9÷} 5204"2

10+

4852.5

.:z 4407.4

3042.7 2622.9l 1831,6

3288.6

2345.

(6-)

3587.~li/ 2

5*

e~

4+

~

...

1897.8

2+

881.

,

,

2 +

O+

8Kr8 Fig. 7. Level scheme of ~4Kr as obtained in the (a, 2n) reaction at E~ = 27 MeV. Transitions with relative intensities larger than 5% of the intensity of the 27 ~ 0~- transition are represented by arrows, whose thickness is a measure of the total transition intensity.

420

H. Rotter et aL / Yrast spectroscopy

the two-neutron hole configuration v(gg/22) for this state, and thus, in connection with the systematics of the 8 + yrast states in the heavier-mass N = 48 isotones, the spin and parity assignment J= = 8 + appears to be quite sure. In addition, the N = 48 level systematics suggests the isomeric 63.5 keV transition to be the 8 + ~ 6 + yrast transition. The 6 + assignment to the final level at 3173 keV has been supported by the present angular distribution and linear polarization data for the 1077.6 keV transition pointing to a stretched E2 or A J = 0 M1/E2 transition. Furthermore, the microsecond-delayed coincidence measurements performed in ref. 13) and in the present work (subsect. 2.2) revealed four transitions to be in cascade, which deexcites the 8 + isomer to the ground state, i.e. the transitions must be of stretched quadrupole nature. Moreover, the spectrum of delayed coincidences allowed the total conversion coefficient of the isometric 63.5 keV transition to be estimated from the intensity balance in the isomeric decay [cf. ref. ~3) and subsect. 2.2]. The comparison of the experimental result with calculated 22) values (table 3) allows the multipolarities E2 or M2 to be selected; the latter, however, can be ruled out on the basis of the much longer lifetime to be expected 2,). An additional argument supporting the spin J = 8 assignment to the isomer is provided by the slope of the excitation function of the 63.5 keV transition, which is in between those of the 6+->4 + and 10+-->8+ yrast transitions (see fig. 2). The excitation function of the 1077.6 keV transition is obviously in favour of the spin assignment J = 6 to the 3173 keV level. The present definite J = = 5 + assignment to the 3289 keV level instead of 6 + [ref. 27)] is based on two experimental results: on the stretched E1 nature of the feeding 298.5 keV transition (tables 1, 2), which proceeds from a well-established 6- level at 3587 keV (see subsect. 3.2) and was not detected in neutron capture work 27.29), as well as on the negative polarization value measured for the deexciting 943.2 keV transition (table 2), which proves the M1/E2 mixing of this transition. At low bombarding energies (E, = 12-16 MeV) a nearly isotropic 950.0 keV y-ray transition was observed which is assumed to be the transition from the wellestablished 02 level 1~), although the level energy obtained [1831.6 (3) keV] is far outside the error bars of that [1837.3 (20) keV] known ~) from the/3 decay of S4Br. The prompt and delayed yy-coincidence measurements revealed the new Tt/2 = 44 ns isomer to be depopulated to the isomeric 8 + yrast state by a cascade of two y-rays of 169.3 and 1968.0 keV. The missing prompt component in the time distribution of the 169.3 keV transition, its total intensity being smaller than that of the 1968.0 keV transition, and the excitation function of the 169.3 keV transition increasing between E, = 20 and 23 MeV stronger than that of the 1968.0 keV transition, show the 169.3 keV transition to be the isomeric one. The stretched E2 character of the two transitions is evident from their large positive A2 values and small negative A4 values in connection with their positive linear polarization (tables 1, 2). Further evidence for the multipolarity E2 of the 169.3 keV radiation is provided by the measured K-shell conversion coefficient of this transition (table 3). Thus, spin and parity 12 + can uniquely be assigned to the isomer at 5373 keV, and 10 + to the

H. Rotter et al. / Yrast spectroscopy

421

5204 keV level fed by the isomeric 169.3 keV transition and the 1268.1 keV y-ray. The latter is deexciting a level at 6472 keV. The 12 + isomer is populated by transitions of 694 and 1198.6 keV. The former did not provide information on spin and parity of the initial level at 6068 keV from the analysis of the singles energy spectra, because the broadened 691.3 keV peak from 72Ge(n, n') interferes strongly with this line, while the 1198.6 keV transition is found to be an E1 transition determining the odd parity of the level at 6572 keV (see subsect. 3.2). Among the y-ray transitions feeding the 8 + isomer a 1740 keV transition has been observed which is component of a complex peak in the singles spectrum and does not occur in the prompt coincidence spectra. Therefore the 1740 keV transition is proposed to feed directly the 8 + isomer and to deexcite a level at 4976 keV. The large negative A2 value of the whole 1740 keV peak, which comprises in addition t o t h e 2 + 2~+ 1 7 4 1 . 3 k e V t r a n s i t i o n o f ~ 4 K r a l s o t h e ~ ~ o+ 1738.0 keV transition 7,s) of 83Kr, is compatible with a J= = (9 +) assignment to the level at 4976 keV. Above 3.9 MeV excitation energy we identified several positive-parity states not decaying via the 8 + isomer. The angular distribution coefficients of the 767.3 and 1546.0 keV y-rays indicate stretched quadrupole transitions. In addition, the angular distribution and linear polarization data of the 886.9 keV transition, feeding a well-established 7 level at 3832 keV (subsect. 3.2), point to a stretched E1 transition. Thus, J ' ~ = 8+ can definitely be assigned to the level at 4719 keV. This level is deexcited by a cascade of two quadrupole transitions of 767.3 and 1856.2 keV to the 4 + yrast level, which leads to the definite assignment o f J ~ = 6 + to the intermediate level at 3951 keV. For the 730.2 keV transition the stretched E2 nature is evident from the angular distribution and linear polarization data and thus enables spin and parity J~ = 10 + to be assigned definitely to the level at 5449 keV, This level is fed by a 1141.5 keV transition, which was observed in the coincidence spectra gated by the 730, 767, 887 or 1546 keV y-rays, while in the singles spectrum this transition was not identified because of the interference with the strong 1143.7 keV transition of ~3Kr.

3.2. NEGAT1VE-PARITYSTATES For some of the levels established earlier ~t), spin and parity could uniquely be determined by the present investigation. The definite J ~ = 5 assignment to the 2771keV level is based on the stretched E1 nature of the deexciting 425.2keV transition, which results f r o m the angular distribution in connection with the linear polarization data and the experimental K-shell conversion coefficient (see tables 1-3). Contrary to refs. 27.2v) we definitively assign J~ = 5- also to the 3220 keV level on the basis of the present angular distribution and linear polarization results obtained for the 448.9 and 1124.5 keV transitions, which depopulate this level to the 5[ and 4f states, respectively. The 1124.5 keV transition is found to be a J ~ J - 1

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1"1. Rotter et al. / Yrast spectroscopy

dipole transition with change of parity and no quadrupole admixture, while the 448.9 keV transition turns out to be a AJ = 0 dipole transition without parity change and quadrupole component. On top of these two lowest-lying 5 states level sequences of negative parity have been established in the present work. The parity of the levels at 3587 and 3832 keV is found to be not changed relatively to that of the 3220 keV level, i.e. to be negative, as following from the experimental K-shell conversion coefficients as well as from the linear polarization of the deexciting 367.6 and 244.5 keV transitions of mixed dipole-quadrupole type (cf. tables 1-3). Moreover, our definite 7- assignment to the new 3832 keV level is based on the multipolarities of the other deexciting transitions of 612.1 and 659.1 keV, which populate levels with well-established spin and parity, taking into consideration also the excitation functions (fig. 2). The 612.1 keV cross-over transition feeding the 52 state is of stretched E2 type, as shown by the angular distribution in connection with the linear polarization data and the K-shell conversion coefficient. The 659.1 keV transition populating the 6 + yrast state is found to be a J ~ J - 1 dipole transition with 6 = 0 and change of parity and exhibits an excitation function similar to that of the 612.1 keV transition. Our definite J ~ = 6 assignment to the 3587 keV level, which was earlier 29) limited in spin and parity to (3-6)-, relies on the feeding from the well-established 3832 keV 7- level by the 244.5 keV transition of mixed M 1 / E 2 type mentioned above and on the deexcitation to the 5~- state by the mixed M 1 / E 2 transition of 367.6 keV. The main arguments for the definite 8- assignment to the 4388 keV level are provided by angular distribution, linear polarization and K-shell conversion coefficient of the 556.6 keV transition which is shown to be a mixed M 1 / E 2 transition populating the 72 level. The analysis of both the 540.7 and 1097.3 keV transitions depopulating the 4929 keV level is complicated, since they are components of a doublet and a triplet, respectively, in the singles y-ray spectrum. The small positive value of A2 for the 540.7 keV transition indicates a dipole-quadrupole mixture of the radiation, while a M2 multipolarity of the 1097.3 keV cross-over transition can be excluded since the B(M2) value, derived from the lifetime, would disagree with the systematics :~). Therefore, spin and parity of the 4929 keV level are suggested to be ( 9 ) . On the basis of the excitation function and the angular distribution of the 1252.6keV transition, spin and parity J = = ( 1 0 ) have been ascribed to the 5641 keV level. This assignment is supported by the comparison of the experimental B(E2) and B(M2) values of the 1252.6 keV transition with the systematics 2,), that rules out a multipolarity M2 of this transition. Thus, a AJ = 1 odd-parity level sequence with E2 cross-over transitions has been established on top of the second 5- state at 3220 keV. A 180.l keV transition is found to deexcite the 3832 keV state (cf. fig. 3), thus fixing the energy Ex = 3651.6 (5) keV of the final state. The angular distribution and linear polarization data on the 180.1 keV transition are consistent with both a AJ = 0 M1 transition with some E2 admixture or a stretched E2 transition. If the measured lifetime of the 3832 keV level (see table 4) is considered in connection with the

H. Rotter et al. / Yrast spectroscopy

423

systematics of reduced transition probabilities 28), an E2 transition can be excluded on the basis of the much longer lifetime to be expected. Hence, for the level at 3652 keV spin and parity J ~ = 7 can be claimed. This result contradicts the J = 5 assignment to a 3650 keV level in S4Kr deduced from proton scattering ~1) which may concern, however, the 3639 keV ( 5 ) level known from (n, y) work 27.29) and populated also in the (a, 2n) reaction. The 3652 keV state is found to decay to the 5~ level as revealed by the coincidence spectra gated by one of the y-rays feeding the 3652 keV level. In fact, the spectra gated by the 180 or 1201 keV y-rays (fig. 3) show the intensity of the 881/882 keV peak to equal twice the intensity of the 425.2 or 1463.8 keV y-rays, thus giving clear evidence for the presence of a 7 1 ~ 5 ~ transition. Its energy of 881.0 (3) keV has been inferred from the level spacing; the intensity has been estimated as I(881.0 keV)/l(881.6 k e V ) = 0.11 (3) from the spectrum gated by the 881/882 keV y-quanta (see fig. 3). The 9 assignment to the 4852 keV level is based on the stretched E2 nature of the depopulating 1200.7 keV transition as shown by the angular distribution and linear polarization data. Further arguments are provided by the excitation function and the stretched dipole character of the deexciting 1616.1 keV transition clearly observed a m o n g the transitions feeding the 8f isomer. Angular distribution and linear polarization of the 1049.4 keV transition populating the 9~ level show this transition to be a stretched E2 one. In accordance with the excitation function of this transition these facts enabled us to ascribe uniquely j r = 11- to the 5902 keV level. The parity of the highest-lying levels in 84Kr established in the present study is proposed to be odd. Indeed, the crucial linear polarization values of the 1198.6 keV transition feeding the 12 + isomer seem to be negative (table 2). In connection with the positive sign of A2 and P,.a obtained for the 1198.6 keV y-ray this transition is indicated to be a A J = 0 E1 transition, and therefore spin and parity of the initial state at 6572 keV should be J~" = ( 1 2 ) . The 443.7 keVtransition (with a large negative A 2 value and a negative linear polarization value) and the 637.4 keV one (with a large negative A2 value) form a cascade of two stretched AJ = 1 M1 transitions built on top of the ( 1 2 ) state at 6572 keV. Thus, a change from even to odd parity in the yrast level sequence seems to occur above 7 MeV excitation energy. The M1 multipolarity assignment to the 443.7 keV transition is supported, in addition, by the comparison of the B(E1) and B(M1) values, deduced from the lifetime, with the systematics 28), that rules out a multipolarity El. A few of the coincidence relations observed (see table 1 and fig. 4) could not be included in the level scheme, e.g. the coincidence found between 443.7 keV and 179 keV, indicating the line at 180 keV to be a doublet. 3.4. TRANSITION PROBABILITIES For 31 of the 37 levels in 84Kr established in the present work the mean lifetime has been measured (table 4). Using the branching ratios of the levels and the mixing

14. Rotter et al. / Yrast spectroscopy

424

TABLE 5 Experimental E2 and M1 transition probabilities in 8aKr J~

J~

E v (keV)

2+ 4+ 6+ 8+ 10 + 12 + 2~ 22~ 47 42~ 5+ 6~ 62 62~ 8~ 82~ 10~ (02~) 2 3+ 52 52 6/ 61 72 7272 81 81 (92) (92) (10,) (10~) 91 111 (12/) (131) (14~-) (53 ) (4/) (54) (62)

O+ 21' 4+ 6+ 8+ 10+ 0+ 2~ 21 22~ 4~ 4f 42~ 5; 6+ 62~ 82~ 2~ 2+ 5~ 3~ 5/ 52 52 6~ 7161 72 7~ 87 87 (9~) 7i 9i 11 i (127) (137) 5~ 5i 6? 5?

881.6 1213.5 1077.6 63.5 1968.0 169.3 1897.8 1016.2 1463.8 447.6 943.2 1856.2 1605.7 662.6 1546.0 767.3 730.2 950.0 1741.3 448.9 519 816.6 367.6 612.1 244.5 180.1 801.1 556.6 1097.3 540.7 1252.6 711.6 1200.7 1049.4 670.4 443.7 637.4 419.0 1228.6 763.0 1636.8

B(E2)~xp (W.u.)a) 14 (9/4) ~) 22 (4) 6.8 (24/14) 2.2 (1) 6.3 (20) 3.6 (4) 2.4 (6) 0.6 (3) 0.16 (4) 2.3 (9) 15 (15/8) 0.6 (7/3) 0.6 (8/3)

B(MI)~x~ (10 3W.u.) b)

21 (7)

73 (45/25)

30 (50/10) 0.2(1) 6 (4/2) 36 (25/15) 1.3 (10/4) 4 (8/2) 5 (3/2) --0.7 30 (15) 25 (20/15) 6 (16/4) />4 3.7 (20) 1.4 (15/9) 17 (10) 14(20/5) 10 (10/5)

0.6 (3) 62 (15) 65(40/20) 100 (70/50) 13 (6) 100(80/40) 60(60/30)

9 (8/4) 11 (5/3) 60 (60/40) 1500(900/500) 300(100) 220 (200/100) 30(20/10) 180 (60) 16(14/7)

~) The B(E2) values are given in Weisskopf units (1 W.u. = 21.8 e 2 fro4). ~) The B(M1) values are given in 10 3 Weisskopf units (1 W.u. = 1.79p~2). ~) A more precise value of B ( E 2 , 2 + - ~ 0 + ) = l l . 4 ( 6 ) W . u . has been obtained from Coulomb excitation experiments 14).

H. Rotter et aL / Yrast spectroscopy

425

TABLE 6 E1 transition probabilities in 84Kr

j~

j~r

E~, (keV)

3[3/ 31 5/ 51 52 52 61 (53) 72 7~ 8~8+ 9~ (92) (12~)

22~ 4[ 42 42 4+ 4~4~ 5[ 4~ 6~ 6[ 72 7/ 8[ 8[ 12~

802.4 605.1 354.8 425.2 675.5 1124.5 874.2 298.5 1543.7 659.1 478.9 886.9 1067.0 1616.l 1692.8 1198.6

B(EI)e×p (10 5 W.u.) ~') 26 (24) 29 (26) <50 h) 60 (25/15) <0.14 c) 0.92 (30) <0.02 d) 23 (8) 7 (4) 6.5 (50/30) <1.2 d) 3.1 (20/10) <0.53 d) 3.0 (30/15) <0.73 d) 34 (20/10)

~') The B(E1) values are given in 10 5 Weisskopf units (1 W.u.= 1.24 e 2 fro2). b) Estimated from I~, (354.8 keV) < 3 x 10 3 iv (881.6 keV). c) Estimated from I~ (675.5 keV) <2x 10 3 iv (881.6 keV). a) Estimated from I v ( E v ) < I x 10 3 I~ (881.6 keV).

ratios of M 1 / E 2 t r a n s i t i o n s (table 1) the r e d u c e d t r a n s i t i o n probabilities of E2, M1 a n d E1 t r a n s i t i o n s or u p p e r limits have b e e n derived a n d c o m p i l e d in tables 5 a n d 6. The i n f o r m a t i o n they c o n t a i n o n the structure of the involved states will be discussed in detail in sect. 4.

4. Discussion and calculations I n the nuclei of the mass-80 region, both the p r o t o n s a n d the n e u t r o n s successively o c c u p y the shell-model states lf5/2, 2p3/2, 2pw2 a n d the i n t r u d e r lg9/2 state. The N = 4 8 n u c l e u s 84Kr is situated n e a r the N - - 5 0 n e u t r o n shell closure a n d is, therefore, expected to have nearly spherical shape at m o d e r a t e excitation energy as suggested by the values of B(E2, 2]~-->0 +) a m o u n t i n g to 11.4 (6) a n d 10.8 (9) W.u. for 84Kr a n d the s e m i m a g i c n u c l e u s 86Kr, respectively ~4). Thus, in the g r o u n d state a n d at low excitation energy ~4Kr s h o u l d be treated as a spherical n u c l e u s with two holes in b o t h the n e u t r o n g9/2 subshell a n d the n e a r - l y i n g p r o t o n f5/2 or P3/2 orbits, i.e. with 8s 38Sr5o as the core nucleus. The lowest-lying 2qp states in 84Kr are expected to arise from excitations of these p r o t o n or n e u t r o n hole pairs, which, moreover, m a y also c o u p l e to low-lying 4qp states as i n d e e d observed (see subsect. 4.1).

426

H. Rotter et aL/ Yrast spectroscopy

4.1. POSITIVE-PARITY STATES The 12 + isomer at 5373 keV should be a 4qp excitation as suggested by the level energy and the low E2 strength of B(E2) = 3.6 (4) W.u. for the isomeric 169.3 keV transition. The predominant 4qp configuration of the isomeric state has been inferred from a comparison of the measured g-factor with predictions estimated for several J ~ = 12 + 4qp configurations by the additivity rule of effective g-factors of lqp and 2qp states as discussed in detail in our previous paper 9). The experimental result gexp(12 +) = + 0 . 1 7 (2) is reproduced only by one 4qp configuration, namely the stretched two-proton two-neutron configuration 1r(fs]2, p3/~)v(gg/~), which yields the estimate gc~(12 +) = +0.18 in excellent agreement with the experimental value of the g-factor. In the present estimate we used for the g-factor of the P3/2 proton the experimental value 3o) obtained for the ground state of the semimagic nucleus S7Rbso. Previously 9) we estimated gc,~c(12 +) = +0.14, using the g-factor of the ground state of SJBr46. Both the two-proton and the two-neutron excitations involved correspond to the well-known low-lying 4+ and 8~ states in 84Kr at 2345 and 3236 keV, respectively. The sum of their excitation energies (5581 keV) is, indeed, rather close to the experimental 4qp energy (5373 keV). Evidence for the 2qp structure of the 4 + state at 2345 keV is given by the non-enhanced E2 transition strength of B(E2, 4 +.+ 2 +) = 2.3 (9) W.u. (see table 5). Additional arguments are provided by systematics. In the semimagic nucleus 86Krs0 the configuration 7r(fs/'2, P312) was assigned to the 4 + yrast state at 2250 keV on the basis of a proton pick-up reaction study 3l). Recently, a half-life of T~/2 = 3.1 (6) ns for this state has been measured 32), resulting in a small E2 transition probability of B ( E 2 , 4 + + 2 + ) = 0 . 0 5 4 ( 1 3 / 9 ) W . u . In 82Kr, the rr(fs]2, p3/~2) configuration was proposed 4) for the 4+ level at 2427 keV, and the ratio B(E2, 4+ .+ 2~)/B(E2, 4+ .+ 2+) was determined to be 0.19 (6) in good agreement with the value 0.14 (2) obtained in ref. 33), both the results being close to the value of 0.07 (4) found for SaKr (table 5). The low-lying two-proton excitation -I 1 + rr(f5/2, P3/2)a gives rise to isomerism also in SSKr49 by coupling this 4 + proton cluster to the odd neutron in the g9/2 hole state 32). In ~Sr the proton subshells P3/2 and ~/2 are completely filled and, therefore, no two-proton state with J ~ = 4 + can be formed at low excitation energy. That seems to be the reason why no 12 + isomer has been found in this nucleus 34-36). As mentioned before (subsect. 3.1) the g-factor of the isomeric 8 + yrast state at 3236 keV proved its dominant two-neutron hole configuration ~3) u(g9/2)" The clear neutron structure of the 8 + yrast state has been found to persist also in the isotone 86Sr as shown by the g-factor 37) g(8~, S6Sr) = -0.243 (4), The low E2 transition rate of B ( E 2 ) = 2 . 2 (1)W.u. of the 8+-+6 + yrast transition in S4Kr as well as its small energy of 63.5 keV suggest the 6 + yrast state to be also a member of the ~'(g9/2) multiplet, whereas the yrast 4 + and 2 + levels seem to be lowered by mixing with other configurations.

H. Rotter et al. / Yrast spectroscopy

427

The second 8+ level of S4Kr located at 4719 keV is deexcited to the two 6 + levels by E2 transitions of single-particle strength (table 5). For the 107-+ 82 transition an E2 rate of B(E2) = 36 (25/15) W.u. was determined that seems to be enhanced and might indicate a collective contribution arising from a deformed nuclear shape which is induced by the alignment of two g9/2 protons. Indeed, in the N = 46 isotones 82Kr and S4Sr the first band crossing in the yrast sequence has been attributed to aligned g9/2 neutrons and the second one to aligned g9/2 protons. This has been concluded for S2Kr from the B(E2) values and a cranked shell model analysis of the bands 4), and for S4Sr directly from g-factor measurements 3s,39). On the other hand, in the lighter Kr and Sr isotopes the g~/2 protons align first 3,4o,39). Furthermore, in the heavier-mass N = 48 isotones S6Sr, SSZr and 9°Mo the 8+ yrare states, located at 4153, 3391 and 3107 keV [refs. 3<4~,42)], respectively, have been interpreted as rr(g~/2) excitations. Thus, a rich systematics supports the conclusion that the second 8 + and 10 + states in S4Kr contain strong components of two aligned g9/2 protons. Their deformation-driving impact on the nuclear shape has been well known for the lighter Kr isotopes 3,4,4o) from B(E2) values and the analysis of the bands in terms of the cranked shell-model. Since in the 6 + state of the ~r(g9/,) multiplet the g9/2 protons are not completely aligned, the 6 + member of this multiplet is expected to lie below the 8+ level. A candidate for this state might be the 6~ level at 3951 keV, which is fed from the 8 + state by an E2 transition of single-particle strength and is deexcited by transitions also with low B(E2) values.

4.2. NEGATIVE-PARITYSTATES By considering level spacings and B(E2) values most of the negative-parity states established were grouped into two band-like level sequences with k J = 1 and ~lJ = 2, built on top of the two lowest-lying 5 states. The AJ = 2 level sequence on top of the 5i state is quite similar to the yrast level sequence up to the 6 + state as to both the level spacings and the B(E2) values amounting to about 10 W.u. There is also 1 5 9 13 a striking resemblance to the low-lying odd-parity level sequence ~-2-~-Y, that was observed in SSKr49 and interpreted as a Pl/2 neutron band 43). The/3 decay of the (5, 6 ) isomeric state of S4Br49, which has been found to be allowed and to populate only the first 5 level 1~) of S4Kr, is very likely to involve the hole transition 7rp3/'2-+vpl)2 according to the systematics of neighbouring odd-mass isotopes 3o) [*3'SSBr(~ g.s.) ¢ , 83"SSKr(½-)]. Shell-model calculations performed for the isotone S6Sr48 indicated 34) a dominant two-neutron structure of the lowest-lying 5 state. These arguments allow one to ascribe the two-neutron hole configuration v(gg/12, P~/'2) as the main component to the first 5 state in S4Kr and the AJ = 2 level sequence built on top of this state. In the second 5 state and the k J = 1 level -1 sequence the proton configuration 7"r(fs/12 or P3/2, g9/2) might be predominant by analogy with the 52 state 4) of S2Kr. Thus, in spite of rather low B(E2) values most

428

H. Rotter et al. / Yrast spectroscopy

of the yrast and near-yrast odd-parity levels in 84Kr could be grouped into sequences resembling bands rather than multiplets. The configuration assignments proposed seem to explain why only one of the two possible E1 transitions of about equal energy has been observed, namely the 1616.1keV 97-~8~ "neutron" transition and not the ( 9 2 ) ~ 8 + transition (1692.8 keV), likewise the 886.9keV 8 ~ 7 ~ "proton" transition rather than the 8~7j transition (1067.0keV). However, some of the E1 transitions expected to occur are missing, e.g., the 71 ~ 6 ~ "neutron" transition, the 5 2 ~ 4 + " p r o t o n " transition and the 5~ ~ 4~ transition. On the other hand, the A J = 0 M1 transitions observed between the two lowest-lying 5- and 7 states, respectively, manifest mutual mixing of the states. This fact may be regarded as evidence for a more complicated structure of the 5 states discussed and of the band-like level sequences built on top of them. Above 6.5 MeV excitation energy three levels with odd parity have been established. The change from even to odd parity of the yrast levels in S4Kr above 7 MeV resembles the situation in ~6Sr discussed by Warburton et al. 35). It is worth mentioning that these high-lying yrast levels are found to be connected by fast M1 transitions [B(M1)~>0.3 W.u.], pointing to recoupling of states within a multiplet of few quasiparticles in a similar way as recently 44) discussed for SSRb. The (12-) state at 6572 keV is very likely to arise from a 4qp excitation. Since the maximum angular momentum of the odd-parity 2qp excitations within the configuration space f5/2, P3/2, P~/2, g9/2 is J = 7, spin and parity J~ = ( 1 2 ) of the 6572 keV state would imply a minimum spin of J = 5 for the even-parity 2qp cluster involved. Thus, the ( 1 2 ) state might be interpreted as the coupling of the low-lying 5- excitations and the 8 + two-neutron hole cluster u(gg~2).

4.3. SHELL-MODEL CALCULATIONS So far the low-lying excitations of S4Kr have been interpreted in the framework of collective models [see references quoted in ref. ~1)]. The identification of several 2qp states such as the 4 +, 8~, 5 i , 5~ states and the discovery of a 12 + isomer in S4Kr indicate strong contributions of two- and four-quasiparticle excitations, respectively, to the high-spin states in the yrast region of this nucleus. A consistent description of the excited states established now in S4Kr needs large-basis shell-model calculations, taking into consideration for both the protons and the neutrons the configuration space in between the shell closures at Z, N = 28 and 50, with 56Ni or ~°°Sn as core. Since such extensive shell-model calculations were not at our disposal, we attempted to describe the excited states of ~4Kr in a drastically truncated configuration space, choosing 8~Sr5o as core. In this crude approach the two valence proton holes are allowed to occupy only the orbitals P3/z and f_s/_~, while the two neutron holes are distributed over the g9/2, Pw-~, P3/2 and G/2 subshells. The formalism of the calculations including electromagnetic transition probabilities and magnetic moments has been described in detail in ref. 45). The SSSr core

429

H. Rotter et al. / Yrast spectroscopy

was a s s u m e d to be inert, a n d p a i r i n g correlations were neglected. The t w o - b o d y i n t e r a c t i o n matrix e l e m e n t s entering the h a m i l t o n i a n were evaluated using an effective i n t e r a c t i o n which was d e t e r m i n e d previously 40) to describe the spectroscopic properties of nuclei of the type " d o u b l y magic core plus two q u a s i p a r t i c l e s " in the 2°sPb a n d ~46Gd regions. I n fig. 8 the e x p e r i m e n t a l results on the positive-parity h i g h - s p i n states as level energies, E2 a n d M1 t r a n s i t i o n probabilities a n d m a g n e t i c m o m e n t s are c o n f r o n t e d with the calculated values. The c o m p a r i s o n shows that level o r d e r i n g a n d excitation energies as well as part of the t r a n s i t i o n strengths are r e p r o d u c e d fairly well, b u t frequently the calculated t r a n s i t i o n probabilities fail to r e p r o d u c e the e x p e r i m e n t a l values. In particular, the u n d e r e s t i m a t e of the experim e n t a l value B(E2, 6~ ~ 4 ~ ) = 6.8 (24/14) W.u. by three orders of m a g n i t u d e (fig. 8) points to a serious l i m i t a t i o n of the present model. F u r t h e r m o r e , the i n a d e q u a t e d e s c r i p t i o n of the t r a n s i t i o n strengths of the positive-parity yrare states (see fig. 8) m a y be due to the drastic t r u n c a t i o n of the configuration space for the protons. Especially, a t w o - p r o t o n 8 + state c a n n o t be formed in the present model, since the

8346Kr48 g=+0.17{2)

(Pf)4 g~

(p f )3,z.(p p)~ 5 +

10+

~

g = ",0.18

I

"~

I CpflJpp/~"

~+

5

I{p.,Ip,41

4+

g = g;)~

( ob)3p(cd) J = q-lob)3 V( cd)~ EXPEREMENT

(~

p;g~ /\

6+

1°

~'\\

~

I

0+

SHELL

MODEL

Fig. 8. Experimental and calculated energies of positive-parity states in the yrast region and reduced transition probabilities and g-factors of 84Kr as obtained in the present work and refs. ,3.~4). For each spin value, at most the two lowest-lying calculated states, which might correspond to experimental levels, and their main configuration contributing generally by/>70% to the state are given. The many-component wavefunctions of the 2+ states are not listed here. The B(E2) and B(M1) values (the latter marked with M~) are given in Weisskopf units. In the present calculations of the B(E2) values effective charge values of %tr=2e for protons and e~ff= e for neutrons were used. The B(M1) values were calculated using effective gyromagnetic factors of g~.~ff- 1.1 for protons, gl.~ff= -0.1 for neutrons and g~,~- 0.5g~.~,.~,.for both protons and neutrons.

430

H. Rotter et al. / Yrast spectroscopy

proton orbit 7"rg9/2 has not been included in the configuration space. However, the simple model used is capable of reproducing fairly well the excitation energies and g-factors of the 8 + and 12 + isomers as well as the B(E2) values of the isomeric transitions, and thus supports the quasiparticle structure inferred from the experimental g-factors. On the other hand, in the given model space there is not more than one possibility each to generate both the 8 + 2qp state and the 12 + 4qp state. Furthermore, the predominance of the two-proton configuration 7r(f;-)2, p3/l) in the second 4 + state of 84Kr clearly emerged from the present shell-model calculations, but the model does not reproduce the experimental value of 0.07 (4) for the ratio B(E2, 42+ -+ 2+)/B(E2, 42+ ~ 22+) because of the vanishing denominator as given by the model. The 10 + yrast state at 5204 keV was previously 9) proposed to belong together with the 12 + isomer to the same 4qp multiplet as suggested by the low 12+~ 10 + E2 transition strength and the small energy splitting. Another possible interpretation is demonstrated by the present shell-model treatment, which ascribes the 4qp configuration ~-(p3-/22)2u(gg/2)8 to the 10+ yrast state. The 2 + proton excitation 7r(p3/22) is known 31) to be the main component of the 2 + yrast state in 86Kr at 1565 keV. Note the fair agreement of the E2 transition rate B(E2, 21+-+ 0t) + = 10.8 (9) W.u. in 86Kr with the strength B(E2, 10~-~ 8~)= 6.3 (20)W.u. in 84Kr. The present model describes this B(E2) value and that of the isomeric transition 12 +-+ 10 + rather well (cf. fig. 8), but the energy splittings 12+-10 + and 10+-8 + are reproduced inadequately. Thus, the structure of the 10 + yrast state in 84Kr remains to be an open question. In the isotone 86Sr the (10~) state at 4709 keV was interpreted 47) as coupling the yrast 2 + excitation of the core nucleus 88Sr5o to the 8 + state u(g9/22). Shell-model calculations of Fields e t aL 34) for 868r, which took into account proton excitations phenomenologically as vibration modes of the 8SSr core, support that interpretation of the 10 + yrast state. Odd-parity states can arise in the present simple model only from neutrons. The drastic truncation of the configuration space for the protons may be again the reason why the present model is incapable of describing the strengths of transitions between negative-parity states. Thus, the attempt to describe the whole set of high-spin states in 84Kr by the present simple shell-model approach, although giving a fair description of some even-parity states, nevertheless cannot be considered as a fully successful step.

5. Summary The present in-beam spectroscopic investigation of 84Kr following the (a, 2n) reaction delivered new experimental data on high-spin states of this nucleus, being among the N = 48 isotones the lightest one studied in-beam so far. The presence of several 2qp states such as the 4 +, 5~-, 52 states in addition to the known 8 + isomer in 84Kr, as well as the identification of a 12 + isomer and its structure give

H. Rotter et al. / Yrast spectroscopy

431

clear e v i d e n c e for strong c o n t r i b u t i o n s o f two- an d f o u r - q u a s i p a r t i c l e excitations, respectively, to the h i g h - s p i n states in the yrast region o f 84Kr. S o m e e n h a n c e m e n t f o u n d for the E2 strength o f the 10 + -* 8 + t r a n s i t i o n has b e e n i n t e r p r e t e d as possible i n d i c a t i o n o f q u a d r u p o l e d e f o r m a t i o n c a u s e d by the a l i g n m e n t o f two g9/2 protons. T w o b a n d - l i k e level s e q u e n c e s with AJ = 1 a n d A J = 2 h a v e b e e n f o u n d , which are built on t o p o f the two l o w e s t - l y i n g 5- states a n d exhibit n o n - e n h a n c e d E2 transition probabilities. S o m e a r g u m e n t s f a v o u r a t w o - n e u t r o n hole c o n f i g u r a t i o n to be ascribed in a first a p p r o x i m a t i o n to the 5 i state, while in the 52 state a t w o - p r o t o n configuration m i g h t be p r e d o m i n a n t . At e x c i t a t i o n energies a b o v e 7 M e V a c h a n g e occurs f r o m even to o d d parity o f the yrast levels, w h i c h are f o u n d to be c o n n e c t e d by fast M1 transitions. S i m p l e s h e l l - m o d e l c a l c u l a t i o n s p e r f o r m e d with SSSr as the core nu cl eu s w i t h i n a drastically t r u n c a t e d c o n f i g u r a t i o n space for the p r o t o n s a l l o w e d a fair d e s c r i p t i o n o f the e x p e r i m e n t a l results only for some e v e n - p a r i t y states to be mad e. A m o r e c o m p r e h e n s i v e s h e l l - m o d e l d e s c r i p t i o n is n o w r e q u i r e d to ex p l o i t the s p e c t r o s c o p i c i n f o r m a t i o n a v a il a b le at present. T h e a u t h o r s are i n d e b t e d to Dr. P. K e m n i t z an d Dr. P. Kleinw~ichter for their p a r t i c i p a t i o n in the early stage o f the investigations. Th e s u p p o r t by the a c c e l e r a t o r staffs is g r a t e f u l l y a c k n o w l e d g e d . This w o r k was s u p p o r t e d by the A k a d e m i e der W i s s e n s c h a f t e n der D D R , the A c a d e m y o f Sciences o f the U S S R and the Royal Swed i s h A c a d e m y o f Sciences.

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