Level structure of 80,82Sr via the 78,80Kr(α, 2nγ) reactions

Nuclear Physics A393 (1983) 224-236 © North-Holland Publishing Company

L E V E L S T R U C T U R E OF s°'S2Sr VIA THE 7s'S°Kr(a, 2n~/) REACTIONS T. HIGO, S. M A T S U K I and T. Y A N A B U

Cyclotron Laboratory, Institute for Chemical Research, Kyoto University, Kyoto 606, Japan Received 22 September 1981 (Revised 29 July 1982)

Abstract:

The level structure of 8°'82Sr was studied with in-beam v-ray spectroscopy via the 78"8°Kr(ot, 2ny)8°'82Sr reactions at E~ = 28.7 MeV. From the angular distributions and y-y coincidence measurements, the ground-state band up to (10 +) and some other states were observed in both nuclei. The deduced levels are compared with current theoretical models. The observed level structure in neutron deficient Sr isotopes indicates a transition from spherical to deformed as neutron number decreases from 50 to 40.

E

N U C L E A R R E A C T I O N S 78'S°Kr(a, 2ny), E = 28.7 MeV; measured E~, Iv(0), y-y-coin. 8°'S2Sr deduced levels, J, rr. IBA analysis.

1. Introduction Recently the level structure of even-even Ge, Se and Kr isotopes'has been studied extensively and many interesting aspects of transitional behaviour of these nuclei have been revealed 1-4); The transition from a spherical 7°Ge to weakly deformed 74"78Ge w a s suggested from the potential energy surfaces obtained by Ardouin et al. 1). It was suggested in 72Se that the enhanced B (E2; 0~ ~ 2~) values, the branching ratio in the 2~- decay and the moment-of-inertia plot of the ground state band up to 12 + can all be understood in terms of the coexistence of deformed and spherical states 2). In the study of the Kr(p, p') reaction, Sakamoto et al. 3) suggested the change of the 2~- and 4~- level structure in Kr isotopes between 78-82Kr and 84-86Kr from the behaviour of the B ( E 2 ; 0 g ~ 2~-) and B ( E 4 ; 0g+r~ 4~-) values. In our recent study of the (p, p') reaction on even Se isotopes, we have observed that the angular distribution of scattered protons leading to the 4~- state abruptly changes between 74-785e and 8°-82Se [ref. 4)]. This fact implies a similar change of the 4~- level structure in Se as in the case of Kr stated above. In contrast to Ge, Se and Kr isotopes, the investigations for Sr isotopes 5) have been rather scarce especially for nuclei with neutron number near 40. No detailed in-beam study of the level structure on light 78'8°'825r has been reported so far except for that by Nolte et al. 6) in which the ground-state band up to 6 + in 78'8°'82Sr 224

225

T. Higo et al. / Level structure

and 2~- in 82Sr were observed. The 82Sr was also studied by the (p, t) reaction by Ball et al. '). To get m o r e detailed information on 8°'82Sr, we investigated these nuclei with in-beam y-ray spectroscopy via the (a, 2ny) reaction. In the present experiment, the ground-state band up to (10 ÷) and some other levels were observed in both nuclei. The deduced level schemes were compared with the rotationvibration model, the variable moment-of-inertia model, the shell model and the p r o t o n - n e u t r o n interacting boson model. In the course of writing this report, an in-beam study o n 8°'82'845r by Fields et al. 8) was published. We also became aware of the conference contributions o n 82"845r by Dewald et al. 9"l°). Our present experimental results are compared and discussed with those of their studies.

2. Experimental procedure and results The 28.7 M e V a-particle b e a m from the Kyoto University Cyclotron was transported and focused onto target position with a spot size of 5 m m height and 10 m m width. No slit was used in the experimental area to reduce the y-ray background. The targets were isotopically enriched 78Kr (92.3%) and 8°Kr (70.1%) gases of 0.5 atm. The contaminants were mainly 8°Kr (7.7%) for the 78Kr target and 78Kr (23.6%) and 82Kr (6.2%) for the 8°Kr target. The gas cell was of cylindrical type and of 1.8 cm diameter with aluminized-mylar foil windows of 1 m g / c m 2 thickness as shown in fig. 1. For singles y-ray measurement, the target cell of 2 cm length was used. The same target cell as above for 78Kr and that of 6.5 cm length for 8°Kr were used in the y - y coincidence experiment. The b e a m was stopped about 2 m downstream from the target and the stopper was shielded with Pb blocks.

2.1. SINGLES -/-RAY SPECTRA AND A N G U L A R DISTRIBUTIONS

Singles y-rays were detected with a 60 cm 3 Ge(Li) detector set at 10 cm apart from the target and at angles of 90 ° , 105 ° , 120 °, 135 ° and 150 ° with respect to the b e a m direction. A n o t h e r Ge(Li) detector of 40 cm 3 volume was placed at 90 ° as a monitor. Typical singles spectra of y-rays from the 78'8°Kr(a, 2ny) 8°'82Sr reactions at 0v = 90 ° are shown in fig. 2. The energy calibration was performed with a 152Eu source. The y-ray energy resolution was 3.5 keV at 1.33 MeV. D

B \

3 crn ........

_'___'

,

,

Fig. 1. A gas-target cell used in the present experiment. A--window for beam inlet and outlet made of aluminized-mylar foil, B---side wall made of brass, C--flange, D--O-ring, and E--pipe for gas inlet.

°I

COUH~SICHRMME L

COUNTS/CHRNMEL

I

_w.

--80St ~5,5

t"55 ~Kr ~SS

r

~

511

5221 511 573•~. 2%0" ~

- - 573.4 82Sr ; ~

r

6 t 7 80Kr

--666.9 1.%Q ---698 82Kr 0

---- 7?6.5 ----7858 ----- 8z,0.6

~

Kr ~

75&.5 8~7 56Fe --900.5 825r 93s.6 (¢) ~(s*)

? 10)2.6 18*J~6+ 1044 82Kr

b~ -t

~

- - 1 0 6 5 6 (10")~(8")

1107.8 (10")~(8"1 ~1113.2 (3")~ 2"

--1175.4 2~0"

1184.7

)

1316.9

? ~'OK

o

_

~o K

~o

a~manns laaa-I / "lv la Og!H ",Z

9"~E

7". Higo et al. / Level structure

227

The accurate evaluation of the efficiencies of y-ray detection at each angle is very important especially in a gas-target geometry such as shown in fig. 1, because various factors affect on the efficiency. The precise calibration of the efficiencies is, however, extremely difficult with y-ray sources, since the target is not a point but finitely broadened, and the profile of the target volume depends on the detailed structure of the beam. With reasonable assumptions of the beam profile, we therefore calculated the efficiencies at each detection angles, by especially taking into account the following points: (1) deviation of the center axis of the beam from the geometrical center axis of the target cell both in its direction and center position; (2) position of the target-cell center with respect to the rotation center of the y-ray detector; (3) broadening of the finite target volume due to the expansion of the window foil of the target gas cell by gas pressure; (4) energy loss of the incident beam in the target and the energy dependence of the reaction cross sections. Among these factors, (1) was most effective on the efficiency variation with respect to the detection angles as shown in fig. 3. The relative efficiencies for each detection angle, finally obtained by taking into account the finite detector size, varies about 15% over the angles measured. With these efficiencies, the angular distribution for a long-lived activity y-ray was reproduced as isotropic within 5 % error, thus justifying our procedure for efficiency evaluation. The measured angular distributions were thus corrected for the efficiencies and also for the dead time in the pulse-height analyzer system. The angular distributions finally obtained are shown in fig. 4. Solid lines are least squares fits with the even Legendre polynomials up to the 4th order: W(O~) = 1 + Q2A2P2(cos 0~) + O 4 A 4 P 4 ( c o s 0v). The geometrical correction factors Q2 and Q4 for the finite solid angle subtended by the Ge(Li) detector'were estimated to be Q2/> 0.98 and Q4 I> 0.92 with the method of Camp etal. H), and thus neglected. The A2 and A4 values are listed in tables 1 and 2.

2.2. y-'y C O I N C I D E N C E

Two Ge(Li) detectors of 60 cm 3 and 40 cm 3 volume are set at ±90 ° to the beam direction and 2.5 cm apart from the target center. The information on E~I, Ev2, (arbitrary units) 1.05

1.oo

(~,,

O

,.,..

w

"' 0.95

x i

i

i

i

I

90* 120' 150" Detection Angle Fig. 3. Calculated detection efficiency of y-rays (relative) versus detection angles at various beam positions with respect to the central axis of the target cell: O---center, ( 3 - - + 3 mm near to, and x - - f a r from the detector.

228

T. Higo et al. / Level structure I

1.4! 1.2~ ,11,1-, 385.7 I.C -'---q~" 1.2 .'oo . ~ / o - ' ~ • 594.8 I£

/~/I

1.2

782.7

+/f 935.6

I.C

1.6

1.4

1.2.

.+/+/

1.0~"

ii

!+

2.5t

1.2

o/o • 573.4

~.01-'-'rl /o~

754.5

1"2l" ,/" _f, 900.5 10~,/ //"

1.21- /"

1.0[_oJ"

6....-• 1012.6

1113.2

,/

1.51-

/

1.o~-,~

~2-1-

/._. 819.4

1.o~,l,j~" 14"[-

e/'~°

785"8

12I- ~,,.z

1.01-,~

1065.6

,..7

,4

1,o~*-3 1.2r . ~ . 1.Oro ~

6o2.o

"

121- f÷--÷.75.4

1:4÷4 90"

,~

2.0]-

120" 150" (ca)

081 J , , , 90* 120° 150" (b)

1.0-, 0.8 ~*~.

,c!, '"~

1486.7

0.6 0.2

~o

5221

90"' 1~'o" 1,~o" I

(b)

Fig. 4. Angular distributions of v-rays from the (a) 78Kr(a, 2n3,)a°Sr and (b) 8°Kr(a, 2nT)a2Sr reactions at E = 28.7 MeV. Solid lines are Legendre polynomial fits.

TABLE 1 Results from the 8°Kr(a, 2n3,)S2Sr reaction

E.

E~

r~

(keY)

(keY)

(%)

Ji ~ Jf

100 19 6.7 62 4.2 16 6.0 35 14 9.0 3.O 20 8.7 7.6 2.1 2.9

2+-*0 ÷ 2+~2 + 2+--*0 + 4+--*2 + (3+)--,2 + (4+)~2 + (4+)~4 + 6+44 + (5-, 4 + ) 4 4 +

573.4 1175.4 1327.9 1686.6 1994.8 2228.4 2814.6 2835.4 3241.0 3336.7 3621.2 3686.5 4348.8

573.4 602.0 1175.4 754.5 1113.2 819.4 666.9 900.5 1486.7 840.6 607.0 1012.6 522.1 785.8 445.5 1107.8

(3) a) (3) (10) (3) (6) (4) (3) (3) (8) (4) (3) (5) (3) (3) (3) (7)

(8+)~6 +

(10+)--*(8 -)

A2 0.20 0.14 0.19 0.30 0.70 0.27 -0.23 0.31 -0.56

(1) (3) (7) (2) (8) (4) (14) (3) (6)

A4 -0.08 -0.04 -0.28 -0.13 -0.30 -0.11 0.01 -0.17 -0.12

(2) (4) (11) (3) (12) (7) (20) (4) (10)

0.26 (3) - 0 . 8 1 (13) 0.26 (3)

- 0 . 1 0 (4) O.75 (18) - 0 . 3 2 (5)

0.33 (16)

- 0 . 3 8 (23)

a The numbers in the parentheses represent the errors in the last significant figures.

229

T. Higo et al. / Level structure

TABLE 2 Results from the 78Kr(~, 2ny)8°Sr reaction

Ex

(keV)

Ev

(keV)

385.7 980.5 1140.3 1570.4

385.7 594.8 754.6 1184.7

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

1763.2 2297.4 2698.8 3764.4

782.7 (2) 1316.9 (15) 935.6 (4) 1065.6 (12)

Iv

Ji~ Jf

A2

A4

100 72 16 13

2+~ 0÷ 4+~ 2+

0.22 (3) 0.26 (4)

- 0 . 0 5 (5) - 0 . 0 4 (5)

(%)

46 5.4 23 14

(3÷)~ 2 +

0.52 (19)

(6+)~ 4 +

0.29 (5)

-0.05 (8)

0.23 (26)

(8+) --,(6+) (10÷) ~ (8+)

0.60 (10) 1.08 (42)

-0.13 (14) 0.62 (45)

a) The numbers in the parentheses represent the errors in the last significant figures.

Tvl-v2 and Tvl-RF of coincident events were recorded on magnetic tapes event by event with 4096-channel A D C ' s via a Y H P 2 1 0 0 computer and analysed off-line. The symbols E~I and E~2 mean the energies of two coincident y-rays, T~1-~2 the time difference between the two coincident y-rays and TV~-RF the time difference between y 1 and the cyclotron RF signal picked up from the dee voltage. The y-ray energy calibration was done with SYCo, 55Mn, 6°Co, 88y, and 152Eu sources and also checked with known transitions in 8°Kr and 82Kr [ref. 5)]. The 25 × 106 and 65 × 1 0 6 events were accumulated for 8°Sr and 82Sr, respectively. P r o m p t events were selected by the coincidence condition on Tv~_v2 and Tvl--RF, of which the resolving time was about 60 ns and 30 ns, respectively. The events were constructed in 2k × 2k matrix form in Evl and Ev2. The spectra gated by specified y-rays were obtained from this matrix. Background contributions were estimated with gates on the background regions around the specified y-ray peak. Examples of gated spectra are shown in fig. 5.

2.3. D E D U C E D L E V E L S C H E M E S

The level schemes obtained from the present experiment are shown in figs. 6 and 7. The energies, intensities and angular distribution coefficients of the observed y-rays are listed in tables 1 and 2. The errors in y-ray energies are typically less than 0.3 keV, which are mainly due to the errors in the calibration curve of the energy versus pulse height. The overall errors including the p e a k fitting errors are written in the parentheses in the tables. The relative intensities of y-rays were determined from the singles y-ray spectra at 0 r = 90 °. The intensities of y-rays not identified clearly in the singles spectra were estimated from the coincidence yield. The errors in the intensity are estimated to be less than 10%. 2.3.1. SeSr. The ground-state band: Members of the g r o u n d - s t a t e band up to (8~-) were assigned from the strong coincidence among relevant y-rays, and their

230

T. Higo et al. / Level

structure

t000 78Kr (a,2ny)80Sr 385.7 key

Gated

r--:

500

o

~ t.~

0

J ,,d

80Kr(a, 2nY)825r .

. o r-,; o

Z Z 80C

~r4

u

Ln. m m

. ~J

.

.

~ d o

"d

_..7 COCO

O 40C u

573.4 keY G a t e d

tt

~o.

'-i ~

~

400

80Kr

(a,2ny)82Sr

602.0 keY G a t e d o

200

0 0

~6o

s6o

860

~obo

Fig. 5. Typical 3'-'g coincidence gated spectra.

angular distributions. The values of the A2 and A4 coefficients for these transitions are in the range of 0 . 2 0 - 0 . 3 1 and - 0 . 0 8 - - 0 . 1 7 , respectively, consistent with the prediction of the oblate-type stretched E2 transition. The 4 3 4 8 . S k e V state (10-~): The l l 0 7 . 8 k e V y-ray is in coincidence with the transition y-rays of the ground-state band up to (8~). Although the angular distribution for this transition has large statistical errors, the A2 and An coefficients are consistent with the prediction of the E2 type transition. We tentatively assigned the 4348.8 keV state (10~-).

T. Higo et al.

/ Level

(10")

3621.2

structure

4348.8

1107.8 __~6.5

I 44%s (8") ~Ln4t0,L _ _ ~ 6 . 7

785.8

522.1 (5-,4") ,11~z81~6

5.4 II

1012.6

o

II

8~.6 I 6"~

II

H

2228.4

JL

(3")

i

1.6.7

16__86.6 I[ 666.9

•

11

l

I

1.~.2

2"

J~

1175.4

231

J/ 4' ,[J.1327.9 1175.4

754.5

II

573,4

82 Sr

Fig. 6. The proposed level scheme of 82Sr in the present experiment. Energies are in keV.

The 1175.4 k e V state 2-~: This state feeds the 2~- state strongly. The angular distribution of the 602.0 keV y-ray feeding the 27 state shows a similar shape to those of the 2~-,2~- transition in 76'78Se [refs. 12.13)] and 78"8°Kr [refs. 14,15)]. Moreover, the angular distribution of the 1175.4 keV y-ray to the ground state has a typical pattern of a 2 + -, 0 + transition. Therefore we assign this state 2~-. The 1686.6keVstate (37): This state feeds preferentially the 2~- state and does not feed the 4~- state. The angular distribution of the 1113.2 keV y-ray feeding the 27 state is consistent with the assignment of a 3 -, 2 transmon. Thus this state is assigned (37). The 511.2 keV y-ray corresponding to the (3 ~-)-, 2~ transition was not observed because of the strong contamination of the 511.0 keV annihilation y-rays. The 1994.8keV state (4~): This state preferentially decays to the 1175.4 keV 2~- state and the angular distribution of the 819.4 keV y-ray feeding the 2~ state is consistent with the assignment of a 4 +-, 2 + transition. This state was found to feed also the 1327.9 keV 4~- state. We assign this state (4~). +

-+-

.

.

232

T. Higo et al. / Level structure

(10")

3764.4

1

1065.6 ([email protected] 2297.4 935.6 (@63.2 1316.9

(3') 1570.4

HT

1184.7

782.7 ~

1140.3

~l

980.5 754.6 594.8 I 4"

IL

I I 385.7

80Sr Fig. 7. The proposed level scheme of 8°Sr in the present experiment. Energies are in keV.

The 2 8 3 5 . 4 k e V state: This state feeds both the 1 9 9 4 . 8 k e V (43) and the 2228.4 keV 67 states. Unfortunately, the angular distributions for these transitions were not observed because of the contaminant overlapping of other y-rays. The 3 6 2 1 . 2 k e V state: This state feeds the 2835.4 keV state and the angular distribution of 785.8 keV y-ray feeding the 2835.4 keV state shows a typical pattern of the stretched E2 type transition. The 3 6 8 6 . 5 k e V s t a t e : This state preferentially feeds the 3241.0 keV (87) state. The 2 8 1 4 . 6 k e V s t a t e (5~, 4 2 ) : This state decays to the 1327.9 keV 41 state and the 1486.7 keV y-ray feeding the 47 state shows a dipole-type angular distribution, and thus this state is most likely assigned 51. However the assignment of this state as 4~ cannot be excluded, because the 4 +-* 4 + transition may show a similar angular distribution as in the case of 76Se [ref. 12)]. The 3 3 3 6 . 7 k e V state: This state was observed to feed the 2 8 1 4 . 6 k e V state. The angular distribution of the 522.1 keV y-ray feeding the 2814.6 keV state shows the negative A 2 value.

T. Higo et al. / Level structure

233

2.3.2. S°Sr. The ground-state band: The ground-state band of up to (8i~) was assigned from the strong coincidence among relevant y-rays and their A 2, A 4 values consistent with the stretched E2 transition. The 3764.4 k e V state (lOaf): The 1065.6 keV y-ray is rather strongly in coincidence with the transitions in the ground-state band up to (8~-). Unfortunately the angular distribution for this transition could not be measured at 150 °, because of further overlapping with a neighboring y-ray due to the increase of the Doppler shift with increasing angles. We tentatively assign this transition (10~-)~ (8~). The 1140.3 k e V s t a t e : This state decays preferentially ' to the 21+ state. The angular distribution of the 754.6 keV y-ray was not observed because of the overlapping 754.5 keV Sasr(4~ ~ 2~) transition from the 8°Kr(a, 2ny) 82Sr reaction. The 1570.4 k e V state (3~): This state feeds preferentially the 2~- state and the angular distribution of the 1184.7 keV y-ray feeding the 2~ state is consistent with a 3+-~2 + transition. No transition to the 4~ state was observed. We tentatively assign this state (3 ~).

3. Discussions 3.1. LEVEL SCHEME OF 82Sr The assignments of the ground-state band (gsb) up to the 6 + and the 2~- states are consistent with those by Nolte et al. 6). Higher spin states (8 +) and (10 +) of the gsb and the 23, (3 ~-), (4~-) and (51, 4~) states are consistent with those by Fields et al. 8) and Dewald et al. 10). The energy levels of the 2835.4 keV state and the 3621.2 keV state are consistent with those by Dewald et al. 10). Dewald et al. lo) proposed a negative parity band (5-, 7-, 9-) based on the 2814.6 keV (51) state and assigned the 522.1 keV y-ray as the (10)--,9- transition. In contrast to their observation, we observed only the 522.1 keV y-ray coincident with the 1486.7 keV (5]-, 4~)-~ 4~ transition. Thus the 522.1 keV y-ray is assigned as the transition from the 3336.7 keV state to the 2814.6 keV (51,43) - + state. 3.2. LEVEL SCHEME OF 8°Sr The assignment of the gsb up to the (6 +) state is consistent with that by Nolte et al. 6). The l l 4 0 . 3 k e V , 1570.4keV (3~), 2 2 9 7 . 4 k e V , 2 6 9 8 . 8 k e V (8~) and 3764.4 keV (10[) states were observed for the first time in the present experiment. Fields et al. 8) assigned the (23) state at 1326.9 keV but our coincidence data showed no evidence for the 941.5 keV transition they observed as the (2~-~ 2~) transition. 3.3. COMPARISON WITH THEORETICAL MODEL CALCULATIONS The rotation-vibration model 16) calculation was performed for the gsb of s°'82"S4Sr. The results are shown in fig. 8. As seen in the figure, the calculated levels

234

T. Higo et al. / Level structure

*,3

~r X

tu 2

-k6

-k4

_

-N4 --~4

2 R E V 80Sr

2

2

R E V 82Sr

R E V 845r

Fig. 8. Calculated energy levels with the (R) rotation-vibration model and (V) variable moment-ofinertia model. The figure E represents the experimental results.

are considerably higher than the experimental ones. We also calculated the level energies of 8°'82'84Sr with the two-parameter VMI model 17.18). The parameters ÷ ÷ ÷ were determined to fit the 21,41 and 61 states. The results are shown also in fig. 8. The agreement with the experiment is good up to 10 ÷ in 8°'82Sr. Shell-model calculations for the energy levels of 8°-86Sr have been reported by Kitching et al. 19) and by Ogawa 20). The calculations of Kitching et al. can only reproduce the levels of Sr isotopes near N = 50, while those of Ogawa show the transitional behaviour of the spectrum from a shell structure to a rotation-like one, in qualitative agreement with the experiment. The p r o t o n - n e u t r o n interacting boson approximation (IBA-2) 21) calculation has been known to reproduce nicely the transition from vibrational to rotational 22.23). We calculated the positive parity level energies with IBA-2 code NPBOS 24). In the calculation the parameter X~ was fixed and x, ed and X~ [see refs. 22) and 24) for the definition of these parameters] were varied smoothly following neutron number of the nuclei. These parameters are listed in table 3 and calculated spectra for 78-865r isotopes are shown in fig. 9. The agreement of the prediction with the experiment for the gsb and other positive parity states is good.

4. Summary We investigated the level structure of 8°'S2Sr via the (a, 2ny) reaction with in-beam y-ray spectroscopy. The ground-state band up to (10 ÷) and some other levels were observed in both nuclei. The gsb of neutron-deficient Sr isotopes shows a transition from vibrational to rotational as neutron number decreases from 50 to 40. The rotation-vibration model does not describe the gsb, while the variable moment-of-inertia model

235

T. Higo et al. / Level structure

+r

J

• 21

o

041

® 6; -'~ 8~

LU

4

10~ e) 2 z v 31

o 42

2*0~ O~

o

4'0

4,'2

4'4

NEUTRON

4'6

4'8

NUMBER

Fig. 9. Energy levels of positive parity states in 78'8°'82'84+86Sr. Solid lines show the calculated levels by IBA-2 model. Spin-parities of the calculated levels are indicated at the left-hand side of each solid line. r e p r o d u c e s it fairly well. T h e p r o t o n - n e u t r o n i n t e r a c t i n g b o s o n m o d e l ( I B A - 2 ) r e p r o d u c e s well t h e e n e r g y levels in 78-86Sr. T h e a u t h o r s w o u l d like to t h a n k t h e c y c l o t r o n c r e w of t h e I n s t i t u t e for C h e m i c a l R e s e a r c h , K y o t o U n i v e r s i t y , for th e o p e r a t i o n of the cyclotron. T h e y also t h a n k Mr. Y. I w a s h i t a for his c o l l a b o r a t i o n in d a t a handling. T h e y are g r eat l y i n d e b t e d to Dr . T. O t s u k a for t h e c a l c u la ti o n of I B A - 2 . TABLE 3 The values of parameters used in IBA-2 calculation for Sr isotopes N N~ ed

K X~

40 5 0.90 --0.16 0.00

42 4 0.90 --0.16 0.30

44 3 0.98 --0.16 0.71

N~ = 5, X~ = -1.05 and Fk = -0.2 for all nuclei.

46 2 1.20 --0.19 1.10

48 1 1.55 --0.30 1.50

236

T. Higo et al. / Level structure

References 1) D. Ardouin, B. Remaud, K. Kumar, F. Guilbault, P. Avignon, R. Seltz, M. Vergnes and (3. Rotbard, Phys. Rev. C18 (1978) 2739 7) J.H. Hamilton, A.V. Ramayya, W.T. Pinkston, R.M. Ronningen, G. Garcia-Bermudez, R.L. Robinson, H.J. Kim and R.O. Sayer, Phys. Rev. Lett. 32 (1974) 239; J.H. Hamilton, H.L. Crowell, R.L. Robinson, A.V. Ramayya, W.E. Collins, R.M. Ronningen, V. Maruhn-Rezwani, J.A. Maruhn, N.C. Singhal, H.J. Kim, R.O. Sayer, T. Magee and L.C. Whitlock, Phys. Rev. Lett. 36 (1976) 340 3) N. Sakamoto, S. Matsuki, K. Ogino, Y. Kadota, T. Tanabe and Y. Okuma, Phys. Lett. 83B (1979) 39 4) K. Ogino, Y. Kadota, N. Sakamoto, Y. Okuma, T. Higo, S. Matsuki and T. Yanabu, to be published 5) C.M. Lederer and S. Shirley, ed., Table of isotopes (seventh edition, A. Wiley-Interscience Publication, 1978) 6) E. Nolte, Y. Shida, W. Kutschera, R. Prestele and H. Morinaga, Z. Phys. 268 (1974) 267 7) J.B. Ball, J.J. Pinajian, J.S. Larsen and A.C. Rester, Phys. Rev. C8 (1973) 1438 8) C.A. Fields, F.W.N. de Boer, E. Sugarbaker and P.M. Walker, Nucl. Phys. A363 (1981) 352 9) A. Dewald, U. Kaup, W. Gast, A. Gelberg, H.-W. Schuh, K.O. Zell and P. von Brentano, Contr. Int. Conf. on nucl. behavior at high angular momentum (Strasbourg, 1980) 10) A. Dewald, U. Kaup, W. Gast, A. Gelberg, K.O. Zell and P. von Brentano, Contr. 4th Int. Conf. on nuclei far from stability (Helsing~r, 1981) 11) D.C. Camp and A.L. Van Lehn, Nucl. Instr. 76 (1969) 192 12) T. Matsuzaki, private communication 13) J.C. Wells, Jr., R.L. Robinson, H.J. Kim, R.O. Sayer, R.B. Piercey, A.V. Ramayya, J.H. Hamilton and C.F. Maguire, Phys. Rev. C22 (1980) 1126 14) H.P. Hellmeister, J. Keinonen, K.P. Lieb, U. Kaup, R. Rascher, R. Ballini, J. Delaunay and H. Dumont, Nucl. Phys. A332 (1979) 241 15) L. Funke, J. Doring, F. Dubbers, P. Kemnitz, E. Will, G. Winter, V.G. Kiptilij, M.F. Kudojarov, I.Kh. Lemberg, A.A. Pasternak, A.S. Mishin, L. Hildingsson, A. Johnson and Th. Lindblad, Nucl. Phys. A355 (1981) 228 16) A. Faessler, W. Greiner and R.K. Sheline, Nucl. Phys. 70 (1965) 33 17) R.A. Sorensen, Rev. Mod. Phys. 45 (1973) 353 18) S.M. Harris, Phys. Rev. Lett. 13 (1964) 663; Phys. Rev. 138 (1965) B509 19) J.E. Kitching, W.G. Davies, W.J. Darcey, W. McLatchie and J. Morton, Nucl. Phys. A177 (1971) 433 20) K. Ogawa, Phys. Lett. 45B (1973) 214 21) T. Otsuka, A. Arima, F. Iachello and I. Talmi, Phys. Lett. 76B (1978) 139 22) F. lachello, ed., Interacting bosons in nuclear physics (Plenum, New York, 1979) 23) U. Kaup and A. Gelberg, Z. Phys. A293 (1979) 311 24) T. Otsuka, User's Manual of NPBOS (1980), and private communication