in-beam gamma-ray spectroscopy of
TRANSCRIPT
PHYSICAL REVIEW C VOLUME 32, NUMBER 6
In-beam gamma-ray spectroscopy of 8 Sr
DECEMBER 198S
P. S. Haskins, F. E. Dunnam, and R. L. ColdwellSpace Astronomy Laboratory and Physics Department, Uniuersity of Florida, Gainesville, Florida 32609
A. C. Rester and R. B.PierceySpace Astronomy Laboratory, University ofFlorida, Gainesuille, Florida 32609
M. L. MugaSpace Astronomy Laboratory and Chemistry Department, University of Florida, Gainesuille, Florida 32609
H. A. Van Rinsvelt, R. W. Smart, * and H. J. M. AartsPhysics Department, University of Florida, Gainesville, Florida 326l 1
J. D. Fox, L. C. Dennis, and C. B. Saw~Physics Department, Florida State University, Tallahassee, Florida 32306
(Received 3 June 1985)
The reaction 7o~e~160,2p2n) Sr with E~160) 80 MeV was used to study the nucleus Sr. Mea-surements were made of the excitation functions, angular distributions, and y-y-t coincidences.From these measurements six new levels were placed in the level scheme of ' Sr at 2683.7, 3609.2,4367.1, 5308.4, 6364.4, and 7827.8 keV. A gamma ray with a very high anisotropy [ A2 ———1.05(7),Aq ——0.12(6)] feeds the (11 ) level at 5914.5 keV; A new band based on the level at 3525.7 keV wasidentified. The sequence of transitions decaying down the negative parity band was reordered toS22-1005-876-694 keV.
I. INTRODUCTION
Recently attention has been focused on the influence ofthe removal of neutrons on nuclear defor'mation in theZ =38—40 nuclei. ' The change in structure as neutronsare removed from Sr to Sr provides an opportunity forone to test a wide variety of nuclear models or to ascertaina single model's applicability through a wide range ofstructures. The nucleus Sr is of particular interest be-cause it seems to be located at the boundary between thespherical and deformed strontium isotopes.
Initial work on Sr was done with heavy-ion ' and(p,t) (Ref. 4) reactions in the early 1970's. The fact thatthe 4+ state was not seen in the (p,t) reactions impliedthat this might be a soft nucleus with structural changesoccurring even at low spin. Not until the early 1980's wasthe Sr level scheme expanded to include higher spinstates. During that period, four different groups studied
Sr with a variety of heavy-ion reactions. In addition,two studies of the radioactive decay of Y were report-d 9, 10
The results of the early work imply that Sr is a vibra-tional nucleus. Observations of the higher spin states ofthe ground-state band led to interpretations of rotationalbehavior. ' The ground-state configuration is welldescribed by a collective model such as the IBM. ' ' '"Only when the side-band levels were investigated to highspin did the more interesting aspects of the Sr structureappear.
II. EXPERIMENTAL PROCEDURES AND RESULTS
The reaction chosen for the study of Sr wasGe(' O,2p2n) Sr, produced with an 80-MeV ' 0 beam
from the super FN tandem Van de Graaff accelerator atFlorida State University. The target consisted of 400pg/cm of 98.5% enriched Ge metal evaporated onto aTa backing with a thickness of about 200 mg/cm .
The Ge(Li) detectors used for the angular distributionand coincidence measurements had efficiencies of 18%and 25% with resolutions of 2.7 and 2.4 keV FWHM,respectively. The coincidence measurements were takenwith a configuration in which the 25% detector wasplaced at 90' with respect to the beam direction and the18% detector at O'. The coincidence results are given inTable I. Although most of the relationships come fromgates set on the 90 detector, some gamma rays were seenonly in gates set on the 0' detector. These are markedwith an asterisk. The italicized energies indicate strongpeaks. A total of 48 of the 60 gamma rays identified asbelonging to Sr have been placed in the level scheme.
With the 18% detector placed at 90' to the beam direc-tion as a monitor, angular distribution data were collectedwith the 25% detector at five angles measured withrespect to the beam axis: 0', 30', 45', 60', and 90'. Acorrection to the measured intensities was made for theabsorption of gamma rays by the target chamber and thefinite solid angle subtended by the detector. The resultsare shown in Table II. Details of the linear polarizationmeasurements are reported elsewhere. ' Results are sumInarized in Table III.
Calibrations were done with a National Bureau of Stan-dards (NBS) standard source. Weighted averages' of theenergies from each of the five angles were adopted for theenergy level scheme. The results are listed in Table II.The errors in the energies include both the statistical er-rors and the error in the fit of the energy versus channel
32 1985 The American Physical Society
P. S. HASKINS et al. 32
Gate
85.4156.9
261.8
269.0380.0403.9
406.5
415.1
423.5
439.9443.3511.0
513.7
522. 1
534.1
537.0569.6
573.6
598.6
602.2
606.7
667.5694.0
712.6
754.9
758.8
786.4
801.1
803.0
820.3
TABLE I. Gamma-gamma coincidence relationships in Sr.
Coincidences
511.0, 573.6, 754.9, 900.8511.0, 522, 8, 529.9, 535.3, 573.6, 598.7, 667.7, 754.5, 875.1,1124.3, 1152.6423.5, 513.7, 522. 1, 793.8, 941.3, 962., 1056.0, 1115.8,1135.5269.0, 381., 423.5, 439.9, 573.6, 754.9, 1489.0282.2, 573.6, 754.9, 900.8, 1003.3, 1013.4423.5, 511.0, 537.0, 569.6, 573.6, 596.8, 755.0, 786.2,801.1, 820.3, 841.3, 876.0, 900.8, 1107.5, 1163.7, 1219.0,1551.0423.5, 511.0, 513.7, 537.0, 573.6, 596.8, 656.0, 801.1, 820.2,876.0406.5, 573.6, 754.9, 667.5261.8, 269.0, 403.9, 511.0, 537.0, 573.6, 602.2, 754.9,786.4, 841.3, 876.0, 1005.4, 1163.7, 1230.0269.0, 511.0, 513.7, 573.6, 754.9, 841.3, 941.3, 1135.5511.0, 573.6, 840.2, 900.8, 1013.4'
85.3, 129., 147., 156.9, 183., 472., 511., 573.6, 595.,602.2, 617., 688.6, 712.4, 754.9, 776.8, 875. 7, 900.8,1039., 1077., 1113., 1129., 1828.4"261.8, 403.9, 415.1, 423.5, 511.0, 573.6, 602.2, 712.4,837.4, 1013.4, 1116.9, 1135.5224. , 261.5, 351.2, 403.9, 415.1, 511.0, 573.6, 602.2,694.0, 754.9, 758.8, 837.4, 876.0, 941.3, 1005.4, 1056.0,1135.5, 1489.0403.9, 423.5, 511.0, 573.6, 841.3,' 876.0403.9, 423.5, 511.0, 573.6, 736.1, 755.0, 1196.6156.9, 218.2, 281.5, 370.9, 403.9, 406.7, 511., 513.7, 522.5,573.6, 1003.3, 1268.785.3, 269.0, 443.3, 511.0, 522.1, 569.6,' 602.2,606.6, 667.5, 694.0, 754.9, 758.8, 786.4, 801.1, 820.3,840.2, 876.0, 900.8, 941.3, 1003.3, 1005.4, 1013.4,1058.9, 1085.9,' 1107.5, 1115-1117, 1135.5,' 1296.2,1393.5, 1489.0, 1551.0, 1828.4"156.9, 439.9, '443.3, 511.0, 573.6, 667.5, 754.9, 900.8, 941.3,1003.3, 1107.5, 1135.5, 1393.5261.8, 403.9,' 439.9, 511-512, 521.4,' 537.0, 573.6,583 ~ 1,' 786.4, 801.1, 820.3, 837.4, 840.2, 1003.3, 1116.9,1135.5, 1281.5511.0, 573.6, 754.9, 786.4, 801.1, 900.8, 941.3, 1116.9,1283.9573.6, 754.9, 786.4, 801.1, 840.2, 1003.3291., 406.5," 415.1," 513.7, 522.1, 573.6, 602.2,754.9, 837.4, , 841.3,' 876.0, 1005.4, 1489.0415.1, 513.7, 522. 1, 561.9, 569.9, 573.6, 602.2, 642. 1,694.0, 813.4, 835.3, 876.0, 1106.0, 1347.8500.8,' 511.0, 522.1, 573.6, 606.6, 667.5, 694.0, 758.8,786.4, 801.1, 837.4, 840.2, 876.0, 900.8, 941.3, 962.2,'1003-1005, 1013.4, 1058.9, 1085.9, 1107.5, 1116.9, 1296.2,1336.5, 1393.5, 1489.0261.8, 269.7, 403.9, 522. 1, 573.6, 755.0, 837.4, 900.8,941.3, 1056.0511., 573.6, 602.2, 606.6, 667.5, 755.0, 801.1, 820.3,840.2, 900.8, 1003.3, 1115-1117, 1175.6, 1336.5403.9, 511.0,' 573.6, 602.1, 606.6, 667.5, 754.9, 758.8,'786.4, 820.3, 840.2, 900.8, 1003.3, 1116.9, 1283.9,"1393.5403.9, 511.0, 522. 1, 573.6, 596.8, 602.2. 755.0, 786.4,840.2, 900.8, 1003-1005, 1085.9, 1296.2'406.5, 415.1, 511.0, 537.0, 573.6, 602.2, 616.9,' 786.4,801.1, 840.2, 956.7,' 1003.3, 1018.2,' 1175.6
IN-BEAM GAMMA-RAY SPECTROSCOPY OF s2Sr 1899
Gate
837.4
840.2
841.3
876.0
900.8
941.3
951.1
1003.3
1005.4
1013.4
1058.9
1085.9
1107.51115.8
1116.9
1135.51163.71175.61196.61268.7
1283.9
1296.2
1336.5
1393.51489.0
1551.01828.4a 80K&b 83S~c veRb
dWeak peak.'y seen only at 0 .
TABLE I. {Continued).
Coincidences
310.0, 403.9, 409.0, 415.1, 439.9,' 513.7, 522.1, 573.6,602.2, 694.0, 758.8, 801-803, 900.8, 1115.8, 1175.6511.0, 573.6, 602.2, 667.5, 754.9, 786.4, 801.1,820.3, 941.3, 1003.3, 1116.9, 1283.9, 1296.2511.0, 522.1, 534.1, 573.6, 602.2, 667.5, 754.9, 786.4,801.1, 820.3, 840;2, 901.1, 941.3, 1003.3, 1056.0, 1175.7, 1296.2269.0, 403.9, 423.5, 511.0, 522.1, 528.2,b 573.6,583.1, 694.0, 755.0, 803.0, 900.8, 1005.4, 1077.6,"1129.," 1281.1, 1489.0380.0, 443.3, 511.0, 573.6, 606.7, 754.9, 801.1, 876.0,941.3, 1003-1005, 1013.4, 1D58.9, 1085.9, 1116.9,1181.0, 1296.2,. 1336.5, 1393.5269.0, 443.3, 522. 1, 573.6, 667.5, 754.9, 840-842,900.8, 1013.4,' 1056.0, 1058.9, 1085.9,' 1296.2, 1336.5, 1489.0'350.7, 370.0, 513.7, 573.6, 617.0, 694.0, 754.9, 782.6,837.4, 882.0, 900.8, 941.3, 1052.0, 1088.0, 1163.7, 1268.7380.0, 511.0, 522.1, 573.6, 602.2, 606.7, 667.5,'694.0, 754.9, 786.4, 801.1', 803.0, 840.2, 876.0, 900.8,
9 ]]75 6d ]181Dd 1283 9ed
415.1, 522.1, 573.1, 602.2, 667.5, 694.0, 755.0, 786.4,801.1, 840.2, 900.8, 1489.0443.3, 511.0,' 537.0, 573.6, 754.9, 803.0, 843.4, 900.8,962.2, 1005.4, 1087.5, 1107.5, 1116.9, 1144.2, 1181.0234., 368., 511.0, 537.0, 573.6, 617.0, 712.4, 754.9,758.8, 900.0, 941.3, 1052.7, 1489.0511.0, 573.6, 583.1, 602.2, 754.9, 900.8, 941.3,1003.3, 1013.4, 1087.0, 1131.403.9, 511.D,
' 573.6, 754.9, 900.8, 1013.4, 1114.5261.8, 269.0, 406.5, 415.1, 423.5, 573.6, 606.6, 712.4,801.1, 837.4, 840.2, 876.0, 900.8, 945.0, 1003.3, 1039.,1107.5, 1116.9423.5, 573.6, 596.8, 602.2, 606.7, 754.9, 786.4, 801.1,820.3, 840.2, 900.8, 1003.3, 1013.4, 1115.8, 1175.6,1283.9261.8 381., 439.9, 513.7, 569.6, 573.6, 602.2, 841.3403.9, 423.5, 573.6, 754.9, 900.8, 945., 1013.4, 1175.6291.5, 572.2, 754.9, 801.1, 820.2, 840.2, 945.0573.6, 598.6, 754.9, 801.1, 840.2, 873.537.0, 573.6, 670.4, 718.2, 786.4, 801.1, 820.3, 837.4,841.3, 1003.3, 1056.0, 1116.9, 1152.2573.6, 694.0, 786.4, 801.1, 837.4, 876.0, 962.2, 1003.3,1116.9, 1175.6403.9, 423.5,' 443.3, 511.0,' 573.6, 608.3,' 754.9,801.1,' 841.3, 900.8, 941.3, 1056.0511.0,' 573.6, 667.5, 754.9, 801.1, 882., 900.8, 941.3,962.2573.6, 754.9, 841.3, 900.8269., 443.3, 522.1, 573.6, 694.0, 754.9, 876.0,' 941.3,1005.4, 1058.9, 1085.9156.9, 316.7, 513.7, 573.6, 758.5, 944.8, 1013.3573.6
number curve. Efficiency calibrations were made with thesame NBS mixed source. The intensities of the Sr gam-ma rays were obtained from the angular distribution re-
suits by the correction of the Ao's for efficiency and nor-malization to the intensity of the 573.6-keV gamma ray.
The spectral analysis was done with the fitting code
1900 P. S. HASKINS et aI. 32
TABLE II. Gamma rays belonging to ' Sr.
(keV)
85.35(04)156.94(05)261.83(04)269.02(05)
379.96(05)403.91(02)406.47(05}415.17(7)'423.51(05)439.88(04)443.28(03)513.7(2)'522.09(03)s34. i 1(os)537.00(04)'569.57(02)'573.64{01)598.56(03)602.15(02)606.65(06)667.53(05)694.04(03)712.4(1)754.9(1)'758.8(1)'786.36(01)801.11(04)
Elevel
(keV)
2683.7(1)3087.1(4)3087.1(4)3511.3(3)3622.7(1)3087.1(4)2402.3(2)2817.5(1)3511.3(3)3525.7(4)3686.0(1)1689.4(1)5914.5(2)
573.64(01)
1175.8(1)2836.3(1)1996.0(1)3511.3(3)2402.3(2)1328.5 (1)4367.1(2)3622.7(1)4423.8(1)4367.1(2)
Iy
6.5(9)0.93(06}i.8(2)1 ' 7(2)
2.0(2)6.7(5)3.2(3)1.5(1.8)6.2{s)3.9(3)3.5(3)
10.3(8)9.6(7)4.3(4)6.5(5)
12.6(9)100.0(7.0)
8.0(6)24.0(1.7)11.7(8)7.s(s)
23.7( 1.7)2.4(2)
69.3(3.6)7.3(6)
22.7(1.5)24.4(1.9)
J;—+Jf
(5)—+5+6 —+46 —+5
8+8+'~8+6 ~(5)(3 )~4+s- (3-)7 —+67~6(8) 8+3+~2+(12 )~(11 )
2+ ~0+
2+'~2+6+' 6+4+'~4+7 —+5(3 )~3+4+ 2+(9)~(7)8+' 6+io+' 8+'
(9)~{7)
A2/Ap
—0.60(09)0.20(14)0.50(14)
—0.17(13)
0.26(14)—0.53(04)—0.50(08)
0.22(03)—0.33(24)—.0.12(07)
0.35(08)0.33(06)
—1.05(07)0.25(10)0.56(05)0.92(03)0.22(01)0.23(04)0.15(04)0.22(06)
—0.14(04)0.33(05)0.22(12)0.31(01)0.43(10)0.28(02)0.34(03)
A4/Ap
0.70(10)—0.12(16)—0.21{16)
0.22(17)
—o.o8(i8)—0.06(6)—0.06(10)—0.22(4)—0.03{05)—0.01(09)—0.30(10)—0.62(83)
0.12(06)—0.23(12)—o.o8(os)
0.03(03)—0.14(01)
o.io(os)—o.o7(os)—0.16(06)—0.28(05)—0.09(07)
0.37(19)—o.is(oi)—0.40(11)—0.21(02)—0.20(03)
RLcFIT. In this code a representative peak, usually fromthe spectrum of interest, is fitted in terms of back-to-backcubic splines and used as the standard. The peaks are fit-ted in terms of this standard shape parametrized withrespect to height, width, and location, while the back-ground error is minimized by fitting the entire spectrumto a single cosine series. The code is iterative in the sensethat first the background is fitted, then the peaks, andthen the background again. The iterations are continueduntil the chi-square value is less than the number of datapoints. The errors in the peak parameters are determinedby generating new data with a Gaussian random distribu-tion about the fit and refitting between three and twenty-five times.
III. LEVEL SCHEME
The level scheme presented in Fig. 1 is in close agree-ment with the one proposed by Dewald. Six new levelshave been added at 2683.7, 3609.2, 4367.1, 5308.4, 6364.4,and 7827.8 keV. The spin uncertainties for the 4 andthe 6 levels at 2825.0 and 3087.1 keV and for the threeodd-spin members of the positive parity band (3+, 5+,and 7+) have been removed. The spin of the 3565.9-keVlevel is given as (7) instead of (6,7). The major differencesbetween the two level schemes are the ordering of the neg-ative parity band above the 3511.3-keV level and the iden-
tification of a new band based on the 3525.7-keV level.These differences are discussed in the following sections.
The decay of the excited residual nucleus proceedsthrough four main bands: the ground-state band, anotherpositive parity band, a negative parity band, and a fourthband with undetermined parity which has been identifiedfor the first time here. The band structure can be clearlyseen in Fig. 2.
The levels of the ground-state band are well establishedthrough the present and other measurements. ' Theenergy, spin, and parity results for the levels of this bandagree with previously published results. The statisticsfor the 10+—+8+ transition were not sufficient for adetermination of spin or parity; the assignment shown isbased on previous studies. ' '
A. Positive parity band levels
The II75.8 keV level is depopulated by two gamma-raytransitions. The most intense is the 602.2-keV transitionwhich decays to the 2+ level in the ground-state band.The angular distribution of this gamma ray requires a LU
of 0.The level at 1689.4 keV is assigned a spin and parity of
3+ based on the angular distribution of the 1115.8-keVtransition which deexcites this level. The value,1115.8+0.2 keV, is the weighted average of the values for
32 IN-BEAM GAMMA-RAY SPECTROSCOPY OF 8 Sr 1901
TABLE II. (Continued).
(keV)
802.95{02)'820.25(01}837.37(03)840.24(02)841.3(3)876.0(1)900.84(01}941.32(04)951.15(04)
1003.26(05)1005.43(08)1013.36(03)1056.03(07)1058.87(08)'1085.90(07)'1107.47(03)1115.8(2)1116.9(1)1135.52(08)1144.20(09)1163.74(09)'1175.6(1)1180.98(06),1196.6(2)'1268.7(5)'1281.1(2)1283.9(4)1296.19(04)1336.49(04)1393~ 5(1)1489.00(02)1551.0(5)'1828.4(1)
Elevel
(keV)
1996.0(1)2S26.8(1)2836.3(1)4367.1(2)4387.0(1)2229.4(1)5308.4(2)3478.0(1)5427.0(1)5392.4(2)3242.7(1)6364.4(2)
4350.2{1)1689.4(1)6543.9(1)2825.0(1)4387.0(1)
1175.8(1)4423.8(1)
3511.3(3)7827.8(8)3525.7(4)3565;9(1)3622.7(1)2817.5(1)
2402.3(2)
Iy
16.0(1.2 }16.6(1.3)9.7(7)
23.3(1.8)7.7(9)7.2(1.3 }
47.5(3.4)10.7(8)5.7(4)
17.3(1.3)8.s(8)
22.1(1.5)3.2(3)5.1(4)1.45(62)4.8(4)9.1(7)9.8(8)2.7(2)6.3(5)1.8(2)2.s(2)2.0(2)2.0(2)1.S(2)1.1(2)0.8(3)7.4(5)3.9(1.4)4.1(1.4)
11.9( 1.6)0.8(2)"o.7(2)b
J;—+Jf
4+ ~2+5+~3+6+'~4+'(9)~79 —+76+~4+(11)~(9)7+~5+(12+ )~10+(11 )—+98+~6+{13)—+(11)
10+~8+3+~2+(14+ ) (12+ )4- ~3+9 —+8+
2+ —+0+10+~8+
7 ~6+(16+')~(14+')7—+6+(7) 6+8+ ~6+5 ~4+
(3 )~2+
A2/Ap
0.85(03)0.42(03)0.45(05)0.23(06)0.52(08)0.33(07)0.37(01)0.22(03)0.42(06)0.44(04)0.27(12)0.48(08)0.50(13)0.43(06)
—0.13(09)—0.21(10)
0.25(08)—0.60(10}
0.07(04)0.07(20)0.08(13)
—0.46(18)0.88(17)
—0.59(22)
—0.43(04)—0.12(06)
0.47{07)—0.21(02)
A4/Ao
—0.08(04)—0.22(03)—0.17(61)—0.52(08)—0.29(09)—o.os(o8)—0.17(02)—0.10(04)—0.46(07)—0.28(04)—0.05(12)—0.14(06)
0.04(15)—0.04(08)
0.08(11)0.18(9)
—0.38(08)0.65(13)
—0.20(06)0.32(29)0.48(19)
—0.20(27)—0.72(19)
0.09{24)
0.04(05)0.04(08)0.23(09)0.00(03)
'Not placed in the level scheme.Intensity is the weighted average of the intensities taken from three or less angular distribution singles spectra.
'Uncertainty is increased to account for contaminant.
the middle member of a triplet which was deconvolutedsomewhat differently in each of the five singles measure-ments which were used for energy determinations. Theother gamma ray depopulating this level has an energy of513.7(2) keV. Because the 513.7-keV transition feeds alevel which is also fed by radioactive decay from Y, 'it is not possible to distinguish between the annihilationgamma ray of 511.0 keV and the 513.7-keV transition inthe coincidence gates. The value, 513.7(2), is the weightedaverage of the third member of a triplet that was deconvo-luted from the high energy tail of the 511.0-keV annihila-tion gamma-ray peak in the singles spectra.
The 1996.0-keV, 4+, level is depopulated by transitionswith energies of 820.3 and 667.5 keV. According to theresults of the angular distribution and polarization mea-surements, ' the 820.3-keV transition is a stretched E2transition to the 1175.8-keV, 2+ level. The 667.5-keVtransition which decays to the 4+ level of the ground-stateband is a mixed E2/Ml transition with a mixing ratio of().28(69)
Two transitions also deexcite the 6+ level at 2836.3
ke V; an 840.2-keV transition to the 4+ level and a 606.7-keV transition to the 6+ level in the ground-state band.Both of these gamma rays are members of doublets. Theangular distribution and polarization data indicate thatthe 606.7-keV transition does not change spin or parity,making it an E2/Ml transition with a mixing ratio of0.18(32).' Although the angular distribution of the840.2-keV transition implies M=0, the addition of theinformation from the polarization experiment supportsthe 6+~4+ assignment. '
The 3622. 7-keV, 8+, state can decay through threetransitions at 380.0, 1393.5, and 786.4 keV. That the786.4-keV gamma ray represents a stretched E2 transitionis supported by both the angular distributions and the po-larization measurements. '
The 4423.8-keV level is assigned a spin and parity of10+ based on the angular distribution and polarization re-sults' for the 801.1-keV transition which deexcites it.There is also an 1181.0-keV transition between this leveland the 8+ level in the ground-state band.
The level at 5427.0 keV is assigned a tentative spin of
1902 P. S. HASKINS et al. 32
TABLE III. Polarization of Sr gamma rays.
E~ (keV)
423.5522.1
573.6602.2606.7667.5694.0754.9786.4801.1'820.3840.2'900.8941.3
1003.31013.41056.01135.51296.21489.0
J;~Jf7 ~6(12 )—+(11 )2+~0+2+ ~2+6+' 6+4+ ~4+7 —+54+~2+8+ ~6+10+ —+8+4+ ~2+6+' 4+'6+~4+(11)~(9)(12+ )~10+8+~6+(13)—+(11)4 —+3+
6+5 ~4+
Pexp
—0.02(12)0.13(07)0.30(03)
—0.09(06)0.19(06)
—0.31(20)0.57(11)0.47(08)0.46(11)0.61(08)0.67(10)0.51(22)0.66(10)0.26(16)0.66(32)
—0.05(14)0.54(57)
—0.52(29)0.49(21)
—0.24(43)
bP„)
0.29(01)
0.55(05)0.47(01)0.37(01)0.51(02)0.70(04)0.03(05)0.60(01)0.31(02)0.72(04)0.89(53)1.01(16) .
—0.29(01)
—0.45(51)—0.70(54)
1.2(1.4)0.18(32)0.28(69)
0.03(05)0.53(47)
Multipolarity
E2/M1E2/M1E2E2/M1E2/M1E2/M1E2E2E2E2E2E2E2E2E2E2E2M2/El[E2/M 1]E1
'Unresolved doublet.Calculated assuming no parity change and no mixing.
'Calculated with A2,„„,A4,„p, and P,„„.
(13) 6364.4
(16 )
78278I
I1283.9
I
(146543.9
5914.5
5392.4
(12 )
I
522. 1
1( (» )
1005.4
1056.0
(11) )( 5308.4I
941.3
1116.9
!
(12+)
1003.3
5427.0
4387.0I
876.0 1144.2
3511.3
2817.5
2402.3
1689.4
573.6
0.0
1F
269.0 I( y 423.5694 0 ~ 8 6
269.0I
4o'6. 5712.4 $ 1489 0 4+
f~ ~
3+
]828.4
4423.8
3622.73478.0
2836.3
2526.8I
837.4
!
6+ ~( 2229 4
900.84+
82O.3
513.7
1135.5 1996.0
1689.4
1175.8
667.5
I
1115.8 602.2
4+ )I 1328.5
754.93+
t
573.6573.6
1175.6
o.o
10+(9( ( 4367. 1 1Q 4350,3
I4'(97.0
758.8 841.3 801.1 11075 + 1181.0 801.1
( 8 ) ) 3686.0511(7( f 3609.2
7 q 35&5 7 (7( f3565 9 8 '(I+I 443.3
8+ l(3$4$ 7 f0.0 (f3087.1 lk 786.4
1 1393 5 + I ' 951.2403 9 4. y 2825.0 6
(5) $ 2683.7 1013 4 + 84025+ Q 156.9 1296.2 6067 5'(1
FICs. 1. Sr level scheme, as deduced from this experiment and previous results. The present results indicate a different orderingfor the band based on the 2817.5-keV level and a new band on the 3525.7-keV level has been identified.
32 IN BEAM GRAMMA RAY SPECTROSCOPY OF sgr 1903
5
2 4 6 IC i6
I () )
FIG. 2. Band structure in Sr. Note the change in slope inthe positive parity band between I =8 and I = 10.
(12+). Because the only observed gamma ray which de-excites this level is a member of a doublet, neither the an-
gular distribution nor the polarization values can be deter-mined accurately. However, the measured values are con-sistent with a stretched E2 transition.
A similar problem arises for the (14+) level at 6543.9keV. Although the angular distribution measurementssupport a spin change of 2, the 1116.9-keV gamma raycannot be resolved from the 1115.8-keV gamma ray in thepolarization measurements. ' The energy is a simple aver-age of the energies of this transition seen in gates in whichthe 1115.8-keV transition is not seen.
The 7827.8-keV level is only tentatively proposed; itsdefining transition at 1283.9 keV is weak, being resolvedin the singles spectra only at 0' and 30'. It appears veryweakly in the coincidence gates, but when the gates forthe members of the positive parity band are compressed,the 1283.9-keV gamma ray appears in each of them.Summing the uncompressed gates at 0' results in a1283.9-keV gamma ray with an intensity that is strongerthan any other gamma ray in the spectrum except forthose already identified as band members. Because thisgamma ray was too weak to be seen in the polarizationmeasurements and was resolved at only two angles in theangular distributions, the spin and parity assignment of(16+) for the 7827.8-keV energy level are based solely onsystematics.
fied in the present work by a weak 1828.4-keV peak in the573.6-keV gate. A gate set on the 1828.4-keV gamma rayshows a 573.6-keV peak as the strongest coincidence. Thespin and parity assignments are based on agreement of en-ergy with the (p, t) reaction results and the occurrence ofother 3 states at about the same energy in related nuclei.
The 2817.5-ke V, 5, level is fed by a transition with en-ergy 694.0 keV and deexcited by two transitions, 1489.0and 415.1 keV. The spin and parity of this level are as-signed on the basis of the angular distribution and polari-zation data' for the 1489.0-keV transition which indicatean E1 transition. This state has been seen in other experi-ments ' ' and identified as a 5 or a 4+ level.
The decay of the 7 level at 3521.3 keV proceeds pri-marily through the 694.0-keV stretched E2 transition tothe 2817.5-keV level. There are also a weak 1281.1-keVtransition to the 6+ level, a 269.0-keV transition to the 8+level in the ground-state band, and a 423.5-keV transitionto the 6 level at 3087.1 keV. Both the angular distribu-tion and the polarization measurements' verify the E2nature of the 694.0-keV transition and therefore the 7spin and parity assignment.
The 4387.0-keV, 9, level decays primarily by a gammaray with energy 876.0 keV. The exact energy, intensity,angular distribution, and polarization of this transitionare somewhat tenuous because there is a strong 875.1-keVcontaminant due to the reaction products Sr and 'Rb.There is a weak 1144.2-keV transition to the 8+, 3242.7-keV level. The spin and parity are based on the apparentstretched E2 nature of the transition seen in our data andthe Zn(' F,p2n) Sr reaction studied by Dewald. Theassignment agrees with the systematics of the X =44 iso-tones (Fig. 3).
The energy of the level at 5392.4 keV is based on thedetermination of the energy of the weaker member of the1003-1005 doublet, which in our data was 1005.4 keV.Dewald assigns an energy of 1006.0 keV to this transi-tion. The spin and parity assignments, (11 ), are basedon the angular distribution and systematics.
The level at 5914.5 keV was assigned a spin of (12)
13
99
B. Negative parity band levels
The 3 state at 2402.3 ke V is probably not a member ofthe negative parity band. The intensity of the 415.1-keVtransition between this level and the 5 state of the nega-tive parity band is only about 12% that of the 1489.0-keVgamma ray in the 694.0-keV gate. The fact that other nu-clei in this region have 3 states at about the same ener-
gy ' ' suggests that this state might be an octupole vi-brational state. This level was first observed in (p, t) reac-tions and assigned an energy of 2405+5 keV. It is veri-
7834 44 36 K "44 38S"44 40 44
80 82 84
FIG. 3. Negative parity bands of the X =44 isotones. Thedata on 'Se are taken from Matsuzaki and Taketani (Ref. 17),
Kr from Sastry et al. (Ref. 15) and Funke et al. (Ref. 18), and84Zr from Price et al. (Ref. 19).
P. S. HASKINS et al. 32
based on the angular distribution which showed it to bedeexcited by a highly aligned dipole transition to the(11 ) level. Although the polarization results are notconclusive, they do indicate that it is more likely that theparity does not change in the transition to the (11 ) statethan that it does. ' Therefore the 5914.5-keV state is as-signed a spin and parity of (12 ). The placement of the522. 1 keV transition in this work differs from that pro-posed by other authors. ' ' This point is discussed in de-tail in Sec. IV 8.
C. Band based on the 3525.7-keV level
A fourth possible band is presented for the first time inthe present work. Although the I=7 level at 3525.7 keVhas also been proposed by. Dewald and Fields et al. , thetransitions which feed it have not been previously placed.The 3525.7-keV level decays through two transitions,1296.2 and 439.9 keV. Each of these gamma rays has anangular distribution which indicates a spin change of one.The chi-square analysis of the polarization plus angulardistribution data of the 1296.2-keV gamma ray' impliesno change of parity although the possibility of a paritychange cannot be statistically ruled out. Based on sys-tematics, one would expect this level to have a spin andparity of 7 . The assignment of the parity for this level(and thus, this band) will have to await the results of fu-ture experiments.
The transitions which decay from the 4367.1-keV levelfeed three levels assigned a spin of 7. All three of thesetransitions have angular distributions which are consistentwith either XI=0 or AI=2. None of the three wasresolved in the polarization data because they all lie undera stronger peak at about the same energy. Therefore thelevel at 4367.1 keV can only be assigned a tentative spinof (7) or (9), with (9) being favored on the basis of sys-tematics.
The 941.3-keV transition which feeds the 4367.1-keVstate has angular distribution coefficients which allowAI =0 or 2. The polarization resolts indicate thathI =2 is the more probable choice and that there is nochange of parity. This does not help with the assignmentof spin and parity for the 5308.4-keV level because of theuncertainty in the assignments for the 4367.1-keV level.According to systematics, it is probably a spin (11) state.
The 5308.4-keV level is fed by the 1056.0-keV gammaray from a level at 6364.4 keV. Although the statisticsfor the angular distribution and polarization results do notallow an unambiguous conclusion, they are consistentwith a stretched E2 characterization. An assignment of(13) for the level would agree with systematics.
The 2825.0-keVlevel is assigned a spin and parity of 4based on the angular distribution and polarization' of the1135.5-keV transition which deexcites it. The 261.8-keVtransition which feeds it has an angular distributionwhich is consistent with a stretched E2 transition. Thespin and parity assignments of this level agree with thoseof Dewald.
At 3087.1 keV is a level which is fed by three transi-tions and decays by three. The assignment of 6 as itsspin and parity agrees with that of Dewald and is basedon the M =1 angular distribution of three transitionsfrom levels with spin 7 and two transitions to levels withspin 5. The polarization of the 423.5-keV transition fromthe 7 level is consistent with no change of parity. '
The angular distribution of the 1336.5-keV transitionfrom the 3565.9-ke V level to the 2229.4-keV, 6+, level inthe ground state band indicates a spin change of 1. Thetentative assignment of (7) is based on systematics and theobservation that a level is somewhat more likely to decayto another level of lower spin. The level at 3686.0 ke V de-cays through a 443.3-keV transition to the 8+ level of theground-state band. The angular distribution of the443.3-keV gamma ray indicates AI=O or 2. The chi-square analysis favors the M =0 assignment.
The tentatively proposed level at 3609.2 keV helps oneto explain coincidences that are not otherwise readily un-derstood. For example, the 941.3-keV gamma ray and the522. 1-keV gamma ray are in coincidence with each other,but no connecting transition is seen in either gate for the(12 )~(l 1 ) transition and the 941.3-keV gamma rayAlthough the (12 )~(11 ) transition appears only in the90' gates (i.e., 90' with respect to the beam), the 522. 1-keVgamma ray is seen in a 0' gate set on the 602.2-keV gam-ma ray. The 522. 1-keV gamma ray is also seen in the758.8-keV gates at both 90 and O'. The spin and parity ofthe 3609.2-keV level is difficult to assign. The 758.8-keVgamma ray has an angular distribution that is consistentwith LU =0 or 2. The 522. 1-keV transition is an E2/M1transition with a AI=1. It decays to the 6 level at3087.1 keV. If the level at 4367.1 keV is 9, then the3609.2-keV level would have a spin of 7.
A tentative level is placed at 419?.0 keV to account fora 511.0-keV gamma ray which feeds the levels at 3686.0and 3242.7 keV. Although the 511.0-keV gamma raymay be annihilation radiation from the decay of somehigh spin isomer of Y which has not yet been observed,the fact that this transition is seen more strongly in the 0gates indicates an anisotropy that would not be charac-teristic of annihilation radiation. The actual placement ofthis gamma ray is highly speculative at this point.
D. Other levels IV. DISCUSSION
There are additional energy levels which are not clearlyassociated with band structure but which may be thelower spin members of bands whose higher spin membersare too weak to be observed in the present reaction. Alevel at 2683.7 keV is fed by a 403.9-keV transition fromthe 6 state and decays by a 156.9-keV transition to the5+ level at 2526.7 keV. This level is assigned a spin of 5based on the angular distribution results.
The experimental data on Sr have been compared withseveral nuclear models. The complex level scheme is typi-cal of transitional nuclei. The level spacings for I (4+are characteristic of those expected in a vibrational nu-cleus. However, in the ground-state band the increasinglevel spacing with spin suggests rotational behavior. Ap-plication of the variable moment of inertia model to theground state band indicates that the moment of inertia
32 IN-BEAM GAMMA-RAY SPECTROSCOPY OP 8 Sr 1905
changes with spin and therefore the structure can be as-sumed to change with spin. Thus the nucleus may be con-sidered soft, i.e., it changes shape with spin. (See Sec. VI.)
The presence of a second excited 2+ state below thefirst excited 4+ state is an indication that this nucleus isnot axially symmetric. ' One can say that Sr is agamma-soft nucleus or that it is a triaxial rotor, bothterms referring to a tendency towards deformation withrespect to the gamma degree of freedom, the first being adynamic condition, the second a static condition.
The large transition probabilities connecting the lowerspin states (I (8) and transition energies which are lowerthan those expected for single particle transitions are indi-cations of collective behavior. The ground-state band andfirst excited positive parity bands up to spin 8+ are bothexamples of collective excitations of the ground state con-figuration. A collective model such as the IBM fits theselower levels very well. ' ' " The lower levels of the firstexcited positive parity band can be interpreted as a quasi-gamma band such as those seen in other even-even transi-tional nuclei in this mass region. These bands arepresumed to arise from a two-phonon vibrational excita-tion of the ground-state configuration.
Above I=8+ noncollective or intrinsic excitations be-gin to influence the structure. These intrinsic quasiparti-cle excitations have rotational bands built upon them.There are three such bands identified so far in this nu-cleus; one with positive parity, one with negative parity,and one with unknown parity. According to two-quasiparticle-plus-rotor calculations one can assume thatthe negative parity band is based on a (g9&z,f5~2) two-quasiproton configuration. It has been suggested thatthe positive parity quasiparticle band is a two-g9/2-quasiproton configuration. The character of the thirdband is not known. It is just these side bands that make
Sr an interesting nucleus for study.
A. Positive parity band
For the positive parity band, the graph of the momentof inertia with respect to the angular frequency based onthe rotational model indicates a sharp change from vibra-tional to rotational characteristics at I =10+ (see Fig. 4).In fact, the assumption that all the angular momenta con-tribute to the moment of inertia leads to an interpretationof rigid rotor behavior above I= 10+. The average exper-imental moment of inertia above 10+ is 47.5 MeV '. IfP=0.287 [from the B(E2,2+ +0+)] aad y—=22.5' (fromthe relationship of the 2+ to the 2+ states), the rigid bodymoment of inertia W„z can be calculated to be W„z——48.7MeV '. Strong transition probabilities between theband members might lead one to interpret this behavior asa vibrational band crossed by a rotational band at I= 10+.However, it is more likely that a quasiparticle bandcrosses the quasigamma band at about 6—8+ with anunusually strong interaction. The strong interaction be-tween the two bands causes the transition energies to becompressed below the crossing, thus giving the appear-ance of vibrational behavior. If the alignment of thequasipaiticles is subtracted from the total angular
'momentum, then the moment of inertia plot refiects the
5p
4O
I
Q) 3P—
10
2O-
10
0.1 o-2 0-3
{t~) (Mev)0 4 0.5
FIG. 4. Moment of inertia as a function of angular frequencyfor Sr.
rotational nature of the quasip article band, but thebehavior is no longer that of a rigid rotor.
The behavior of the positive parity band in Sr is verysimilar to that of the ground-state band in Zr in whichPrice et al. ' suggest the observation of rigid rotorbehavior. The two nuclei are isotones and their levelschemes are very similar, the outstanding difference beingthat the forward bend is observed in different bands in thetwo nuclei. Price et al. ' treat the Zr data with the for-malism of the cranked shell model. The kinematic mo-ment of inertia, W(1) =I„/co, and the angular momentumaligned along the rotation axis, I„=[(I+1/2) —K ]'~,
30
20—Q
15
10
82S
84Z
I I I
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
4 op (Mev)FICz. 5. Kinematic moments of inertia as a function of angu-
lar frequency for Sr and "Zr. The data on Zr are taken fromPrice et al. (Ref. 19).
1906 P. S. HASKINS et al. 32
are each plotted as a function of the rotational frequency,fuu. Comparison of their plots of A" vs fun and I„vs fico
(Figs. 5 and 6) with those for the ground-state band ofSr shows similar behavior. In both moment of inertia
plots (Fig. 5), the moment of inertia exhibits large changeswith small changes in rotational frequency up to a givenfrequency after which there is very little change.
The plots of aligned angular momentum versus rota-tional frequency (Fig. 6) both show sharp gains in align-ment which are attributed to the breaking of quasiparticlepairs. ' ' In the case of Zr the calculations suggest thatthe alignments are due first to two g9/2 quasiprotons andthen to two g9/2 quasineutrons. ' The alignment in Sr isattributed to two g9/2 quasiprotons. A second align-ment of quasiparticles was not seen in this experiment.
There are soine differences in the preceding interpreta-tion for these two nuclei. In Zr the transition to rigidrotor behavior occurs at Ace=0. 9 MeV, more than twicethe frequency of the apparent Sr transition at fun=0. 4MeV. In Zr both protons and neutrons have undergonea bandcrossing. Only the protons have undergone a band-crossing in Sr. Without measuring the quadrupole mo-ment of Sr, one cannot find a set of shape parametersthat might be consistent with the rotation of a nucleuswith no pairing as Price et ai. ' were able to do.
The most plausible explanation of the first excited posi-tive parity band in Sr is that it is made up of two dif-ferent bands which cross at about I=6+. The lower ener-
gy band is a %=2+ quasigamrn. a band based on theground-state configuration, and the higher energy band(I & 6+ ) is probably a two-quasiproton configuration.However, the behavior of the moment of inertia plot canbe interpreted in one of two possible ways: either the twobands interact very strongly or the nucleus becomes a rig-id rotor above spin 10. Strong interaction between aquasiparticle band and the ground-state configuration isnot unknown in this region of the nuclear chart( Zr, Kr), ' ' however, the interaction usually occurswith the ground-state band rather than the quasigammaband. The interpretation of rigid rotor behavior i.s based
on an interpretation of the moment of inertia which con-siders the total angular momentum as the quantity whichcontributes to the moment of inertia. If one considers themoment of inertia to be a collective property, then thealigned angular momentum should be subtracted from thetotal angular momentum, the result being the value whichshould be used to determine the moment of inertia and ro-tational frequencies. If this is done, the collective degreeof freedom is still rotational, but it no longer behaves likea rigid rotor. The excitation of aligned quasiparticles insoft nuclei may stabilize the deformation and decrease thepairing correlations, ' but any evidence of rigid rotorbehavior would have to come at higher spins and higherrotational frequencies than those seen in the present ex-periment.
B. Negative parity band
The negative parity band is based on the 5 state at2817.5 keV. The 3 state at 2402.3 keV is associated withan octupole vibration (as discussed in Sec. III). Therehave been some difficulties with the determination of theordering of the transitions above the level at 3511.3 keV.The problems have been the following:
(1) The 876.0-keV transition is part of an 875-876 doub-let in which the 875-keV gamma ray is the stronger of thetwo and belongs to two contaminants ( Sr and 'Rb).
(2) The 1005.4-keV transition is the weaker half of a1003-1005 doublet in which both gamma rays belong to"Sr.
(3) The 522.1-keV transition is a highly aligned dipoletransition and is therefore very anisotropic.
These problems have made the intensity determinationsdifficult. Because of this, the ordering of the negativeparity band transitions is based on two factors, the highdegree of alignment of the 522.1-keV gamma ray and thecoincidence relationships. Although the relative ordering
35
30
25
20—X
15
10
1.0
09
0.8
07
0.6
0.5
0.4
-00 0.2 0.4 0.6 0.8 1.0 l. 2 1.4
%co (MeV)
FIG. :6. Aligned angular momenta as a function of angularfrequency for Sr and Zr. The data on Zr are taken fromPrice et al. (Ref. 19).
0.3
0.25 7 9
SPIN (fl)13
FIG. 7. Plot of the attenuation factor with respect to spin forthe negative parity band in Sr.
32 IN-BEAM GAMMA-RAY SPECTROSCOPY OF 8 Sr 1907
1000— + +4~2
O+ +
O'O
Ol + +8~6
I
O I
1500CHANNEL NUMBER
2~0
lQOO— + +4~2
C)+ +6~4
500— +- +~ 8~6
~OI
P)OC)
I
OOOO
I
1500CHANNEL NUMBER
2000
FICx. 8. Summed ground-state band gates at 0' and 90'. Note the disappearance of the 522-keV gamma ray in the 0' gates.
of the 694-, 876-, and 1005-keV transitions is suggested byboth our data and that of Dewald, the placement of the522.1-keV transition is a point of difference.
One indication that the 522.1-keV gamma ray is higher
in the level scheme than other authors suggest is the highdegree of alignment seen in the angular distribution data.The A2 and A4 values fall very close to the A,„valuesfor a 12—+11 or a 10~11 transition. This indicates an a2
1908 P. S. HASKINS et aI.
2~01.3
00c) ~ P9
CL 07
0.5
+ ++ +4 2
E2E2
5 4
E1
+10
6+
5+
432+
87'
+65
+4+32'
+16
12
10
87+6+5+43-2
+
+12
10
4+
2
P312 ~11
P.lt
500l
700l I
900 1100E~(keV}
l
1300
FIG. 9. Anisotropy of the 522.1-keV transition.
I
1500
0 0+ 0 084
Zi78 80 82
Ge Se Kr SrFIG. 11. Positive parity bands of the N =44 isotones. Data
are from Refs. 15, 17—19, and 27.
of almost one. For a mixing ratio of —0.70(54), ' thecalculated aq would be 0.90(16). A plot of the experimen-tal a2 vs I (Fig. 7) shows the expected behavior of highalignment at the entry levels decreasing to smaller align-ments for the lower spin states.
In the (a,2n) reactions only the 522.1-keV gamma ray isseen feeding the 2817.5-keV level. ' The question arises:Are there actually two 522-keV gamma rays or is the highanisotropy of this gamma ray responsible for a misinter-pretation of the data? The 522.1-keV gamma ray has avery large intensity at 90' and almost none at O'. If one isviewing the reaction at +90' as Higo et al. and Fieldset al. did in their coincidence measurements, the 522. 1-keV gamma ray appears much stronger than its integratedintensity indicates. Figures 8 and 9 illustrate the degreeof anisotropy of the 522. 1 keV transition. Figure 8 showsthe summed ground-state band gates (573-755-901-1013-1107) set on the 0' and the 90' detectors. Although thereis no evidence of a 522. 1 keV gamma ray at 0', there is astrong peak at that energy in the 90 gate. The ratio of in-tensities of a gamma ray at 0' to that at 90', taken from
I
14
the angular distribution measurements, is plotted in Fig. 9for several transitions in Sr. The stretched E2 transi-tions of the ground-state band have ratios greater than oneas expected. The E1 transition from 5 to 4+ has a ratioslightly less than one. The 522.1-keV transition has a ra-tio of 0.10. No other gamma ray in this study exhibitssuch a strong anisotropy.
Additional support for our ordering of the negative par-ity band comes from the systematics of the iY =44 iso-tones (Fig. 3). The negative parity bands of Se and Krfollow the same spacing as we suggest in Sr up to 9In Zr the states match up to 11
V. SYSTEMATICS
78Sr 80Sr 82
10 10+
84S
+ +8 8
The collective behavior of the N =44 isotones is quitesimilar. The ground-state band levels agree closely at lowspin, especially among the nuclei with Z =38+2 (Fig. 10).This agreement is probably due to the influence of the de-
+10
+12
+10 +
10
+12
+10
o 3
(3CCLLI
++
10
+ +8
+ +8
+ +6 6
+4
76 78 80 82 84326644 3 Se44 36K144 388&44 40Z t44
FIG. 10. Ground-state bands of the %=44 isotones. In ad-dition to the references indicated in Fig. 3, the Ge data arefrom Lecomte et al. {Ref.27).
+ +6 6
6 6+
+ +4 4
+ +1 — + + 4 4
4+
2
2+
+2+
2'0+
0+ + +0
EXP VMI EXP VMI EXP VMI EXP VMI
FIG. 12. VMI fits to the neutron-deficient strontium iso-topes. Data on nuclei other than Sr are taken from Refs. 9and 28.
32 IN-BEAM GAMMA-RAY SPECTROSCOPY OF Sr 1909
TABLE IV. Parameters for VMI fit to Sr nuclei. Parametersare defined in the following equations:
(~) 1 C(~ ~ )1 I(I 1 )
1 I{I 1)2W
anda =[(1/~)(dW/dI) jl=o= 1/(2CW )
in which C is the stiffness parameter, Wp the moment of inertia,and cr is the softness parameter.
BWI o/BWo that might suggest a second-order phasetransition. The negative value of Wo can be associatedwith a preference for spherical symmetry. There seemsto be a fundamental change in structure between Sr and
Sr, both lying in the middle of the g9/2 neutron shell.Although the Sr nucleus appears to be soft with a nearlyspherical ground state, the level energies and transitionstrengths in Sr would seem to indicate a more deformedground state.
Nucleus Wp VI. SUMMARY84Sr
82Sr80Sr78S
1.48 X 100.92X 10'0.84X10'1.07 X 10'
—0.02X10 '0.14X 10-'0.56 X 10-'0.99X 10
2614.019.390.360.05
formed shell gap at Z =38.' At higher spins (I )8) thedifferences in level spacings can be attributed to the ef-fects of quasiparticle excitations.
The similarity of the negative parity bands of the%=44 isotones is shown in Fig. 3. The positive paritybands exhibit the sharpest differences in structure (Fig.11). This may be due to an anticorrelation with protonnumber of the interaction between the gamma band andthe quasiparticle band ( Vz, ) suggested by Funke et al.The positive parity quasiparticle band seems to interactmost strongly with the quasigamma band at Z =38 ( Sr)and with the ground state band at Z =36 or 42 ( Kr,
Zr). Why this occurs and whether it is a more generalphenomena is a topic for further study.
The Z =38 isotopes, on the other hand, show a sys-tematic compression of the ground-state-band energies asneutrons are removed from X =50 to X =40. Thiswould indicate that the differences in structure of thesemedium mass nuclei at the spins studied so far (I & 16)are related to the neutron shell structure. The ground-state bands of the neutron deficient strontium nuclei havebeen fitted in Fig. 12 with the variable moment of inertia(VMI) model; the parameters used are listed in Table IV.As neutron pairs are removed and the residual nucleus be-comes more deformed, the moment of inertia becomeslarger and o. becomes smaller, indicating that the nucleusis becoming more rigid. The change of sign of Wo be-tween Sr and Sr indimtes a discontinuity in
Although the ground-state band of Sr exhibitsbehavior typical of a slightly deformed asymmetric rotor,the side bands exhibit the most interesting behavior. Inthe negative-parity band, the (12 )~(11 ) transition hasa high degree of anisotropy. The moment of inertia of thepositive parity band could be considered to indicate achange from vibrational behavior to the type of rotationalbehavior expected from a rigid rotor. ' If this sequence oftransitions mn be represented by the crossing of two dif-ferent bands, a quasiparticle band and a quasigammaband, then the interaction between those two bands isunusually strong.
The transitional nucleus Sr exhibits complex behaviorthat indicates an interplay between several degrees of free-dom such as collective rotational and vibrational excita-tions, single-particle excitations, and core deformation.More precise transition probabilities are needed to under-stand the collective aspects of the structure. Microscopiccalculations should be done to better define the influenceof the single-particle excitations.
The neutron-deficient strontium isotopes appear toevolve from spherical to highly deformed as neutrons areremoved from the valence shell. Bemuse Sr is located atthe point at which a transition from vibrational to rota-tional collective excitations takes place, knowledge of itsbehavior can contribute to an understanding of how andwhy the evolution occurs.
ACKNOWLEDGMENTS
This research was supported in part by U.S. Depart-ment of Energy Contract No. DE-F605-84ER10410.The assistance of the staff members of the Tandem Ac-celerator Laboratory at Florida State University is greatlyappreciated.
'Present address: Mantech International Corporation, AtlanticBeach, FL 32233.
Present address: Laboratory for Space Research, Leiden, theNetherlands.
~Present address: Department of Radiology and RadiationTherapy, Thomas Jefferson University, Philadelphia, PA19107.
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