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Second backbending in the yrast line of 156Er
Volume 102B, number 4
PHYSICS LETTERS
18 June 1981
SECOND BACKBENDING IN THE YRAST LINE OF 156Er T. BYRSKI, F.A. BECK, C. GEHRINGER, J.C. MERDINGER, Y. SCHUTZ and J.P. VIVIEN Centre de Recherches Nucl~aires and Universit~ Louis Pasteur, 67037 Strasbourg, France
and J. DUDEK i , W. NAZAREWICZ 2 and Z. SZYMAblSK1 1 Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland
Received 26 March 1981
High spin yrast states of lS6Er were investigated using the reactions 141Pr(19F,4n~,) and 123Sb(37Cl,4n.r), the latter in connection with a sum-crystal. In addition to the backbending at I = 12 B, a second one is found at I -- 26 ~ and the yrast band is extended up to I = 32/L These results are interpreted in terms of a Hartree-Fock-Bogolyubov Cranking (HFBC) method. It is demonstrated that for deformations in the vicinity of the Strutinsky equilibrium deformation, both a 2qp proton band crossing the yrast band or a 4qp neutron band crossing the yrast band can cause strong secondary backbending.
The existence of irregularities in the yrast level spacing (backbending) for nuclei o f the rare earth region has recently attracted considerable theoretical attention; in particular, two approaches, the H a r t r e e F o c k - B o g o l y u b o v Cranking (HFBC) [ 1 ] and the coreplus-quasiparticle model focus on the particle alignment to explain this phenomenon. It was suggested [ 1 - 3 ] that sharp backbending can be understood as a result of weak coupling between two interacting bands. The existence or non-existence of backbending is related to the oscillatory behaviour o f this coupling which depends strongly on the shell filling [3]. The observation o f a second discontinuity in the yrast band o f N = 90 nuclei, 158Er [4] and 16°yb [5], supports this picture. To study the effect of variation o f the neutron number we searched for the existence o f a second backbending in 156Er, as predicted in ref. [6]. A previous experiment [7] performed on 156Er identified the yrast band levels up to 1 = 24 ÷, with the onset o f the first backbending at I = 12 +. 1 Supported in part by the Polish-American Maria Sk/odowska Fund, Grant No. P-F7037 P. 2 Address: Institute of Physics, Technical University, 00-662 Warsaw, Poland.
The experiments were performed at the Strasbourg MP tandem accelerator. The excitation functions measured in steps o f 5MeV (between 90 and 110 MeV) in the 141pr(19F, 4n)156Er reaction led to the choice o f a bombarding energy o f 95 MeV. The 1 mg/cm 2 metallic target was rolled as a foil onto a 0.1 mm lead backing. The 7 - 3 ' coincidences were measured with an array of three Ge (Li) detectors. F r o m the relative 3'1-72 yields at 0 ° and 90 °, DCO ratios R = W(90 °, 0°)/W(0 °, 90 ° ) were also derived from the summed coincidence spectra. All 3 ' - 7 coincident spectra obtained with gates set on the 7-rays deexciting the 14 + to 24 + states exhibit a 766 keV 7-ray line which is different from the 765 keV line known to belong to the negative-parity band [7], since the spectra do not show the presence of any other transitions of this band. The 766 keV 7-ray line is attributed, on the basis o f the relative intensity and the DCO ratio, to the decay of the F r = 26+excited state of 156Er leading to the existence o f strong second backbending in the yrast band o f this nucleus. After the upgrading o f the Strasbourg MP tandem accelerator to V = 16 MV we performed a second experiment using the 123Sb(37C1, 4n)156Er reaction with the aim of populating more strongly the high-spin states. A sum crystal was used to discriminate against
0 031 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
23 5
Volume 102B, number 4
PHYSICS LETTERS
Table 1 Relative intensities for the ?-ray transitions of the yrast line in IS6Er observed (a) in the 141pr(19F, 4n)ZS6Er (E(19F) = 95 MeV) and, (b) in the 123Sb(37C1,4n)lS6Er (E(37C1) = 170 MeV) reactions. Transition I i ~ If 2~ 0 4~ 2 6~ 4 8--- 6 10 ~ 8 12 ~ 10 14 ~ 12 16 ~ 14 18 ~ 16 20 ~ 18 22 ~ 20 24 ~ 22 26 --, 24 28 ~ 26 30 --, 28 32 --* 30
E7
/3, (%)
(keV) 344.2 452.7 543.4 618.4 674.2 681.7 a) 522.7 544.0 625.1 710.2 772.1 826.9 766.0 a) 681.7 a) 766.0 a) 799.8
(a)
(b)
100 89(2) 85(2) 70(2) 42(2) 22(2) 12(1) 10(1) 9(1) 7(1) 5(1) 3(1) 3(1)
100 93(3) 90(3) 80(3) 62(3) 48(4) 24(3) 24(3) 23(3) 22(3) 22(3) 20(3) 35(3) b) 15(3) 35(3) b) 10(3)
a) Doublet not resolved. b) Sum of the intensities for the 26+-24 + and 30+-28 + transitions.
~:) 1200,
+e~ +1 ,,=.
N
I
800"
%% .1 ~" ~, l
+1
18 June 1981
the other reaction channels. It was possible to increase the incident bombarding energy of the chlorine beam to as high as 170 MeV without having large contributions from other channels, even if the 5n channel is more strongly populated in the direct spectrum than the 4n channel at this energy. As compared to the first experiment, an increase of 12fi is thus obtained for the angular m o m e n t u m transfer as well as stronger feeding of the highspin states (see table 1). Fig. 1 shows, for both experiments, the spectra obtained with a sum gate set on the 14 +, 18 +, 20 +, 22 + and 24 + decay transitions. Similar spectra were observed for each of the gates. Besides the fact that the second experiment confirms the existence of a 766 keV 7-ray in the yrast line of 156Er we also notice several differences : like the 544 keV line, which is known [7] to contain the 6 + - 4 * and 1 6 + - 1 4 + transitions, the 682 keV and 766 keV line intensities are much higher than those expected for the decay of the 12 + and 26 + excited states. Since these lines are also in coincidence with themselves, we conclude to the existence of two 682 keV and two 766 keV ?-rays in the yrast line as indicated in table 1. A 800 keV 3'-ray line also observed in the gated spectra is interpreted as the transition between the 32 + and the 30 + excited states. For the theoretical interpretation, we approximated
+~ ~ +1 +l ¢o o++
++ .~.=o
t ouD
+1
123$b~7CI, 4n ) 156Er Sum Gotes 1/.+--2/.+ + Gore EEl f
~
+1
.÷1 ÷1 .I
t.00,
z
0
o u
t.500,
I
I
I
I
t
I
1/'1pr119F,/.n1156Er +-24÷
3000,
1500"
I
I
i
i
"
I
"
I
CHANNEL NUMBER
Fig. 1. Coincident "y-rayspectra from the 141pr(;gF, 4n)lS6Er and 123Sb(37C1,4n)lS6Er reactions obtained with a sum gate set on the 14+, 18+, 20+, 22+ and 24+ decay transitions. 236
Volume 102B, number 4
PHYSICS LETTERS
the nuclear hamiltonian by the deformed W o o d s Saxon potential with the parameters taken from ref. [8] supplemented by monopole pairing with the parameters taken from ref. [9]. The approach thus no longer contains any adjustable parameter. Rotation was accounted for by adding ( - W / x ) to the hamiltonian, and the corresponding solution o f the HFBC equations was obtained in the pairing self-consistent way [10]. The calculations were performed at the Strutinsky equilibrium deformations fl2,eq = 0.20 and fl4,eq = 0.02 and also at a number of deformations in the vicinity o f the equilibrium in order to study the stability o f the final results with respect to variations of the deformation. Results o f previous calculations for 1 6 ° y b show [10] that the first backbending in 16°yb is due to the alignment o f one o f the li13/2 neutron pairs, while the !
I
I
23
18 June 1981
second one is due to that o f one o f tlae l h 11/2 proton pairs. The calculations for 156Er were performed using exactly the same method as for 16°yb. The results o f calculations are compared to the experimental data in fig. 2, and in table 2. There are no ambiguities concerning the first backbending which is well reproduced by the calculations. There is, however, some difficulty in the unique interpretation of the data for spins corresponding to the second backbending in 156Er. This is due to a sensitive dependence of the theoretical results on the nuclear deformation. In order to display this effect we repeated calculations at a number of quadrupole and hexadecapole deformation points. For quadrupole deformation 132 ~ 0.17 there is a strong alignment and strong second backbending effect due to the lh11/2(5/2 ) proton orbital. The corresponding aligned angular momentum values are listed in table 2. For increasing quadrupole deformation, the lh11/2(5/2 ) orbital is deplaced away from the Fermi level and is, as a consequence less active [11 ] in the alignment; its role in backbending decreases as well. However, for increasing 132 The neutron 2qp and 4qp band crossing be-
28 ii.
(Hey "1]
"'--.
30
Table 2 28 150
18 20 ,P- . . . . . . . 1/. e----- ~ -
100
L/" _ " ~ ~
22
1-~6
3~32
18
20
- --'~0
22
\ 0
50 4 . ~~ . ~ 7 ~ - ~ 6 ~_.~S~
-~6
EXPT
~
2
_.....
/~oo..
-----
/.~2 =0'23
I
I
I
• 05
• 10
"15
(~fi(~|2 (MeV 2)
Fig. 2. Comparison of the experimental moment of inertia (full line) with two versions of the HFB calculations differing in quadrupole deformations (hexadecapole deformation fixed at/34 = 0.02). The calculated results do not contain band interaction contributions. The experimental curve has been obtained using the usual relation 2 9/~/2 = 21x/W with I x = [(I + 1/2)2 _ K 2 ] 1/2. The experimental quantities ?/co being related to the mean value o f l (I = 1, 3, 5 ...), we have interpolated these data in order to get [lx, co] values for even/.
Aligned angular momenta in and ip (in units ofh ) corresponding to various deformations. Numbers in parentheses indicate the initial cos and final tof values (in MeV) at which the alignment process of a quasiparticle pair starts and ends. A sharp effect occurs when taf ~. w s. If however t~f is significantly larger than cos, then there may exist also some significant contributions to aligned angular momentum originating from a coherent effect of many other quasiparticles. Note that at deformation/32 = 0.17 the two neutron pairs align their angular momenta in the same frequency range just giving rise to an overestimate of the total aligned angular momentum. It is also poss~le that the nucleus stays well deformed up to I ~ (2224)~ and then starts shrinking as predicted in ref. [ 12 ]. In such a case one should compare the experimental data (in fig. 2) with the long-dashed line for I < (22-24)/i while the calculated results for 1 t> (22-24)h lie somewhere in between the long-dashed and short-dashed lines. /32
0.12 0.17 0.20 0.23 expt.
First backbending
Second backbending
in
ip
in
11.4(0.20-0.23) 10.4(0.24-0.27) 9.6(0.22-0.24) 10.2(0.26-0.28) 10
7.5(0.20-0.23) 6.1(0.29-0.33) 2.6(0.25-0,36) 2.7(0.28-0.40) 8
7.0(0.25-0.36) 5.6(0.24-0.28) 5.6(0.33-0.38) 5.6(0.39-0.41) 8
237
Volume 102B, number 4
PHYSICS LETTERS
comes more and more pronounced leading to a strong second backbending effect at/32/> 0.23, ~4 --"0.02. Thus depending on a slight variation in deformation the nature of the calculated backbending changes from a proton to a neutron effect. Unfortunately it is not possible to choose unambiguously between the two possibilities on the basis of the experimental data we have. In this.respect some further information, e.g. concerning the high-spin excitations in the neighbouring 155Er and 157Er nuclei will be helpful. One can argue on the basis o f theoretical results [12], that 156Er shrinks rather than elongates with increasing spin thus favouring a proton-effect hypothesis. Nevertheless it seems interesting to demonstrate on the basis of HFBC pairing self-consistent calculations that protons and neutrons may compete in producing secondary anomalies along yrast lines of collective rotating nuclei.
238
18 June 1981
References [1] R. Bengtsson and S. Frauendorf, Nucl. Phys. A327 (1979) 139 and references therein. [2] F.S. Stephens and R.S. Simon, Nucl. Phys. A183 (1972) 257; C. Flaum and D. Cline, Phys. Rev. C14 (1976) 1224. [3] R. Bengtsson, I. Hamamoto and B.R. Mottelson, Phys. Lett. 73B (1978) 259; F. Grtimmex, K.W. Schmid and A. Faessler, Nucl. Phys. A326 (1979) 1. [4] I.Y. Lee et nl., Phys. Rev. Lett. 38 (1977) 1454. [5] F.A. Beck et al., Phys. Rev. Lett. 42 (1979) 493. [6] M. Prolszajczak and A. Faessler, Z. Phys. A283 (1977) 349. [7] A.W. Sunyar et al., Phys. Lett. 62B (1976) 283. [8] J. Dudek and T. Werner, J. Phys. (NY) G4 (1978) 1543. [9] J. Dudek, A. Majhofer and J. Skalski, J. Phys. (NY) G6 (1980) 447. [10] S. Cwiok et al., Nucl. Phys. A333 (1980) 139. [11] J. Dudek, J. de Phys. Suppl. C-10 (1980) 18. [12] G. Andersson et al., Nucl. Phys. A268 (1976) 205.
PHYSICS LETTERS
18 June 1981
SECOND BACKBENDING IN THE YRAST LINE OF 156Er T. BYRSKI, F.A. BECK, C. GEHRINGER, J.C. MERDINGER, Y. SCHUTZ and J.P. VIVIEN Centre de Recherches Nucl~aires and Universit~ Louis Pasteur, 67037 Strasbourg, France
and J. DUDEK i , W. NAZAREWICZ 2 and Z. SZYMAblSK1 1 Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland
Received 26 March 1981
High spin yrast states of lS6Er were investigated using the reactions 141Pr(19F,4n~,) and 123Sb(37Cl,4n.r), the latter in connection with a sum-crystal. In addition to the backbending at I = 12 B, a second one is found at I -- 26 ~ and the yrast band is extended up to I = 32/L These results are interpreted in terms of a Hartree-Fock-Bogolyubov Cranking (HFBC) method. It is demonstrated that for deformations in the vicinity of the Strutinsky equilibrium deformation, both a 2qp proton band crossing the yrast band or a 4qp neutron band crossing the yrast band can cause strong secondary backbending.
The existence of irregularities in the yrast level spacing (backbending) for nuclei o f the rare earth region has recently attracted considerable theoretical attention; in particular, two approaches, the H a r t r e e F o c k - B o g o l y u b o v Cranking (HFBC) [ 1 ] and the coreplus-quasiparticle model focus on the particle alignment to explain this phenomenon. It was suggested [ 1 - 3 ] that sharp backbending can be understood as a result of weak coupling between two interacting bands. The existence or non-existence of backbending is related to the oscillatory behaviour o f this coupling which depends strongly on the shell filling [3]. The observation o f a second discontinuity in the yrast band o f N = 90 nuclei, 158Er [4] and 16°yb [5], supports this picture. To study the effect of variation o f the neutron number we searched for the existence o f a second backbending in 156Er, as predicted in ref. [6]. A previous experiment [7] performed on 156Er identified the yrast band levels up to 1 = 24 ÷, with the onset o f the first backbending at I = 12 +. 1 Supported in part by the Polish-American Maria Sk/odowska Fund, Grant No. P-F7037 P. 2 Address: Institute of Physics, Technical University, 00-662 Warsaw, Poland.
The experiments were performed at the Strasbourg MP tandem accelerator. The excitation functions measured in steps o f 5MeV (between 90 and 110 MeV) in the 141pr(19F, 4n)156Er reaction led to the choice o f a bombarding energy o f 95 MeV. The 1 mg/cm 2 metallic target was rolled as a foil onto a 0.1 mm lead backing. The 7 - 3 ' coincidences were measured with an array of three Ge (Li) detectors. F r o m the relative 3'1-72 yields at 0 ° and 90 °, DCO ratios R = W(90 °, 0°)/W(0 °, 90 ° ) were also derived from the summed coincidence spectra. All 3 ' - 7 coincident spectra obtained with gates set on the 7-rays deexciting the 14 + to 24 + states exhibit a 766 keV 7-ray line which is different from the 765 keV line known to belong to the negative-parity band [7], since the spectra do not show the presence of any other transitions of this band. The 766 keV 7-ray line is attributed, on the basis o f the relative intensity and the DCO ratio, to the decay of the F r = 26+excited state of 156Er leading to the existence o f strong second backbending in the yrast band o f this nucleus. After the upgrading o f the Strasbourg MP tandem accelerator to V = 16 MV we performed a second experiment using the 123Sb(37C1, 4n)156Er reaction with the aim of populating more strongly the high-spin states. A sum crystal was used to discriminate against
0 031 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
23 5
Volume 102B, number 4
PHYSICS LETTERS
Table 1 Relative intensities for the ?-ray transitions of the yrast line in IS6Er observed (a) in the 141pr(19F, 4n)ZS6Er (E(19F) = 95 MeV) and, (b) in the 123Sb(37C1,4n)lS6Er (E(37C1) = 170 MeV) reactions. Transition I i ~ If 2~ 0 4~ 2 6~ 4 8--- 6 10 ~ 8 12 ~ 10 14 ~ 12 16 ~ 14 18 ~ 16 20 ~ 18 22 ~ 20 24 ~ 22 26 --, 24 28 ~ 26 30 --, 28 32 --* 30
E7
/3, (%)
(keV) 344.2 452.7 543.4 618.4 674.2 681.7 a) 522.7 544.0 625.1 710.2 772.1 826.9 766.0 a) 681.7 a) 766.0 a) 799.8
(a)
(b)
100 89(2) 85(2) 70(2) 42(2) 22(2) 12(1) 10(1) 9(1) 7(1) 5(1) 3(1) 3(1)
100 93(3) 90(3) 80(3) 62(3) 48(4) 24(3) 24(3) 23(3) 22(3) 22(3) 20(3) 35(3) b) 15(3) 35(3) b) 10(3)
a) Doublet not resolved. b) Sum of the intensities for the 26+-24 + and 30+-28 + transitions.
~:) 1200,
+e~ +1 ,,=.
N
I
800"
%% .1 ~" ~, l
+1
18 June 1981
the other reaction channels. It was possible to increase the incident bombarding energy of the chlorine beam to as high as 170 MeV without having large contributions from other channels, even if the 5n channel is more strongly populated in the direct spectrum than the 4n channel at this energy. As compared to the first experiment, an increase of 12fi is thus obtained for the angular m o m e n t u m transfer as well as stronger feeding of the highspin states (see table 1). Fig. 1 shows, for both experiments, the spectra obtained with a sum gate set on the 14 +, 18 +, 20 +, 22 + and 24 + decay transitions. Similar spectra were observed for each of the gates. Besides the fact that the second experiment confirms the existence of a 766 keV 7-ray in the yrast line of 156Er we also notice several differences : like the 544 keV line, which is known [7] to contain the 6 + - 4 * and 1 6 + - 1 4 + transitions, the 682 keV and 766 keV line intensities are much higher than those expected for the decay of the 12 + and 26 + excited states. Since these lines are also in coincidence with themselves, we conclude to the existence of two 682 keV and two 766 keV ?-rays in the yrast line as indicated in table 1. A 800 keV 3'-ray line also observed in the gated spectra is interpreted as the transition between the 32 + and the 30 + excited states. For the theoretical interpretation, we approximated
+~ ~ +1 +l ¢o o++
++ .~.=o
t ouD
+1
123$b~7CI, 4n ) 156Er Sum Gotes 1/.+--2/.+ + Gore EEl f
~
+1
.÷1 ÷1 .I
t.00,
z
0
o u
t.500,
I
I
I
I
t
I
1/'1pr119F,/.n1156Er +-24÷
3000,
1500"
I
I
i
i
"
I
"
I
CHANNEL NUMBER
Fig. 1. Coincident "y-rayspectra from the 141pr(;gF, 4n)lS6Er and 123Sb(37C1,4n)lS6Er reactions obtained with a sum gate set on the 14+, 18+, 20+, 22+ and 24+ decay transitions. 236
Volume 102B, number 4
PHYSICS LETTERS
the nuclear hamiltonian by the deformed W o o d s Saxon potential with the parameters taken from ref. [8] supplemented by monopole pairing with the parameters taken from ref. [9]. The approach thus no longer contains any adjustable parameter. Rotation was accounted for by adding ( - W / x ) to the hamiltonian, and the corresponding solution o f the HFBC equations was obtained in the pairing self-consistent way [10]. The calculations were performed at the Strutinsky equilibrium deformations fl2,eq = 0.20 and fl4,eq = 0.02 and also at a number of deformations in the vicinity o f the equilibrium in order to study the stability o f the final results with respect to variations of the deformation. Results o f previous calculations for 1 6 ° y b show [10] that the first backbending in 16°yb is due to the alignment o f one o f the li13/2 neutron pairs, while the !
I
I
23
18 June 1981
second one is due to that o f one o f tlae l h 11/2 proton pairs. The calculations for 156Er were performed using exactly the same method as for 16°yb. The results o f calculations are compared to the experimental data in fig. 2, and in table 2. There are no ambiguities concerning the first backbending which is well reproduced by the calculations. There is, however, some difficulty in the unique interpretation of the data for spins corresponding to the second backbending in 156Er. This is due to a sensitive dependence of the theoretical results on the nuclear deformation. In order to display this effect we repeated calculations at a number of quadrupole and hexadecapole deformation points. For quadrupole deformation 132 ~ 0.17 there is a strong alignment and strong second backbending effect due to the lh11/2(5/2 ) proton orbital. The corresponding aligned angular momentum values are listed in table 2. For increasing quadrupole deformation, the lh11/2(5/2 ) orbital is deplaced away from the Fermi level and is, as a consequence less active [11 ] in the alignment; its role in backbending decreases as well. However, for increasing 132 The neutron 2qp and 4qp band crossing be-
28 ii.
(Hey "1]
"'--.
30
Table 2 28 150
18 20 ,P- . . . . . . . 1/. e----- ~ -
100
L/" _ " ~ ~
22
1-~6
3~32
18
20
- --'~0
22
\ 0
50 4 . ~~ . ~ 7 ~ - ~ 6 ~_.~S~
-~6
EXPT
~
2
_.....
/~oo..
-----
/.~2 =0'23
I
I
I
• 05
• 10
"15
(~fi(~|2 (MeV 2)
Fig. 2. Comparison of the experimental moment of inertia (full line) with two versions of the HFB calculations differing in quadrupole deformations (hexadecapole deformation fixed at/34 = 0.02). The calculated results do not contain band interaction contributions. The experimental curve has been obtained using the usual relation 2 9/~/2 = 21x/W with I x = [(I + 1/2)2 _ K 2 ] 1/2. The experimental quantities ?/co being related to the mean value o f l (I = 1, 3, 5 ...), we have interpolated these data in order to get [lx, co] values for even/.
Aligned angular momenta in and ip (in units ofh ) corresponding to various deformations. Numbers in parentheses indicate the initial cos and final tof values (in MeV) at which the alignment process of a quasiparticle pair starts and ends. A sharp effect occurs when taf ~. w s. If however t~f is significantly larger than cos, then there may exist also some significant contributions to aligned angular momentum originating from a coherent effect of many other quasiparticles. Note that at deformation/32 = 0.17 the two neutron pairs align their angular momenta in the same frequency range just giving rise to an overestimate of the total aligned angular momentum. It is also poss~le that the nucleus stays well deformed up to I ~ (2224)~ and then starts shrinking as predicted in ref. [ 12 ]. In such a case one should compare the experimental data (in fig. 2) with the long-dashed line for I < (22-24)/i while the calculated results for 1 t> (22-24)h lie somewhere in between the long-dashed and short-dashed lines. /32
0.12 0.17 0.20 0.23 expt.
First backbending
Second backbending
in
ip
in
11.4(0.20-0.23) 10.4(0.24-0.27) 9.6(0.22-0.24) 10.2(0.26-0.28) 10
7.5(0.20-0.23) 6.1(0.29-0.33) 2.6(0.25-0,36) 2.7(0.28-0.40) 8
7.0(0.25-0.36) 5.6(0.24-0.28) 5.6(0.33-0.38) 5.6(0.39-0.41) 8
237
Volume 102B, number 4
PHYSICS LETTERS
comes more and more pronounced leading to a strong second backbending effect at/32/> 0.23, ~4 --"0.02. Thus depending on a slight variation in deformation the nature of the calculated backbending changes from a proton to a neutron effect. Unfortunately it is not possible to choose unambiguously between the two possibilities on the basis of the experimental data we have. In this.respect some further information, e.g. concerning the high-spin excitations in the neighbouring 155Er and 157Er nuclei will be helpful. One can argue on the basis o f theoretical results [12], that 156Er shrinks rather than elongates with increasing spin thus favouring a proton-effect hypothesis. Nevertheless it seems interesting to demonstrate on the basis of HFBC pairing self-consistent calculations that protons and neutrons may compete in producing secondary anomalies along yrast lines of collective rotating nuclei.
238
18 June 1981
References [1] R. Bengtsson and S. Frauendorf, Nucl. Phys. A327 (1979) 139 and references therein. [2] F.S. Stephens and R.S. Simon, Nucl. Phys. A183 (1972) 257; C. Flaum and D. Cline, Phys. Rev. C14 (1976) 1224. [3] R. Bengtsson, I. Hamamoto and B.R. Mottelson, Phys. Lett. 73B (1978) 259; F. Grtimmex, K.W. Schmid and A. Faessler, Nucl. Phys. A326 (1979) 1. [4] I.Y. Lee et nl., Phys. Rev. Lett. 38 (1977) 1454. [5] F.A. Beck et al., Phys. Rev. Lett. 42 (1979) 493. [6] M. Prolszajczak and A. Faessler, Z. Phys. A283 (1977) 349. [7] A.W. Sunyar et al., Phys. Lett. 62B (1976) 283. [8] J. Dudek and T. Werner, J. Phys. (NY) G4 (1978) 1543. [9] J. Dudek, A. Majhofer and J. Skalski, J. Phys. (NY) G6 (1980) 447. [10] S. Cwiok et al., Nucl. Phys. A333 (1980) 139. [11] J. Dudek, J. de Phys. Suppl. C-10 (1980) 18. [12] G. Andersson et al., Nucl. Phys. A268 (1976) 205.