- Email: [email protected]
Band crossing in 162Dy: Characterisation of negative-parity yrast and yrare sequences
Volume 104B, number 1
PHYSICS LETTERS
13 August 1981
BAND CROSSING IN 162Dy: CHARACTERISATION OF NEGATIVE-PARITY YRAST AND YRARE SEQUENCES P.M. WALKER Science and Engineering Research Council, Daresbury Laboratory, Warrington WA4 4AD, UK 1 and Cyclotron Laboratory, Michigan State University, East Lansing, M148824, USA F.W.N. de BOER Physics Department, University of Fribourg, e/o SIN, 5234 Villigen, Switzerland 1 and Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309, USA and C.A. FIELDS Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309, USA Received 4 June 1981
The crossing of an octupole band by a rotation-aligned two-quasiparticle band has been observed in detail in 162Dy. Both the yrast and yrare states are identified from the band heads (I = 2 and I = 5) to high spin (1 ~ 14), with band crossings in both the even-spin and odd-spin sequences.
The form o f rotational bands in deformed nuclei illustrates the dynamic competition between collective and intrinsic degrees o f freedom. In particular, band crossings make evident the changing circumstances which favour different excitation modes in different angular-momentum domains. Frequently, the combined influence of the method of population o f the states, and the mixing between the crossing bands, results in only the lower (.yrast) sequence being identified experimentally. One observes yrast anomalies (backbending) but the question of the nature of the unfavoured (yrare) states is left open. The present letter considers one such observation o f the negative-parity yrast and yrare states (i.e. the two negative-parity sequences of states that lie lowest in energy) through the band-crossing region. The character o f both the bands is deduced from the excitation and deexcitation modes. This explicit band crossing has been observed in 1 Present address.
162Dy, following the 160Gd(a, 2n) reaction at 28 MeV. Using standard ")'-ray and conversion-electron techniques (including detailed 3 ' - 7 coincidence studies) at least six rotational bands have been identified up to I ~> 10. The complete results will be published elsewhere [ 1] but here we concentrate on the two lowest negative-parity bands, illustrated in fig. 1. The negative-parity yrast sequence changes above I = 7, from the octupole band to the two-quasiparticle (2qp) band. The placement of the levels in the two bands as indicated in fig. 1 is based initially on the connecting inband transitions (and the knowledge o f the low-spin members of the octupole band from other work [2]). In the band based on the I = 5, 1486 keV level, all even-spin members have both I ~ I - 2 and I ~ I - 1 branches. These specify uniquely all the band members except the I = 9 member; we show later that the I = 9, 1940 keV level is strongly mixed with the I = 9, 1960 keV level, so that in which band each is placed is somewhat arbitrary. The even-spin levels in the band above the 1148 keV level form a sequence with smooth be-
0 0 3 1 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
19
Volume 104B, number 1 3135
[
PHYSICS LETTERS
114-)
464 / (13-)
2779
/----I-12+0~ 877~
)
13-
2684
4
437
~
781412+0
(12-)37111 I '2021[248__3 2332 / 01-) 10+0__ 957~ / / ' - - - ~ 9"2 --355 /
388
196o /
,+o_1o3,~/~---@ + ~ 355 / 72
4+0 1125//
9- /
1 316
/
3+2 ~334 / / 1 1 4 8
-
4~$
3 9--
,- ~ // " 7-2 11141683
1019~8+0
1576
762~8+0 1135~6+0
,~,,~, ~_
/ 2~3o 1390 J,,__,~.5 -
32-
~. 906--10+0
1940
/
1210
2281
2111
./~
1637 [__,-
+ ~ 6 6 0-10~9/" ~5+2~ 348 /
11_~, t
~
2.~ 5- ~
2qp
~
938~6+0 1221~4+0
2+o_113o// oc,o,,o,. 0,2.. 2+2~ 260/
Fig. 1. Partial level scheme for 162Dy, showing levels in the two lowest-lying negative-parity bands, populated in the 16°Gd(c~,2n) reactions, and their ,y-ray decay modes identified in this work. The thickly drawn levels represent the negative-parity yrast sequence. Excitation energies are given in keV, with their I n assignments (assignments in parentheses and dashed transitions are tentative). Other levels which are fed from those illustrated are labelled by the quantum numbers InK.
haviour inEversus I ( I + 1) space, and are also connected by i n - b a n d / 4 1 - 2 transitions (the 4 ~ 2 transition is not identified in this work, though it is known from neutron capture studies [3]); even-spin levels with I = 2 - 1 0 also have characteristic decay to the ?-vibrational band. The odd-spin members decay only to the ground-state band (gsb), but they are easily placed in the band, based on (i) their smooth spacings in E versus I ( I + 1) space, and (ii) the absence of any other candidates for band members [ 1 ]. The interesting features of the in-band/out-of-band branching ratios cannot be dealt with in detail here (but see ref. [ 1 ]) though the transitions between the two bands will be considered below. Previous knowledge [2] of these two bands has been confined to the lowest three or four members. This is valuable for the characterisation of the states. In partic20
13 August 1981
ular, the I ~ = 3 - , 1210 keV level is strongly populated by inelastic deuteron scattering [4] and Coulomb excitation [5], yielding a B(E3) value of about 9 single-particle units. Therefore, the band above the I ~r = 2 - , 1148 keV level appears to be based on the single-phonon octupole vibration. We note that some significant involvement of the {~-- [523]p, ~+ [411]p}2- two-quasiproton configuration is indicated by the population of the I = 2, 1148 keV band head following 162Tb/3-decay [6]. This is not inconsistent with the octupole character of the excitation [2]. The excited members of the octupole band decay promptly to the gsb or the ?-vibrational band, and t h e / = 2 band head has a short half-life (0.2 ns [7]). In contrast, t h e / n = 5 - , 1486 keV level has a longer half-life (2 ns [8]) establishing it as a band head and suggesting a K = 5 assignment, based on a 2qp excitation. The strong population of this I = 5 level following 162Ho/3 + decay [9] suggests the (s+ [642]n ' 5-[523] n }5 - two-quasineutron assignment. The present data support this assignment by using the angular distribution coefficients for the in-band I -+I - 1 transitions. The negative A 2 values [ 1 ] imply negative mixing ratios and hence (c.f. ref. [ 10]) negative g-factors (gK --gR < 0); this is only consistent with neutron configurations. The involvement of the s+ [642], i13/2 neutron in the 2qp band is of special interest, because these neutrons are well known to be strongly influenced by the Coriolis force [ 11]. This leads to an alignment of intrinsic angular momentum with the rotation, i.e. rotation alignment, which in turn gives a high effective moment of inertia. The latter feature is illustrated at the top of fig. 2. The 2qp band is seen to have 2 9 / h 2 ~ 130 MeV -1 at low fi~o, compared with values of about 100 MeV -1 and 80 MeV -1 in the octupole and ground-state bands, respectively (the gsb is not illustrated). Thus, although the 2qp band is not favoured energetically at low spin (compared to the octupole band) on account of the larger energy required to promote two quasiparticles, the high moment of inertia leads to the 2qp band falling below the octupole band at high spin. While the moment-of-inertia curves for the 2qp and octupole bands are separately fairly smooth, the curves for the negative-parity yrast states (thick lines in fig. 2) show sudden increases at h2co 2 ~ 0.02 MeV 2, characteristic of the band crossing that can be seen in detail in fig. 1. The mixing between the 2qp and octupole bands is evident in three specific features, to be discussed below. First, the I = 9 level energies are significantly perturbed.
Volume 104B, number 1
PHYSICS LETTERS
/2q~3 odd
130 -
162Dy
120-
>m
110 -
100-
90-
~2w2 ( MeV 2) 0.01
0 02
0.03
0.04
0.05
I
t
I
I
I
9-
006
,o-9
7-
s;
60
1;o
(I/t~)2
Fig. 2. Moment-of-inertia diagram for bands in 162Dy, In the upper section 2~/~ 2 = (41 - 2 ) / [ E ( 1 ) - E ( I - 2)1 is shown as a function of//2w z = [E(1) - E ( 1 - 2)]2/4. The thick full lines connect the values for the negative-parity yrast states (with separate odd-spin and even-spin sequences) while the thin full lines connect the yrare extensions. The open symbols represent the estimated values before the mixing of the/rr = 9levels. Parentheses indicate tentative values. In the lower section the inverse moment of inertia (//2/2 9 = [E(I) - E ( 1 - 1)]/ 2/) is shown as a function o f I 2 for the 2qp band only. The line joins the values resulting from a 2qp-plus-rotor calculation (with a 50% reduction of the theoretical matrix elements ins+ volving the g [642] neutron orbital).
Second, there are transitions between the bands. Third, there is/3 + decay from the I = 6 isomeric state in 162Ho to both the presently considered I = 5 levels in 162Dy. The l o g f t value for the strong branch has been taken (above) to imply the two-quasineutron assignment for the 2qp level. The l o g f t for the weak branch implies some significant (<~ 5%) admixture of the same twoquasineutron configuration in the I = 5, 1390 keV member of the octupole band. Considering the I = 9 energies, one can see (fig. 2) in the moment-of-inertia curves for the odd-spin 2qp and octupole bands, that there are significant irregularities. Furthermore, the experimental I = 9 energies are only 20 keV apart. If we use a mixing strength o f about 10 keV, then the unperturbed I = 9 energies are within a few keV of one another. The unperturbed
13 August 1981
moment-of-inertia curves then follow the dashed lines (and open symbols) in fig. 2, showing smoother behaviour. With 10 keV mixing between levels of equal I, none of the other levels would be perturbed more than 3 keV, and all but the I -- 9 levels contain more than 90% of their parent configuration. The experimental I = 9 levels are estimated to contain about 50% of each of the 2qp and octupole parent configurations. The decay of the I = 10, 2qp state supports this suggestion, because there are comparable branches to each of the I = 9 levels. (The I = 10 octupole state decays to neither I = 9 level, a consequence, essentially, of the lower Kvalue of the octupole excitation. Transitions from the I = 9 levels themselves go directly to the gsb in each case, similar to the other odd-spin levels, so that the mixing effects are not evident in these transitions.) The mixing between the bands is also shown by the cross-band 8-+ 6 (2qp ~ octupole) transition. This transition is part of the even-spin yrast sequence. Using again 10 keV mixing between the bands, the B(E2, I ~ I - 2) ratio favours the in-band transition over the cross-band transition by a factor o f about two, only. The energy factor favours the cross-band transition, so that its experimental observation is consistent with these considerations. One would expect to see weakly the crossband 8 ~ 7 (2qp ~ octupole) transition, but its energy of 171 keV coincides with the in-band 10 ~ 9 transition, and it is difficult to establish experimentally. Other significant features to consider are the A I = 1 level spacings and decay modes in the 2qp band. The odd-spin states are favoured energetically and decay primarily out-of-band, while the even-spin states decay only in-band. A similar situation has been found in other 2qp bands, and has been described in a 2qp-plus-rotor Coriolis coupling representation [ 10]. Results for the A I = 1 level spacings in the 162Dy 2qp band are illustrated at the b o t t o m of fig. 1. More details will b e given elsewhere [ 1 ], but for the present we note that (i) the high moment of inertia is reproduced, even though the gsb value is used for the basis states, (ii) the energy favouring of the odd-spin states is reproduced, and (iii) the calculation follows better the values (open circles) corresponding to the I = 9 energy before mixing with the octupole band, supporting the previous evidence for the perturbation o f the experimental I = 9 level energies. The 2qp-plus-rotor calculation uses a basis in which the ~- [523] neutron remains strongly coupled to the deformation, while the s+ [642] neutron mixes, 21
Volume 104B, number 1
PHYSICS LETTERS
through the AK = 1 Coriolis matrix elements, with all the other i13/2 orbitals; i.e. the i13/2 neutron becomes rotation aligned. As with other similar bands [10] we call this mixed 2qp band a "semi-aligned" side band. Overall, a satisfactory interpretation of the properties of the 2qp band is seen to be possible. The crossing of an octupole band by a 2qp band has been inferred on previous occasions, well illustrated by the octupole bands in t h e n = 88 isotones [12] and 152Sm (N = 90) [13]: the states that are favoured energetically are observed through the crossing region, but the unfavoured states remain unknown. This leaves unanswered significant questions, in particular the nature of the crossing 2qp band. Generally, observed band crossings have been restricted to cases where the knowledge of the yrare states is very limited, leading to ambiguities in the interpretation. The negative-parity bands in 162Dy provide an example where all the yrare states are identified, enabling them to be clearly characterised. A discussion of the structure of octupole bands would be incomplete without noting the two high-spin characteristics suggested by Vogel [ 14], namely either the taking-on of 2qp character, or the alignment of the octupole phonon with the rotation. The former is illustrated by the negative-parity yrast states in 162Dy (figs. 1 and 2) and the latter is seen in the yrare extension of the octupole band. These features may be quantified in terms of the alignment of intrinsic (or vibrational) angular momentum with the rotation. The degree of alignment, is, is estimated [15] simply from the difference in the total angular momentum between the excited band and the gsb, at a given rotation frequency. In an octupole band i s should not exceed 3h, since the octupole phonon carries only 3 units of angular momentum; in contrast an i13/2 neutron may align up to 6.5h. Experimentally, in the 2qp band ic~ rises from 2.8 to 4.3h with increasing rotation frequency, consistent with the partial alignment of an i13/2 neutron. (We note that there is more alignment than is possible for an octupole phonon. Also, it should not be surprising that the i13/2 neutron is not fully aligned: the corresponding 1qp i 13/2 band in 161Dy [16] for example, also has i s ~ 4h.) In the odd-spin members of the octupole band the corresponding rise in ic~ is from 1.0 to 3.0h, consistent with the aligned-octupole interpretation; however, the even-
22
13 August 1981
spin members show a remarkable increase in is, up to 3.7/~ at the highest observed spins. This corresponds to the significant up-bending in the moment-of-inertia curve (fig. 2) and is indicative of a crossing with another (unidentified) 2qp band. In summary, we have identified an octupole band and a 2qp band from their band heads to high spin. The bands have been characterised by their excitation and deexcitation modes with a variety of population mechanisms, namely Coulomb excitation, inelastic scattering, neutron capture, radioactive decay and fusion-evaporation reactions. The negative-parity yrast states are formed by the octupole band for I ~< 7 and by the 2qp band forI>~ 8. The mixing between the bands is about 10 keV in the crossing region, leading to level-energy perturbations and cross-band transitions. The 2qp band is able to become yrast at high spin due to the involvement of an i13/2 neutron, which gives an intrinsic contribution to the total nuclear angular momentum. We wish to thank P. Vogel for useful discussions. This work was supported in part by the US National Science Foundation under Grant No. Phys-78-22696, and the US Department of Energy.
References [1 ] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [ 16]
F.W.N. de Boer et al., to be published. A. Byrne, Nucl. Data Sheets 17 (1976) 97. A. B/icklin et al., Phys. Rev. 160 (1967) 1011. T. Grotdal, K. Nyb¢, T. Thorsteinsen and B. Elbek, Nucl. Phys. All0 (1968) 385. R.N. Oehlberg et al., Nucl. Phys. A219 (1974) 543. L. Funke et al., Nucl. Phys. 84 (1966) 424. B. Sethi and S.K. Mukherjee, Phys. Rev. 166 (1968) 1227. V. M6nig, Z. Phys. 225 (1969) 327. M. J¢rgensen, O.B. Nielsen and O. Skilbreid, Nucl. Phys. 24 (1961) 443. P.M. Walker et al., Phys. Lett. 86B (1979) 9; Nucl. Phys. A343 (1980)45;A365 (1981)61. F.S. Stephens, Rev. Mod. Phys. 47 (1975) 43. F.W.N. de Boer, L.K. Peker, P. Koldewijn and J. Konijn, Z. Phys. A284 (1978) 267. J. Konijn et al., Phys. Lett. 99B (1981) 449. P. Vogel, Phys. Lett. 60B (1976) 431. A. Bohr and B.R. Mottelson, J. Phys. Soc. Japan 44 (1978) Suppl. 157. S.A. Hjorth, A. Johnson and G. Ehrling, Nucl. Phys. A184 (1972) 113.
PHYSICS LETTERS
13 August 1981
BAND CROSSING IN 162Dy: CHARACTERISATION OF NEGATIVE-PARITY YRAST AND YRARE SEQUENCES P.M. WALKER Science and Engineering Research Council, Daresbury Laboratory, Warrington WA4 4AD, UK 1 and Cyclotron Laboratory, Michigan State University, East Lansing, M148824, USA F.W.N. de BOER Physics Department, University of Fribourg, e/o SIN, 5234 Villigen, Switzerland 1 and Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309, USA and C.A. FIELDS Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309, USA Received 4 June 1981
The crossing of an octupole band by a rotation-aligned two-quasiparticle band has been observed in detail in 162Dy. Both the yrast and yrare states are identified from the band heads (I = 2 and I = 5) to high spin (1 ~ 14), with band crossings in both the even-spin and odd-spin sequences.
The form o f rotational bands in deformed nuclei illustrates the dynamic competition between collective and intrinsic degrees o f freedom. In particular, band crossings make evident the changing circumstances which favour different excitation modes in different angular-momentum domains. Frequently, the combined influence of the method of population o f the states, and the mixing between the crossing bands, results in only the lower (.yrast) sequence being identified experimentally. One observes yrast anomalies (backbending) but the question of the nature of the unfavoured (yrare) states is left open. The present letter considers one such observation o f the negative-parity yrast and yrare states (i.e. the two negative-parity sequences of states that lie lowest in energy) through the band-crossing region. The character o f both the bands is deduced from the excitation and deexcitation modes. This explicit band crossing has been observed in 1 Present address.
162Dy, following the 160Gd(a, 2n) reaction at 28 MeV. Using standard ")'-ray and conversion-electron techniques (including detailed 3 ' - 7 coincidence studies) at least six rotational bands have been identified up to I ~> 10. The complete results will be published elsewhere [ 1] but here we concentrate on the two lowest negative-parity bands, illustrated in fig. 1. The negative-parity yrast sequence changes above I = 7, from the octupole band to the two-quasiparticle (2qp) band. The placement of the levels in the two bands as indicated in fig. 1 is based initially on the connecting inband transitions (and the knowledge o f the low-spin members of the octupole band from other work [2]). In the band based on the I = 5, 1486 keV level, all even-spin members have both I ~ I - 2 and I ~ I - 1 branches. These specify uniquely all the band members except the I = 9 member; we show later that the I = 9, 1940 keV level is strongly mixed with the I = 9, 1960 keV level, so that in which band each is placed is somewhat arbitrary. The even-spin levels in the band above the 1148 keV level form a sequence with smooth be-
0 0 3 1 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
19
Volume 104B, number 1 3135
[
PHYSICS LETTERS
114-)
464 / (13-)
2779
/----I-12+0~ 877~
)
13-
2684
4
437
~
781412+0
(12-)37111 I '2021[248__3 2332 / 01-) 10+0__ 957~ / / ' - - - ~ 9"2 --355 /
388
196o /
,+o_1o3,~/~---@ + ~ 355 / 72
4+0 1125//
9- /
1 316
/
3+2 ~334 / / 1 1 4 8
-
4~$
3 9--
,- ~ // " 7-2 11141683
1019~8+0
1576
762~8+0 1135~6+0
,~,,~, ~_
/ 2~3o 1390 J,,__,~.5 -
32-
~. 906--10+0
1940
/
1210
2281
2111
./~
1637 [__,-
+ ~ 6 6 0-10~9/" ~5+2~ 348 /
11_~, t
~
2.~ 5- ~
2qp
~
938~6+0 1221~4+0
2+o_113o// oc,o,,o,. 0,2.. 2+2~ 260/
Fig. 1. Partial level scheme for 162Dy, showing levels in the two lowest-lying negative-parity bands, populated in the 16°Gd(c~,2n) reactions, and their ,y-ray decay modes identified in this work. The thickly drawn levels represent the negative-parity yrast sequence. Excitation energies are given in keV, with their I n assignments (assignments in parentheses and dashed transitions are tentative). Other levels which are fed from those illustrated are labelled by the quantum numbers InK.
haviour inEversus I ( I + 1) space, and are also connected by i n - b a n d / 4 1 - 2 transitions (the 4 ~ 2 transition is not identified in this work, though it is known from neutron capture studies [3]); even-spin levels with I = 2 - 1 0 also have characteristic decay to the ?-vibrational band. The odd-spin members decay only to the ground-state band (gsb), but they are easily placed in the band, based on (i) their smooth spacings in E versus I ( I + 1) space, and (ii) the absence of any other candidates for band members [ 1 ]. The interesting features of the in-band/out-of-band branching ratios cannot be dealt with in detail here (but see ref. [ 1 ]) though the transitions between the two bands will be considered below. Previous knowledge [2] of these two bands has been confined to the lowest three or four members. This is valuable for the characterisation of the states. In partic20
13 August 1981
ular, the I ~ = 3 - , 1210 keV level is strongly populated by inelastic deuteron scattering [4] and Coulomb excitation [5], yielding a B(E3) value of about 9 single-particle units. Therefore, the band above the I ~r = 2 - , 1148 keV level appears to be based on the single-phonon octupole vibration. We note that some significant involvement of the {~-- [523]p, ~+ [411]p}2- two-quasiproton configuration is indicated by the population of the I = 2, 1148 keV band head following 162Tb/3-decay [6]. This is not inconsistent with the octupole character of the excitation [2]. The excited members of the octupole band decay promptly to the gsb or the ?-vibrational band, and t h e / = 2 band head has a short half-life (0.2 ns [7]). In contrast, t h e / n = 5 - , 1486 keV level has a longer half-life (2 ns [8]) establishing it as a band head and suggesting a K = 5 assignment, based on a 2qp excitation. The strong population of this I = 5 level following 162Ho/3 + decay [9] suggests the (s+ [642]n ' 5-[523] n }5 - two-quasineutron assignment. The present data support this assignment by using the angular distribution coefficients for the in-band I -+I - 1 transitions. The negative A 2 values [ 1 ] imply negative mixing ratios and hence (c.f. ref. [ 10]) negative g-factors (gK --gR < 0); this is only consistent with neutron configurations. The involvement of the s+ [642], i13/2 neutron in the 2qp band is of special interest, because these neutrons are well known to be strongly influenced by the Coriolis force [ 11]. This leads to an alignment of intrinsic angular momentum with the rotation, i.e. rotation alignment, which in turn gives a high effective moment of inertia. The latter feature is illustrated at the top of fig. 2. The 2qp band is seen to have 2 9 / h 2 ~ 130 MeV -1 at low fi~o, compared with values of about 100 MeV -1 and 80 MeV -1 in the octupole and ground-state bands, respectively (the gsb is not illustrated). Thus, although the 2qp band is not favoured energetically at low spin (compared to the octupole band) on account of the larger energy required to promote two quasiparticles, the high moment of inertia leads to the 2qp band falling below the octupole band at high spin. While the moment-of-inertia curves for the 2qp and octupole bands are separately fairly smooth, the curves for the negative-parity yrast states (thick lines in fig. 2) show sudden increases at h2co 2 ~ 0.02 MeV 2, characteristic of the band crossing that can be seen in detail in fig. 1. The mixing between the 2qp and octupole bands is evident in three specific features, to be discussed below. First, the I = 9 level energies are significantly perturbed.
Volume 104B, number 1
PHYSICS LETTERS
/2q~3 odd
130 -
162Dy
120-
>m
110 -
100-
90-
~2w2 ( MeV 2) 0.01
0 02
0.03
0.04
0.05
I
t
I
I
I
9-
006
,o-9
7-
s;
60
1;o
(I/t~)2
Fig. 2. Moment-of-inertia diagram for bands in 162Dy, In the upper section 2~/~ 2 = (41 - 2 ) / [ E ( 1 ) - E ( I - 2)1 is shown as a function of//2w z = [E(1) - E ( 1 - 2)]2/4. The thick full lines connect the values for the negative-parity yrast states (with separate odd-spin and even-spin sequences) while the thin full lines connect the yrare extensions. The open symbols represent the estimated values before the mixing of the/rr = 9levels. Parentheses indicate tentative values. In the lower section the inverse moment of inertia (//2/2 9 = [E(I) - E ( 1 - 1)]/ 2/) is shown as a function o f I 2 for the 2qp band only. The line joins the values resulting from a 2qp-plus-rotor calculation (with a 50% reduction of the theoretical matrix elements ins+ volving the g [642] neutron orbital).
Second, there are transitions between the bands. Third, there is/3 + decay from the I = 6 isomeric state in 162Ho to both the presently considered I = 5 levels in 162Dy. The l o g f t value for the strong branch has been taken (above) to imply the two-quasineutron assignment for the 2qp level. The l o g f t for the weak branch implies some significant (<~ 5%) admixture of the same twoquasineutron configuration in the I = 5, 1390 keV member of the octupole band. Considering the I = 9 energies, one can see (fig. 2) in the moment-of-inertia curves for the odd-spin 2qp and octupole bands, that there are significant irregularities. Furthermore, the experimental I = 9 energies are only 20 keV apart. If we use a mixing strength o f about 10 keV, then the unperturbed I = 9 energies are within a few keV of one another. The unperturbed
13 August 1981
moment-of-inertia curves then follow the dashed lines (and open symbols) in fig. 2, showing smoother behaviour. With 10 keV mixing between levels of equal I, none of the other levels would be perturbed more than 3 keV, and all but the I -- 9 levels contain more than 90% of their parent configuration. The experimental I = 9 levels are estimated to contain about 50% of each of the 2qp and octupole parent configurations. The decay of the I = 10, 2qp state supports this suggestion, because there are comparable branches to each of the I = 9 levels. (The I = 10 octupole state decays to neither I = 9 level, a consequence, essentially, of the lower Kvalue of the octupole excitation. Transitions from the I = 9 levels themselves go directly to the gsb in each case, similar to the other odd-spin levels, so that the mixing effects are not evident in these transitions.) The mixing between the bands is also shown by the cross-band 8-+ 6 (2qp ~ octupole) transition. This transition is part of the even-spin yrast sequence. Using again 10 keV mixing between the bands, the B(E2, I ~ I - 2) ratio favours the in-band transition over the cross-band transition by a factor o f about two, only. The energy factor favours the cross-band transition, so that its experimental observation is consistent with these considerations. One would expect to see weakly the crossband 8 ~ 7 (2qp ~ octupole) transition, but its energy of 171 keV coincides with the in-band 10 ~ 9 transition, and it is difficult to establish experimentally. Other significant features to consider are the A I = 1 level spacings and decay modes in the 2qp band. The odd-spin states are favoured energetically and decay primarily out-of-band, while the even-spin states decay only in-band. A similar situation has been found in other 2qp bands, and has been described in a 2qp-plus-rotor Coriolis coupling representation [ 10]. Results for the A I = 1 level spacings in the 162Dy 2qp band are illustrated at the b o t t o m of fig. 1. More details will b e given elsewhere [ 1 ], but for the present we note that (i) the high moment of inertia is reproduced, even though the gsb value is used for the basis states, (ii) the energy favouring of the odd-spin states is reproduced, and (iii) the calculation follows better the values (open circles) corresponding to the I = 9 energy before mixing with the octupole band, supporting the previous evidence for the perturbation o f the experimental I = 9 level energies. The 2qp-plus-rotor calculation uses a basis in which the ~- [523] neutron remains strongly coupled to the deformation, while the s+ [642] neutron mixes, 21
Volume 104B, number 1
PHYSICS LETTERS
through the AK = 1 Coriolis matrix elements, with all the other i13/2 orbitals; i.e. the i13/2 neutron becomes rotation aligned. As with other similar bands [10] we call this mixed 2qp band a "semi-aligned" side band. Overall, a satisfactory interpretation of the properties of the 2qp band is seen to be possible. The crossing of an octupole band by a 2qp band has been inferred on previous occasions, well illustrated by the octupole bands in t h e n = 88 isotones [12] and 152Sm (N = 90) [13]: the states that are favoured energetically are observed through the crossing region, but the unfavoured states remain unknown. This leaves unanswered significant questions, in particular the nature of the crossing 2qp band. Generally, observed band crossings have been restricted to cases where the knowledge of the yrare states is very limited, leading to ambiguities in the interpretation. The negative-parity bands in 162Dy provide an example where all the yrare states are identified, enabling them to be clearly characterised. A discussion of the structure of octupole bands would be incomplete without noting the two high-spin characteristics suggested by Vogel [ 14], namely either the taking-on of 2qp character, or the alignment of the octupole phonon with the rotation. The former is illustrated by the negative-parity yrast states in 162Dy (figs. 1 and 2) and the latter is seen in the yrare extension of the octupole band. These features may be quantified in terms of the alignment of intrinsic (or vibrational) angular momentum with the rotation. The degree of alignment, is, is estimated [15] simply from the difference in the total angular momentum between the excited band and the gsb, at a given rotation frequency. In an octupole band i s should not exceed 3h, since the octupole phonon carries only 3 units of angular momentum; in contrast an i13/2 neutron may align up to 6.5h. Experimentally, in the 2qp band ic~ rises from 2.8 to 4.3h with increasing rotation frequency, consistent with the partial alignment of an i13/2 neutron. (We note that there is more alignment than is possible for an octupole phonon. Also, it should not be surprising that the i13/2 neutron is not fully aligned: the corresponding 1qp i 13/2 band in 161Dy [16] for example, also has i s ~ 4h.) In the odd-spin members of the octupole band the corresponding rise in ic~ is from 1.0 to 3.0h, consistent with the aligned-octupole interpretation; however, the even-
22
13 August 1981
spin members show a remarkable increase in is, up to 3.7/~ at the highest observed spins. This corresponds to the significant up-bending in the moment-of-inertia curve (fig. 2) and is indicative of a crossing with another (unidentified) 2qp band. In summary, we have identified an octupole band and a 2qp band from their band heads to high spin. The bands have been characterised by their excitation and deexcitation modes with a variety of population mechanisms, namely Coulomb excitation, inelastic scattering, neutron capture, radioactive decay and fusion-evaporation reactions. The negative-parity yrast states are formed by the octupole band for I ~< 7 and by the 2qp band forI>~ 8. The mixing between the bands is about 10 keV in the crossing region, leading to level-energy perturbations and cross-band transitions. The 2qp band is able to become yrast at high spin due to the involvement of an i13/2 neutron, which gives an intrinsic contribution to the total nuclear angular momentum. We wish to thank P. Vogel for useful discussions. This work was supported in part by the US National Science Foundation under Grant No. Phys-78-22696, and the US Department of Energy.
References [1 ] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [ 16]
F.W.N. de Boer et al., to be published. A. Byrne, Nucl. Data Sheets 17 (1976) 97. A. B/icklin et al., Phys. Rev. 160 (1967) 1011. T. Grotdal, K. Nyb¢, T. Thorsteinsen and B. Elbek, Nucl. Phys. All0 (1968) 385. R.N. Oehlberg et al., Nucl. Phys. A219 (1974) 543. L. Funke et al., Nucl. Phys. 84 (1966) 424. B. Sethi and S.K. Mukherjee, Phys. Rev. 166 (1968) 1227. V. M6nig, Z. Phys. 225 (1969) 327. M. J¢rgensen, O.B. Nielsen and O. Skilbreid, Nucl. Phys. 24 (1961) 443. P.M. Walker et al., Phys. Lett. 86B (1979) 9; Nucl. Phys. A343 (1980)45;A365 (1981)61. F.S. Stephens, Rev. Mod. Phys. 47 (1975) 43. F.W.N. de Boer, L.K. Peker, P. Koldewijn and J. Konijn, Z. Phys. A284 (1978) 267. J. Konijn et al., Phys. Lett. 99B (1981) 449. P. Vogel, Phys. Lett. 60B (1976) 431. A. Bohr and B.R. Mottelson, J. Phys. Soc. Japan 44 (1978) Suppl. 157. S.A. Hjorth, A. Johnson and G. Ehrling, Nucl. Phys. A184 (1972) 113.