Nuclear Physics A520 (1990) 225c-240c 225c North-Holland

DOUBLE BLOCKING IN DOUBLY ODD DEFORMED NUCLEI

Andres J. KREINER

Laboratorio Tandar, Departamento de Fisica, CNEA Buenos Aires, Argentina

A wealth of two quasiparticle structures is found and classified in doubly odd deformed l - [521]) and the semi nuclei. Particularly interesting are the doubly decoupled (~'h~ ® t9

decoupled (~'hl ® t~ i½ a ) bands. In this last structure both critical, ~'h~ and b i ~ , orbits are blocked showing the largest delay in crossing frequency among all the known bands in this mass region and the alternative deblocking of either one of these orbits brings tile cros- sing frequency down. A systematic study of all the shifts in crossing frequency shows that tile roles of ~h~ and t9 i ~ are largely equivalent suggesting that both pairs simultaneously participate in the structure of tile S band in this region of the chart of nuclei.

1. INTRODUCTION

In the light rare-earth region the first backbending is interpreted 1 as due to the breaking

of a pair of i '~ neutrons occupying low-fl state (fl = ], ~) in a prolate deformed field. This

interpretation is supported by blocking experiments performed in neighboring odd N nuclei

in which the ground-to-S band crossing frequency is higher in the i½3 bands than in the even-

even neighbors, since tile maximally aligned state is already occupied. Moreover, the i '~ bands

show large alignments (i,, ~- 6h for the positive signature component ct = -~, and __ 5h for

a = - ~ ) which are consistent with the alignment gains in the S hands.

In the heavier rare-earth region, however, the i½3 shell is much more occupied and the

r and s Also, the alignments are i1~ orbitals closest to the Fermi surface correspond to f~ = ~ ~.

much smaller ( i , ~ 2 - 3h) than in the lighter region. Here the nature of tile S band and the

first crossing in far less clear and for many years this subject has remained controversial 2-11.

On the other hand, a prominent feature of rotational spectra in this mass region is the

presence of low-lying decoupled h~ proton bands in which the first crossing is also delayed.

1 - I component of the h~ intruder shell (the 2 Tile large positive quadrupole moment of the f~ = 2

(541] orbit) is believed to drive the nucleus to a larger deformation, thus hindering the action

of the Coriolis force on the pair of i½3 neutrons. However, this conjecture is not supported by

lifetime measurements s in the decoupled h~ band in lSllr. In addition, cranked shell model

1- [541] orbit (namely right at the Fermi surface calculations with a realistic position for the

as indicated by the odd-proton spectra) give equal crossing frequencies ("~ 0.3 MeV) for both

0375-9474/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

226c A.Z Kreiner / Doubly odd deformed nuclei

a pair of h~ protons and a pair of i½3 neutrons. In particular the quasiparticle character of

the ~- [541] excitation tends to quench its quadrupole moment (since the single-quasiparticle

contribution is u 2 - v 2 times the single-particle one, u and v being the usual BCS occupation

amplitudes which would be about equal in this case) thus, reducing a possible polarization

tendency. The proton alignments in these bands are sizeable (i v "~ 3 - 4h) and in particular

somewhat larger than in the i½ -3 neutron bands.

Hence, the question is to decide which is the role played by a pair of h~ protons. Which

pair (t9 i l ] 2 or ~'h~ 2 ) is breaking first or are they breaking at essentially the same frequency?.

Blocking experiments in odd mass nuclei are somewhat ambiguous since one does not

have control on the other type of nucleon. In this regard doubly odd nuclei may provide

a unique opportunity to study this problem because here one can block simultaneously the

two sensitive orbitals and then deblock them alternatively (if one has sufficiently complete

sI~ectroscopic information), to determine the shifts in crossing frequencies for the individual

bands. To actually be able to carry out this program we need a clear identification of the

different structures. Indeed a classification scheme is emerging 12-14 and we shall discuss some

examples as we move on.

In this work we discuss results for several doubly odd nuclei: 172Ta [ref.10], l*s'lS°Re [refs.

11, 15] and 182'184Ir [refs. 16, 17].

2. DOUBLY DECOUPLED BANDS (DDB's)

This structure actually turns out to be 14'1e'18'19 the equivalent of a decoupled band (in

an odd nucleus) but in a doubly odd system and it involves both a valence proton and a

neutron occupying predominantly ~ = ~ orbitals with large decoupling parameters. The

interest of decoupled rotational bands, derives, in particular, from the fact that the features

of the collective and intrinsic motion can be clearly identified and separated (like, at the ot'her

extreme in rigid strongly-coupled bands.) The constancy of the intrinsic structure in the

decoupled case manifests itself in the constancy (in certain regions of angular momentum I or

angular velocity hw) of quantities like the alignment, i, and also allows one to reliably extract

the inertia parameters characterizing the motion of the core in presence of quasiparticles.

1 - [521] structure. The proton is in a decoupled state The best known case is the ~'h~ ® t9

(the single j value of the decoupling parameter is a v = 5) while the neutron is in a rather pure

~/ = ~ orbit (an ~ 1). For the nuclei considered both ~-h~ and t9 ~- [521] lie right at their

respective Fermi levels 2°.

A.J. Kreiner / Doubty odd deformed nuclei 227c

2.1. Addit ivi ty Properties

A striking additivity of the deviations of the inertia parameters with respect to those of an

appropriate ee core is documented in Table 1 to be a systematic feature of DDB's (compare

columns 4 and 5).

Table 1.Inertia parameters and alignments extracted from the first three transitions in gsb's

(even-even nuclei), t9 ~- [521] (odd S), ~ h~ (odd Z) and DDB's bands (odd-odd nuclei), a

denotes the signature.

(it2MeV-') (h 'MeY -1) (It) (It) 17°Hf 0 + 0 29.26 172Hf 0 + 0 31.32 l n H f ~- t 39.14 0.41

2 2

17SHf 1- ! 38.90 0.42 2 2

lnTa s - z 38.94 2.14 2 2

~TSTa 5- 1_ 39.21 2.35 2 2

172Ta 3 + 1 48.63 48.82 2.27 17aTa 3 + 1 46.42 46.79 2.72

2.55 2.77

174W 0 + 0 26.05 17sw 0 + 0 27.20 17s W ! - l 34.89 0.44

2 2

177 W o) 1-- t 33.49 0.445 2 2

179 W 1-- ! 32.09 0.45 2 2

177Re 9- 1_ 30.64 3.11 2 2

17SRe 5 + 1 39.45 3.07 17SRe 5 + 1 36.95 36.93 3.55 3.56

18°0s 0 + 0 21.98 lS20s 0 + 0 23.28 lSlOs 1_- 1 28.35

2 2

1830s !- t 29.49 2 2

181ir 9_- t 22.40 2 2

lSZlr 9- ! 24.29 2 2

lS2lr 5 + 1 26.72 lS4Ir 5 + 1 30.73

°) Values for 1TTW are

0.53

0.49

3.81

3.88 28.77 4.48 4.34 30.50 4.41 4.37

interpolated from l~gW and-179W. "

In other words, ~,~, determined experimentally is equal, with a high degree of precision,

:So, " + S ~ " + 6 ~ v (where 6~ ; ; v -- ~eo;v --or, with i = n or p). ~ , tends to

follow an analogous rule 19 but with less precision. A similar additivity property holds for the

alignments, namely z,~ v't=p = z n't=p + tp"~P (columns 6 and 7 and Fig. 1).

228c " A.Z Kreiner / Doubt, odd deformed nuclei

lO

S

8

4

2

0 0

ALIGNMENTS

. . . . I . . . . I . . . . I '~--~ ' I . . . . _ /

,, l / 2 - [ s l i I ~, ,, 1 /2 - Io211 J " l o

x / ~ R e a - I o t ~ R e a = + I / 2 \ = ~ w ° = + I / 2 \ 8

+ I~ l l l a = +I/2 /~ ~ 6

4 e..........~ o o - -

, I . . . . I . . . . o 0.1 0 . 2 0,3 0.4

(MeV)

ALIGNMENTS

. . . . I . . . . I . . . . - n 1/2 - [5411 i~ ix t / 2 - 1 5 a i ]

t - ' ' ' ' I . . . .

x l~Ir ° . 1

o i t l l r a = + I / Z

- 0 ioios 0 = + I / 2

¢

c i = ~ l " I . . . . I , , , , , , , ,

o . 1 0 . 2 o . 3 0 . 4

(MeV) 0 .5

Figure 1: Alignments for 17aRe (ref. 11, left frame) and ls~Ir (ref. 16, right frame) DD- and associated bands.

Let us illustrate the procedure for the case of 17SRe. The core is always the even-even

nucleus with a proton and a neutron less, in this case 17sw with parameters 9o = 27.20 and

91 = 134.47. Since the ~- [521] band is unknown in ITTW we interpolate its parameters

from 17sW and 179W obtaining 90 = 33.49, 91 = 128.87 and i~ =p =0.445. For 17TRe we have

9o =30.64, 91 = 61.98 and i~ =p =3.11. The deviations with respect to 176W of the parameters

of 177W and '77Re are:

c~.ezP ~ e ~ p c~.ezP 6 9 ~ v = 6.29> 6~1, ~ = -5.60 and 6~Sov = 3.44, 6~lv = - 72.49 respectively. Hence we

obtain -o,,v¢'¢c°lc = 27.20 + 6.29 + 3.44 = 36.93 (vs. 9onv~=V = 36.95), ~lc~l,,V = 134.47 - 5.60 - 72.49

= 56.38 (VS. ~V~,V = 54.28) and i~, =P + i~ =v = 0.445 + 3.11 = 3.56 = z-v'c"t~ (vs. i~, p = 3.55).

The agreement is certainly impressive in this case. This agreement suggests that neutron and

proton "fluids" behave largely in an independent way.

It is worth noting that 9 ~ v for lrSRe is 36% larger than 9o~ (for 17sW). This can

mainly be traced to the rather large blocking of pairing correlations by the odd proton and

neutron quasiparticles. The large decrease of 91,,p (meaning a significant gain in rigidity) is

also consistent with this interpretation.

Fig. 2 shows also a similar alignment plot for the case of ls2Ir. These parameters seem to

provide reliable "local" references and give information about the changes experienced by the

associated cores in presence of quasiparticles.

Let us briefly discuss another potential implication of the additivity properties which bears

A.J. Kreiner / Doubty odd deformed nuclei 229c

on the question of core shape polarization.

It is the current opinion that the prolate b~ quasiproton drives tile nuclear shape t,~ larger

deformations as compared to those of the ee core. Now, if the odd proton system would indeed

have a significantly larger deformation, should one expect such precise additivity properties?

The moment of inertia is a complex quantity which depends on pairing and deformation (and

possibly quite sensitively on both variables). The odd neutron system has approximately

thesame deformation as the ee one, while the odd proton and thus also the doubly odd

system would be more deformed if there is shape polarization due to the h~ proton. The

quantities related to the neutron in the odd N system do not contain the increased deformation

information while they should be affected in the doubly odd one if the deformed field is

something felt equally by all nucleons. On the other hand, if only blocking is active (i.e.

no deformation increase), the effects should be additive because proton and neutron pairing

correlations are largely decoupled in heavy nuclei. A similar remark holds for tile alignments.

0.0

-0 .5

v

c-

O

- 1 . 5

- 2 . 0

ROUTHIANS

-0 .5

- i . 0

- L S ×

<> t~'Re a = + I / 2 ~'x

- 0 " ~ W a - + I / 2 - 2 0

+ t"~'W a : + I / 2

ROUTHIANS

x In2 l r t t = 1

o t S l l r a = ~ - 1 / 2

D St tOs a - + i / 2

I . . . . I . . . . I , , , , I . . . . . . . . I . . . . J . . . . I . . . . I . -2s 0 . 1 0 . 2 0 . 3 0 4 0 . 1 0 . 2 0 , 3 0 . 4 0 . 5

co (MeV) 6~ (MeV)

Figure 2: Routhians for 17aRe (left frame) and lS~Ir (right frame) for DD- and associated bands.

2.2. Crossing Frequencies

Some of the DDB's have been measured to high enough angular momenta to reach states

well beyond the first backbend allowing tile extraction of crossing frequencies. Figure 2 shows

the relative Routhians for ls2Ir and arSRe along with the same information for related bands.

These relative Routhians, e', have been constructed referring each nucleus to its own "local"

reference extracted from the first few transitions along each band (see table 1). It is well

230c A.Z Kreiner / Doubty odd deformed nuclei

known that the ground-to-S band crossing frequency can be obtained from the intersection

of the two slopes in the e' vs. hw plots befnre and after the first backbend. These crnssing

frequencies, ?gw¢ are given in Table 2.

Table 2. Fist-crossing frequencies for yrast bands in even-even cores, 9 ~- [521], ~'h~ and

DDB's.

Nucleus I "~ hw¢ ~ 6hw~ ~v 6hw,,p ~ _____ ( M e V ) ___(_M_e_V_)(_MeV) -

17°Hf 0 + 0.265(5) ~7~gf ½- 0.220(5) -0.045 171Ta ~- 0.310(10) +0.045 172Ta 3 + 0.265(10) 0.000 0.000 178W 0 + 0.275(5) ~TsW 1- 0.255(5) -0.020

2

177Re 9- 0.325(5) +0.050 17aRe 5 + 0.305(10) +0.030 0.030 la°os 0 + 0.270(10) '810s ½- 0.215(5) -0.055 1sli t -~- 0.300(5) +0.030 2 ls2Ir 5 + 0.250(10) -0.020 -0.025

") Uncertainties in hw¢ are

crossing.

estimated at 5-10 keV depending on the sharpness of the

The crossing frequency of the DDB's is intermediate I°'22 between the first backbend fre-

quency of neighboring odd neutron and odd proton nuclei. The shift in crossing frequency of

the DDB (with respect to that of the associated even-even core) is almost identical to the sum

of the shifts in crossing frequencies for the neighboring odd N and odd N nuclei.

As an example one has: &we ( 'Tsw) + 6hwo WbW) + 6hwc ( " R e ) = 0.305 MeV) (vs.

hw~,,,p ('TSRe) = 0.305(10) MeV). One may say that the presence of the h~ proton delays

the crossing in the ~ ½- [521] bands or equivalently that the ~- [521] neutron facilitates the

crossing in ~'h~ bands.

This behaviour would be consistent with the increased-deformation picture, since the pres-

ence of the ~- [521] neutron would bring the crossing frequency of the neutron S band down

while the increased deformation would bring it up.

However, the hwc value for the DDB is also consistent with the alternative interpretation.

The presence of the ½- [541] proton would block the ~'h] 2 component (i.e. the lowest c~ = !2

h~ trajectory) while the occupation of the ½-[521] orbital would facilitate the decoupling of a

pair of i ~ neutrons as indicated above.

A.J. Kreiner / Doubly odd deformed nuclei 231c

The current view on the structure of the S-band in this region of the periodic table is that

of a pair nf aligned i)~ neutrnns. Its crnssing frequency would correspond to the value given

in table 2 for the ee nuclei. The rather low tttvc value for odd neutron nuclei is interpreted

as a particular blocking effecC 1. The neutron pairing correlations are decreased in the odd

N system with respect to the even-even one since the pair of time reversed orbits associated

with ~- [521] is blocked. This means that the neutron pairing gap, A,, is smaller and hence

the.energy to break a pair of i ~ neutrons is smaller leading to a smaller htoc . The effect

1+ [660] is thought to be particularly large because the ~- [521] and the highly-alignable

i ~ parentage orbital responsible for the first backbend are both prolate, this being a mani-

festation of quadrupole pairing. 21 On the other hand, in this region of mass the amplitude of

l+ [660] orbit is not expected to be very large since it lies far below the Fermi surface the

(as reflected in the small alignment of the i ~ bands). One the other hand, the rather high

value of hw~ for the h 9 proton is interpreted as a deformation effect. This highly prolate

quasiproton configuration is believed to drive the nucleus to larger deformation, increasing

the spacing among the highly-alignable low-Q quasineutron orbitals and also their distance to

the Fermi surface, thus hindering the action of the Coriolis force on the pair of i ~ neutrons

and resulting in larger crossing frequencies. This conjecture is, however, not supported by

lifetime measurements s in the dec6upled ~rh a band in lSllr. In addition, cranked shell model

calculations performed here, with a realistic position for the 7r~- [541] orbit (namely right at

the Fermi surface as indicated by the odd proton spectra) give equal crossing frequencies for

both a pair of h a protons and a pair of i ~ neutrons, of about 0.3 MeV. (A standard Nilsson

potential with/3 = 0.25, t~ = 0.063,/~, = 0.411,~p = 0.063,#p = 0.605 and A~ = Ap = 0.8

MeV have been used.) Another argment is that the quasiparticle character of the ½- [541]

excitation tends to quench its quadrupole moment (since the single-quasiparticle contribution

is u ~ - v ~ times the singleparticle one, u and v being the usual BCS occupation amplitudes

which are about equal in this case) thus reducing a possible polarization tendency.

An alternative scenario t°'22 for the behavior of h 9 bands could be, the at least partial

participation of a pair of h a protons (together with a pair of i ~ neutrons) in the structure

of the S-band. Here the first backbend would be delayed because the highly alignable ½-

[541] orbital would be blocked in the odd proton system. This interpretation would require

some kind of coupling or linkage between the two S-band configurations (namely fiha 2 and

~, i ~ 2 ), otherwise if they are independent, one should observe two distinct backbendings. The

two pairs may be coupled attractively by a proton-neutron residual interaction and drag each

232c " A.J. Kreiner / Doubly odd deformed nuclei

other. Although the crossing frequency of the DDB behaves in a rather additive (or linear)

way, the crossing itself is far less sharp than in the associated odd N and odd Z bands (see

Figs. 1-4). This may reflect one of two circumstances: a) an increased interaction strength

between ground and S band in the odd-odd nucleus, or b) the inappropriateness of the reference

parameters in the crossing region and beyond.

3. SEMIDECOUPLED (STAGGERED) BANDS

3.1. Staggering Behaviour

A structure in which one of the particles is decoupled (e.g. @h~ ) and the other in an orbital

with ~ significantly larger than 1 (but Coriolis distorted, e.g. t) i ~ ) is known as (staggered)

semidecoupledla,ls,2a, 24.

In this structure (~'h~ ® t9 i ~ ) both "critical" orbits are blocked.

The two distinctive features of this structure are that it starts with a sequence of low

energy M1 transitions and that it displays a pronounced odd-even staggering.

23n'- -

2%

21/2"- ~51 lej2 o- -

211 17/2"- ~ . . . 1,79

13&

9/2"-) -

T"/Tw1 ~

(V,)" - - 2312"- -

23/2" 305

~5 2V2"- ' - (1))'- - 18'/

106 1121 - 1~2" -

275 222 257 17/2"-

1~2" 1oo m)'- ~u ~66 • ( I01"- ~ ' - 156 I73 i)/2"-- L 1~2 1/,9 ( 9 ) ' - - 8 0 ,123

& (8 ) ' - 11/2"- ~-96

1 8 1 ~ 1 0 5 182ir10 S 1~30SIO ? Z3~'- -

[~)-_ - 23/2"~ ( l&) '~ 2'71

29¢ 30& 307 [q,'2"- "-

(12}'-~ 2112"-T- "-I~., 226 _ (1~ I77 1W2"- 170 152

(12)'-~ - "-T-- 216 229 19/2 213 (12)° 230 17/2"-

(M)'-~ 1~ 1'//2"~12162 (11)° IL,6 185 (IQ'J 15/2" 15.~'- 110)" 156 164

162 13/ 13/2"- 19)" 10& (9)'2 TOT IYZ" 95 138

11/2" & (6)" 1112 °- (e)'4 leo wz" 9 "~u , . , 2 " -

r1~e lo 3 l n W m 1"oRe m lmWlo 7

(1/,)'-I"-

(I))'-,T-

(I:n'-.T-

(II)'-T-

n(J'-T-

(9)"-/-

161i~ ~ (7)" 9

(161"- - 2?5

( I )~ ' - - 2:)1

riD"- - 217

(11)'~ - 179

(10) ' - - 160

( 9 ) ' - 131

(e)'- ~o~ ( 7 ) ' - (6) _-oo

182Nelo 7

2VZ" (1~0"- -

19/2" IIi) 220 (12)'- L 268 247

17/2" 186 (11)'- L 164

ISle" 176 (10~'- " 166

I)/2" (91"- '9 [Z)

11/2" (6)'- 84 m" ~9 (5)"

1850S109 186Ir 109

Figure 3: Systematics of t9 i½3 and Sh~ ® i i~s bands (Refs. are: 16, 17 and 18 for ~s2'~s4'lSSlr; 11, 12 and 15, and 25 for 17s'ls°'lS2Re).

A.J. Kreiner / Doubly odd deformed nuclei 233c

Figure 3 shows a comparison between the initial portions of ~h~ ® t9 il~ and t9 i ~ bands in

doubly odd and odd neutron nuclei respectively for all tile prolate cases known ill Ir and Re to

date. The impressive similarity in the neutron number dependence of the staggering behavior

(or signature splitting) between odd and neighboring doubly odd cases leaves no" doubt, in my

opinion, about the common origin of the staggering, namely the signature dependence of the

Coriolis interaction (in this case acting on the neutron).

1500 , ' ' I ' ' I / ~ ' 17 I /

ooo - is _

o ~ 13 h-'

500 - ~ ~ . . _ _ _ _ ~ 12 •

1°

9

95 i 100 i Nlhn) 105 l 110 5/2 ° 7/2* 9/2 *

Figure 4: Calculated energies of some yrast states (relative to I=4) for the ~'h~ ® ~ i ~ bands as a function of the neutron Fermi level.

A two quasiparticle plus rotor model ~a'24 (TQPRM) is able to reproduce both above men-

tioned features only for the ~'h~ ® i i ~ configuration. Since the proton is completely decou-

pied, only its favored (c~ =~ ) trajectory participates (tile unfavored one is shifted to much

higher energies) in the description of the yrast states of the doubly odd system. The staggering

just reflects tile splitting of the two i ~ neutron signatures present in the neighboring odd-N

nuclei. As seen in fig. 3 the staggering becomes more pronounced as the neutron number

decreases and the neutron Fermi level penetrates deeper into the i!~ shell approaching the

lower f~ components.

Fig. 4 shows a TQPRM calculation for this structure as a function of neutron number N

(tile positions of the f~ = a s-, ~ and ~ components are marked on the N scale).

One clearly sees how the staggering becomes more pronounced up to a point where favored

2 3 4 c ' A . J . Kreiner / Doubly odd deformed nuclei

(odd spins) and unfavored (even spins) states become degenerate. Going even further will

inwrt them getting into the double decoupling regime of this structure.

3.2. Grossing frequencies

As already mentioned, in this structure both critical orbitals are blocked and it is the most

stable one as a function of frequency showing the least variation both in alignment and in

dynamical moment of inertia. In these bands the first crossing is clearly delayed with respect

to both odd N i ~ and odd Z h~ structures in neighboring nuclei so that it is the structure

with the largest delay. Also here the backbend is very smooth possibly indicating a large

interaction strength.

tO

8

6

4

2

0

ALIGNMENTS

. . . . . l . . . . I . . . . ~ . . . . l ' f

n 1 / 2 - I 5 4 1 ] i t V l i 3 / l

x ta= l r a - I

¢ l U l r a = 0

o i l i l r a = + I 1 2

+ lelOs a = + 1 / 2 ~ x

= :e lOs a = - 1 / 2 , / z . ~ - '~

,

. . . . I . . . . I . . . . I . . . . I , O,I 0 . 2 0 3 0 . 4

co (MeV)

O 0

- 0 5

e-

= 0

- 1 . 5

-2 .0 0

ROUTHIANS

. . . . r . . . . I . . . . I . . . . I '

o l ~ l r a = 0

C] IStlr a - + I / 2

+ l lnos a = + I / 2

= I=~Os a = - I / 2

, , l , l . . . . l . . . . . l , 0 . I 0 . 2 0 3 0 4

(MeV)

Figure 5: Alignments (left frame) and Routhians (right frame) for lS2lr semidecoupled- and associated bands.

Tile shifts in crossing frequency seem also to fulfill the following relation: 6hw¢,, v "~ 6ttw,, v

+ 6hw . . . . (The _~ sign stems also from the fact that in some of the cases it is not clear if we

have completely passed the crossing.) This is documented in figs. 5 and (5 and in Table 3.

The delay and the smoothness of the crossing can also be clearly seen in fig. 7 (left frame)

where the dynamic moment of inertia ~(~) is plotted as a function of frequency for the case

of 17SRe. Fig.7 also shows (right frame) ~(~) for the different bands in the isotone :7~Os for

comparison.

A.J. Kreiner / Doubly odd deformed nuclei 235c

.4

178Re Semldecoupled(phg/2 x n113/2) lO

1Q 17SW

.413/2 -IQ 17SW 8' • t~gn lt21n~ 7

6 5

. 4 3'

2'

1'

o o.o o:1 0:2 0:3 0:4

hw [MeV]

0.0 178Re Semldecoupled Routhlans

-0.5"

-1.0"

~-1.5"

3 -2.0"

n113/2 -1Q 175W • phg/2 1i2 177Re

-2.5 o o o:1 0:2 0:3

hw [MeV]

~, pn 0 ] ~ X • n113/2 1/2 175W •

0. 014

Figure 6: Alignments (left frame) and Routhians (right frame) for ~TSRe semidecoupled- and associated bands.

Table 3.

semidecoupled bands.

First-crossing frequencies for yrast bands in even-even cores, b i~ , ~'h~ and

Nucleus (ol, r) hwc 6hwc ,-v 6hcv,~ c, tc (MeV) (MeV) (MeV)

17°Hf (0, +) 0.265(5) l n H f (~,+) 0.320(10) + 0.055 17'Ta ( ] , - ) 0.310(10) + 0.045 172Ta (1 , - ) > 0.350(10) > 0.085") 0.100 " w (0, +) 0.275(5) l'sW (~, +) 0.310(10) 0.035 Z77 Re ( ~ - ) 0.325(5) 0.050 ~TSRe (1, - ) 0.350(10) 0.075 0.085 zs°Os (0,- I - ) 0.270(10)

's'Os (}, +) 0.290(5) 0.020 's'1, (~ , - ) 0.300(5) + 0.030 lS2Ir (1 , - ) > 0.315(10) > 0.045") 0.050

") Backbending not yet fully reached.

236c " A.J. Kreiner / Doubty odd deformed nuclei

2 0 0

DIN. MOM. INER.

. . . . I . . . . I . . . . I . . . . I ' ' n 1/2-[541] ~ v i,a,,= x t'mRe a - I

o I~Re a = 0

- o Z~Re a = + 1 / 2 ¢ t w ~ a = + 1 / 2

t~lf f ot = - I / 2

150

!. 100

5 0

DIN. MOM. INER.

. . . . I . . . . I . . . . I

× L ~ o s 1/2"[521] a = +1/2 o t'~Os 7 / 2 " [ 5 1 4 ] a - + 1 / 2

t:] t '~O s 7 / 2 - [ 5 1 4 ] a = - 1 / 2

* "~Os il3,~ a = + 1 / 2

n t nOt l i l=r a a = - 1 / 2

' ' ' I ' ' '

. , I . . . . . . I . . . . I . . . . I , , , I . . . . 0 , , , , I . . . . I . . . . I

0 0.1 0.2 0 3 0 4 0.1 0 2 0.3 0.4

co (MeV) co (MeV)

Figure 7: Dynamic moment of inertia for lrSRe semidecoupled and associated bands (left frame) and for structures in lrgos (right frame).

4. O T H E R BANDS

These bands comprise cases in which one or both critical orbitals are deblocked.

4.1 Compressed structures

Structures of the type ~ m® g, i1~ or ~-h~ ®g,y, where x and y differ respectively from

h~ and i ~ are called compressed 12'1a since their main distortion is a much smaller "effective"

K value (one extracts from the first two transition energies along these bands) as compared

to the band-head spin.

These structures show no signature splitting 11. Let us illustrate this feature in the case

of ~r ~-2 [514] ® ~ i ~ . For ~" 9-2 [514] both signature components are degenerate while for

i1~ they are split. Hence the yrast band in the doubly odd system is signature unsplit

because it is built by coupling the two degenerate proton components with the favored (c~ = 12)

r-1514 ] and 7? s2+[402]® ~ i ~ For all these neutron trajectory. Other examples are ~-h~ ® i 2

cases the additivity of crossing frequency shifts is poorer but still the effect of g, i12 a or ~h~ is

always retardatory.

4.2. Normal Structures

One interesting example is the/rh~ -[514}® ~ ~-[5141 structure in iS°Re [refs. 12 and 151.

This band has a rather well defined K and follows the I(I+1) law near the band head state 1~'13.

As evident from fig.8 it shows in fact an unhindered crossing, being consistent with the fact

that non of the critical orbits are occupied.

A.J. Kreiner / Doubly odd deformed nuclei 237c

v

. . . . I . . . . I ' '

,~ 9/2-[514l x v 7/2"[S14] - x I S ° R e ~ . |

v |mR e a = 0

0 l ~Re a = +1 /2

÷ tWRe a = - I / 2

u IvIW (x = + 1 / 2

- + I ~ W cz = - I / 2

ALIGNMENTS

.... I .... I ....

/

o . . . . I . . . . I . . . . I . . . . I , , , , 0 0.1 0.2 0 3 0.4 o.s

co (MeV)

Figure 8: Alignments for IS°Re (refs. 12 and 25) normal- and associated bands.

5. ELECTROMAGNETIC PROPERTIES

5.1. DCO ratios

DCO ratios 20 are extremely useful tools to characterize these structures since they sensi-

tively depend on the mixing ratio 6 and in particular on its sign.

For instance the semidecoupled band is characterized by a large negative value of 6 which

reflects the presence of the i ~ neutron and the decoupled h~ proton. Another illustrative

5+ [402] ® b i ~ . Both are example is given by the two structures ~'h~ ® b }- [514] and I)

very similar, they are equal-parity compressed structures but they differ in the sign of ~ (For

calculating M1 matrix elements we have used both the two quasiparticle plus rotor model and

the semiclassical approach 27 obtaining very similar results).

5.2. B(M1) / B(E2) ratios

These ratios are also sensitive indicators of configuration both below and above the crossing

(see also ref. 5). We obtain as a rule very good agreement below the crossing and particularly

at the beginning of the bands but in general there is not enough data above the crossing where

it is crucial s to decide the nature of the crossing. Fig.9 illustrates this point for the ~'h~ ®~}-

[514] band in ~TSRe (ref. 28). There are no free parameters in the calculation since g-factors

are taken from Nilsson wave functions and alignments from experiment. The rise cannot be

reproduced by any calculation, but the one involving a pair of h~ protons comes closest.

238c • A.J. Kreiner / Doubly odd deformed nuclei

o l

~t

A

0

v t ~ t

0.5 ¸

0 . 4 ¸

0.3 ¸

A (NI 0 . 2

m 0.I

, - I

v 0.0

1 7 8 R e p h 9 / 2 x n 7 / 2 - [ 5 1 4 ]

• e x 9

• th

• th p**2

th n**2

th (pn)**2

S 1 0 1 5 2 '0 2 S

z ( i n i ) [h]

Figure 9: B(M1)/B(E2) ratios as a function of spin of the decaying state (I(ini)). Dots correspond to theoretical values for the ~'h 9 ® t~ ~- [514] configuration below the backbending. The other three theoretical curves correspond to three different options for the structure of

- 9 2 the S band:p * *2 = 7rh~ ,n * *2 = b i ~ 2 and (pn) * *2 = #h~ ~ ®tgi~ 2.

6. SUMMARY AND CONCLUSION

Given hw .... in the (Z-l) even-even neighbor one has:

a) For oddZ:hw~ (~ ' h l ) > h w ....

h,~o (other bands) < ~,~o (,~h~)

In general: hw¢ (other bands) < hw¢,,,

b) For odd N: h~,o (,~ i~ ) > t~,o . . . .

hwc (other bands) < hwc (fi i ~ )

In general: hwc (other bands) < hw ....

c) For odd-odd: hwc (~'h 9 @ b i ~ ) has the highest crossing frequency.

The deblocking of either one of these orbitals brings the frequency down and:

hwo (,~h~ ® ~ y ) >hwc (~y)

~ o ( , ? x ® ~ i ½ s ) > h ~ o (~x)

At a quantitative level, shifts in crossing frequencies for semidecoupled and DDB's behave

in a rather additive (linear) way.

.4.J. Kreiner / Doubly odd deformed nuclei 239c

The roles of ~rh~ and ~ i½ a are largely equivalent. It is likely that the first backbend

in this region involves at the same time both pairs ~'h~ 2 and i i½32 . In this regard it is

interesting to note that the total alignment one expects for example in the ls°Os region from

~h~ 2 ® ~ i½32 configuration is in good agreement with the experimental value (_~ 10h). In

fact if we take the alignments from the two a = ~ components of both fi'h~ (ip = 3.8h) and

i½3 (in = 2.8h) in lSllr and lslOs respectively (see table 1) we obtain ip( ¢rh~ 2 ) + in

(~5 i-1~ 2 ) = (6.6 + 4.6) h = ll.2h. Since there are in general no two distinct crossings both

pairs seem to interact and drag each other. Double blocking experiments may be a valuable

complementary tool to study the nature of band crossing.

However (and fortunately) more higher spin and precise data (e.g. on B(M1)/B(E2) ratios)

is needed to resolve this issue.

ACKNOWLEDGEMENTS

I would like to thank all the colleagues from different laboratories (TANDAR, BNL, Orsay,

Grenoble, Stony Brook, Sao Paulo, Strasbourg and ORNL) who over several years now have

believed in this project. I am particularly indebted to D.Hojman and V.Vanin for their help.

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