Double blocking in doubly odd deformed nuclei

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

225c

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 nuclei. Particularly interesting are the doubly decoupled (~'h~ ® t9 l - [521]) and the semi decoupled (~'hl ® t~ i½a ) 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 crossing 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 eveneven 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 i1~ orbitals closest to the Fermi surface correspond to f~ = r~ and s~. Also, the alignments are 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 controversial2-11. 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. Tile large positive quadrupole moment of the f~ = 2I component of the h~ intruder shell (the 21 (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 calculations with a realistic position for the 1- [541] orbit (namely right at the Fermi surface 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. The best known case is the ~'h~ ® t9 1 - [521] structure. The proton is in a decoupled state (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. Additivity 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-') 17°Hf 172Hf lnHf 17SHf lnTa ~TSTa 172Ta 17aTa

0+ 0+ ~2 12 s2 52 3+ 3+

0 0 t2 !2 z 2 1_ 2 1 1

29.26 31.32 39.14 38.90 38.94 39.21 48.63 46.42

174W 17sw 17sW 177W o) 179W 177Re

0+ 0+ !2 1-2 1-2 92 5+ 5+

0 0 l 2 t2 !2 1_ 2 1 1

26.05 27.20 34.89 33.49 32.09 30.64 39.45 36.95

0+ 0+

0 0

17SRe 17SRe

18°0s lS20s lSlOs 1830s 181ir lSZlr lS2lr lS4Ir °) Values

(h'MeY -1) (It)

(It)

48.82 46.79

0.41 0.42 2.14 2.35 2.27 2.72

2.55 2.77

36.93

0.44 0.445 0.45 3.11 3.07 3.55

3.56

21.98 23.28 1_- 1 28.35 0.53 2 2 !t2 29.49 0.49 2 9_- t 22.40 3.81 2 2 9- ! 24.29 3.88 2 2 5 + 1 26.72 28.77 4.48 4.34 5 + 1 30.73 30.50 4.41 4.37 for 1TTW are 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 = zn't=p + tp"~P (columns 6 and 7 and Fig. 1).

"

228c

A.Z Kreiner / Doubt, odd deformed nuclei

ALIGNMENTS lO

....

I ....

,, l / 2 - [ s l i I S

I

/~Re a

-

o

t~Re a

= +I/2

+ I~lll

....

_

"lo

= +I/2

/~

\

8

~

6

I ....

- n 1/2-[5411

\

= +I/2 a

ALIGNMENTS

I '~--~' I . . . . / J

~, ,, 1 / 2 - I o 2 1 1

x

= ~w°

I ....

x

l~Ir° .

o

itllr a

0 ioios

-

I ....

t-'

'

'

'

I

. . . .

i~ ix t / 2 - 1 5 a i ] 1

= +I/Z

0 = +I/2

8

4

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

o

-

¢

-

2

, I ....

0 0

0.1

0,3

0.2

I ....

o

,

,

c,

0.4

,

i= o.1

(MeV)

~ l "

I ....

0.2

o.3

I, ,,, 0.4

0.5

(MeV)

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 6 9 ~ v = 6.29> 6~1, ~ = -5.60 and 6~Sov

c~.ezP = 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 t h e s a m e 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. ROUTHIANS

ROUTHIANS 0.0

-0.5 -0.5

-i.0 v c-

-LS ×

O

x I n 2 l r tt = 1

<> t~'Re a = + I / 2 -1.5

-2.0

- 0 "~W a

-

+I/2

+ t"~'W a :

+I/2

....

I .... 0.1

o tSllr a

~' x

= ~-1/2

D SttOs a - + i / 2 -20

J .... 0.2

I .... 0.3

co (MeV)

I.-2s 04

I 0.1

. . . .

I 0.2

. . . .

I , , , , 0,3

I 0.4

. . . . 0.5

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 "~ _____ 17°Hf 0+ ~7~gf ½171Ta ~172Ta 3+ 178W 0+ ~TsW 12 177Re 917aRe 5+ la°os 0+

hw¢ ~ 6hw~ ~v 6hw,,p ~ ( M e V ) ___(_M_e_V_)(_MeV)0.265(5) 0.220(5) -0.045 0.310(10) +0.045 0.265(10) 0.000 0.000 0.275(5) 0.255(5) -0.020 0.325(5) +0.050 0.305(10) +0.030 0.030 0.270(10)

'810s

½- 0.215(5)

-0.055

1slit ls2Ir

-~2 5+

+0.030 -0.020

0.300(5) 0.250(10)

-0.025

") Uncertainties in hw¢ are estimated at 5-10 keV depending on the sharpness of the crossing. The crossing frequency of the DDB's is intermediate I°'22 between the first backbend frequency 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 presence 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 is thought to be particularly large because the ~- [521] and the highly-alignable 1+ [660] i ~ parentage orbital responsible for the first backbend are both prolate, this being a manifestation of quadrupole pairing. 21 On the other hand, in this region of mass the amplitude of the l+ [660] orbit is not expected to be very large since it lies far below the Fermi surface (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 measurementss in the dec6upled ~rha 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.

(V,)" - -

305

2VZ"

(1~0"- -

(I:n'-.T-

19/2" IIi) 268

(12)'- L220 247

17/2"-

(II)'-T-

17/2" 186

~ ' - ~66 156 i)/2"-- L,123

n(J'-T-

ISle" 176

(9)'- -80

(9)"-/-

I)/2"

(11)'- L 164 (10~'- " 166 (91"-

(8)'-

11/2"- ~-96

161i~9 ~ (7)"

11/2"

~5

(1))'- 106 1121275 257

1~2" • 1oo 1~2

(1/,)'-I"-

2312"- -

23/2"

1/,9 &

(m)'I01"-

~u I73

2V2"-

'-

18'/

1~2"-

222

(I))'-,T-

'9

[Z)

(6)'- 84

m" ~9 (5)"

181~105

23n'- 2% 21/2"- ~51 lej2 o- 211 17/2"~ . . . 1,79 13& 9/2"-) T"/Tw1~

[~)-_ 23/2"~ 29¢ 30& (12}'-~ 2112"-T_ 170 152 (12)'-~ "-T-229 19/2 213

182ir10 S

1~30SIO ? Z3~'- (161"- (l&)'~ 2'71 2?5 307 [q,'2"- "(I)~'- (1~

"-I~.,

I77

1W2"-

(12)° 230 17/2"-

(M)'-~ 1~ 1'//2"~12162 (11)° IL,6 185 (IQ'J 15/2" 110)" 156 15.~'- 164 162 13/ 13/2"19)" 10& (9)'2 TOT IYZ" 95 138 (e)'4 leo 11/2" wz" & (6)" 9 1112°- "~u ,.

r1~elo 3

lnW m

1"oRem

,2"-

lmWlo 7

186Ir 109

2:)1

226 216

1850S109

riD"- 217 (11)'~ 179 (10)'- 160 (9)'-

131

(e)'- ~o~ (7)'(6) _-oo 182Nelo 7

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

/

~

'

17I

/

ooo

-

is

o

13

~

h-'

500

_

~..____ ~

-

~

12

•

1° 9

95

i 5/2 °

100

i

Nlhn)

7/2*

105

l

110

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 ( T Q P R M ) is able to reproduce both above mentioned features only for the ~'h~ ® i i ~ configuration. Since the proton is completely decoupied, 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 T Q P R M calculation for this structure as a function of neutron number N (tile positions of the f~ = as-, ~ and ~ components are marked on the N scale). One clearly sees how the staggering becomes more pronounced up to a point where favored

234c

'

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. ROUTHIANS

ALIGNMENTS l ....

. . . . . tO

8

n 1/2-I541 -

¢ lUlr

= 0

a

~ ....

l '

. . . .

r

. . . .

I

. . . .

I

I'

. . . .

f

] it V l i 3 / l

x ta=lr a o ililr a

I ....

O0

I -05

= +I12

+ lelOs a = + 1 / 2 = :elOs a

=

~x

,/

-1/2

6

z . ~ -'~

e= 0

4

o l~lr -1.5

,

2

0

. . . .

I O,I

. . . .

I

. . . .

0.2

co (MeV)

I 03

. . . .

I, 0.4

-2.0

a

= 0

C] IStlr a -

= +I/2

= I=~Os a

= -I/2

,, 0

+I/2

+ llnos a

l,l

.... 0. I

l . . . . . 0.2

03

l, 04

(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.

235c

A.J. Kreiner / Doubly odd deformed nuclei

178Re

Semldecoupled(phg/2

x

n113/2)

178Re Semldecoupled

lO

Routhlans

0.0 1Q 17SW

8'

•

.413/2-IQ 17SW

-0.5"

t~gn lt21n~

7

.4

6 5 .4

-1.0" ~-1.5"

3'

3

2'

-2.0"

~, •

pn 0 n113/2 1/2 175W

•

n113/2-1Q 175W phg/2 1i2 177Re

1'

o o.o

o:1

0:2 0:3 hw [MeV]

0:4

0.

-2.5

oo

o:1

0:2 0:3 hw [MeV]

]~X •

014

Figure 6: Alignments (left frame) and Routhians (right frame) for ~TSRe semidecoupled- and associated bands. Table 3. First-crossing frequencies for yrast bands in even-even cores, b i ~ , ~'h~ and semidecoupled bands. Nucleus

(ol,r)

17°Hf lnHf 17'Ta 172Ta

(0, +) (~,+) (],-) (1,-)

hwc (MeV) 0.265(5) 0.320(10) 0.310(10) > 0.350(10)

6hwc ,-v (MeV)

"w

(0, +)

0.275(5)

l'sW

(~, +)

Z77Re ~TSRe

(~ -)

(1, - )

0.310(10) 0.325(5) 0.350(10)

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.

+ + >

6hcv,~c,tc (MeV)

0.055 0.045 0.085") 0.100 0.035 0.050 0.075

0.085

236c

A.J. Kreiner / Doubty odd deformed nuclei

"

DIN. MOM. INER.

DIN. MOM. INER. .... I .... I .... n 1/2-[541] ~ v i,a,,=

200

x t'mRe a -

I ....

....

I ' '

×

I

o I~Re a = 0 - o Z~Re a = + 1 / 2 ¢ tw~ a = +1/2

150

!.

L~os

I ....

I ....

1/2"[521] a

I

'

'

'

I

,

,

,

I

'

'

I

. . . .

'

+1/2

=

o t'~Os 7 / 2 " [ 5 1 4 ]

a-

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

a = -1/2

+1/2

* "~Os il3,~ a = + 1 / 2 n t n O t l il=r a a = - 1 / 2

t~lff ot = - I / 2 100

50

,,,,I

0

0

.... 0.1

I .... 0.2

I

03

.

,

I

.

.

.

.

04

co (MeV)

.

.

I

0.1

. . . .

I

02

. . . .

0.3

0.4

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

For all these

cases the additivity of crossing frequency shifts is poorer but still the effect of g, i12a 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

ALIGNMENTS

.... I .... I'' . . . . ,~ 9/2-[514l x v 7/2"[S14] - x

IS°Re

~

.

|

v

|mR e a

= 0

0

l~Re

= +1/2

a

I ....

I ....

/

÷ tWRe a = -I/2 u - +

IvIW (x = + 1 / 2 I~W

cz =

-I/2

v

o

. . . .

0

I . . . . 0.1

I . . . . 0.2

I 03

....

I, ,,, 0.4

o.s

co (MeV)

Figure 8: Alignments for IS°Re (refs. 12 and 25) normal- and associated bands. 5. E L E C T R O M A G N E T I C P R O P E R T I E S 5.1. DCO ratios DCO ratios 20 are extremely useful tools to characterize these structures since they sensitively 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 example is given by the two structures ~'h~ ® b }- [514] and I) 5+ [402] ® b i ~ .

Both are

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

•

ol

178Re

ph9/2

x

n7/2-[514]

0.5 ¸ ~t A

0

0.4 ¸

•

ex 9

•

th

•

th p**2 th

n**2

th (pn)**2

v t~t

0.3 ¸

A (NI

0.2

m 0.I ,-I v

0.0

S

10

z (ini)

15

2'0

2S

[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®~i½s)>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 The roles of ~rh~ and ~ i½a are largely equivalent.

239c

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.

REFERENCES 1) F.S.Stephens and R.S.Simon, Nucl. Phys. A183, (1972) 257. 2) A.Neskakis et al., Nucl. Phys. A261, (1976) 189, and references therein. 3) J.D.Garret and S.Frauendorf, Phys. Left. 108B, (1982) 77. 4) G.D.Dracoulis et al., Nucl. Phys. A401, (1983) 490, and references therein. 5) L.L.Riedinger et hi., Proceedings of the Twenty-Second Zapokane School on Physics, Poland, 1987 (unpublished); V.P.Janzen et al., Phys. Rev. Left. 61, (1988) 2073. 6) W.Walus et al., Phys. Scr. 34, (1986) 710, and references therein. 7) U.Garg et al., Phys. Left. 151B, (1985) 335. 8) R.Kaczarowski et hi., in Proceedings of the International Conference on Nuclear Physics, Florence, Italy, 1983, edited by P.Blasi and R.A.Ricci (Tipografia Compositore, Bologna, Italy, 1984), Vol. 1. p. 181. 9) M.N.Rao et al., Phys. Rev. Lett. 57, (1986) 766. 10) A.J.Kreiner et hi., Phys. Left. 215B, (1988) 629. 11) D.Santos et al., Phys. Rev. C39, (1989) 902; A.J.Kreiner et al., Phys. Rev. C40, (1989) 487.

240c

'

A.J. Kreiner / Doubly odd deformed nuclei

12) A.J.Kreiner et al., Phys. Rev. C36, (1987); 23¢19 C37, (l.qSR) 1335E, aml references therein; A.J.Kreiner in Proceedings of the International Conference on Contemporary Topics in Nuclear Structure Physics, Cocoyoc, Mexico, 1988, edited by R.F.Casten e¢ al. (World Scientific, Singapore, 1988) pp. 521-541. 13) A.J.Kreiner, in Proc. XII Workshop on Nuclear Physics, ed. by C.Cambiaggio e[ al. (World Scientific 1990) pp. 137-155. 14) A.J.Kreiner in Exotic Nuclear Spectroscopy, ed. by Win. McHarris, (Plenum Press, New York, 1990), Chap.26. 15) Ts. Venkova et al., Progress Report, Jfilich, 344, (1986)49 . 16) A.J.Kreiner, P.Thieberger and E.K.Warburton, Phys. Rev. C34, (1986) I~1150, A.J.Kreiner et al., submitted to Phys. Rev.C. 17) A.J.Kreiner, J.Davidson, M.Davidson, P.Thieberger, E.K.Warburton, J.Genevey, and S.Andr~. Nucl. Phys. A489 (1988) 525. 18) A.J.Kreiner, D.E.Di Gregorio, A.J.Fendrik, J.Davidson and M.Davidson, Phys. B.ev. C29 (1984) B.1572, Nucl. Phys. A432 (1985) 451. 19) A.J.Kreiner and D.I'Iojman, Phys. B.ev. C36, (1987) R2173. 20) A.J.Kreiner and D.FIojman, Notas de F~sica, Universidad Aut6noma de M~:dco, Vol.10, N° 1 (1987) 171. 21) J.D.Garret, in Proc. Conference on High Angular Momentum Properties of Nuclei, Oak Ridge, Tennessee, 1982 ed. by N.R.Johnson (Harwood, 1982) pp. 17-48 and references therein. 22) A.J.Kreiner, Proc. Conf. on High-Spin Nuclear Structure and Novel Nuclear Shapes, Argonne National Laboratory - PMY-88-2, (1988) 297. 23) A.J.Kreiner, M.Fenzl, S.Lunardi and M.A.J.Mariscotti, Nucl. Phys. A282 (1977) 243. 24) A.J.Kreiner, Z.Phys. A288, (1978) 373. 25) M.F.Slanghter, R.A.Warner, T.L.Khoo, W.H.Kelly, and W.C.McHarris, Phys. Rev. C29, (1984) 114. 26) K.S.Krane, R.M.Steffen and R.M.Wheeler, Nucl. Data Tables All (1973) 351. 27) F.D~nau and S.Frauendorf, ibid 21, pp. 143-160, F.D/Snau, Nucl. Phys. A471 (1987) 469. 28) A.J.Kreiner, V.R.Vanin, F.A.Beck, C.Bourgeois, Th.Byrski, D.Curien, G.Duchene, B.I-Iass, F.LeBlanc, J.C.Merdinger, M.G.Porquet, P.Romain, S.Rouabah, D.Santos and J.P.Vivien, to be published.