Shears bands in 201Pb and 202Pb

N U C L E A R

P H Y S I C S A

ELSEVIER Nuclear Physics A 592 (1995) 365-384

Shears bands in 2°lpb and 2°2pb

G. Baldsiefen a, p. Maagh a, H. Hiibel a, W. Korten a, S. Chmel a, M. Neffgen a, W. Pohler a, H. Grawe b, K.H. Maier b, K. Spohr b,

R. Schubart c, S. Frauendorf d, H.J. M a i e r e

a institutfiir Strahlen- und Kernphysik, Universitiit Bonn, Nussallee 14-16, D-53115 Bonn, Germany

b Hahn-Meitner-lnstitutfiir Kernforschung, Glienicker Str. 100, D-14109 Berlin, Germany

c II. Physikalisches lnstitut, Universitdt GOttingen, Bunsenstr. 7-9, D-37073 G6ttingen, Germany

d Forschungszentrum Rossendo~ PosOrach 510119, D-01314 Dresden, Germany

e Ludwig-Maximilians-Universitiit Mfinchen, Am Coulombwall 1, D-85748 Garching, Germany

Received 7 April 1995

Abstract

High-spin states in 2°lpb and 202pb have been investigated using in-beam y-my spectroscopic

techniques. Seven regular sequences of enhanced dipole transitions, with weak E2 crossovers in

some cases, have been found, one of which is firmly connected to low-lying levels in 2°lpb. These

bands are interpreted to be built on high-spin proton-particle neutron-hole excitations. Tilted-axis

cranking calculations show that the angular momentum along the bands is predominantly generated

by a continuous and simultaneous reorientation of the proton and neutron spins into the direction

of the total angular momentum (shears effect).

Keywords: NUCLEAR REACTIONS 192Os( 14C,xn); E = 76 MeV; measured yy-coin, E~, ~-y(0), DCO ratios. 201.2o2 Pb deduced levels, J, ~r, shears bands. Compton-suppressed Ge detectors, BGO detectors. Tilted-axis cranking calculations.

1. Introduct ion

Cascading sequences of magnetic dipole transitions are well established experi-

mentally in many nuclei o f the light-mass Pb region [ 1-3] . These structures are built

on high-spin proton-particle neutron-hole excitations with very small oblate deforma-

tion. Soon after their discovery it was realized [ 1,3,4] that they cannot be interpreted

as collectively-rotating high-K bands, mainly because they carry too little quadrupole

collectivity [5 -8 ] to account for the moments of inertia of the observed regular bands.

The proton contribution to the structure of the dipole bands is a par t ic le-hole excitation

with high spin across the Z = 82 shell gap. This excitation induces a small oblate

0375-9474/95/$09.50 (~) 1995 Elsevier Science B.V. All fights reserved SSD! 0375-9474(95)00305-3

366 G. Baldsiefen et al./Nuclear Physics A 592 (1995) 365-384

deformation. However, the bands discussed here are not directly built on these high-

K states [9-19]. Rather, it appears to be essential that high-spin neutron i13/2 hole

excitations are coupled to these proton configurations. The proton-particle neutron-hole

interaction favours a perpendicular orientation of their spin directions with the total

nuclear angular momentum pointing into a direction somewhere between these two

spins. The physics in the case of such a coupling is well described within the framework

of the tilted-axis cranking (TAC) model [4]. The results of the TAC calculations show

that the angular momentum along the dipole bands is generated predominantly by a

reorientation of the proton and neutron spins in small but regular steps into the direction

of the total angular momentum. The effect may be viewed as the closing of the blades of

a pair of shears, the two blades representing the proton and neutron spins, respectively.

Therefore these bands have been called "shears bands" [1].

For a full understanding of this interesting nuclear structure effect it is desirable

to scan the region of nuclei where these bands exist. In this work we report on a

spectroscopic investigation of high-spin states in 2°lpb and 2°/Pb. It is of particular

interest to search for shears bands in these nuclei because for near-spherical shape the

neutron i13/2 subshell is occupied and it takes more energy to populate the neutron-hole

states that are suggested to be essential for the formation of the shears bands. We find

seven shears bands in these two nuclei, two of which have been reported in our earlier

work [20]. One of the bands in 2°lPb is firmly connected to the spherical level scheme

and, consequently, its spin and excitation energy are experimentally established. Indeed,

it turns out that this band has a higher excitation energy than the band with the same

configuration in neighbouring 199pb.

In the following section the experimental procedure will be described and the results

will be presented. The level schemes are presented in Section 3 and the properties of

the bands will be discussed within the framework of the TAC model in the last section.

2. Experimental procedure and results

High-spin states in 2°lpb and 202pb were populated in the reaction 192Os(|4C,xn) at

a beam energy of 76 MeV. The 14C beam was provided by the VICKSI accelerator

of the HMI Berlin. The target consisted of a pill pressed from osmium metal powder,

enriched in 192Os to 99.0%, with an average thickness of approximately 100 mg/cm 2.

The beam was degraded and stopped in the thick target, but no appreciable amounts of

the next heavier Pb isotope, 2°3Pb, were produced because of the small reaction cross

section at a beam energy close to the Coulomb barrier. Because of the large stopping

power of osmium [21] most of the y-rays within the shears bands are emitted after the

recoiling Pb nuclei have come to rest and their energies are not Doppler-shifted. Only the

highest-spin transitions show Doppler-broadening. The thick target was mainly chosen

for the search for bands and their connections to known lower-spin states including the

measurement of coincidences across long-lived isomers in 2°lpb and 2°2pb. Gamma-ray

coincidences were measured with the OSIRIS spectrometer array which comprises 12

G. Baldsiefen et al./Nuclear Physics A 592 (1995) 365-384 367

Compton-suppressed Ge detectors as well as a multiplicity and sum-energy detector of

48 BGO scintillation counters. A total of 150 x 106 coincidence events within a hardware

time window of 100 ns were recorded. They consist of the energy deposited in at least

two Ge detectors, the times with respect to the beam pulse of the cyclotron and the sum

energy and multiplicity recorded by the BGO ball.

In the off-line analysis the coincidence events within a prompt time window of 38 ns

and with a BGO detector fold F > 5 and sum energy H > 1 MeV were sorted into an

E~I - E~2 matrix. Gates were set on all y-ray lines to obtain, after proper background

subtraction, one-dimensional coincidence spectra. The analysis revealed seven cascades

of coincident y-rays in 2°lpb and 2°2pb with energy spacings typical for the shears bands

in this mass region [ 1 ]. In Figs. 1 and 2 summed coincidence spectra for some of these

bands are displayed. The total relative intensities for each band are shown in the insets.

A correction for internal conversion assuming M1 multipolarity for the AI = 1 transitions

was applied. The transitions belonging to the new bands are in coincidence with several

of the transitions between the spherical states in 2°lPb and 2°2pb, respectively, as can be

seen in Figs. 1 and 2.

The transition energies, intensities, DCO ratios and spin assignments for the bands

and the spherical transitions in 2°lpb and 2°2pb are summarized in Tables 1 to 4.

The intensities within the bands were corrected for internal conversion assuming pure

M1 and E2 multipolarities for the AI = 1 and 2 transitions, respectively. Since the

multipolarity for many of the transitions in the spherical level scheme are not known,

y-ray intensities instead of total intensities are given in Tables 2 and 4. The y-ray

intensities were determined from the total-projection spectrum of a coincidence matrix

which was created without restricting conditions on the time and the BGO-detector sum-

energy and multiplicity. For weak transitions and doublets intensities were determined

from individual coincidence spectra; they were then normalized to reference transitions

in the total-projection spectrum. Since a hardware coincidence-time window of about

100 ns was used in the experiment, a loss of intensity is observed for coincidences

across the long-lived isomers [12,13,15] and in those cases our intensities may be

different to previous data where intensities have been determined from singles spectra

or coincidence spectra with different time windows.

Directional correlation (DCO) ratios were determined from a coincidence matrix with

the forward and backward detectors on one axis and the near-90 ° detectors on the other

axis. Gates were set on all strong clean transitions along both axes of this matrix to

obtain the intensities I t (30 °) and I~(90°). The DCO ratios were then normalized to

1.0 for known stretched E2 transitions.

3. Level schemes

In our work we have concentrated on the search for shears bands and their decay to

previously known levels. It was not our aim to extend the spherical level schemes of 2°lpb and 2°2pb.


z.

6

0

2000-

1 0 0 0 -

3000-

+

e4

+

¢ -- •

• 0 100 200 300 400 500 600

~' ~, lkeVl +

'2- I + o ,

I • ~ o I I ~- ~I~

I ~ ~I, I+

i1' P

2000- I~"

• +

r,,,-

1000- ~ I I

+

el.

I

2 o l p b _ Band 2

.~o

• ,0 o ' l

7-i7 _ + . Q ~ 0 I00 200 300 400 500 600

~ ; ~ + +

• u'~ +

I o ~ , ¢ ~. + I

I I ~1 I ,t , ,~ ~ ,~ U, I I"" ,,~ r... r - - o4 I ~ ~ _

i l ~ l I I i I <:"

.~ 6 0 . ~ ~

m ~ 0 100 200 300 400 500 600

0

e.) 4 0 0 -

200

I

¢ • ¢',1

I

+

200 40(

+": g +

ei ~, " + o.

600 800

E n e r g y (keV)

Fig. 1. Summed coincidence spectra of bands 1 to 3 in 201Pb. Transitions marked by dots belong to the bands,

those marked by plus signs belong to spherical states. Coincidences with group 3 transitions are marked G3.


~ = ':I { { ~ 20,pb .~n. 4

• ~ 0 100 200 300 400 500 606

0 ~ ~ + +

I . ~ + ,o -

2o0 _ _ =1 I ~ , - , ' ~ , " 'o

,~1 I , ~ 1

12o 2°]Pb - Band 5 • 9o { i ~

30 ~ I

400 ~" o

, ~ + • ~.~ I00 200 300 400 500 600

~ o Ef IkeVl 0 ~. ~ +

- , I I ' , . , ~ + ' * " ° + +

200 I~t ~' ~ ~" ~ ~ _

Ii I I I I I I ~

600 ~. ~, ,20 1 I 2°2pb - Band 1

i. | + 30) • i

o ~

400 0 i00 200 300 400 500 600

~ l ~, lkeVl +

~. +

~ + + ~

I ' ' o', ~ ~411

200- I

'~l~ q | i ~ ' t T - ~ l I ' ql~r~" '~ ' ~'~W T I~" ~ q ~ v - - ~ l - ~ r Pl ~1~ ~ " t I ~ l ~ ' Y l

~ T ~ - ' " ' ~ ~ r 1 t

200 400 600 800

Energy (keV)

Fig. 2. Summed coincidence spectra of bands 4 and 5 in 2°~pb and of band 1 in 2°~pb. Transitions marked by dots belong to the bands, those marked by plus signs belong to spherical states.


Table 1 Transition energies, total intensities, DCO-ratios and spin assignments of the bands assigned to 2ol Pb

E r [keV] /tot [%] RDCO / i ---* If

Band 1 109.2 89(28) 0.71(15) 181.6 100(21) 0.66(6) 263.8 99(10) 0.71 (6) 340.8 87(8) 0.69(5)

404.0 75(7) 0.70(6) 459.0 52(6) 0.70(6) 505.7 17(6) 0.67(11) 558.5 7( l ) 0.65(18)

518.4 10(2) 0.69(10) 744.6 11 (4) 1.10(33)

862.8 10(4) 0.92(34) 964.7 10(3) 0.77(18)

Band 2 101.7 72(23) 0.55(14) 129.7 77(15) 0.57(8) 171.6 86(12) 0.58(6) 220.5 100(15) 0.58(5) 275.9 92(10) 0.56(3) 333.1 46(9) 0.57(5) 334.6 43 ( 1 l ) 0.60 ( 5 ) 393.3 28(4) 0.64(10) 394.8 31(7) 0.60(13) 442.5 9(5) 0.68(16) 453.9 19(6) 0.62(14)

Band 3 139.6 100(18) 0.69(17) 175.8 99(28) 0.68(19) 222.3 100(15) 0.64(10) 276.4 94( 15 ) 0.66(9) 332.3 69( 11 ) 0.69(13) 388.1 51(7) 0.59(14) 441.3 39(10) 0.64(16) 491.7 26(5) 0.64(17) 539.8 12(3) 0.66(26) 829.4 12 ( 5 ) 1.20 ( 65 ) 933.1 10(4) 0.82(30)

103t.4 12(4) 1.19(49)

Band 4 176.5 93 (19) 0.83(19) 225.7 100(17) 0.88(17) 278.2 91 (10) 0.85(14) 326.7 64(12) 0.79(16) 380.4 36(7) 0.89(11) 429.7 16(7) 0.79(30) 483.1 19(7) 0.73(26) 530.2 15(3) 0.85(20)

37/2 39/2 41/2

43/2 45/2 47/2 47/2 49/2 49/2

51/2 51/2

~35/2 --*37/2 ----~39/2

--~41/2 ---*43/2 ---*45/2 ---~45/2 --~47/2 ---*47/2

--*49/2 ---~49/2

G. Baldsiefen et al./Nuclear Physics A 592 (1995) 365-384

Table 1--continued

371

E v [keV] ltot [%1 RDCO li ~ If

Band 5

152.9 94(21) 0.55(23) 198.6 96(9) 0.63(11) 250.0 100(11) 0.68(11) 312.0 75(10) 0.58(11) 374.4 57(7) 0.68(14) 436.0 39(10) 0.77(21) 493.4 37(7) 0.76(20)

3.1. 2° lpb

Five bands have been assigned to 2°lpb. They are shown in the level scheme of that

nucleus in Fig. 3. Bands 1 and 2 were already found in our previous work [20] but

both bands were not linked to the previously known spherical levels. On the basis of the

data presented here we have connected band 2 to the known states and established its

spins and excitation energy. The other bands still remain unconnected, mainly because

of contaminations in the coincidence spectra and insufficient statistics.

For the purpose of our discussion we have separated the spherical levels into three

groups which are divided by the long-lived 29 /2 - and 41/2 + isomers. The energy of

the 13/2 + state as well as the spins and lifetimes of the 13/2 +, 25 /2 - , 29 /2 - and

41/2 + isomers are adopted from the work of Rosengard et al. [ 15]. We confirm most

of the levels of groups 1 and 2, as well as the 447 keV transition of group 3, that were

reported previously [ 15]. We also confirm the 79 keV isomeric transition which was

observed in the conversion-electron spectroscopy of Sun et al. [ 13]. A total of 42 new

transitions have been placed into the spherical part of the level scheme, most of them

belonging to group 3 of excited states above the 41/2 + isomer.

The five bands carry 11(4), 11(3), 8(3), 7(4) and 8(4)% of the total intensity of

the population of group 3 of levels. Band 1 decays via several pathways into group 1.

The strongest transitions in this decay are the 610 keV (not shown in the level scheme

of Fig. 3) and the 1341 keV transitions; they carry 36(4) and 22(3)% of the intensity

of the band, respectively. Band 1 also seems to be in weak coincidence with transitions

of group 2. However, these coincidence relationships are not clear, mainly because of

contaminations in the gating transitions. Thus, our data do not allow to establish the

decay scheme of band 1.

The band head of band 2 at (6146+d) keV decays in a single-step via the 1640 keV

transition into the 35/2 state at (4506 + d) keV. Its DCO ratio is compatible with

stretched quadrupole or non-stretched dipole multipole order. This transition carries only

5(2)% of the decay of band 2. Our data do not allow to establish the remaining decay

pathways. There exists, however, a second connection between band 2 and the spherical

level scheme at the two very close-lying levels at (7378 + d ) and ( 7 3 8 0 + d ) keV, both

with spin 47/2. This spin assignment is based on the DCO ratios of the transitions that


Table 2 Transition energies, y-ray intensities, DCO-ratios and spin assignments in 201Pb

Ey [keV] lr [%1 RDCO 17 ~ 1~ r

Group 1 166.4 3.3(0.2) 1.08(9) ?--.21/2+ 222.4 58.0(1.2) 0.93(10) 25/2---- ,21/2- 350.5 34.5(1.4) 0.95(13) 19/2+ ~ / 2 + 354.5 63.4(1.9) 1.I0( 11 ) 19/2+ ~ 17/2+ 360.6 26.3( 1.1 ) 0.96(9) 21/2+ ---, 17/2+ 594.5 3.0(0.3) 0.73(21) 2 1 / 2 - 4 2 1 / 2 + 600.5 70.9(1.4) 0.80(8) 21/2----,19/2+

664.1 1.3(0.1) 1.08(25) - 667.6 2.8(0.2) 1.03(16) -

830.7 2.7(0.3) 1.13(16) ?--.21/2+ 834.0 3.8(0.3) 0.94(11) ?---.21/2+ 913.0 100.0(2.0) 1 . 0 8 ( 8 ) 17/2+---~13/2+ 917.0 37.0(1.5) 0.81(11) 15/2+---,13/2+

1341.0 3.4(0.1) 0.89(16) ?---~25/2-

Group 2 79.5 10.2(1.9) 1 .05(41) 41/2+---~37/2+

142.5 1.1(0.1) 1.00(35) 35/2---*35/2 287.2 42.1(0.8) 0.76(5) 35/2----*33/2- 293.9 12.8(0.8) 0.78(7) 33/2+---,31/2 387.0 3.3(0.1) 0.90(15) 33/2+4--,33/2 - 422.5 32.5(1.6) 0.83(14) 33/2+---+31/2-

573.2 9.0(0.8) 0.63(11) 35/2---*33/2+ 628.4 27.0(1.4) 1 . 0 0 ( 9 ) 37/2+---*33/2+

715.7 5.5(0.8) 0.66(12) 35/2--*33/2+ 728.0 61.5(1.8) 0.89(4) 37/2+---~35/2- 791.0 22.8(1.1) 0.61(4) 31/2---~29/2- 826.6 89.4(1.8) 1 .00(14) 33/2----~29/2- 919.4 8.8(2.5) 0.87(12) 31/2---,29/2-

1640.0 1.7(0.1) 1.13(26) 35/2---*35/2

Group 3 98.2 0.8(0.1) 0.74(21) 45/2----,43/2

136.2 0.6(0.1) 0.89(28) 47/2---*45/2+ 153.7 2.0(0.1) 1.02(15) 45/2---+41/2 159.4 2.3(0.1) 1 . 0 6 ( 1 3 ) 45/2--+45/2+ 179.3 6.8(0.7) 0.70(6) 53/2--~51/2 190.4 < 1.0 0.81(18) 39/2---~41/2+ 19%2 4.1(0.1) 0.70(11) 51/2---+49/2+ 232.2 0.6(0.03) 0.81(25) 49/2+---~47/2 253.7 0.9(0.1) 0.78(28) 41/2---~39/2 259.2 1.8(0.1) 0.63(13) 51/2---,49/2 269.9 4.0(0.7) 0 . 6 4 ( 1 2 ) 39/2--~37/2+ 302.0 4.5(0.1) 0.79(13) 45/2---~43/2 331.1 1.7(0.2) 0.77(18) 51/2---~49/2 380.6 3.2(0.3) 0.84(29) 49/2---*47/2 382.0 3.8(0.1) 0.66(15) 49/2--+47/2 447.3 31.5(0.6) 0.76(5) 43/2---~41/2+ 455.8 3.2(0.2) 0.71(7) 55 /2~53/2 470.7 7.1(0.4) 0.94(12) 47/2---*45/2 548.3 2.7(0.1) 0.67(9) 49/24-*47/2


Table 2- -cont inued

373

E r [keV] /~, 1%1 Roco 1~ r ~ 1~

586.1 1.8(0.3) 0.76(13) 47/2---,45/2+ 600.2 2.9(0.4) 0.98(16) 45/2---~45/2 663.9 3.1(0.2) 0.8(12) 53/2--,51/2 682.3 1.0(0.1) 0.73(18) 49/2+---~47/2 717.3 27.7(0.6) 1.05(6) 49/2--,45/2 902.2 23.9(0.2) 0.55(5) 45/2---,43/2

1005.5 1.9(0.1) 0.76(20) 41/2--~39/2 1190.1 13.6(0.4) 1 .07(13) 45/2+---~41/2+

1251.3 3.5(0.1) 0.74(17) 43/2---~41/2+ 1312.0 19.6(1.2) 0.73(13) 51/2---~49/2 1312.3 5.8(0.4) 0.97(11) 49/2+---~45/2+ 1388.1 1.9(0.1) 0.72(29) 47/2---~45/2 1389.4 1.4(0.1) 0.64(37) 47/2--,45/2 1683.8 3.8(0.2) 1 .01(17) 45/2+---~41/2+ 1749.5 1.9(0.1) 0.93(19) 3 9 / 2 4 3 5 / 2 -

populate and depopulate these states and finally connect them to levels of known spins.

The band-head spin is then 35/2 compatible with the non-stretched dipole nature of the

1640 keV transition mentioned above. Because of their proximity the two close lying

states must be heavily mixed and it is impossible to decide which level belongs to the

band and which is a state of group 3. The pairs of transitions populating and depopulating

these states, the (380.6, 382.0 keV), (393.3, 394.8 keV) and the (333.1,334.6 keV),

(1388.1, 1389.4 keV) pairs, respectively, have equal transition intensities. The (381,

382 keV) doublet was not resolved in our previous work [20] and was erroneously

interpreted as the continuation of the band. Above the 49/2 state there is another forking

Table 3 Transition energies and total intensities

of the bands assigned to 2°2pb

E r [keV] /tot [%1

Band 1 161.5 100(19) 243.3 83(12) 332.9 46(7) 407.6 27(5) 466.5 32(8) 517.7 15(9)

Band 2 183.0 100(23) 240.1 92(11) 296.3 72(12) 361.9 43(7) 419.5 28(5) 487.2 40(8)


Table 4

Transition energies, ~,-ray intensities and spin assignments in 2°2Pb

E r [keV] 1 r [%] 1~ ~ 1~ r

46.0 12+ ~ 10q-

122.5 16+ --* 15

129.7 16 ----} 15

179.8 99.8(9) 12+ ----} 11--

202.7 4.2(0.8) ( 1 8 - ) --* 1 9 -

215.0 2.5(0.5) 14+ ~ 13+

231.8 14.3(1.9) 15 ---* 16+

271.1 11.3(1.7) 12 ----} 1 1 -

354.6 46.7(5.6) 16+ ~ 16+

626.7 - 13+ ~ 12

689.4 22.4(2.9) ( 2 0 - ) ----} 19--

717.6 29.7(3.3) 13+ ~ 12+

785.5 20.3(2.6) ? --~ 12+

796.9 24.2(2.9) 17-- ---* 16+

831.1 8.2(0.7) 13 ---+ 12+

840.6 72.8(7.3) 2 1 - ---} 19--

853.6 29.7(4.2) 14+ ~ 12+

888.1 100(8) 1 1 - ---* 9 -

933.2 8.2(1.4) 14+ ~ 12+

1021.5 13.3(2.1) 10+ ~ 9 -

1151.1 59.4(5.3) 1 7 - ~ 16+

1160.5 17.3(2.6) 18+ ---, 16+

of the band. It is not certain and because of the strong mixing of the close-lying levels

probably irrelevant, which of the sequences is the continuation of the band. The sequence

with transition energies of 334.6, 393.3 and 453.9 keV, however, gives a somewhat

smoother moment of inertia and is therefore taken as the continuation of the band.

For the remaining bands in 2°lpb (bands 3, 4 and 5) our data do not allow to establish

the connection to the previously known levels. For bands 4 and 5 the coincidence rela-

tionships to the low-spin transitions are somewhat ambiguous because of contaminations

in the gating transitions.

3.2. 2°2pb

The two new bands which we assign to 2°2pb are shown in the level scheme in Fig.

4. Band 1 is in coincidence with the transitions below the 16 + 110 ns isomer [ 12]. In

addition it is most likely in coincidence with the 1151 keV transition above that isomer

and with a 1629 keV line which was not placed in the previously known level scheme

[ 12]. The latter transition is also in coincidence with the 1151 keV transition.

Band 2 is only tentatively assigned to 2°2pb because it is weak and the coincidence

relations are not clear. If it belongs to that nucleus, it probably has higher spins than

band 1 and feeds into the states around and above 6 MeV of the normal level scheme.

G. Balds ie fen e t a l . / N u c l e a r Phys ics A 592 (1995) 3 6 5 - 3 8 4 3 7 5

1.0

c -

o ¢ n ~ ~ ~ ~ ~ ~1 ~o

r.. r~ r..

rr)

t - o

t2£3

. j .j . j t ~ j .d ~-

o -

c..9

¢

to

- I

m ~

m ~

o

C) N

+

I

¢-I

I ¢-I


Bend 1

517.7 1,

466.5

407.6

332~

161.5t 243.3

(Bend 2)

487.2 1

419.5

2°'pb ,619 296.3

240.1 183.0

2 1 - ~ 6 0 8 2 + d ' <- 9 • <2o-)-r <--~ ?-?-;- 2 ~

840.5 689.2

III ? 1 9 - 1 7 - ~ ( 1 8 ) 202.7 5242 + d'lO7ns

I I L 1151.1 I 1160.5

933.2 . . . . 6267 853.3 7852 831.1

. I "i~.2~ 1 "~" I 24.2ns

1021.5

! 1 1 ,,,h 9- ~ 2170

Fig. 4. Level scheme of 2°2pb. Band 2 is only tentatively assigned to this nucleus. The spherical levels are

taken from Ref. [121.

4. Discussion

At first, when the magnetic dipole bands were discovered in several lead isotopes,

it was thought that they result from a collective rotation of oblate nuclei [ 1 ]. In fact,

similar sequences of AI = 1 transitions with AI = 2 crossover transitions are known

in many deformed nuclei where they are built on states with nucleon configurations

with their spins strongly coupled to the deformation axis. However, for the dipole bands

discussed here there exist several important differences, and soon it became clear that

they cannot be interpreted as normal collective bands [ 1,3,4].

The bands are built on high-spin proton-particle (h9/2 and/or i]3/2) excitations coupled

to one or more i13/2 neutron-hole states. The high-K h9/2 and i13/2 protons have a strong

oblate deformation-driving effect and the occupation of the 9/2 [505] and 13/2 [606]

Nilsson orbitals polarizes the stiff core towards slightly oblate deformation (f12 ~<

0.1, ~ ,~ 70 ° [ 1 ] ). High-K excitations with oblate deformation do indeed exist in - 2 2 + - 2 •

several light-mass Pb isotopes e.g. the (Sl/2h9/2)8 and (Sl/2h9/2113/2)11- isomers in

the even-even isotopes between 192pb and 198pb [9-19]. However, no regular bands

have been observed to be built on these states. Obviously, the collective rotational

states of such weakly-deformed nuclei lie too high in energy above the other available

near-yrast states and are not populated in (heavy ion, xn) reactions. The regular bands


t _ 3

~ o

~-~ O ~ Jrt

I

377

0 10 20 0 10 20 :)a('h) J~(h)

Fig. 5. Angular momentum coupling at low and high rotational frequency for band 2 in 201Pb with the

configuration ABEll (see text).

are only observed to be built on states where the high-K proton-particle excitations are

coupled to low-K i13/2 neutron holes. This cannot be a deformation effect, since the il3/2

neutron-hole excitations are very little deformation-driving. In fact, i13/2 neutron-hole

states are known systematically in the Pb isotopes [9-19,22]. They can be regarded as

spherical shell-model states and also on these excitations no bands are built.

The second argument for the peculiar nature of the dipole bands in the Pb region is

connected to their small quadrupole deformation. It was evident when the first bands

of this type were found [ 1 ] that the E2 transition probabilities are much smaller than

the M1 transition rates. Subsequent lifetime measurements [5-8] showed that, indeed,

the quadrupole collectivity is very small. It is surprising that nevertheless very regular

bands with a substantial moment of inertia are observed. However, the normal relation

between the moment of inertia of the bands and the quadrupole deformation does not

hold: e.g. the ratio of the moment of inertia over the square of the quadrupole moment

lies about an order of magnitude higher than for normal well-deformed rotational bands.

A further argument is the lack of signature splitting at high spins for most of the

dipole bands in the Pb region. Normal high-K bands develop a signature splitting when

the rotational angular momentum becomes much larger than the intrinsic nucleon spin.

For such bands K is almost constant and the increment of the angular momentum is

generated by the collective rotation perpendicular to the symmetry axis. Consequently

the orientation of the total nuclear spin approaches the axis perpendicular to the axis of

deformation and signature becomes a good quantum number due to the symmetry for

180 ° rotation around this axis.

These deviations from normal collective rotation have led to the interpretation of the

dipole bands in terms of the "shears mechanism" [4,1 ]. The proton-particle neutron-hole

interaction favours a perpendicular coupling of the large proton and neutron spins and

the resulting total nuclear spin points into a direction somewhere in between these spins.

The coupling scheme is shown in Fig. 5. The left-hand part of the figure shows the sit-

uation near the band head. The proton and neutron spins are coupled - together with a

small collective angular momentum R - to the total spin J. The collective part, which is

microscopically composed of all the small proton and neutron angular momenta besides

378 G. BaMsiefen et al./Nuclear Physics A 592 (1995) 365-384

A

:E

LU

8

6

4

x

2 xx x x

0 i |0

I i I r

X

o~ O X

o×§ o a O I x X x

x x

x

~x X x

X X

i I i

20 30

Fig. 6. Experimental energies as a function of spin for shell model states (crosses) and for band 2 (dots) in 201Pb.

the large proton h9/2, i13/2 and neutron i13/2 spins, represents only a minor contribution to

the total spin. The total J is the conserved quantity and, clearly, K is not a good quantum

number, even at the band head. TAC calculations [ 1,4] show that the angle between the

total spin and the 3-axis (symmetry axis) remains almost fixed within the bands. The

gain in angular momentum along the bands is predominantly generated by a reorientation

in small but regular steps of the proton and neutron spins into the direction of the total

spin J, as is indicated in the right-hand pan of Fig. 5. Since this effect has some resem-

blence to the closing of a pair of shears, the bands have been named "shears bands" [ 1 ].

Only band 2 in 2°lpb is firmly connected to the spherical levels and its excitation

energy and spins are known. We will therefore focus on this band in the following

discussion. With the known excitation energy of band 2 we can now compare its location

to the other states in 2°lpb. The excitation energy as a function of spin is displayed in

Fig. 6. It shows that band 2 lies about 1.5 MeV above yrast near the band head and

approaches the yrast line at high spins. It certainly lies higher in energy compared to

the yrast states than the corresponding bands in the lighter Pb isotopes [ 1,3].

The band-head spin of band 2 is 35/2, the same spin as was assigned to band 2 in

199pb [ 1 ]. Furthermore, the moments of inertia of these bands are similar. The spherical

configuration {Tr -2 • - (Sl/2h9/2113/2) 11 (~)/2 "-2 -1 (113/2P3/2) 27/2 } 35/2 + was assigned to

band 2 in 199pb [ 1 ]. In the simplified nomenclature adopted in our previous work, this

would be written as ABEl l. Here, the neutron quasi-panicles are denoted by letters

(A,B,C . . . . as in the cranking model) and the proton contribution is labeled by the spin,

i~ = 11 in this case. On the other hand, the band-head energy is much higher, about

6.2 MeV in 2°lpb compared to about 4.8 MeV in 199pb. This reflects the fact that the

neutron i13/2 subshell is filled for 2°lpb and it takes appreciably more energy to decouple

and align an i13/2 neutron pair (AB). In the neighbouring even--even Pb isotopes the

(vi~-3~2) 12 + states have energies of 2.80, 3.00 and 3.24 MeV for J9spb, 2°°pb and 2°2pb,

G. Baldsiefen et al./Nuclear Physics A 592 (1995)365-384 379

respectively. Furthermore, the 11- proton 2p2h states, which are not known in 2°°Pb

and 2°2pb, may be expected to lie at higher energies than in the lighter Pb isotopes

[ 16]. We can estimate the energy of 11 - excitation using the experimental energies of

the (Irh~/2)8+ states in the neighbouring Po isotopes [23] and the 7ri13/2 - h9/2 energy

differences in the Bi isotopes [24,25] and obtain

E( 11-,2°° Pb) ~ E( 11-,2°2 Pb) ~ 3.2 MeV.

Then, with the average energy of the (~'i13/2)12 + state, E( 12 +) ~ 3.1 MeV, we obtain

for the band-head energy of band 2 for the ABE11 configuration

E(ABE11,2°1Pb) ~ 6.3 MeV

which is in good agreement with the experimental energy of about 6.2 MeV.

The dynamical moments of inertia j(2) = dI ( to) /d to for all bands assigned to 2°lpb

and 2°2pb are shown in Fig. 7. As can be seen the moment of inertia of band 3 in 2°lpb

is very similar to that of band 2. One may speculate that these two bands have a similar

structure and we tentatively assign the configuration ABF11 to band 3. However, a final

assignment by a comparison to TAC calculations can only be made when spins and

excitation energy are experimentally determined.

Band 1 in 2°lpb has a moment of inertia that is similar to the one of band 1 in 199pb

below the band crossing [ 1 ]. Furthermore, similar to 199pb, it deexcites into a level of

rather low spin, i.e. the 25 /2 - state at 2719 keV. This band may therefore have the

same configuration, A11, as was assigned to band 1 in 199pb. However, in the lighter

isotopes [ 1,3] a crossing of that band with the ABC11 band with three aligned i13/2

neutrons is observed at a frequency around ha~ = 0.3 MeV. In the case of 2°lpb where

the i13/2 neutron subshell is filled the decoupling and alignment of the BC neutron pair

will take more energy and that may be the reason why this band crossing is not observed

here. Indeed, also in the corresponding Hg isotope with the same neutron number, 199Hg,

the BC alignment is not observed experimentally, while in the lighter Hg isotopes it

occurs around hto = 0.3 MeV [26-28].

These arguments are illustrated in Fig. 8 which shows a schematic diagram of the oc-

cupation of the neutron orbitals for several configurations in the isotopes 198pb to 2°2pb.

As can be seen, in 199pb the BC alignment takes only little energy because of the close-

lying orbitals below the N = 120 energy gap. For 2°lPb with 119 neutrons, however, there

is only one hole in these levels for the neutron configuration A and the BC alignment in-

volves an excitation of a neutron pair across the gap into the orbitals originating from the

3/2 [501 ] Nilsson state. Generally, Fig. 8 shows that in the heavier isotopes it takes more

and more energy to produce the necessary neutron holes in the il3/2 orbitals which are

essential to form the shears bands. Thus, it is an interesting question how far up in neu-

tron number these bands can be observed experimentally. Once the N = 120 energy gap

has to be crossed in order to produce i13/2 neutron-hole excitations for the isotopes above

199pb, there exists a large variety of different configurations with one or two neutrons in

the levels above that gap. Only some of those involving quasineutrons A to F are shown.


>

E

>

35

30

25

20

15

20

15-

10

I ' f ' I I • I •

201pb --zx-- Band 1

: - - o - - Band 2

! - - v - - Band 3

\ ~ - - o - - Band 4 [

\ ~ ------o-~ Band 5

I I I I !

202D1 ~ ~ Band 1 & L /

Band 2

I

0,1 0,6 I I I I

0,2 0,3 0,4 0,5

hm [Me V]

Fig. 7. Dynamical moments of inertia for the five bands assigned to 2ol Pb and the two bands assigned to 202 Pb.

None of the two bands assigned to 2°2pb is connected to the spherical states. An

interpretation of their structure can therefore only be speculative. We observe that the

moment of inertia of bands 1 in 2°lpb and 2°2pb (see Fig. 7) show a different slope

than most of the other bands. That may be an indication for similarities in their structure

and, since we very tentatively suggest the configuration A11 for band 1 in 2°lPb, we

might assume A B l l or A E l l for band 1 in 2°2pb. On the other hand, we do not find the

"identical" partner bands in neighbouring 2°lpb and 2°2pb that would be expected. As

was pointed out earlier [ 1,29], bands which differ by the quasineutron E or F should

have very similar transition energies. These neutron levels originate from the completely

decoupled pseudospin/k = 0 1/21521] orbital. In Fig. 8 the expected pairs of identical

bands are connected by dashed lines. This explanation for the occurrence of identical

bands is completely analogous to the one used for the identical superdeformed yrast and

excited bands in 15°Gd, 151Th and 152Dy [30,31]. In 2°lPb the closest similarity exists

G. Baldsiefen et aL /Nuclear Physics A 592 (1995) 365-384 381

) o: °. o ; ) ; ; °;

t . ^ ~ "x . . . . . . ° o oo \ ^ o . - v \ - • ~ \ _ . - v \ - - v EFl/21521]

^ ~ ) ~ o " o " o ) - o o ) ' o - o " '~" - A / - s c o { c c {e. ~ c ~ / o - o - B /2[660]

o_ :o /_ . o _o ,,_o o ; L o _o c,,,,0,,, E8 AB-CE ~ A;C ABE ~S EBcE/T~ ;BC ;BE/~B A~CE

ABCF ABF ABCF \ ABF ~ ABCF

198ph 199ph 200ph / 2Olph ) 202ph

Fig. 8. Schematic illustration of the occupation of neutron-hole orbitals in different aligned configurations for 198Pb to 2°2pb taken at a small rotational frequency. The odgin of the levels at ho) = 0 is indicated by the

Nilsson quantum numbers.

between bands 2 and 3, see Fig. 7. As in 199pb [ 1 ], these bands might therefore differ

by the quasineutrons E and F. However, in the case of 2°lpb no interband transitions -

as they were observed for 199pb - were found.

In order to substantiate the ideas outlined above more quantitatively we have per-

formed calculations within the framework of the TAC model, as proposed in Ref. [4]

and applied to 199pb and 2°°pb in Ref. [ 1], where the details of the formalism are

described. We use the deformation parameters fl = 0.1 and ~ = 60 °, no pairing for the

proton system and a pair gap of A = 0.75 MeV for the neutron system. The neutron

chemical potential is chosen independent of the rotational frequency to give neutron

number N = 119 for fu~ = 0.3 MeV.

The calculated quasineutron routhians as a function of the rotational frequency and as

a function of the tilting angle are shown in Figs. 9 and 10, respectively. Compared to

1.0

A

0.5

0.0

0.0 0,1 0.2 0.3 0.4 ~uJ (MeV)

Fig, 9. Quasineutron routhians as a function of the rotational frequency for rotation perpendicular to the

symmetry axis (O = 90°).


~E

3 , - ¢U

i , i , i , i , , , i , i , i i ,

0.510 ~C 0.0 . . . . . . . . . . . . . . . . . . .

0 ° 2 0 ° &O ° 6 0 ° 8 0 °

Fig. 10. Quasineutron routhians as a function of the tilting angle for a rotational frequency of hto = 0.2 MeV.

the case with two neutrons less the/Jil3/2 levels are shifted to higher energies and the

BC crossing frequency lies about 90 keV higher than in 199pb, as Can be seen in Figs.

7 and 8 of Ref. [ 1 ]. This reflects the shift of the Fermi level out of the ~'il3/2 subshell

(compare also Fig. 8).

The energies of the shears bands as a function of spin and the spins as a function of

the rotational frequency are calculated for the configurations A11, ABC11, ABE11 and

ABF11. The results are compared to the experimental data for band 2 in 2°lpb in Figs.

11 and 12. For the other bands the comparison cannot be made because they are not con-

nected to the low-lying states and their excitation energies and spins are not known exper-

imentally. For band 2 experiment and theory agree very well for the ABE11 configuration

which was already suggested on the basis of the more qualitative arguments given above.

5. Conclusion

High-spin states in 2°lpb and 2°2pb were populated in the 192Os(14C,xn) reaction and

investigated using the OSIRIS y-ray spectrometer array. Five (three new ones from this

A

u.I

I I ' I ' I ' I ' I ' r

I i I ~ I i I I I i I i 2 1

l, I~ IB 22

Fig. 11. Experimental (band 2) and calculated energies as a function of spin for 2o] Pb.


I * I ~ I ' I ~ I i I ' I ' I

I i I I I L I I 1 I I i I I I

0.1 0.2 0.3 0.4

hw (MeV)

Fig. 12. Experimental (band 2) and calculated spins as a function of the rotational frequency for 2Ol Pb.

work) dipole bands were assigned to 2°lpb and two to Z°2Pb. One of the bands in 2°lpb

is connected to the low-lying states and its spins and excitation energy are determined.

The "shears" mechanism [ 1 ] is used for the interpretation of the dipole bands. This is

an efficient way to form regular bands in these nuclei with very small deformation. The

angular momentum along the bands is mainly generated by a step by step reorientation

of proton h9/2 and /o r i13/2 particle spins and neutron il-~'~2 hole spins into the direction

of the total spin - similar to the closing of the blades of a pair of shears.

Til ted-axis cranking [4] calculations substantiate these ideas and give excellent agree-

ment with the data for band 2 in 2°lpb for which excitation energies and spins are now

known.

Acknowledgements

This work was partly supported by the Bundesminister fiir Forschung und Technologie,

Germany, and partly by the Deutsche Forschungsgemeinschaft.

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Shears bands in 201Pb and 202Pb