High-spin states in 183Pt

Nuclear Physics North-Holland

A511 (1990) 92-116

HIGH-SPIN

STATES

IN ‘83Pt

J. NYBERG Manne

Siegbahn

Insfitute

of Physics,

Royal

Frescativiigen

24, S-10405

ofTechnology,

Insiitute

S-10044

Stockholm,

Stockholm,

Physics Department

I, The

Sweden

and The Niels Bohr Institute,

Tandem

Accelerator

Laboratory,

DK-4000

Roskilde,

Denmark

A. JOHNSON Manne

Siegbahn

Institute

of Physics, Frescativiigen

24, S-10405

Stockholm

and Physics Department

M.P. CARPENTER’,

Department

Institute

The University

M.L. HALBERT,

Heav.v Ion Research

Accelerator

S-10044

Facility,

of Tennessee, Knoxville,

N.R. JOHNSON,

Oak Ridge

J.C. WADDINGTON Tandem

of Technology,

Stockholm,

C.R. BINGHAM, L.H. COURTNEY, V.P. JANZEN’, A.J. LARABEE4, Z.-M. LIU’ and L.L. RIEDINGER

of Physics,

C. BAKTASH, Holifield

I, The Royal

Laboratory,

McMasfer

National

Sweden

S. JUUTINEN’,

TN 37996-1200,

USA

I.Y. LEE and Y. SCHUTZh Laboratory,

Oak Ridge,

TN37831,

USA

and D.G. POPESCU’ Universiry,

Hamilton,

Ontario,

Canada

L8S 4Kl

Received 2 October 1989 (Revised 10 November 1989) Abstract: High-spin states in ‘s3 Pt have been studied for the first time using the reactions “‘%m(‘“S, 5n) Rotational bands built on the Nilsson configurations $-[521], ?[514] and and ‘7”Yb(‘h0,3n). ;+[624] were observed up to spin values of y-yfi. Quasiparticle alignments and band crossing frequencies were investigated in these bands. A large signature splitting was observed in the vi,,,,-band structure. The experimental results were compared with total routhian surface calculations, in which the shape of the nucleus could be followed as a function of rotational frequency for different quasiparticle configurations.

’ Present address: Argonne National Laboratory, Physics Division, 9700 Cass Avenue, Argonne, IL 60439, USA. ’ Present address: Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada KOJlJO. 3 Present address: Department of Physics, University of Jyvlskyli, SF-40100 Jyvlskylii 10, Finland. 4 Present address: Buena Vista College, Storm Lake, Iowa, USA. 5 Permanent address: Lanzhou University, Lanzhou, P.R. of China. ’ Permanent address: GANIL Laboratory, B.P. 5027, F-14021 Caen Cedex, France. ’ Present address: Department of Nuclear Physics, Australian National University, Canberra, Australia. 0375.9474/90/$03.50 (North-Holland)

@ Elsevier

Science

Publishers

B.V.

_I. Nyherg et al. / Hi&spin

E

state.7

93

““Sm(‘“S, Sn), E = 153 MeV, ““Yb(“O,3n), E = 81-84 MeV; NUCLEAR REACTION measured E,, I,(0), I,, y?(t), yX (X-ray)-coin. “‘Pt deduced levels, J, 57, S. Enriched targets, Ge (Compton suppressed) detectors, 47r NaI(TI) ball. Calculated experimental routhians, aligned angular momentum, signature splitting, total routhian surfaces.

1. Introduction

A transition from oblate to prolate ground state shapes has been established with decreasing neutron number for Pt and Hg nuclei in the mass region around A = 186-188. The study of the high-spin structure of transitional nuclei in this region is of great interest since coexistence of prolate and ablate, as well as triaxial shapes has been predicted ‘) and inferred in various experiments ‘-‘). The occurrence of high-j orbitals, which are close to the Fermi surface and which strongly feel the Coriolis interaction in a rotating nucleus, also give rise to pronounced spin-alignment effects in these nuclei. Both i,1,2 neutrons and h
driving

effects of involved 2. Experimental

quasiparticles. methods

The high-spin structure of lX3Pt has been investigated in three separate experiments. The first experiment was performed at the Holifield Heavy Ion Research Facility using the 25 MV tandem accelerator. High-spin states were populated via the ‘s4Sm(34S, 5n)lX3Pt reaction at 163 MeV. The nucleus Ix4Pt was also strongly populated in this experiment and results from the analysis of lX4Pt can be found in ref. ‘). Two stacked foils of lT4Srn, each with a thickness of about 500 pg/cm’ and separated by about 0.5 mm, were used as targets. In this experiment yy-coincidences were measured using seven Ge detectors placed at various angles throughout the ORNL Spin Spectrometer. Six of the Ge detectors were surrounded by NaI anti-Compton shields. The remainder of the Spin Spectrometer held 64 NaI detectors which were

94

J. Nyberg

et al. ,I High-spin

used to select the 5n-channel

by gating

about 50 x lo6 yy-coincidences

remained

from this experiment The second

on sum-energy after selection

were used to construct

experjment

was performed

accelerator

using the reaction

a thickness

of 1.4 mg/cm2,

states and multiplicity.

A total of

of the 5n channel.

The data

the main part of the level scheme of ‘*‘Pt. at the Niels Bohr Institute

FN tandem

‘70Yb(‘“0, 3n)“‘Pt at 82 and 84 MeV. The target, with was enriched to 85.4% in “‘Yb. A catcher foil of

3 mg/cm’ Pb was placed immediately behind the target in order to stop all the recoiling nuclei. Four Ge detectors (three n-type coaxial and one planar) with BGO anti-Compton shields from the NORDBALL detector system were placed around the target. About 2.3 x lo6 yy-coincidences were collected and the energy of the y-rays together with their time difference were recorded. An overlap coincidence time of 150 ns was used in this experiment. The main purpose of this experiment was to study the low-energy y-rays and the characteristic X-rays in addition to searching for isomer& states in r8’Pt, The third experiment was performed at the McMaster Accelerator Laboratory using the FN tandem accelerator. The nucleus Ix3Pt was produced via the reaction ‘70Yb(‘h0, 3n) at 81 MeV. The target (85% enrichment) had a thickness of 1.9 mg/cm’. In this experiment, angular distributions of y-rays were measured at 5 angles between 0” and 90” relative to the beam using one Ge detector. A multiplicity filter consisting of 6 NaI detectors positioned symmetrically around the beam axis was used to discriminate against y-rays from radioactive decay and other lowmultiplicity events.

3. Experimental

results

The level scheme of ls3Pt obtained in the present experiments is shown in fig. 1. In this level scheme only the band heads and some of the other lowest lying excited states were known earlier from studies of the radioactive decay of ‘83Au [refs. “*“)I. In the analysis of the coincidence data the E,-E, events were sorted into a two-dimensional matrix after proper gain-matching of the Ge spectra. The matrix was first symmetrized and the procedure of ref. 13) was then used to subtract a background

from it. This procedure

allows

for a complete

subtraction

of all the

Compton-Compton and Compton-photo events in the matrix. Events where at least one y-ray was from the continuum were also subtracted. In the construction of the level scheme, the order of the transitions was established by the intensity relationship of the peaks in the individual gates. For the strongly coupled bands additional support was obtained from checking the energy balance of the transitions. An example of some gated -y-ray spectra is shown in fig. 2. In one of the experiments a planar Ge detector was used together with three other coaxial detectors. Thus, it was possible to analyse yX-coincidences and to find to which element a peak belonged. All the strong transitions shown in fig. 1 were found to be in coincidence with Pt X-rays. The neighbouring even-even isotopes, ‘82Pt

95

J. Nyberg et al. / High-spin states

4 5256

4912f

--I--1749)

1 4025

41/Z--)

-T602

3423

3712-

-+

3397

(37/Z-)

551

2373

29/z-

473.1

456.6 1444

2i/2-

4321 1012

I?&?-

---I---

3647

3130 314

t

sz25h6

218.0 96 0

YZF

1/z-

35

+

,393 *r (712-k

160

196

1150 --_________

Fig. 1. Level scheme

of ‘lisPt.

121 ,

(Q/2+]

243

t

(1112')

96

in

b) gate

IOOOl-

: 255,339

and

c) gate : 619,671 and 714ke

100

Fig. 2. Summed

coincidence

I.

I.

/

200

300

400

spectra

/,

/.

500

600

Energy (keV)

/

,]

700

for some gates on peaks due to transitions 2 and (c) band 4.

in (a) band

1, (b) band

and ls4Pt, have been studied quite extensively during the last few years ‘4*2),and it is clear that the rotational bands in fig. 1 do not belong to these nuclei. It was thus concluded that atI the transitions in fig. I belong to “‘Pt. This is also supported by results from recent studies of the decay of ““Au [refs. “,l’)]. Some weak transitions that could not be definitely placed in the level scheme were also observed. These include a sequence of y-rays with energies 198, 204, 217, 232 and 244 keV, which are all in coincidence with each other and with Pt X rays. The association of these y-rays with “‘Pt is supported by the fact that they are seen in both reactions used to populate lRiPt. Properties of y-ray transitions assigned to lx3Pt in this experiment are listed in table 1. The spin and parity, I”, of the states were deduced from the measured angular distributions of the y-rays combined with previous knowledge of I” for the band heads. The spin and parity assignment of the ground state ( TIj2 = 7 min)

J. N_vherg et al. / High-spin states TABLE

Measured coefficients,

97

I

y-ray energies, intensities, angular distribution coefficients, dipole/quadrupole assigned multipolarities and spins for transitions in ‘“‘Pt observed in the lXIYb(KJO 3n)I”lPt

4

Multipolarity

6

(keV)

73 96 112.2 115.0 121 132.1 139.3 141.2 147 160.0 161 161.2 164 179.6 196 205 214 218.0 234.5 239 244.2 254.6 259 213.5 275 290 299.2 313.0 314 339.4 356.4 369.5 376 384.7 404.1 409.0 416 421 432.1 437.7 445.9 454.8 456.6 463.2 473.1

2.7 (0.5) 6.3 (0.9)

-0.61 -0.34

(0.05) (0.07)

0.03 (0.06) -0.02 (0.08)

5.0 (0.5) 5.2 (0.5) 1.6 (0.5)

-0.14 (0.04) -0.27 (0.05) -0.3 (0.1)

-0.14 (0.05) 0.20 (0.07) 0.1 (0.2)

2.6 (0.5)

-0.65

(0.07)

0.25 (0.08)

-2.5 i 0.2

E2/Ml

-0.47

(0.03)

0.05 (0.03)

-1.7io.5

E2/Ml

32 (3)

25.2 (0.9) 22.5 (0.9) 5.4 (0.9) 30 (2)

0.29 (0.03) 0.35 (0.04) -0.82 (0.04) 0.23 (0.04)

-0.13 -0.08

-0.6’;; -0.1:;;;;

E2/Ml E2/Ml E2/Ml

(0.04) (0.05 1

0.12 (0.04) -0.05 (0.05)

E2/Ml EZ/Ml

E2 E2 -1.1:;;;

E2/Ml E2

100 (5)

0.20 (0.03)

-0.03

(0.04)

E2

47 (2)

0.28 (0.03)

-0.07

(0.04)

E2

0.03 -0.07 0.20 -0.08

(0.04) (0.05) (0.07) (0.04)

E2 E2 E2/Ml E2

38 (2) 41 (2) 1.4 (0.5) 101 (5) 37 (2) 6.8 (0.7) 45 (3)

39 (3) 32 (3) 34 (2) 68 (3) 32 (2) 34 (2) 16.2 (0.9)

0.21 0.32 -0.94 0.33

(0.03) (0.03) (0.07) (0.03)

0.30 (0.03) -0.36 (0.04) 0.25 (0.03)

0.38 0.04 0.18 0.33 0.39 0.33 0.32

(0.06) (0.05) (0.04) (0.03) (0.04) (0.04) (0.04)

-0.04 (0.05) 0.08 (0.06) -0.07 (0.05)

-0.06 0.15 0.03 -0.02 -0.09 -0.02 -0.08

(0.07) (0.08) (0.05) (0.04) (0.05) (0.06) (0.05)

-

1.4”’I iJ 5

E2 E2/Ml E2

E2 E2 E2 E2 E2 E2 E2

Assigned

mixing reaction

levels

J. Nyberg et al. / High-spin stares

98

TABLIZ l-continued

EY

hIA0

WV) 485.4 498.4 504.2 511 515.0 520. I 536.3 550 551 567

WA0

6

Multipolarity

11.7 (0.9) 21.6 (0.9)

0.22 (0.04) 0.3 (0.1) 0.28 (0.04)

0.01 (0.05) 0.0 (0.1) -0.04 (0.05)

E2 E2 E2

60 (4) 19.8 (0.9) 26.1 (0.9) 24 (3)

0.20 0.30 0.33 0.46

0.06 (0.0s) -0.08 (0.05) 0.07 (0.05) -0.2 (0.1)

E2 E2 E2 E2

25 (2)

(0.04) (0.04) (0.04) (0.08)

0.2 (0.1) 0.29 (0.03)

22 (3) 49 (3)

0.0 (0.1) -0.03 (0.0s)

E2 E2

578 589 592 602 620.0 622 624 660 671 714 749 “) ‘) ‘) “) ‘1 ‘)

0.25 (0.05)

16 (2)

Contaminated Contaminated Contaminated Contaminated Contaminated Doublet.

by by by by by

‘“*Pt ‘WPt “‘Pt “‘Pt y-ray

is based on systematics other two band heads,

y-ray. y-ray y-ray y-ray from

-0.16 (0.07)

E2

Assigned _____I?

levels I”f

(:I)

($;I

($) (p”,

(&

ip+, (9-t (Y--, (5

(F) (F”) cP-) (3-1 (f-) 0)

($I’

(Y+, s-

&+,

&+, ‘)

cp-) (p--) (8’) ($F)

(Y-1 (?‘I (p’) (p-) ($F)

(4-) (Y) (p’)

(y-1 (Jj’}

(q-, (XJ’)

(9-j ($5’)

(W (?!‘I (9’) (B’,

(y-, (p’) (Y’, ($2’)

(target impurity), (target impurity). (target impurity). radioactive decay.

of decoupled 0 =i bands I?). The spin and parity of the namely I” = (z-) at 35 keV ( TI12 = 43 s) and I” = (t’) at

196 keV are assigned using systematics of Nilsson states in this mass region ‘I, ‘2.‘s,‘6) and are therefore given in parenthesis in fig. 1 and table 1. The multipolarity of some of the transitions observed in the y-y-coincidence experiment could not be deduced from the angular distribution measurement due to contamination of the peaks in the singles y-ray spectrum or due to insufficient statistical accuracy. This applies especially to the highest lying transitions, where the I” values were not measured, but inferred from the continued rotational band structure. It should be mentioned that the (160, 3n) reaction, used to populate ‘*% in the angular distribution experiment, had a strong competition from the 4n channel, thus making the analysis more difficult.

J. Nyberg

The large negative bands

2 and

transitions concluded

mixing

3 and bands

et al. / High-spin

ratios obtained 4 and

states

99

for several of the transitions

5, show that they probably

connecting

are Ml/E2

mixed

(and not El/M2 which would lead to long lifetimes). It can thus be that band 2 has the same parity as band 3 and that band 4 has the same

parity as band 5. From recent studies

“,‘2) of the radioactive decay of isotope-separated “‘Au, many new excited states in IR3Pt were found. Some of these, namely the ones at E = 35, 96, 150, 196 and 243 keV, coincide with states observed in this work. The multipolarity of the transitions connecting these states with the band heads and the deduced I” values of the states agree well with our findings except in one case. In ref. I’), it was found that the 115 keV transition decaying to the isomeric I” = (?) state was an E2 transition. We also observe such a transition but with a multipolarity consistent with a stretched dipole. In our measurement the 115 keV transition nicely connects the two lowest lying states in bands 2 and 3. The 121 keV transition, connecting the (y’) and (4”) states, is very weak in our measurement. It seems that most of the decay proceeds via the 73 and 48 keV transitions. The 48 keV transition was not observed in this work, but it was reported in the work of Roussiere I’). In the “prompt” yy-coincidence experiment the 161 keV transition de-populating the (f’) state was barely observed. This is possible if the (g+) state has a long life-time. This was pointed out already by Macias-Marques et al. ‘I), who claimed that the 161 keV line was strongly attenuated in the coincidence data and that it probably was connected with a state having a long half-life ( T,,2~ 50 ns). Our measurement of delayed y-y-coincidences showed that there is a delayed 161 keV line and that it must depopulate a state with a much longer half-life than 150 ns (which was the overlap coincidence time in our experiment). As a comparison it should be mentioned that the corresponding :’ to ;- transition with an energy of 108 keV in “‘OS has a half-life of 316 ns [ref. I’)]. No other delayed transitions, were observed in the experiment. which could be connected to ‘?t, In the work on radioactive decay of IX3Au the signature partner of band 1 was also observed “*‘2). In this experiment such a band was not populated. The branching ratios for the AZ = 2 and AZ = 1 transitions in the strongly coupled bands could not be extracted with sufficient statistical accuracy in this work. Generally the Al = 2 transitions are much stronger than the AZ = 1 transitions except at the very bottom of the bands where they are of comparable strength.

4. Discussion 4.1. QUASIPARTICLE

PROPERTIES

Neutron single-particle energies tion p2 in fig. 3. The single-particle

are shown as a function energies were calculated

of quadrupole deformausing the Woods-Saxon

100 -7.0 : -7.5

\

-

!Y+ -8.0 i\

/j ?\

\ \

‘,P”f/

1. \

,

‘I

/

/

‘1’

I/

z’\

\

/i’

\

3

Fig. 3. Neutron single-particle levels calculated with the Woods-Saxon potential for N = 106. The hexadecapole deformation /3? was set to zero in this calculation. Some of the levels are labelled with the asymptotic quantum numbers Q”[Nn, I]. They correspond to the largest component of the wave function expanded in the Nilsson basis states at I& = 0.24.

potential with “universal” parameters “) appropriate for neutron number N = 106. The levels lying close to the Fermi surface for N = 106 at a prolate deformation of &=0.20-0.25 are, using the Nilsson notations, I’ [624] and z-‘[633] with positive parity and <- [503], $-[514], $-[512] and i- [521] with negative parity. All these band heads have been identified 1’,1_7)in lxzPt and they agree nicely with the systematics of band-head energies in this mass region assuming a prolate deformation of the nucleus. In lXiPt the ground state has been labelled as ?[521] and the isomeric state In the present study rotational bands at the excitation energy 35 keV as ?[514]. built on the j-(521] (band l), z .[514] (bands 2,3) and !.‘[624] (bands 4,.5) singleparticle levels have been observed (see fig. 1). The two signatures of the k[521] band should have a large signature splitting which may explain why the unfavoured signature

was not observed

in the experiment.

No states corresponding

to oblate

shapes have been identified in IX’Pt, neither at low “) nor at higher spins. In order to compare the experimental results to the calculations described below the experimental quantities must be expressed in the rotating frame of reference. The standard plot of quasiparticle angular momentum and energy in the rotating frame versus rotational frequency are shown in fig. 4. Each of these quantities is extracted from measured spins, level energies and transition energies as discussed by Bengtsson and Frauendorf I”). The calculated angular momentum and energy of the rotating non-excited core are subtracted using the values of the reference parameters J,,, J, and A,,, given in the figure caption. The choice of the reference parameters is difficult in this transitional region, where the nuclei are relatively soft against changes in deformation as a function of rotational frequency and quasipartitle configuration. The mean values of J1, and J, which gave a fairly constant

J. Nyberg

et al. / High-spin

rfates

101

hw(MeV)

hw(MeV)

Fig. 4. (a) Aligned angular momentum, i, and (b) routhian, e’, for the rotational bands observed in “‘Pt. The reference parameters were J,, = 22Sh’ MeV-I, J, = 120h” MeV-’ and _tcIc= 1.05 MeV. The K-values used were K =$ for band I (open squares), K =i for bands 2 (filled triangles) and 3 (open triangles) and K =z for bands 4 (open circles) and 5 (filled circles).

alignment above the crossing in the ground bands of “‘Pt [refs. “,‘“)I and Ix4Pt were [ref. ‘)I were chosen as reference parameters for Ix3Pt. The same parameters used for all rotational bands, and their numerical values are given in fig. 4.

4.2. EXPERIMENTAL

BAND

Examining fig. 4a, angular momentum experiment. Band I, interpreted a very small initial 0.23 MeV with a total

CROSSINGS

AND

QUASIPARTICLE

one can see that all bands over the whole frequency

ALIGNMENTS

show an increase in the aligned range that was covered in the

as the cy = t-4 signature of the 4~[521] band structure, shows alignment but experiences a pronounced upbend at Prw = alignment gain of about 9h. This number is somewhat uncertain

since the crossing is not completed at the last observed transition. Bands 2 and 3, interpreted as the two signatures of the ?[514] band structure, show almost identical behaviours up to hw ;= 0.28-0.29 MeV, where the LY= -4 branch seems to experience an additional band crossing (or another kind of interaction). The alignment gain with frequency in this structure is not as sharp as in band 1 and the alignment frequency is shifted upwards to about 0.27 MeV. The total alignment gain is estimated to be of the same order as that of band 1, although the highest lying transitions needed to deduce this figure are lacking. Bands 4 arzd 5, interpreted as the two signatures of the f+[624] structure, emanating from the vililz subshell, show a rather large initial alignment (i -3h) due to the i ,3,7 neutron. Also, these bands experience an alignment at hw ^- 0.26-0.27 MeV but with a smaller alignment gain (-5-6h) than the other bands. The onset of an additional alignment might also be imagined at the highest frequencies in the (Y= +$ branch. One interesting feature here is the crossing of the alignment curves of the

102

J. Nyberg

et al. / High-spin

states

two signatures at hw = 0.27 MeV as seen in fig. 4a. This might be an indication of different shape driving effects of the quasiparticles in the two signatures of the i,3,2 band structure and is the subject of a further discussion below. The reason for the alignment increases in lg3Pt is not obvious from fig. 4a. The high-j orbitals in this mass region that are the best candidates for alignment processes are i,3,Z neutrons and h 9,2 (and perhaps i,3,2) protons. The vi,,lz alignment should occur below ho = 0.3 MeV in the vicinity of ‘83Pt. A suggestion of an additional band crossing (rrh& at low frequency has been made for fX5A~,0s[ref. “)I, ‘s6Au,07 and ‘8XA~,09[ref. ““)I and for ‘8sPt,07 [ref. “I)]. However, as discussed by Carpenter et al. ‘), the dependence of the crossing frequency on the particular shape parameters of the nucleus in a given excitation makes it dithcult to extrapolate the proposed trend to 183Pt,0s. Detailed calculations of the influence of rotation on the nuclear shape have been undertaken as described below in order to obtain a better interpretation of the observed structure of ‘83Pt. The experimental quasiparticle routhians, e’(w), given in fig. 4b, also show some interesting features. Bands 2 and 3 have no signature splitting while bands 4 and 5 have a large one, with Al?(w)

= e’(w, a = -$--e’(w,a

= +$)

(1)

being as large as 120 keV at ztw =0.25 MeV and decreasing slightly at the highest observed frequency. For an axially symmetric nucleus with y =O’, the signature splitting should be almost zero for bands built on a large-0 orbital like ;+[624]. For non-axial nuclei this may be altered as discussed below.

4.3. TOTAL

ROUTHIAN

SURFACE

CALCULATIONS

In order to investigate the influence of rotation on the shape of the nucleus, deformation self-consistent Strutinsky-Bogolyubov cranking calculations were performed using a non-axial Woods-Saxon potential with parameters given in ref. I’). Average pairing effects were included as the BCS pairing for the vacuum state at ho = 0 MeV, A,, coupled with a phenomenological approximation for the pairing gap at non-zero rotational frequencies. This approximation takes the form

where w,==O.40 (0.50) for even(odd)-N and w,=OSO (0.60) for even(odd)-2. For odd-N and odd-2 the value of A, was reduced to 87.5% of its initial value in order to simulate pair blocking brought about by the odd particle. The deformation space covered p2 cos (y + 30”) from 0.05 to 0.40, p2 sin (y + 30”) from -0.20 to 0.30 and

J. Nyberg er al. / High-spin states p4

from -0.08

varied

to 0.00 around

the liquid

drop value.

from 0.0 to 0.9 MeV. More complete

found in ref. 22). The total routhian

of a nucleus

103

The rotational

calculations

frequency

in this mass region

(2, N) of fixed many-quasiparticle

was can be

configuration

v is given by E’(w, b, N, Z, v) = &,,(w

= 0, b, N, Z v)

+~(~~l~“I~W)~,N,Z,“-(~Wl~WI~W)~,=Nr)L.v~ and the angular

momentum

projection

on the rotational

3

(3)

axis by

Ix(w, L%N, Z, v) = (‘J+ IJx IWp^,~,z,v.

(4)

For the construction of total routhian surfaces (TRS), i.e. a potential energy surface in the (&, y)-plane, the energy in eq. (3) is minimized with respect to the deformation parameter p4. The first term on the right hand side of this equation represents the Strutinsky energy at hw = 0 MeV while the second term represents the energy gain due to collective rotation and quasiparticle alignment. In the discussions presented below the configurations are sometimes labelled by the spherical shell model quantum numbers or by the Nilsson quantum numbers. It should be pointed out that these quantum numbers only are valid at zero rotational frequency for spherical and axially symmetric shapes, respectively. The only good quantum numbers for the wave function in eqs. (3) and (4) are the parity and the signature quantum numbers (r, CX).In some cases it is nevertheless convenient to refer to a rotational band by the spherical or Nilsson labels.

4.4. INTERPRETATION

Bands dominant

OF

EXPERIMENTAL

RESULTS

built on three different Nilsson configurations have been observed. features of these bands are apparent in the plots of fig. 4:

The

(i) All five rotational sequences have a band crossing in the range of 0.23 < hw < 0.27 MeV. (ii) The exact nature of the crossing in the two signatures of the vi,3,2 band is different. The crossing occurs more sharply in the unfavoured signature, (7~, (Y)= (+, -$), giving it temporarily more aligned angular momentum than the favored signature, ( + , + i). (iii) The vi,,,2 structure has a large energy splitting between the two signatures, the vh,,, structure has none. The alignment features of the five observed bands are indeed curious, since a naive interpretation would be that all bands have the same rotational alignment process taking place. An i,3,2 neutron alignment, however, would be blocked in the vi,3,2 bands 4 and 5, while an h,,, proton crossing should be observed in all bands,

104

J. Nyherg et af./ ~igh-spifl ~tatcs

assuming

similar

shape

parameters.

tions are used in this section atic, and also to address 4.41.

TRS and cranked

to provide

signature

explanations

splitting

~a~~u~uie~ shape ~ffra~ete~.~. Total

the four lowest lying one-quasiparticle combination.

The variation

shell model

(CSM)

calcula-

for this band crossing

system-

differences

between

the observed

routhian

surfaces

were calculated

configurations

of the shape

parameters

bands. for

of each parity

and signature

as a function

of rotational

frequency is listed in table 2 for the first (i.e. the ones that are lowest in energy) (+, +f), (+, -i), (--, +i) and (-, -I) configurations. As an example of the calculations, some surfaces for the lowest (+, +1) configuration are also shown in fig. 5. As can be seen in table 2 there are three rather well localized minima for all four configurations. The first one is a minimum around /3? = 0.20-0.25 and y = 0” to -15”. This minimum is yrast in the spin range up to 30-35h and it is believed to be responsible for all the observed rotational bands in the present study. Different properties of this minimum will be discussed below. The second minimum has a deformation around & = 0.12-0.15, y = -7.5” to -9O”, i.e. the nucleus has a very small quadrupole deformation to the non-collective axis at y = -120”. This minimum

and a triaxial shape close is yrast in the spin range

30-55h for the The +5”. It

for the configurations (+, +i), (+, -i) and (-, +k) and in the range 40-5511 (-, -iI configuration. third minimum has a large deformation with &=0.36-0.41 and y=O” to is yrast above spin %A, except for the (-, -iI configuration, where it is yrast in the spin range 30-4Oti. The (-, - !J configuration consists of one j,,!, neutron and two iI?,: protons and its structure is very similar to that found in the well deformed minima in the A = 130 mass region “). There the important high-j orbits are ui,3,2 and ~h,li-7 (i.e. they have orbital angular momenta which are one unit smaller). No indications of the second and third type of minimum have been observed in this experiment and they will therefore not be discussed further. Let us now discuss the structure of the first type of minimum in some detail. The two lowest lying positive-parity configurations of opposite signature correspond to the :‘[624] Nilsson orbital. In these configurations, the nucleus is initially axially symmetric, but develops a triaxial shape with y < 0 as the rotational frequency increases (see fig. 5 and table 2). This is logical since the Fermi surface lies at the K = 5 level of the i ,3,2 subshell, which results in a drive of the deformation of the nucleus to negative values of y. It is apparent from table 2 that, below the first crossing (which corresponds to an alignment of neutrons at &w = 0.25 MeV), the lowest vi ,3,?. orbital [(+, i-i), commonly called A] drives the nucleus not only to larger negative y-vralues but also to smailer values of &. In comparison, the other signature of the vi,3,2 structure [(+, -i), called B] has less shape driving tendency, especially in y. At )Iw = 0.21 MeV, y has a value of -15” for configuration A, but -8” for B. It is perhaps logical that the crossings observed in these two bands would

J. Nyherg

et al. / High-spin

.states

105

TABLE 2 Calculated equilibrium deformation (p?, r,P4) for the four lowest lying configurations in “‘Pt as a function of rotational frequency hw. Also listed in the table are the total routhian E’, the total energy E = E’+ WI,, the angular momentum projection on the rotational axis for neutrons (I,,,), protons (!,,,) and their sum (I, = I,,+ r,,,). In the rightmost column the number and type of high,j particles involved in the contiguration is indicated in some cases (the low- and medium-j particles are not shown) hw

(MeV) (i)

(ii)

Cmjiguration:

PA

Y

”

(

TT,

a) = (+,

+

f),

E’

(MeV)

E

I

I

( MeV)

(G

G”,

also called A

0.050 0.090 0.130 0.170 0.210 0.250 0.289 0.329 0.369 0.409 0.449 0.489 0.529 0.569

0.231 0.225 0.215 0.213 0.215 0.211 0.202 0.197 0.197 0.204 0.209 0.21 I 0.208 0.207

-0.3 -3.3 -9.8 -12.5 -13.7 -14.9 -15.7 -15.5 -15.4 -13.8 -11.8 -12.4 -13.8 -13.4

-0.025 -0.025 -0.029 -0.030 -0.032 -0.035 -0.039 -0.041 -0.042 -0.041 -0.041 -0.042 -0.041 -0.038

~ 1.96 -2.15 -2.42 -2.77 -3.19 -3.75 -4.55 -5.50 -6.53 -7.70 -9.06 ~ 10.62 -12.30 - 14.08

-1.78 - 1.64 -1.38 -1.09 -0.67 0.36 1.65 2.27 3.03 4.44 6.19 7.64 9.08 11.10

3.4 5.0 7.1 8.7 10.5 14.6 19.2 21.0 22.4 23.9 25.3 26.9 28.5 29.8

0.3 0.6 0.9 1.2 1.6 1.9 2.2 2.6 3.4 5.8 8.6 10.4 12.0 14.5

3.7 5.6 8.0 9.9 12.1 16.5 21.4 23.6 25.9 29.7 34.0 37.3 40.4 44.3

0.289 0.329 0.369 0.409 0.449 0.489 0.529 0.569 0.609 0.649 0.689 0.729

0.146 0.141 0.135 0.131 0.129 0.129 0.130 0.131 0.130 0.130 0.126 0.120

-75.1 -75.6 -81.1 -90.8 -91.2 -91.3 -91.3 -91.4 -91.6 -90.8 -89.8 -90.9

-0.007 -0.005 0.001 0.002 0.002 0.002 0.002 0.002 0.003 0.001 -0.001 -0.001

-3.40 -4.97 -6.63 -8.73 -10.94 - 13.07 -15.14 -17.16 -19.15 -21.13 -23.19 -25.28

6.41 6.77 8.89 10.84 10.65 10.39 10.30 10.32 10.45 10.97 12.22 12.86

23.9 25.2 31.5 37.0 37.0 36.7 36.6 36.7 36.9 37.5 39.8 40.6

10.0 10.5 10.5 10.8 11.0 11.3 11.5 11.6 11.7 12.0 11.6 11.8

33.9 35.7 42.0 47.8 48.1 48.0 48. I 48.3 48.6 49.5 51.4 52.3

0.329 0.369 0.409 0.449 0.489 0.529 0.569 0.609 0.649 0.689 0.729

0.366 0.400 0.406 0.406 0.403 0.398 0.391 0.382 0.378 0.373 0.367

0.010 0.020 0.02 I 0.021 0.020 0.020 0.019 0.018 0.017 0.017 0.016

-3.89 -5.48 -7.52 -9.71 - 12.05 - 14.53 -17.13 -19.91 -22.84 -25.93 -29.21

6.05 9.80 12.00 13.72 15.65 17.85 20.06 22.70 25.28 28.17 3 1.55

15.2 24.3 29.0 31.9 34.8 37.7 40.2 42.6 44.7 46.7 48.6

14.9 17.1 18.7 20.3 21.8 23.5 25.2 27.4 29.4 3 I .9 34.8

30.2 41.4 47.7 52.1 56.6 61.2 65.4 70.0 74.2 78.5 83.4

-$I.

also called B

-1.78 -1.65 -1.48 ~ 1.24

3.4 5.0 6.2 7.4

0.3 0.6 0.9 1.2

3.7 5.5 7.1 8.6

Co~jiguration: 0.050

0.090 0.130 0.170

0.23 1 0.227 0.224 0.222

2.2 1.2 1.o 1.1 1.4 1.9 2.6 3.7 4.0 4.4 4.8 (T-T,a) = (+,

-0.2 -1.8 -4.1 -6.2

-0.025 -0.025 -0.026 -0.026

-1.96 -2.15 -2.40 -2.71

(i~ill,2)’

( vi I2J

(vj,,,z)‘,

(7ri,,,z)z

(~i,2,2)i

106

J. Nyberg

et al. / High-spin

TABLE hw (MeV)

”

’

0.210

0.222

-8.1

0.250

0.223

-9.7

0.289

0.209

0.329

A

states

2-continued

E’

E

I,,

I

(fi)

(G

(MeV)

(MeV)

-0.027

-3.08

-0.93

8.7

1.6

10.3

-0.028

-3.53

-0.54

9.9

2.1

12.0

-13.1

-0.035

-4.12

1.32

16.5

2.3

18.8

0.193

-14.8

-5.01

2.44

20.0

2.6

22.6

0.369

0.194

-14.6

-0.040 -0.041

-5.99

3.16

21.4

3.4

24.8

0.409

0.201

-13.0

-0.041

-7.12

4.60

22.9

5.7

28.6

0.449

0.207

-10.5

-0.041

-8.45

6.33

24.4

8.6

32.9

0.489

0.209

-11.5

-0.042

-9.96

7.70

25.9

10.2

36.1

0.529

0.206

-13.6

-0.041

-11.60

9.22

27.3

12.0

39.4

0.569

0.205

-13.9

-0.037

-13.34

11.06

29.0

13.9

42.9

0.289

0.144

-85.7

-0.014

-3.40

6.31

22.6

10.9

33.5

0.329

0.141

-83.3

-0.010

-4.94

5.84

22.3

10.4

32.7

0.409 0.449

0.134 0.125

-89.0

0.489

0.126

-88.9

0.000

0.529

0.127

-89.0

0.001

0.569

0.128

-89.3

0.001

-89.9

0.000 -0.001

-8.25

9.94

33.6

10.8

44.4

-10.34

10.69

35.8

11.1

46.8

-12.41

10.67

35.9

11.3

47.2

-14.43

10.64

35.9

11.5

47.4

-16.41

10.73

36.0

11.7

47.7

0.609

0.128

-89.1

-18.36

10.84

36.2

11.8

48.0

0.649

0.126

-88.0

-0.002

-20.34

11.63

37.2

12.1

49.3

0.689

0.122

-88.2

-0.004

-22.42

12.84

39.6

11.6

51.2

0.729

0.117

-89.5

-0.004

-24.49

13.46

40.4

11.7

52.1

0.329

0.361

2.2

0.006

-3.98

5.63

14.3

14.8

29.2

0.369

0.388

1.6

0.016

-5.52

8.88

22.1

16.8

39.0

0.409

0.403

1.3

0.021

-7.51

11.77

28.5

18.6

0.449

0.405

1.2

0.021

-9.69

13.66

31.8

20.2

47.1 52.0

0.489

0.401

1.5

0.021

-12.04

15.60

34.7

21.8

56.5

0.529

0.397

2.2

0.020

-14.51

17.71

37.5

23.4

60.9

0.001

0.569

0.392

2.8

0.019

-17.10

19.77

39.6

25.2

64.8

0.609

0.385

3.8

0.019

-19.83

22.14

41.5

27.4

68.9

0.649

0.382

4.2

0.018

-22.71

24.52

43.4

29.4

72.8

0.689 0.729

0.378 0.372

4.7

0.018 0.017

-25.74

27.31

45.2

31.8

77.0

-28.95

30.58

47.1

34.6

81.7

(iii)

Configuration:

5.3

CT,ff) = (-, -t,.

(vi&

(uj,,,,)‘,

(CJ

also called E

0.050

0.240

-0.2

-0.023

-1.99

-1.91

1.3

0.3

1.6

0.090

0.241

-0.4

-0.022

-2.08

-1.81

2.4

0.6

3.0

0.130

0.243

-0.8

-0.022

-2.24

-1.65

3.6

1.0

4.5

0.170

0.244

-1.3

-0.022

-2.46

-1.36

5.1

1.4

6.4

0.210

0.245

-2.3

-0.022

-2.77

-0.93

7.0

1.8

8.8

-0.024

0.250

0.240

0.20 1.73

13.7

-0.032

-3.23 -3.93

2.3

0.220

-5.3 -12.4

11.4

0.289

17.0

2.6

0.329

0.215

-13.8

-0.034

-4.79

2.42

18.7

3.2

19.5 21.9

0.369

0.180

-15.2

-0.040

-5.77

4.19

24.0

3.0

27.0

0.409

0.178

-15.4

-0.041

-7.02

5.74

27.3

3.9

31.2

0.449

0.202

-12.1

-0.042

-8.44

7.66

27.8

8.0

35.9

0.489

0.206

-12.7

-0.044

-10.06

8.84

28.5

10.1

38.6

0.529

0.202

- 14.4

-0.042

-11.79

10.41

29.6

12.4

42.0

0.569

0.201

-13.7

-0.038

-13.61

11.57

31.2

13.1

44.3

(4/d’

(uf,,A’,

(%J

107

J. Nyberg et al./ High-spin states

TABLE 2-continued E'

E

(MeV)

(MeV)

0.329

0.137

-83.6

-0.003

-5.08

8.16

29.8

10.4

40.2

0.369

0.135

-83.2

-0.002

-6.94

8.44

31.2

10.4

41.6

0.409

0.134

-81.7

-0.001

43.3

0.449

0.130 0.130

0.000 0.003

-10.90

0.489

-83.1 -83.9

0.529

0.131

-84.2

0.569

0.131

-84.6

0.609

0.130

8.87

32.5

10.9

9.45

34.2

11.1

45.3

-12.99

9.97

35.6

11.3

46.9

0.004

-15.10

10.37

36.6

11.5

48.1

0.003

-17.18

10.79

37.5

11.7

49.2

-84.9

0.004

-19.27

11.27

38.3

11.9

50.2

-8.86

/

0.649

0.129

-85.1

0.004

-21.37

11.79

39.0

12.1

51.1

0.689

0.128

-85.2

0.003

-23.50

11.68

39.6

11.5

51.1

0.729

0.128

-85.7

0.004

-25.59

11.96

40.1

11.5

51.5

0.210

0.400

0.2

0.02 1

-1.60

2.31

13.9

4.7

18.7

0.250

0.399

0.021

-2.43

0.020

-3.47

18.8

6.2 11.3

22.2

0.389

3.12 5.24

16.0

0.289

0.3 1.6

0.329

0.388

2.2

0.019

-4.98

7.01

20.9

15.5

0.369

0.392

2.1

0.019

-6.62

8.15

23.1

16.9

36.4 40.0

0.409

0.393

2.0

0.019

-8.46

9.44

25.3

18.5

43.7

0.449

0.392

2.2

0.019

-10.45

10.91

27.5

20.1

47.6

0.489

0.391

2.2

0.019

-12.59

12.46

29.5

21.7

51.2

0.529

0.385

3.0

0.017

-14.84

14.73

32.5

23.4

55.9

0.569

0.383

3.7

0.016

-17.23

16.99

34.8

25.3

60.2

0.609

0.385

3.7

0.017

-19.78

20.27

38.4

27.4

65.8

0.649

0.40 1

3.1

0.019

-22.55

23.51

41.8

29.2

71.0

0.689

0.409

2.9

0.019

-25.49

26.20

43.7

31.3

75.1

0.729

0.408

3.7

0.022

-28.70

30.52

47.9

33.4

81.3

($A’

30.1 (G,,,,)‘,

(+,,,z)2

(iv) Conjguration: (rr,m)= (-,+$), also calledF 0.050

0.240

-0.2

-0.023

0.090

0.241

-0.4

-0.022

-1.99 -2.09

-1.91

1.3

0.3

1.6

-1.82

2.4

0.6

3.0

0.130

0.243

-0.8

-0.022

-2.24

-1.65

3.6

1.0

4.5

0.170

0.244

-1.3

-0.022

-2.46

-1.37

5.1

1.4

6.4

-0.93

0.210

0.245

-2.4

-0.022

-2.77

0250

0.233

-9.5

-0.026

-3.24

7.0

1.8

8.8

0.56

12.9

2.3

15.2

0.289

0.217

-16.0

-0.032

-3.99

1.89

17.8

2.5

0.329

0.212

-17.9

-0.034

-4.87

2.46

19.2

3.0

20.3 22.3

0.369

0.174

-24.1

-0.035

-5.88

4.70

25.6

3.1

28.7

0.489

0.207

-16.2

-0.037

-10.08

9.30

29.1

10.5

39.6

0.529

0.203

-17.4

-0.037

-11.82

10.96

30.6

12.5

43.1

0.289

0.152

-76.4

-0.013

-3.46

4.13

16.2

10.0

26.2

0.329

0.149

-69.4

7.18

26.3

10.3

36.6

0.369

0.151

-68.4

-0.001

-4.86 -6.44

8.30

29.1

10.8

39.9

0.409

0.138

-78.1

-0.003

-8.30

9.36

32.3

10.9

43.1

0.449

0.129

-86.9

-0.002

-10.40

11.11

36.8

11.1

47.9

0.489

0.126

-90.4

-0.001

-12.65

11.87

38.9

11.3

50.1

0.529

0.125

-91.5

-0.001

-14.89

11.90

39.1

11.5

50.6

0.569

0.125

-92.4

-0.001

-17.07

11.90

39.2

11.7

50.9

0.609

0.124

-93.1

-0.001

-19.21

11.89

39.3

11.8

51.1

0.649

0.122

-93.6

-21.35

12.08

39.5

12.0

51.5

0.001

0.000

(4/Z)’

(+J,

(&J

108

.i. Nvberg et al. / ~j~~-.~~jn states TABLE 2-continued

0.689

0.120

-94.5

0.001

-23.49

12.26

39.9

12.0

51.9

0.729

0.117

-98.0

0.002

-25.59

12.93

40.1

12.8

52.9

0.329

0.370

2.0

0.018

-4.03

6.27

16.3

15.0

31.3

8.35 11.99

20.7

16.8

28.7

18.7

37.6 47.4 52.4

0.369

0.387

1.8

0.019

-5.52

0.409

0.407

1.9

0.021

-7.41

0.449

0.411

1.8

0.022

-9.60

13.93

32.1

20.3

0.489

0.408

2.5

0.021

-11.95

15.80

34.8

21.9

56.7

0.529

0.404

3.2

0.020

-14.44

17.73

37.2

23.6

60.8

0.569

0.402

3.9

0.019

-17.04

19.76

39.3

25.3

64.7

0.609

0.402

4.4

0.018

-19.76

21.94

41.1

27.4

68.5

0.649

0.402

4.6

0.019

-22.61

24.16

42.8

29.3

72.1

0.689

0.402

4.8

0.019

-25.59

26.66

44.4

31.5

75.9

0.729

0.399

4.7

0.018

-28.72

24.45

46.1

33.7

79.8

, (vjj1s,2J',tS,312)L

be somewhat different in their detailed nature [see point (ii) listed above], since the shapes are not exactly the same according to the calculations. In the TRS calculation, the two lowest lying configurations of negative parity and opposite signature correspond to rotational bands built on the I-[5141 Nilsson orbital, originating from the spherical hV12subshell. They are identified with bands 2 and 3 observed in the experiment (see fig. 1). The shape parameters for these negative parity bands are rather different from those for the positive parity bands (see table 2). At ho = 0.21 MeV, the two signatures have very similar deformations, & = 0.25 and y = -2”. The Vh,/, orbital influences the nuclear shape much less than the vi ,3,1 orbital because of its smaller j-value. The 4-15211 configuration, originating from the p3/? subshell and corresponding to band 1 in the experiment (fig. l), lies higher up in energy in the TRS calculation. It can be found as the third negative-parity configuration and it is easily identified at low rotational frequencies because of its large signature splitting. The shape parameters for this configuration are not included in table 2 but they are rather similar to the lowest lying negative-parity configuration. To get aid in the understanding of the involved configurations, cranked shell model calculations were performed with two sets of deformation parameters, namely (& = 0.25, p4 = -0.02, y = -2”) and (p7 = 0.22, p4 = -0.03, y = -12”). These parameters represent the shapes of the lowest negative and positive parity configurations, respectively, at a frequency around tao = 0.21 MeV, just before the first crossing. The CSM calculations were performed with the same treatment of the pairing correlations as in the TRS calculations. The CSM diagrams for quasineutrons and quasiprotons are shown in figs. 6 and 7, respectively. 4.4.2. Crossings. As mentioned above in (i), the band crossings in all of the observed bands occur at similar frequencies, 0.23 < hw < 0.27. The angular momenta

109

0.30 0"

0.20

Y

0.10

0.00

-0.10

-60° *x11*

-0.10

0.10

0.20

0.30

040

x =& cm fy c 3oq Fig. 5. Total routhian surfaces calculated for the lowest lying fr, cu) = (i-, +:) configuration in “‘Pt at fiw = 0.05, 0.21, 0.33 and 0.45 MeV. The contour lines are separated by 0.1 MeV, and the local minima are marked with black dots. See table 2 for more detailed information about the equilibrium deformations.

J. Nyberg et al. / High-spin states

110

0.0

0.1

0.2

0.3

0.4

0.5

hw (MeV) Fig. 6. Quasineutron routhians, e’, calculated for N = 105 using the deformation parameters (a) pa = 0.25, p4= -0.02, y= -2”(upperdiagram) and(b) & =0.22,p4= -0.03, y = -12”(lowerdiagram).Thedifferent lines correspond to different quantum numbers (n, a) as follows: solid line (+, +4), dotted line (+, -f), dash-dotted line (-, +f) and dashed line (-, -4). The highly alignable arbitals with positive parity originate from the i,,,* sub-shell. Details of the calculations are given in the text.

of the four configurations are ‘listed in table 2 for each frequency so that the occurrence of band crossings in the calculations can be noted. Considering the frequency progression for band (+, + 4) in table 2, one can see that a crossing takes place soon after liw = 0.21 MeV. This is evidenced by a decline in &. and an increase in I,. The alignment of neutrons is clearly responsible for this crossing, as the proton contribution to the angular momentum is small and constant in this frequency range. The biggest increase in calculated I,, (4.6A) occurs between Fzw= 0.25 and 0.29 MeV for (i-, i-i). This is clearly the vi,3,2 (BC) crossing occurring in band A. The first crossing in the signature partner (-I-, - $) occurs at the same frequency but is sharper both in gain of f,, (6.kh) and in drop in &. This is the vi,3,2 (AD) crossing in band B. The difference in these crossing features is clearly seen in experiment: the crossing in B is sharper than that in A (see fig. 4a). The correct detail of the calculations is rather surprising.

.I. Nyberg et al. / ~igb-s~~n

states

Fig. 7. Same as in fig. 6 but for protons at Z = 78. The highly originate from the h9,z sub-shelf and those of positive-parity

The fact that the crossings

occur at roughly

111

aiignable orbit& with negative parity originate from the i,,,z sub-shell.

the same frequencies

in bands

2,3,4

and 5 can also be observed in the TRS calculations. Looking at the entries for the negative parity bands in table 2, one can see a crossing occurring in both signatures at the same place as for the positive-parity bands, namely between Frw = 0.21 and 0.29 MeV. Once again, the rise in angular momentum occurs in the neutron system (AB) crossing. This is a curious phenomenon - the (table 2), and must be the ~~~~~~ primary (AB) and the blocked (BC and AD) crossings occur at approximately same rotational frequencies, both in the data and in the theory. The experimentally measured crossing in band 1 appears at a slightly smaller rotational frequency than in bands 3 and 4 (hw = 0.23 MeV compared to ~0.26 MeV). The AB crossing is responsible for the quasiparticle alignment also in band 1. This difference in crossing frequency is not fully reproduced in the TRS calculation, where the AB crossing appears at roughly the same frequency as in the lowest lying negative parity configuration. The reason for this discrepancy may be due to differences in the pairing correlations in the involved configurations. As explained

112

J. Nvherg

above the pairing calculation. could

correlations

A fully

negative-parity

are treated

self-consistent

show if pairing

et al. / Hi&pin

is responsible

states

in a phenomenologicai

calculation,

with

for the different

way in the present

particle-number crossing

in the

bands.

It is clear that small & and negative

y-values

lower the vi,X/z crossing

both AB and BC. Thus, the (+, +$) band in “‘Pt has the AB crossing a predicted

projection,

frequencies

frequencies, blocked

and

BC crossing

at &w = 0.29 MeV. The deformation parameters for the negative-parity bands lead to higher vi ,3!_1crossing frequencies and an AB alignment at 0.25 MeV, The VI,~,~ crossings in the positive- and negative-parity bands in lxiPt (the former blocked, the latter unblocked) will therefore occur at similar frequencies due to the shape differences of the vi 1.1,2and Yhyi2 bands. This is also illustrated in the quasineutron Routhians shown in fig. 6. The experimental observation is thus verified in this case. The CSM quasiproton calculations for the two shapes are given in fig. 7. It is clear that the lowest proton crossing results from the alignment of a &?g12 pair and is high in frequency (hw = 0.45 MeV) for y = -12”, and lower (~0.38 MeV) for y = -2”. In both cases, however, the 7rhsi2 crossing is calculated to be beyond the range of detection in our measurements. A low-frequency hg,? proton crossing has been proposed to occur in lxsPt [ref. “)J, rssAu [ref. “)I and in lXh~‘XXA~ [ref. “‘)]. Carpenter et al. ‘f have discussed the dilemma associated with the possibility having a low-frequency rhgjl crossing. The data of refs. 9*2i,70) are indicative

of of

such a crossing, based on “blocking effects ” in different bands in adjacent nuclei and on the behavior of measured Ml/E2 ratios (for ‘““Pt). However, calculations cannot place the rrhgil? crossing below ho = 0.3 MeV unless two conditions are met: y is zero or positive, and the proton pairing is signi~cantly reduced in an odd-Z nucleus I). Whife y is close to zero for the one-quasiparticle negative-parity bands (according to the TRS calcutations), it is not possible to have a reduced proton pairing in ‘“‘Pt. Consequently, a low-frequency rhyiZ crossing is unlikely in the bands observed in 18’Pt. 4.4.3. S~~~~~ure ~pi~ttj~g. Two medium-K bands are observed in “‘Pt, based on the $-[514] and 2*[624] Nilsson states. As seen in fig. 4b, there is no energy splitting between the two signatures in the former, but significant splitting in the latter. As discussed

by Frauendorf

and May I”), this energy splitting is rather dependent on the value of y, By virtue of the smallerj, the vh 9,z orbital does not drive the nucleus very much in -y, so it is logical that this structure would have a small signature splitting. After the crossing, when y is more negative a signature splitting develops in the negative parity configuration as well. The z,G,.1,7band, however, can assume significant splitting already before the crossing because of the transition to a shape with y < 0. Another impo~ant factor is the eqnil~brium hexadecapole deformation, which is large and negative having values between -0.022 and -0.040 for all the bands shown in table 2. It is well known 15) that large hexadecapole deformations may also affect the single particle the signature splitting. A large negative value of fi4 “contracts”

J. Nyberg et al. / High-spin states

levels and brings signature

the low-0

splitting

orbitals

closer to the Fermi surface.

as it is only the R =f component

produce this splitting. The calculated signature

splitting,

The negative-parity

show no signature

bands

113

This increases

of the wave function

AE’ in eq. (l), can be extracted splitting

up to hw 20.3

the

that can

from table 2. MeV while

the positive-parity bands show a sizable splitting. The signature splitting starts to develop at hw = 0.15 MeV between the positive-parity bands, it is 116 keV at hw = 0.21 MeV and increases then rapidly to about 600 keV at hw = 0.41 MeV. To check the effect of the p4 values on the signature splitting, a detailed analysis was done at hw = 0.21 MeV for the two lowest lying positive-parity configurations (A and B) varying p4 from -0.08 to 0.00. For the A configuration the equilibrium y-deformation changed from -15” to -10” with increasing p4 values. The value of /3? did not change from its equilibrium value in this case. The same behaviour was found also for the other signature, except that y was about 5” larger (more positive). Of course, the decreasing values of (~1 and Ifi41 reduced the signature splitting until it became only 30 keV for p4 = 0.00. For a fixed point in the (,!I?, y)-plane (& = 0.21 and y = -16”, i.e. close to the equilibrium deformation) the signature splitting was reduced by a factor of two when p4 was changed from its equilibrium value around -0.03 to 0.00. The calculations thus show that the negative values of y and p4 together promote a signature splitting in the positive-parity bands of Ix3Pt. The experimental value for the signature splitting in the vi,_q,2 band of “‘Pt is 87 keV at hw =0.21 MeV, which is slightly smaller than the calculated value of 116 keV at 0.21 MeV. In view of the sensitivity of this quantity to the detailed parameters used in the calculation, the agreement should be viewed as rather good. To test the TRS calculations over a wider range of nuclei, we have compared calculated and measured signature splittings in the vi,,,, band of adjacent W [refs. zx.‘y,3”)], OS [ref. 3’,32.3’)], P [ref. X,“,Zh)] and Hg [refs. ‘,‘,“)I nuclei with N = 99-107. The results are summarized in fig. 8a and 8b. The calculated equilibrium y and p4 values for the (+, +$) configuration are shown in fig. 8c and 8d, respectively, for all these nuclei.

The rotational

frequency

was kept at hw = 0.21 MeV in fig. 8,

i.e. at a value below the first crossing. Several interesting trends are apparent from the comparison of theory and experiment in fig. 8. (a) Trend with N. The TRS calculations predict a dramatic rise in AE’ for N = 105 as compared

to N = 107 for each of the four elements

considered,

and this increase

is clearly present in the data (see fig. 8a, 8b). The y-value becomes more negative for each of these N = 105 isotopes as compared to N = 107, but the effect is rather small (fig. 8~). The p4 value decreases in each case when going from N = 107 to 105 (fig. Sd), which should rather lead to a slight decrease of the splitting. It therefore seems that the observed increase in AE’ is mainly caused by other effects, like the Fermi surface coming closer to the R = f orbital for the i,,jz shell, when reducing N by two units. After the predicted steep rise in AE’ with decreasing N, the calculations yield a leveling and then rapid decline with a deep minimum at N = 101 (fig. 8b). For each

J. Nyberg et al. / High-spin states

114

h

N Fig. 8. (a) Experimental and (b) calculated energy splitting, AE’, between the two signatures, A and B, of the vi,,,, band, as a function of neutron number N at hw = 0.21 MeV for W (squares), OS (circles), Pt (diamonds) and Hg (triangles). Also shown in this figure are the calculated equilibrium deformations (c) y and (d) p4 for the signature A, i.e. (+, +f), of the vi,,,, band at hw = 0.21 MeV.

element, (toward although known).

the 0’). the The

sharp decline The data (fig. effect seems to Pt data seem

seems to be associated (fig. 8c) with a decrease in y 8a) do not show such an N = 101 minimum for W, be present in the OS data (unfortunately ‘750s99 is not parallel to those for OS, although “%,,,, has not yet

been studied. The calculations give another steep rise in AE’ between N = 101 element. This rise is associated with a return to rather negative y The only known N = 99 isotope is ‘73W, and indeed its signature largest of the W isotopes in the range considered. (b) Trend with Z. Generally the behaviour of the signature

and 99 for each values (fig. 8~). splitting is the splitting

in the

vi,3,2 bands is very similar in experiment and theory as a function of Z for constant N. For N = 107 the largest AE’ is obtained for Z = 76 and Z = 78 (they are very similar in magnitude) both in fig. 8a and in fig. 8b. For the N = 105 isotones the TRS calculation over-estimates AE’ for Z = 78, experimentally AE’ attains its largest value for Z = 76. In the case of N = 103 there is again a very good agreement between experiment and calculations - the Z = 76 isotope has the largest AE’.

5. Summary High-spin states in the transitional nucleus ‘% have been investigated for the first time. Alignment processes were observed in three different band structures built

J. Nyberg

on neutron employed

P,,~, hgIz and

i,),z orbitals.

Total

in order to study the shape evolution

configuration and rotational fully described as alignment i ,3,2 neutron the positive

et al. / High-spin

orbital.

states

routhian surface calculations were ‘83Pt as a function of quasiparticle of

frequency. The observed of pairs of i,3,2 neutrons,

The similarity

and negative-parity

in the observed

bands

115

band crossings were successalso in the case of a blocked band

were reproduced

crossing

frequencies

for

in the TRS calculations.

The reason for this similarity is a difference in the shape of the nucleus in the positive and negative parity bands, which brings the AB and BC (or AD) crossings close together in rotational frequency. A large signature splitting was observed in bands, while no splitting was observed in the vhs,z bands. The TRS the yi13,, calculations give similar results and it was found that large negative values of y and p4 together enhance the signature splitting in the vi,3,2 bands. A systematic study of measured and calculated signature splittings in the vi,3,Z bands for the W, OS, Pt and Hg isotopes with N = 99-107 has been presented. The TRS calculations reproduce the general features of the behaviour of the signature splitting very well. The authors wish to thank Drs. R. Bengtsson, W. Nazarewicz and R. Wyss for fruitful discussions and Dr. G.B. Hagemann for assisting in the experiment at the Niels Bohr Institute. This work was supported in part by the Swedish National Research Council. Research at the University of Tennessee is supported by the U.S. Department of Energy under contract DE-FG05-87ER40361. Oak Ridge National Laboratory is operated by Martin Marietta Energy Systems under contract DEAC05-840R21400 with the U.S. Department of Energy. The McMaster University Tandem Accelerator Laboratory operates under a grant from the Canadian Natural Sciences and Engineering Research Council.

References 1) R. Bengtsson, T. Bengtsson, J. Dudek, G. Leander, W. Nazarewicz and J.Y. Zhang, Phys. Lett. B183 (1987) 1 2) M.P. Carpenter, CR. Bingham, L.H. Courtney, V.P. Janzen, A.J. Larabee, Z.M. Liu, L.L. Riedinger, W. Schmitz, R. Bengtsson, T. Bengtsson, W. Nazarewicz, J.Y. Zhang, J.K. Johansson, D.G. Popescu, J.C. Waddington, C. Baktash, M.L. Halbert, N.R. Johnson, I.Y. Lee, Y. Schutz, J. Nyberg, A. Johnson, J. Dubuc, G. Kajrys, S. Monaro, S. Pilotte, K. Honkanen, D.G. Sarantites and D.R. Haenni, Nucl. Phys. A, accepted for publication 3) G. Hebbinghaus, W. Gast, A. Kramer-Flecken, R.M. Lieder, J. Skalski and W. Urban, Z. Phys. A328 (1987) 387 4) W.C. Ma, A.V. Ramayya, J.H. Hamilton, S.J. Robinson, J.D. Cole, E.F. Zganjar, E.H. Spejewski, R. Bengtsson, W. Nazarewicz and J.Y. Zhang, Phys. Lett. Bl67 (1986) 277 5) R.V.F. Janssens, P. Chowdhury, H. Emling, D. Frekers, T.L. Khoo, W. Kuhn, Y.H. Chung, P.J. Daley, Z.W. Grabowski, M. Kortelahti, S. Frauendorf and J.Y. Zhang, Phys. Lett. B131 (1983) 35 6) F. Hannachi, G. Bastin, M.G. Porquet, C. Schiick, J.P. Thibaud, C. Bourgeois, L. Hildingsson, D. Jerrestam, N. Perrin, H. Sergolle, F.A. Beck, T. Byrski and J.C. Merdinger, Z. Phys. A325 (1986) 371 7) F. Hannachi, G. Bastin, M.G. Porquet, C. Schiick, J.P. Thibaud, C. Bourgeois, L. Hildingsson, D. Jerrestam, N. Perrin, H. Sergolle, F.A. Beck, T. Byrski, J.C. Merdinger and J. Dudek, Nucl. Phys. A481 (1988) 135

116

J. .A(vberg el a!. / High-spin

slates

8) S. Pilotte, G. Kajrys, S. Monaro, M.P. Carpenter, V.P. Janzen, L.L. Riedinger, J.K. Johansson, D.C. Popescu, L3.D. Rajnauth and J.C. Waddington, Phys. Rev. C40 (1989) 610 9) A.J. Larabee, M.P. Carpenter, L.L. Riedinger, L.H. Courtney, J.C. Waddi~~ton, V.P. Janzen. W. Nazarewicz, J.Y. Zhang, R. Bengtsson and G.A. Leander, Phys. Lett. 8169 (1986) 21 10) M.P. Carpenter, C.R. Bingham, L.H. Courtney, S. Juutinen, A.J. Larabee, Z.M. Liu, L.L.. Riedinger. Z-Y. Zhang, A. Johnson, J. Nyberg, C. Baktash, M.L. Halbert, N.R. Johnson, I.Y. Lee, Y. Schutz, K. Honkanen, D.G. Sarantites and D.R. Haenni, XXIV Int. Winter Meeting on nuclear physics, Bormio, Italy, 1986, p. 647 11) M.I. Macias-Marques, C. Bourgeois, P. Kilcher, B. Roussiire, J. Sauvage and M.C. Abreu, Nucl. Phys. A427 (1984) 205 12) B. Roussit?re, Doctoriai Thesis, UniversitC de Paris-Sud, ORSAY (lQ86) 13) G. Palameta and J.C. Waddington, Nucl. Instr. Meth. A234 (1985) 476 14) D.G. Popescu, W. Schmitz, J.K. Johansson, G. Kajrys, D.D. Rajnauth, J.C. Waddi~gton, M.P. Carpenter, V.P. Janzen, L.L. Riedinger, S. Monaro and S. Pitotte, University of Tennessee Progress Report 88-03 (1988) 27; !V. Schmitz, Master Thesis, University of Bonn (1957). 15) Nuclear Data Sheets 52 (1987) 715 16) A. V~s~nathan, E.F. Zganjar, J.L. Wood, R.W. Fink, L.L. Riedinger and F.E. Turner, Phys. Rev. Cl9 (1979) 282 17) H. Kawakami, M. Ishihara, N. Yoshikawa, K. tshii, H. Kusakari and M. Sakai, J. Phys. Sot. Jpn. 36 (1974)623 18) W. Nazarewicz, J. Dudek, R. Bengtsson, T. Bengtsson and 1. Ragnarsson, Nucl. Phys. A43S (1985) 397; S. Cwiok, J. Dudek and W. Nazarewicz, to be published 19) R. Bengtsson and S. Frauendorf, Nucl. Phys. A327 (1979) 139 20) V.P. Janzen, Z.-M. Liu, M.P. Carpenter, L.H. Courtney, A.J. Larabee, L.L. Riedinger, J.K. Johansson, D.G. Popescu and J.c’. Waddin~ton~ to be submitted to Nucl. Phys. 21) V.P. Janzen, M.P. Carpenter. L..L. Riedinger, W. Schmitz, S. Pilotte, S. Monaro, D.D. ~a.in~utb, J.K. Johansson, D.C. Popescu, J.C. WaddingtoI~, Y.S. Chen, F. D&au and P.B. Semmes. Phys. Rev. Lett. 61 (1988) 2073 22) R. Wyss, W. Sat&a, W. Nazarewicr and A. Johnson, submitted to Nurl. Phys. 23) R. Wyss, J. Nyberg, A. Johnson, R. Bengtsson and W. Nazarewicz, Phys. Lett. 8215 (lQ88) 211 24) S. Frauendorf and F.R. May, Phys. Lett. 3125 (1983) 245 25) J.D. Garrett and S. Frauendorf, Phys. Lett. B108 (1982) 77 26) M.J.A. de Voigt, R. Kaczarowski, H.J. Riezebos, R.F. Noorman, J.C. Aacelar, M.A. Deleplanque, R.M. Diamond and F.S. Stephens, submitted to Nucl. Phys. 27) F. Hannachi, G. Bastin, M.G. Porquet, J.P. Thibaud, C. Bourgeois, L. Hildingsson, N. Perrin, H. Sergolle, F.A. Beck and J.C. Merdinger, Z. Phys. A330 (1988) 15 18) P.M. Walker, G.D. Dracoulis, A. Johnston, J.R. Leigh, M.G. Slocombe and I.F. Wright, J. of Phys. G4 (1978) 1655 29) F.M. Bernthai, C.L. Dors, B.D. Jeltema, T.L. Khoo and R.A. Warner, Phys. Lett. B64 (19761 147 30) J. Pedersen, S. Bj~rnholm, J. Borggreen, J. Kownacki and G. Sletten, Phys. Ser. T5 (1483) 162 31 j G.D. Dracoulis, C. Fah~ander and A.P. Byrne, Nucl. Phys. A401 f 1983) 490 321 R.M. Lieder, G. Sletten, J. Borggreen and J. Pedersen, Nucl. Phys. A375 i 1982) 291 33) A. Neskakis, R.M. Lieder, M. duller-Ve~gian, H. Beuscher, W.F. Davidson and C. Mayer-Biiricke, Nucf. Phys. A261 (1976) 189