Neutron-hole states in 204Tl

cl

I.E.1 : 2.G

Nuclear Physics A342 (1980) 431- 453 ; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NEUTRON-HOLE

STATES

IN *04TI ’

P. A. SMITH, R. J. PETERSON, R. A. EMIGH and R. E. ANDERSON ++ Nuclear Physics Laboratory, Department qf Physics and Astrophysics, University of Colorado, Boulder. CO 80309 USA

Received 24 July 1979 (Revised I7 December 1979) Abstract:

The level scheme of the doubly odd nucleus ‘04Tl has been studied via the 205Tl(p, d)‘04TI reaction at an incident energy of 26.1 MeV and with an energy resolution of better than 10 keV (FWHM). Seventy-seven levels are observed below 3.2 MeV excitation, The extraction of /-transfers and spectroscopic factors for most levels was accomplished by the comparison of experimental angular distributions with DWBA calculations. Extensive configuration mixing is implied from the large number of levels populated. The state at 1.289 MeV, which is populated via I = 6 transfer, is most likely the 6+ level. This knowledge and the known location of the 7+ isomer at I.103 MeV completes the experimental determination of the doublet involving the 7r3s,,, and vii,,,, orbitals.

E

NUCLEAR REACTION 205TI(p, d), E = 26.1 MeV; measured u(&, 0). z04TI deduced levels, 1, J, H, spectroscopic factors. Enriched target, magnetic spectrometer.

1. Introduction Shell-model calculations have been quite successful in predicting the spectra1 properties of nuclei two or more nucleons removed from ‘O’Pb [refs. ‘-*)I. These calculations have been based on theoretical effective interactions ’ - 3, and empirical matrix elements determined from the two-particle spectra 4-*). Although the latter approach has been shown to predict a high-spin subset of the spectra of threeparticle nuclei with good accuracy, it has not been applied to nuclei with proton holes. This may be due in part to a lack of information on the proton hole spectra needed to determine the residual interaction matrix elements. The low-lying level scheme of the doubly odd nucleus 20‘W is determined by the residual interactions among one proton hole and three neutron holes. To select states of a given singlehole parentage from amongst the many levels of this nucleus, we have studied the (p, d) neutron pickup reaction on 205Tl. The 3s+ proton hole that forms the “‘Tl ground state’- 1‘) couples to the angular + Research supported in part by the US Department of Energy. ” Present address: MS 846, Los Alamos Scientific Laboratory, Los Alamos, NM 87545. 437

438

P. A. Smith et al. / Neutron-hole states

momentum of the transferred neutron to produce the spectrum seen in the 205Tl(p, d)204T1 reaction. From simple shell-model considerations and neutron pickup studies on the isosopes of lead ’ 2, ’ 3), it is found that the prominent neutron orbitals are the 3p,, 2f+ 3p,, 1i,, 2f+ and 1h,. Neutron pickup from ‘08Pb generally finds the sum rule strengthexhausted by one state ofeach angular momentum r2), although some problem has been noted for the y’ state at 1.63 MeV [ref. 13)]. The situation is slightly more complex in 20sPb although only one strong transition is noted for each orbital 14, “). The present work examines this same neutron structure in the presence of a proton hole via the 205Tl(p, d)204Tl reaction. In the simplest picture, assuming an inert “*Pb core, only two states of angular momentum J = j?+ would be found for each j pickup. This would result in a total of twelve states, that is, six pairs which correspond to the six neutron orbitals j in 205,207Pb. In contrast, the worst possible configuration mixing for levels which can be formed from the neutron orbitals active between N = 82 and N = 126 and proton orbitals between Z = 50 and Z = 82 would result in a total of 142 states, of which 92 levels are accessible from an assumed seniority one +’ target ground state via the (p, d) reaction. These would encompass 32 I = 1 pickups, 48 I = 3 pickups, 26 I = 5 pickups and 17 I = 6 pickups. Some final states would be accessible by two different I-transfers, e.g. a single state populated by both I = 1 and 1 = 3 pickup must have a spin-parity of 2-. Although the residual interaction cannot be determined in the presence of extensive configuration mixing, simple accounting for the distribution of pickup spectroscopic strength to 204T1 is a good test of the shell model for nucleons removed from 208Pb. 2. Experimental

procedure and DWBA

analysis

The 205Tl(p, d)204T1 reaction was observed with 26.1 MeV protons from the University of Colorado AVF cyclotron. Reaction products were analyzed by a magnetic spectrometer incorporating a position sensitive helical cathode proportional counter at the focal plane. Deuterons were identified by their energy-loss in a plastic scintillator located behind the proportional counter and by the proper time-of-flight from the target to the scintillator. Two spectrometer settings were used to study a wider range of excitation energies. The thallium target consisted of a thin (130 pg/cm’) layer of highly enriched (99.5 ‘A) material evaporated onto a 20 pg/cm2 thick carbon backing. The enriched thallium isotope was obtained from Oak Ridge National Laboratory. At the center of the detector a resolution of 7 keV (FWHM) was obtained with a deterioration to 10 keV towards the two ends of the counter. Sample spectra are shown in fig. 1. A solid state counter located at a fixed angle in the scattering chamber was used to provide the relative normalization. The absolute normalization of the data was accomplished by comparing measured forward angle elastic scattering cross sections with those calculated from the optical model parameters presented in table 1. The

P. A. Smith et al. / Neutron-hole states

439

900.0

E&26.1 MeV e,,=15.0° 400.0

100.0 ‘j; E 2 2 902 t cz ‘C(4.439) \

400.0

47,48 I--

40

“NW

100.0

Channel Number spectra from the 207T1(p,d)204TI reaction. The ‘04Tl levels are numbered identified by energy in table 2. Major contaminants are identified.

Fig. I. Deuteron

and

TABLE 1 DWBA parameters “)

Particle

V.

rr

a,

IV,

4Wo

ri

ai

Vs.,,

P ‘) d *) neutron well

56.20 97.30 ‘)

I.17 I.15 1.24

0.75 0.79 0.65

3.02 0.15

31.20 55.62

1.32 1.33

0.65 0.91

24.80 13.40 25.00

r_

a_,

I.01 0.98 1.24

0.75 I .OO 0.65

rc

Sb)

1.25 1.25 1.25

0.70 0.45

The finite-range parameter = 0.621. ‘) Potentials have units of MeV and lengths have units of fm. These parameters are for 0.0 MeV excitation in the final nucleus. b, Non-locality parameter. ‘) Ref. z’). *) Ref. “). ‘) Well depth varied to reproduce binding energy.

uncertainty in the absolute cross sections is estimated to be less than +20 y0 since the optical-model calculations for forward angle proton elastic scattering are relatively insensitive to the choice of proton parameters. The excitation energies of the final states were determined from the known low-

P. A. Smith et al. / Neutron-hole states

440

205Tl(p,d)204Tl Ep=26.1 MeV

1 1

Y

1°okW

50

60

70

&.,,,. (dwt

Fig. 2. Angular distributions which have I = transfer in the 205TI(p, d)‘04Tl reaction.

1

101 0

’

IO

’

‘

20 30 40 8 cJn.(d*6)

’

.

SO

60

J

70

Fig. 3. Angular distributions which have I = transfer in the 205TI(p, d)2”4TI reaction.

1

P. A. Smith et al. / Neutron-hole

states

IOOcm

441

.

.

j

205TI(p,d)204TI Ep=26.1 MeV

.

.

.

.

:

lo

cl

&,,,. (dcd

Fig. 4. Angular distributions which have 1 = 1 transfer in the 205Tl(p, d)‘04T1 reaction.

10

20

50

40

es.m ~~~91

50

60

70

Fig. 5. Angular distributions which have I = 3 transfer in the zOSTl(p,d)‘04Tl reaction.

P. A. Smith et al. / Neutron-hole states

442 loo0

.

.

mooI

1

.

20sTl~p,d)z04TI ! Ep=26.1 MeV

.

.

.

.

.

1

205Tl(p,d)204Tli Epa26.1 MeV.

1’3

I=3 100, 2.475 YOV:

IO: I 7

2.796

lo

P-4 A--

0 Fig. 6. Angular distributions which have I : 3 transfer in the ‘05Tl(p, d)20“Tl reaction.

e,.,,(mJ)

50

60

70

Fig. 7. Angular distributions which have I = 3 tr’ansfer in the ‘05TI(p, d)‘04Tl reaction

P. A. Smith et af. / Neutron-hole states

100

1000

1.969 MeV

0

IO

20

30 8,.,.

40

!KJ

60

70

(WI

Fig. 8. Angular distributions which have I = 1 + 3 or I = (3) transfer in tiie zo5Tl(p, d)“W reaction.

l__o 8,.,, 0

IO

(dd

Fig. 9. Angular distributions which have I = I + 3 orl= : (3) transfer in the ZoSTIIo. reaction. \-, dlzo4T1 I

energy

4 4 4 4 4 5 6

1.046 D

1.103 I.118 1.133 1.176 1.204 1.250 I.289

20 21 22 23 24 25 26

I I

2

I I

2

2 2 3 2 2 3 2 3

0.473 0.489 0.535 0.628 0.675 0.735 0.762 0.859 0.870 0.904 0.966 1.012

0.428 D

6

AE WV) ‘1

1 8 9 10 11 12 13 14 I5 16 17 18 19

0.000 0.142 0.300 0.320 0.349

WV)

1 2 3 4 5

Peak

1 6

1

3

I 1

6

3

I

3 I+3 3

I 1 (1+3)

3

I 1 1 1 I

1 3 3

1 1

I+3

/-transfer

Present

Comparison

7+ 0-2o-22-40-20-26+

(22) 2-422-40-22-4-

20-20-20-22-44o-20-20-2o-20-22-40-20-2-

Jnd)

260 280 180 15 190 215 220

1240 620 70 1280 50 240 670 35 15 200 110 35 140

1180)

720 1580 2740 1560

I 720

work

4.61 0.150 0.096 0.037 0.11 0.12 4.36

0.51 + 1.46 0.36 0.81 1.39 3.09 0.17 0.058 0.65 0.32 0.038 0.065 0.10 0.13 0.15 (0.010+0.034) 0.18 0.076+0.22 0.23 0.017 0.32

PS ‘)

results with results from

TABLE 2

d) ““‘TI reaction

(p, d) reaction

of ““Tl(p,

1.280

1.205

(I.112

1.040

0.900 0.960

10.748

0.628

5

t

II

I

I

(3)

0.345 0.415 0.475

(1))

1

(0.310

(1 f3)

0.144

Itransfer

0.000

energy

(P. d) “)

the literature

I.375

I .202 I.252

I .052 1.118 1.120

1.014

0.7360 0.7590

0.6269

0.489

0.422 0.4342

0.3193

0.000 0.1414

energy

y-ray b,

(7+)

(4-)

2-

J”

2

s

$ F 2

$ ; %

%

2

$

a

P

6 8 8

8 8

6 5

5

5 5

10 10 5

5 5 5 5

5 5 10

1.405 1.424 1.463

I .489 1.516

1.545 1.584

1.652

I.683 1.709

1.753 1.810 1.834

1.908 1.933 1.951 1.969

1.991 2.049 2.084

2.116 2.146 2.166 2.191

2.228 2.243 2.271

28 29 30

31 32

33 34

35

36 31

38 39 40

41 42 43 44

45 46 47

48 49 50 51

52 53 54

5 8 9

5 5 5 5

6

1.388

21

0-2(5-)

1

5(6)

250 90 55

2-4(2-4-) 2-4-

(3) 3

3

60 45 25 20

2-4(2-) 0-4-

35 205 < 10

140 135 80 50

3

2-4-

(2-) 2-42-40-4-

(1+3) 1(+3)

3

(1+3) 3 3 1+3or3

3

2-4-

55 70

o-2-

< 10 15 500

35

(4-)

5(6)

1

40 40

0-2-

1

25 < 10 < 10

25

15 15

0-22-

2-4-

(2-4-) 0-2-

(3) 1

1 1+3

3(+1)

0.76 (0.30) 0.18

0.15 (0.017+0.063) < 0.018( +0.045)

0.62

(0.059 +0.20) 0.35 0.29 < 0.017+0.073 or0.11

I .32

0.036 1.54( I .56)

0.024

0.022 1.03(0.93)

(0.037) 0.008

0.015 0.004+0.016

0.31(+0.084)

2.230

(2.130)

2.040

11.925;

t1.822;

1.680

I.545

3

3

(2.249) (2.270)

2.213

2.153

2.049 2.081 2.107

I.946 1.963

1.846 1.902

1.815

1.706 1.739

1.671

1.635

I .524

1.475

1.398

E

2.415 2.492

2.570 2.642 2.613 2.105 2.728 2.196 2.807 2.831 2.934 2.968 2.986 3.002 3.045 3.067 3.093 3.117 3.142

59 60

61 62 63 64 65 66 61 68 69 70 71 12 13 74 15 76 17 2-42-42-42-42-42-42-4(0-2_)

(2-4-)

(3)

2-42-4-

3 3 3 3 3 .3 3(+1) (1)

3 3

2-42-42-4-

(2-4-)

J” d,

< <

< < <

<

<

20 40 30 15 15 20 15 15 IO 10 IO 15 25 10 10 IO

60

30

60

95 80 30

IO

PS ‘)

(0.055)

0.19 0.076 0.14 0.11 0.54 < 0.039 < 0.068( +0.009) (0.017)

0.20 0.11

0.31 0.15 0.097

(0.026)

2 (continued)

energy

____ I-

transfer

(P>d) “) ~y-ray Y

2.491 2.536 2.575 (2.638)

2.422 2.454

2.314 (2.344)

energy

_

“) Ref. 16). b, Results are a combination of refs. 16. 23-28). ‘) These uncertainties are the standard deviations of the energies obtained from the calibration spectra. d, In most cases, only the least restrictive spin assignments are given. ‘) Orbits are assumed to be 3p, ,2, 2f,,,, 1h,,, and 1i,,;, for I = 1,I = 3, I = 5 and I = 6, respectively. Multiply by 0.94 to convert 3p, ,* to 3p,,, and by 0.85 to convert 2f,,, to 2f,,,.

6 8 6 8 8 10 10 IO 10 10 15 15 10 IO 10 15 20

9 8

3 3 3

2.374 2.397 2.420

56 57 58

6 6 9

(3)

2.320

55

9

/-transfer

energy (MeV)

Peak

Present (p. d) reaction work

TABLE

b

P. A. Smith et al. 1 Neutron-hole states

447

lying levels of 20?Il [ref. ‘“)I and from the known levels of 92Nb [ref. “)J and looRu [refs. 18*19)] seen in the (p, d) calibration spectra taken under the same experimental conditions as the *‘4Tl data. The resulting uncertainties in assigned energies are generally better than &8 keV. Spectroscopic factors were extracted by comparison to non-local, finite-range distorted-wave Born approximation (DWBA) calculations *‘) using the opticalmodel parameters listed in table 1. These parameters are obtained from global analysis of proton *l) and deuteron **) elastic scattering data. The spectroscopic factors are obtained by

The summed spectroscopic factor for pickup from the filled shell j is 2j+ 1 in this convention. Because of the small angular momentum mismatch for the (p, d) reaction at 26.1 MeV, the low I-transfers are-favored and best determined. The DWBA calculations were performed for each j” at 0.0, 1.0, 2.0 and 3.0 MeV excitation energy. The DWBA cross sections for an arbitrary excitation were interpolated from these results. Angular distributions were obtained for a great number of the states noted in the spectra of fig. 1. Angular distributions, collected by f-transfer, are shown in figs. 2-9, where comparisons are made to the DWBA predictions. Since no striking j-dependence is noted in the DWBA predictions, only those shapes for pt or ft pickup are compared to the data for 1 = 1 and I = 3 transfers, respectively. A more complete discussion of each l-transfer is found in sect. 3.

3. Experimental results 3.1. ANGULAR

DlSTRIBUTIONS

The angular distributions for the levels populated in this study are collected by I-transfer in figs. 2-9. Levels for which the I-transfer is not conclusive have the most probable I-transfer(s) placed in parentheses in table 2 and the figures. The fourteen levels which have ambiguous angular distributions and, consequently, for which no I-transfer assignment could be made, are not shown. In many cases these levels are weakly populated and are observed clearly at only a few angles. The uncertainties shown for the data point are statistical and are given by a least squares fitting procedure used to analyze the spectra. Levels populated by 1 = 1 transfer arise from the pickup of a neutron from the p, or p+ orbit, resulting in states with j” = O-, l- or j” = l-, 2-, respectively. Similarly, I = 3 transfers populate levels having final state spin-parities of 2-, 3- (f,) or 3-, 4- (f,). Angular momentum transfers of1 = 5 result in levels having j” = 4-, 5- (g& and transfers of 1 = 6 result in levels

P. A. Smith et al. / Neutron-hole states

448

having j” = 6+, 7+ (iY). Unless information from presently justifies it, the least restrictive spin-parities are listed in table 2. 3.2. THE I = 1 PICKUP

available

studies

RESULTS

Since the (p, d) reaction at 26.1 MeV kinematically emphasizes I = 1 pickup, it is most sensitive to low spin (O--2-) final states in this experiment. The same states are most likely to be seen in the analysis of thermal neutron capture on 203T1 [refs. 23-25)]. The results summarized in table 2 show a good correspondence between the present results and levels inferred from the y-ray spectrum 16). One previously unidentified low-lying state at 300 keV is noted from the present work. Angular distributions assigned to pure I = 1 pickup are shown in figs. 24. The state located at 2.831 MeV is the only tentative assignment. Angular distributions resulting from I = 1 + 3 neutron pickup are shown in fig. 8. A single state populated by the sum of I = 1 and 1 = 3 angular distributions must have a spin of 2-. Peaks narrow enough not to be obvious doublets with this sum of l-transfers are labelled as (2)- in table 2. The 0.428 MeV peak is clearly wider than other nearby peaks and corresponds to a known doublet, one member of which is known 16*26-28) to have a spin of 4-. In this case the j-transfer must be $- for the I = 3 contribution. A total of between twenty-five and thirty-one levels populated by I = 1 curves are noted up to an excitation of 2.831 MeV. There is a chance that some of these may be doublets, even with an energy resolution of less than 10 keV. The total spectroscopic sum (assuming p+ pickup) for 1 = 1 transfer is ZC’S = 5.39. This spectroscopic sum compares well to the maximum value of 6 and to the observed value of 4.32 for pt and p+ pickup from 206Pb up to an excitation energy of 2.352 MeV [ref. ‘“)I. The results summarized in table 2 show a clear clustering of the I = 1 strength at the lower excitation energies. The centroid of the I = 1 strength in 204T1 (located at 0.506 MeV) is bound by 322 keV less than that in 205Pb, but weak, high-lying states may have been missed in the 206Pb(p, d)205Pb reaction 14). A maximum number of thrity-two I = 1 states is allowed for the entire spectrum of active nucleons above N = 82 and 2 = 50 for the couplings of lowest seniority. That up to thirty-one levels are observed is evidence of the very extensive mixing of these hole states. The largest single I = 1 spectroscopic factor is 1.31 (assuming the p+ orbital for the 0.320 MeV state), which is near the value of 1.5 predicted for a (7c3s+@ v3p,), - state in a weak coupling scheme. The 2- ground state shows obvious evidence of configuration mixing as the level is populated by some I = 3 strength and the 3p, spectroscopic factor is 0.5 instead of the weak coupling prediction of 2.5. 3.3. THE

I = 3 PICKUP

RESULTS

Reliable 1 = 3 assignments are made for many (p, d) reaction angular distributions

P. A. Smith

et al.

/

Neutron-hole

449

states

observed to final states in *‘4Tl as shown in figs. 5-7. Mixed transitions with 1 = 1 transfers are shown in fig. 8 while l-transfers likely containing some I = 3 strength are presented in fig. 9. Spectroscopic factors are listed in table 2. In contrast to the 1 = 1 results, the f = 3 transitions are found predominantly at higher excitations. The summed spectroscopic factors based on $- transfer provide 12.67 out of a maximum allowed sum of 14. A sum equal to 9.5 is found for pickup on *06Pb [ref. 14)]. The excitation energy centroid of the I = 3 strength is 1.336 MeV above the ground state, which is 21 keV less bound than the 1 = 3 centroid observed in the (p, d) reaction on *06Pb [ref. 14)]. A total of between thirty and thirty-eight 1 = 3 transitions are identified in this work. A maximum of forty-eight states can be populated if the active orbits between 132Sn and *‘*Pb are thoroughly mixed and if only the lowest seniority states are considered.

3.4.

HlGHER

I-TRANSFER

RESULTS

One of the few known spins in *O‘W is that for the 62 ps isomeric 7+ state located in the region of 1.115 MeV excitation. The parentage of this state seems to be largely

MeV

Ep-26.1 I.103

MeV

-

1=6

0

10

20

30

40

50

60

70

e c.m. ‘d*g’

Fig. IO. Angular distributions which have I = 5 or I = 6 transfers in the 205Tl(p, d)‘04Tl reaction.

450

P. A. Smith et al. 1 Neutron-hole states

due to the coupling of vli, and ~3s~ holes as inferred from its observed magnetic moment 29). Consequently, a large I = 6 pickup strength would be expected in the (p, d) reaction. Two very clear I = 6 angular distributions are seen at 1.103 and 1.289 MeV. These two angular distributions are identical, even where they deviate from the DWBA predictions as shown in fig. 10. The spectroscopic factors are 4.61 for the 1.103 MeV level and 4.36 for the 1.289 MeV level. The 1.103 MeV level corresponds to the 1.l 18 MeV level determined from *05Tl(y, ny) reaction studies using Nal (Tl) counters. Due to the relatively poor resolution of such counters the energy determined in the present study is likely to be on a firmer basis. A close doublet at 6+ and 7+ states is expected from the (7r3.s;’ @ vii;.,‘) configuration multiplet. The 6+ state must lie at a higher excitation than the 7+ level for the latter to be isomeric. Furthermore, a 25+ 1 intensity weighting predicts that the 7+ level should be fifteen percent more intense than the 6+ level. Experimentally, the 1.103 MeV level is less than five percent more intense than the 1.289 MeV level. The 1.289 MeV level is most likely the 6+ member of this doublet. The centroid of these two I = 6 excitation energies is 1.190 MeV above the ground state and is less bound than the I = 6 centroid in *05Pb by 387 keV. The 7+ state is strongly populated by the *06Pb(d, a)*04Tl reaction 30) and the 6+ state is not observed as would be expected from the (d, a) reaction systematics which show preferential population of states with J” = L n+ 1. The only two I = 6 transitions observed in this work are those to the 1.103 and 1.278 MeV levels discussed above and they represent only sixty-four percent of the total i, strength available. This is consistent with the results seen from neutron pickup from *‘*Pb [ref. 13)] while the *06Pb(p, d)*05Pb results 14) indicate that the i, orbital is about ten percent weaker in *05Pb than in *07Pb. Thus, the relatively low spectroscopic factors for the i, pickup noted in ref. 13) persist in 20‘?l. Since it is likely that some of the missing i, strength would have been observed in either the present work or one of the experiments listed in ref. 13), the most probable explanation is that some absolute normalization problem exists with the DWBA calculations. Only the two levels located at 1.584 MeV and 1.709 MeV can be firmly assigned I = 5 transfers. These angular distributions are shown in fig. 10. The total spectroscopic strength for these two levels is 2.56 compared to a theoretical value of 10.0. The *06Pb(p, d) *05Pb reaction study 14) measured approximately ninety-five percent ofthe strength seen in the *‘*Pb(p, d)*07Pb reaction studies ’ 3), but only fifty percent of the h, strength was observed in the latter reaction. Experimentally, one would reasonably expect a summed strength of only - 4.8. The centroid of these two states is 1.659 MeV above the ground state or 1629 keV more bound than the I = 5 centroid in *05Pb. Consequently, we conclude that either some of the 1 = 5 strength lies at higher excitations or that the same problem with the magnitude of the i, spectroscopic factor is present for I = 5 transfer. The relatively constant and intrinsically low cross sections for I = 5 and 6 = 6 transfer make identification difficult

P. A. Smith

et al. 1 Neutron-hole

states

451

if any fragmentation is present and this strength could easily be lost in the many peaks at higher excitation. Nonetheless, the level density below m 1.8 MeV is such that any of these levels would probably be seen in this work. It is possible many of the levels observed in the region of 3.0 MeV that are not assigned f-transfers are populated with some I = 5 or 1 = 6 strength. 4. Discussion The fragmentation of the neutron I = 1 and 1 = 3 pickup strength from “‘Tl is quite extensive as indicated by the large number of levels populated. This is in striking contrast to the neutron pickup results from ‘O’Pb [ref. 14)], where the simple shell-model scheme so successful for neutron pickup from 208Pb [refs. 31*32)] is still noted. A determination of the average two-nucleon residual interaction in 206Pb by application 14) of the energy-weighted sum rule of Bansal and French 33) found very weak neutron-neutron strengths. The neutron-proton interaction is much stronger and evidently has caused extensive mixing both in the 205Tl ground state and in the low-spin levels of ‘04T1. Significant mixing of the 205T1 groundstate wave function has also been implied in a 205Tl(t, P)~“T~ reaction study 34). Application of the method of Bansal and French to 20sT1 must await accurate and complete neutron stripping data on “‘Tl. With such data the shifts in centroid binding energy noted for each I-value may be converted to quantitative residual interaction matrix elements. Only a beginning has been made on this neutron stripping experiment 3). To carry through a careful analysis of the Bansal and French sum for the 1 = 5 and I = 6 orbitals, neutron transfer reactions favoring larger angular momentum transfers are desired. The (3He, a) and (a, 3He) reactions on “‘Tl and ‘03T1 respectively would be an ideal source of such data if high resolution could be obtained. The positive parity states of 204T1 seen by 1 = 6 transitions show little mixing. A total of nine 6+ and eight 7+ states are possible, but a simple weak coupling scheme is found. The expected experimental I = 6 strength is essentially exhausted by the known 7+ state at 1.103 MeV and a likely 6+ state at 1.289 MeV. The 3~ protonhole and 1i, neutron-hole evidently have only a weak residual interaction, which is in notable contrast to the spectrum of negative parity states. The configuration for these levels can be represented in the form

where K = 0, 1, 2, . . ., 12. If one neglects all values of K except for K = 0,then the configuration can be written approximately as (n3s;’ @ 206Pb(g.s.) 6 vli$,‘),+,,+. The term 206Pb(g.s.) is a normalization

factor which can be included by calculating

452

P. A. Smith et al. 1 Neutron-hole

states

TABLE 3

Comparison Spin of matrix element 6+ If Separation “) See text for details

of (x3s,i

0 vl i;i,:/,),.

204TI

seniority

, , matrix elements “) lo6TI

1

theoretical

Z04TI

seniorities

I and 3

(MeV

(MeV)

(MeV)

- 0.264 -0.450 0.186

-0.109 -0.529 0.420

0.022 -0.371 0.393

on how the matrix

elements

were determined.

the matrix elements with respect to 206Pb(g.s.). These values are given in table 3. The energy difference between the two values, 6+ and 7+, is 0.186 MeV. No comparison to the experimental (7~s; ’ 0 vl iii?‘), +,7 + levels in 206T1 [ref. 35)] can be made since the 6+ member of this configuration has not yet been firmly identified. The 7+ member has been identified via the 208Pb(d, ~z)“~Tl reaction 36). Nonetheless, the theoretical studies of Kuo and Herling ‘) predict 6+ and 7+ levels composed primarly of the (7~3s; 1 @ vli$‘) configuration to be located at 2.05 MeV and 1.63 MeV respectively in 206T1. This study is consistent with the presently known experimental information on 206T1. Derived two-body matrix elements from these predictions are given in table 3. The energy difference of these two matrix elements is 0.420 MeV does not compare well with the value 0.186 MeV obtained above. Most likely the wave function for the 6+, 7+ levels in 204T1 contain higher seniority components as 204T1 is four holes removed from the 208Pb core. If we assume that these levels take the form (7~3s;~ 0 x(vliY)i)K2 0 vli$1)6+,7+, where K = 0, 1, 2,. . ., 12, then the two-hole matrix elements can be calculated using standard shell model methods 37). The results are given in table 3. The energy difference for these matrix elements is 0.393 MeV, which is much closer to the value of 0.420 MeV obtained from 204T1. Better agreement probably could be obtained if high seniority components from other neutron orbitals were included. It is clear, nonetheless, that high seniority components contribute measurably to the wavefunctions for the 6+ and 7+ levels located at 1.289 and 1.103 MeV in 20“T1. Similar residual interaction comparisons between the negative parity states observed in this work and the calculated and experimental levels of 206T1 are precluded due to the extensive mixing noted in this experiment. It is with pleasure that the authors thank J. Alvistur for his thorough and diligent help with the reduction of these data. Further thanks are due to L. Smith for her help in the final states of the preparation of this work.

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