High spin states in 9 6 T ~ populated through the (a ,n) reaction

H. A. MACH, M. W. JOHNS, A N D J . V. THOMPSON' 'McMrrsrer Ul~ioersify, H ~ ~ n i l r o ~ t , O I I ~ . , C N I I N ~ ~ ~ I L8S 4KI

Received August 6, 1979

High spin states of y 6 T ~ populated by the (a,n) reaction using alpha beams from 13 to 27 MeV have been studied. Gamma-ray energies and intensities, gamma-gamma coincidence prob- abilities, gamma-ray angular distributions, and electron conversion coefficients were determined at 18 MeV. In addition, some results taken at 14 MeV are reported.

The high spin structure observed in this work includes the following levels: 49.3(6+), 3 18.8(6+). 574.7(7+). 926.9(9+), 946.5(8+), 1062.1(8+), 1138.8(8+), 1447.2(9+), 1702.8(10+). 1861.6(9+), 1922.3(1 I+), 2147.5(11+), 2213.5(101+'), 2317.2(12+), 2396.8(1Ic+)), 2599.0((13)+), 2642.4((14)+), and 3020.1(12'+)).

These experiments also clarify and extend the information obtained by previous workers. In particular, evidence is adduced for low-lying states at 0.0(7+), 34.3(4+). 45.3(5+), 120.3(3-), 177.0(5+), 226.2(2-), 227.0(4+), and 254.3(3+).

The work identifies many other states of intermediate energy. Attenuation coefficients for states in y 6 T ~ are calculated using a theoretical model.

On a CtudiC les etats de spin eleve de 9 6 T ~ peuplis par la reaction (a,n). en utilisant des faisceaux alpha de 13 a 27 MeV. Les Cnergies et les intensitis des raies gamma, les probabilites de coincidences gamma-gamma, les distributions angulaires des rayons gammaet les coefficients de conversion electronique ont etC determines a 18 MeV. On rapporte de plus quelques rksultats de mesures faites 5 14 MeV.

La structure spin eleve observie dans ce travail inclut les niveaux suivants: 49.3(6+), 3 18.8(6+), 574.7(7+), 926.9(9+), 946.5(8+), 1062.1(8+), 1 138.8(8+), 1447.2(9+), 1702.8(10+), 1861.6(9+), 1922.3(1 I+), 2147.5(1 I+), 2213.5(10(+'), 2317.2(12+), 2396.8(1 I(+'), 2599.0((13)+), 2642.4((14)+), and 3020.1(12(+').

Ces experiences clarifient et accroissent aussi I'ensemble des risultats obtenus anterieurement par d'autres chercheurs. Elles apportent en particulier des preuves de I'existence de niveaux de basses energies a 0.0(7+), 34.3(4+), 45.3(5+), 120.3(3-), 177.0(5+), 226.2(2-), 227.0(4+). et 254.3(3+).

On identifie aussi dans ce travail plusieurs autres Ctats d'energie intermediaire. Des coefficients d'attenuation pour des etats de 96Te sont aussi calculCs en utilisant un modele

theorique. Can . J . Phys., 58. 174(1980) [Traduit par le journal]

Introduction 18 MeV, the spectra are dominated by transitions 96TC has been extensively studied by the (p,n) from the high spin states extending to 3 MeV which

reaction which preferentially populates low spin f01-m the f ~ c u s of the present work. states. As a result of the work of Doukellis et al. (1) The experimental results to be discussed are and of Kern and his co-workers (2, 3), we have based on excitation functions, on angular distribu- available a fairly complete level structure for the tion functions, y-y coincidence probabilities, and low-lying states of 96Tc. Their conc~usions are in electron conversion coefficients determined at both the main confirmed by the (d,2n) experiments of 14 and 18 MeV. Since this Paper is primarily con- Madueme and Arita (4). In addition to these, this cerned with high spin states, most of the data pre- nucleus has been studied by Emigh et al. (5) sented was taken at 18 MeV. A subsequent Paper through the (3He,d) reaction and by Bini et (6) dealing with states of low and intermediate spin will using the (a ,n) reaction with an alpha energy in the be based mainly on the 14 MeV data. 10-14 MeV range.

The (a,n) reaction populates a large number of Experimental Details states not observed in the (p,n) or (d72n) studies. Alpha beams provided by the McMaster Tandem With an beam of 14 MeV, a rich structure of Van de Graaff Accelerator were used with self- states of low and intermediate spin is excited, in- supporting targets of 93Nb ranging in thickness cluding most of those observed in the proton and from 0.9 mg/cm2 for the electron measurements to deuteron work. When the beam is raised to 2.5 mg/,-m2 for gamma-ray measurements. Gamma-

'Present address: Ontario Hydro, Pickering, Ont., Canada. ray excitation functions were carried out in 0008-4204/80/020 174- 17$0 1 .OO/O

a1980 National Research Council of Canada/Conseil national de recherches du Canada

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MACH ET AL. 175

the alpha energy range from 13 to 27 MeV. These made it possible not only to distinguish the gamma rays of y 6 T ~ from those of y 5 T ~ , y 5 , y 6 M ~ , and y'Nb but to differentiate between y6Tc trans- itions from high spin and low spin states.

Angular distributions were obtained from foul- experiments; one at 18 MeV which accentuated transitions between high spin states and three at 14 MeV in which the transitions between low spin states were predominant. For two of these experi- ments, the beam was stopped in a lead foil (152 mg/cm2 at 18 MeV, 98 mg/cm2 at 14 MeV) be- hind and in contact with the target. This arrange- ment permitted the determination of angular dis- tributions in the 0 to 90" range (seven angles), for transitions of energy greater than 150 keV. For lower energies, corrections for lead absorption and incoherent scattering were so large as to make the data useless. In the other two experiments (at 14 MeV), the beam was stopped in a tantalum foil 30 cm from the target. This arrangement restricted the measurements to angles greater than 15" with a consequent reduction in the precision of the A , coefficients deduced from the data. The high reso- lution 1 cc Ge(Li) detector used resolved the 85.3- 86.1 keV doublet sufficiently to provide high qual- ity angular distribution functions for these two transitions, as well as for a large number of gamma rays in the 30-350 keV energy range.

In all four experiments, the normal corrections were made for counting losses, for the finite solid angle subtended by the detector at the target, and, where applicable, for the differential absorption in the lead stopping foil. Corrections for lack of cen- tering were made by comparing the intensity of a number of decay lines in the fixed and movable detectors in the spectra recorded at each angle. The combined uncertainty in the data created by these corrections is of the order of 1%.

It was particularly useful in the analysis to have data at both energies because several key transi- tions were found to be unresolved doublets, of which one appeared alone in the 14 MeV spectrum while the other was dominant in the 18 MeV spec- trum.

Three independent gamma-gamma coincidence experiments were carried out at 18 MeV. The first, designed to study coincidences between medium and high energy gamma rays, was performed in a metal chamber which allowed the detectors to be located about 5 cm from the target but which effec- tively eliminated coincidences with gamma rays of energy less than 100 key . The second experiment was performed in a Lucite chamber with minimal

absorbers present which allowed detection of coin- cidences for gamma rays of energy greater than 26 keV. Although the 1 cc Ge(Li) and 10 cc intrinsic germanium detectors used had very low detection efficiency for transitions above 500 keV, this ex- periment established strong y-y cascades involv- ing both the 49 and 85 keV gamma rays. The third experiment was pelformed in the Lucite chamber with the 10 cc intrinsic and a 17% Ge(Li) detector. With the improved statistics ofthis experiment (2 x lo7 coincident pairs), the role of many of the weaker transitions and close doublets in the level scheme became clear. In all three experiments, standard fast-slow coincidence electronics was used with an approximately Gaussian TAC peak of width -8 ns. The coincidence data were written on magnetic tape in a format which recorded the ener- gies of both the start and stop pulses and the time delay between them for each coincident pair. To accommodate the differential delays in detecting high and low energy transitions and to ensure that events associated with states of short but measur- able lifetimes were not missed, a 200 ns window was set on the TAC spectrum in scanning the tapes to obtain spectra in coincidence with a single photopeak.

Many of the gates were analyzed using a much narrower TAC window (-20 ns). Comparisons between the broad and narrow window analyses showed that chance events made a negligible con- tribution to the spectra.

The conversion electron spectrum was recorded using an on-line seven gap "orange" magnetic spectrometer in the manner already described (7). The effective momentum resolution in this experi- ment including the effects of target thickness was about 1% in the high energy region.

Experimental Results (a) Gamma-ray Energies and Intensities

Figure 1 presents the gamma-ray spectrum ob- tained with the 10 cc intrinsic germanium detector, with an alpha beam of energy 18MeV. The identified peaks are nearly all associated with high spin states. Many of the weaker unlabelled,peaks are also in y 6 T ~ , associated with low spin states. These are much more prominent in spectra taken at 14 MeV.

Columns 1 and 2 of Table 1 present a partial list of the energies and intensities identified with y 6 T ~ in the present work. Those shown include transitions from the high spin states of concern in this paper plus a selection of the transitions between low spin

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CAN. J . PHYS. VOL. 58. 1980

I I

CHANNEL N U M B E R

FIG. I . The gamma-ray spectrum of y 6 T ~ recorded with a I0 cc Ge detector and an 18 MeV alpha beam.

states which offer support to the high spin struc- tures.

Throughout this work, the position has been taken that evidence from y-y coincidence data supported by excitation functions is required be- fore conclusively associating a transition with 9 6 T ~ . This rule has been relaxed for a few cases of strong transitions whose excitation functions were characteristic of 9 6 T ~ .

(b) Excitation F~rnctiorzs Figure 2 presents a number of characteristic ex-

citation functions for transitions in 9 6 T ~ and 9 T c . Quadrants 1, 2, and 3 show the characteristic downward shift in the peak of the excitation func- tion as one looks at transitions from initial spin states of lower and lower spin. Functions for most

of the prominent transitions of interest in this work are shown in these three quadrants. The fourth quadrant presents a characteristic excitation func- tion for 9 5 T ~ , functions for transitions between states of medium spin and the function for the 255 keV doublet which contains both a high spin and a medium spin component. While these excita- tion functions had little predictive power in the development of the level structure, they do provide corroborative evidence for the correctness of the level scheme.

(c) Gamma-Ganlma Coincidence Measurements Figure 3 presents coincidence spectra gated by

13 of the most important transitions in 9 6 T ~ . These represent a selection from the more than 120 gates for which spectra were analyzed. Each of the seven

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MACH

spectra on the left of Fig. 3 is associated with a single transition, and the group of spectra presents evidence for most of the levels in the decay scheme. Evidence that the 183 and 255 keV transitions are both doublets is presented at the right of Fig. 3.

The level structure was tested by deriving coin- cidence probabilities from the coincidence spectra and comparing these with those deduced from the level structure and the measured photon intensities of Table 1. In a number of cases where the gamma ray of interest was unresolved from a contaminant line, or was too weak to be observed in the direct spectrum, the coincidence spectra were used to deduce photon intensities.

The third column of Table 1 presents the classification of the observed gamma rays in 9 6 T ~ . These classifications were primarily derived from the coincidence data.

(d ) Angular Distributions Figure 4 presents a selection of the 150 measured

angular distribution functions. Each distribution was least-squares fitted to a function of the form W ( 8 ) = A,[1 + A 2 P 2 + A,P,]. Table 1 presentsA, and A, coefficients resulting from either the 14 or I8 MeV measurements, depending on which seemed more reliable.

Angular distributions for a given Ji + Jf transi- tion may be predicted theoretically as a function of the mixing ratio 6 = (JfIIL + 1 llJi)l(JfllLllJ,) and the population parameters of the initial state. The population distribution among the 177 substrates for levels populated in (a,xn) reactions can be well represented by a Gaussian of width o . Thus a two- parameter search for a minimum in the surface x2(o,6) is required to find the best fit of the experi- mental data to the model. Unfortunately, except for transitions where large positive A , coefficients have been determined with high statistical accu- racy x,,~,,~' is found at the bottom of a narrow valley of almost constant depth. The search thus fails to identify a unique value of 6 but rather a range of values (typically of the order of 10" in arctan 6), each associated with an appropriate value of o , which yield equally acceptable values of x,,,,. At- tempts to limit the range of 6 values have been made by many workers, using the statistical model in the formation and decay of the compound nucleus to estimate the appropriate attenuation coefficients or equivalent o values to be used with a state of given spin.

The estimates ofo made in the present work have been carried out using a modification of the method used by Shibata et ul. (8) for states excited by the 93Nb(a,2ny)95T~ reaction. The work of these au-

ET A L . 177

thors was in turn an extension of the work of Ejiri et 01. (9) on the alignment of levels in the ground state band of nuclei produced through (a,2ny) reactions on targets of zero spin. The details of the present calculation are described in the Appendix.

The o values corresponding to the calculated coefficients, which are given in column 8 of Table 1, range from about 1.5 for low spin states to 3.2 for those of highest spin. The values so obtained are in good agreement with those found from the two- parameter search for the few cases where the search led to a unique solution.

Table 1 also presents the A,, A,, and 6 values corresponding to the Ji + Jf transition indicated (the sign convention for 6 is that used by Yamazaki (10)). The experimental coefficients and those pro- vided by the model agree very closely. The quoted uncertainties in 6 are those corresponding to x2 = xmin2 + I (1 1) with an additional allowance for the uncertainty in o .

The 183 keV peak is a doublet involving the low excitation 228 + 45 keV and the high excitation 2397 + 2213 keV transitions. The high excitation component is responsible for 33 and 4% of the total peak intensity at 18 and 14MeV, respectively. Thus the angular distribution measurement at 14 MeV yields pure A , and A , coefficients for the low excitation component, characteristic of a AJ = 1 transition. The fact that the coefficients for the composite peak at 18 MeV are the same as those for the "pure" peak at 14 MeV gives a strong indica- tion that the high excitation component is also of AJ = + 1 character. The 255 keV peak is also a doublet involving high and low excitation components. However, in this case, the ratio of intensities only changes from 60 to 30% so that neither the 14 MeV nor the 18 MeV angular distributions are "pure". Because the angular distributions determined at 14 and 18 MeV are identical and both characteristic of AJ = + 1 transitions, it appears that both compo- nents must be dipole in characteristic. The conclu- sions drawn for both the 183 and 255 keV doublets are consistent with the requirements of the level structure of Fig. 6, based on the properties of other transitions. The angular distribution and the inter- nal conversion data for the stronger component of the 183 keV doublet show clearly that this transi- tion is MI rather than E2 as claimed by Madueme and Arita (4).

The 487, 721, and 946 keV peaks in the 18 MeV spectra are contaminated to the extent of about 10% by Y5Mo decay lines or 9 5 T ~ lines. At 14 MeV no 95Mo is created. The sequence of angles used was chosen to minimize distortion of the distribu- tion rising from the buildup of activity.

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TABLE 1. Properties of transitions in "Tc - 4 CC

Experimental coefficients Calculated coefficients Energy Assignment 6(L -1- I/L) (keV) lntensity Classification A, x 100 A, x 100 J,* + J," A, x 100 A,, x 100 x 100 o a, x 100 Multiplicity

M I < E l ' E l = M l * MI/E2 M1 M1 M1 M1

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Experimental coefficients Calculated coefficientsb Energy Assignment 6 ( L -I- 1/L) (keV) lntensity Classification A2 >: 100 A* x 100 Jin + Jln A, x 100 A4 x 100 >: 100 u a, x 100 Multiplicity

alntensities (measured at 18 MeV) are relative to the value o r 100 ror the 525 keV transition. bThe range of A2 and A4 values permitted by the uncertainty in u are indicated in parentheses. <The argument forthis assignment is given in the text. dThe angular distribution coefficients and u parameter quoted were determined at 14 MeV for this transition, rather than at 18 MeV. .Data were taken from ref. 3. 'Part o f an incompletely resolved doublet intensity derived from y-y coincidence measurements. qA spin of 8 + fits equally well. The 8 + chbice would make the 885 keV state the yrast level, and one would expect to observe a strong deexciting transition. hThis level may be a doublet. If it is not, one of the deexciting gamma rays must be M2 in character. ITransition only observed in the y-y coincidence spectra. ja obtained from a two-parameter search for a minimum in the surface x2(u, 6) at Em = 18 MeV.

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CAN. J . PHYS. VOL. 58. 1980

ENERGY OF a PARTICLES (MeV)

FIG. 2. Excitation functions for transitions in 9 6 T ~ , expressed in terms of photons per microcurie of charge collected. The vertical scale for each gamma ray has been arbitrarily adjusted for clarity for presentation.

(e ) Itzternal Corzuersiorz Data The electron spectrum was scanned at 18 MeV

from Bp 1100 to 2500 together with selected sec- tions from Bp 4000 to 4700. A comparison of the electron and gamma-ray spectrum is shown in Fig. 5 and column 9 of Table 1 presents the K- conversion coefficients for the measured transi- tions. The errors quoted are statistical and do not include allowances for systematic errors intro- duced through uncertainties in the electron and gamma-ray detection efficiencies. The quality of the data is such as to clearly distingilish E 1 from M1

transitions but is not adequate to give useful M 1/E2 mixing ratios. Since the energy range from 400 to 900 keV showed strong impurity transitions to- gether with a large number of weak y 6 T ~ transitions and since the difference between a~ for M1 and E2 transitions is very small in this energy region, no attempt was made to study this portion of the spec- trum.

The electron data were analyzed by the compu- ter program ANABEL designed to provide a more sophisticated fitting tool than that used by earlier workers in this laboratory (7). In this program, the

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281 k e V Gote

395 keV Gate

. .

169 keV Gate - $E $ 2 N

100 N -

W 5 0 0 keV Gate

I

cr ). 2 500'f 1; ' 371 keV Gate

4co JE 525 keV Gote

49 keV Gate

263 keV Gote -1 loo

183 keV Gate j::

351 keV Gate

-. 10

a N 444 keV Gate LD W 0 C C C

k 255 keV Gate 1500

273 keV Gate

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

CHANNEL NUMBER CHANNEL NUMBER

FIG. 3. Coincidence spectra recorded in the 17% Ge(Li) detector corresponding to a selection ofgates set up on the 10 cc Ge detector. The beam energy was 18 MeV.

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182 CAN. J . PHYS. VOL. 58. 1980

FIG. 4. Angular distributions for 30 selected gamma rays in y 6 T ~ . The data for the 128 keV transition were recorded at 14 MeV; the remaining data were taken at 18 MeV. The solid curves correspond to the "calculated coefficients" given in Table 1.

energies of the stronger peaks are allowed to float and the energies of the nearby weaker peaks (both K and L and M) fixed with respect to the stronger ones. After the multipolarity and mixing ratio of a strong peak was determined through a combination of its angular distribution and electron intensity, KIL and KIM ratios were estimated and used to define the intensities of each L and M ~ e a k relative

parameters over the momentum range defined by one window. These parameters were required to change slowly over the total spectrum. Whereas the earlier program with fixed positions for all the peaks tended to fail on complex spectra, ANABEL has consistently provided reduced X' values ap- proaching unity for very complex structures.

The resDonse function of the electron detector in to its K peak in the fitting process. The analysis was the beta-ray spectrometer was measured at various then repeated with both the energies and intensities electron energies using the beta spectrum of ' 9 8 A ~ . of such peaks fixed with respect to the strong ones. The response function consisted of a Gaussian

The peak shape in ANABEL was assumed to be peak and a Wood-Saxon tail one tenth of the height a skewed Gaussian with constant width and tailing of the Gaussian. The electron distribution was

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MACH ET A L

-

J I

-

6 926

Y L Z L B W t l 96 f8

9 6 b 8

f ILE

- W + l 8 81s

0 9 E E Y 0 9 E E

2 S Z E BBIE

E OlF N E O I E c==Iz -

Y S f 0 2

Y EEBl

Y 6 f E I

- - - -

1 1 1 1 1 1 I I I 1 1 1 1 1 1 \. 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 I

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184 CAN. J . PHYS. VOL. 58. 1980

measured at various pp values during the experi- ment. The electron detection efficiencies ranged from 0.65 and 0.77 depending on the gains and discriminator settings used.

Normalization between the gamma-ray and electron intensity scales was provided through the 927 and 995 keV transitions whose angular dis- tributions suggest that they are stretched E2 in character. Since the theoretical ct, vs. energy curves for M 1 and E2 transitions cross at -700 keV and are only slightly separated up to 1 MeV, these transitions would provide a good calibration even if they were of M1 f E2 character.

Discussion The results of the present investigation are sum-

marized in Fig. 6 which shows a large number of high spin states up to an excitation energy of 3 MeV connected by dipole and quadrupole transitions and a number of lower spin states seen in earlier work. The transitions included in Table 1 and Fig. 6 all show excitation functions characteristic of y 6 T ~ and nearly all the relationships between them are based on y-y coincidence data.

The level scheme of Fig. 6 has been tested by comparing the coincidence probabilities derived from a large number of coincidence spectra with those deduced from the level scheme. In general, the two sets of values agree within 25% for all but very weak transitions.

In addition to the gamma rays tabulated in Table 1 and placed in Fig. 6 there are many other moder- ately weak transitions which show excitation func- tions characteristic of y 6 T ~ . Many of these are clearly related to the low spin states observed in the (p,n) and (d,2n) studies. Inasmuch as these transi- tions are much more intense in the (a,n) spectra taken at 14 MeV than in those recorded in the pres- ent studies at 18 MeV, they will be discussed in a subsequent paper.

The ground state decays to y6Mo with a 4.28 day half-life (12). The 34.3 keV state has a lifetime of 51.5 min and decays to the ground state of y 6 T ~ via an M3 transition (98%) and to y6Mo by electron capture (2%). The spins and parities of these two states are well established as 4+ and 7+, respec- tively, from these decay studies and these assign- ments will be accepted as a starting point for the discussion to follow.

The present experiments confirm the existence of the doublets of energy 85.3, 86.1 and 219.3, 220.0 keV which led Doukellis et al. (1) to propose a pair of states at 34.3 and 35.0 keV. While it is clear that one of these is the 4+ level at 34.3 keV, there is no evidence from either their experiments or ours

to distinguish between 35.0 or 33.6 keV for the energy of the other. The argument in favour of the 35.0 keV choice seems to rest on the work of Ageev et al. (13) who found no L-conversion lines corre- sponding to what would be a strong 33.6 keV tran- sition were the second option chosen. We thus reject the 33.6 keV choice.

Most of the states to the left of Fig. 6 with excita- tion energies below 500 keV have been identified in earlier work. However, the present experiments provide a significant number of additions to the supporting data available. Results from unreported (3He,d) experiments in this laboratory and recent work by Emigh et al. (5) indicate that the ground state, at least one of the 34.3,35.0 keV pair, and the 45.3 and 49.3 keV states are all of positive parity. These experiments also suggest that the 120.3, 3 15.2, 35 1.1, 549.9, 865.3, and 976.4 keV states are of negative parity. These results are consistent with the data of Table 1 and in agreement with the con- clusions of Doukellis et al. (1) and of Kern and his co-workers (2, 3) for the parities of states up to and including the 351.1 keV level. The fact that the 549.9, 865.3, and 976.4 keV states are not popu- lated in the (p,n) reaction suggests very strongly that their spins are greater than 4. This argument will often be used to distinguish between high and low spin assignments in thediscussion thatfollows.

Evidence from the particle transfer work refer- red to above and the isobaric analog resonance measurements of Doukellis et al. (1) and Miracle and Kern (3) requires that the 120.3 keV state has negative parity. The 86.1 keV transition from this level to the 4+ state at 34.3 keV is of the AJ = + 1 type from our angular distributions and is E l in character from the internal conversion data of Miracle and Kern (3). Moreover, the 120.3 keV state is strongly populated in the (p,n) reaction. J K for this state is thus uniquely determined as 3-; neither the 4- or 2- assignments proposed by earlier workers (1, 4) can be reconciled with the present data.

The spin and parity of the 35.0 keV state have been the subject of much speculation. Given the 3- assignment to the 120.3 keV state, the AJ = k 1 character of the 85.3 keV transition (known to be El from ref. 3) leads to J K = 2+ or 4+ for the 35.0 keV state. The 2+ choice can be eliminated by considering the properties of the negative parity states at 3 15.2 and 549.9 keV. The spin of the latter state is limited to 5 by the presence of the AJ = + 1 transition of energy 515.8 keV and by the fact that the level is not observed in the (p,n) studies. With 5- for the 549.9 keV level, the properties of the 194.9-234.8 keV cascade and the 279.9 keV transi-

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MACH ET A L .

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186 C A N . J . PHYS.

tion uniquely define J" = 4- and 4+ for the 3 15.2 and 35.0 keV states, respectively. The 3+ assignment for the 35.0 keV level favoured by Doukellis et nl. (1 ) is inconsistent with our data.

The four levels at 120.8, 315.2, 549.9, and 976.4 keV appear to form a relatively well-defined band structure, as shown in graph D of Fig. 6. The last two members ofthe structure are not pop~~lated in the (p,n) work but are strong in both the 14 and 18 MeV (cr,n) experiments.

Since the 254 keV state is more strongly popu- lated in the (p,n) than in the (cr,n) reaction, its spin is less than 5. It deexcites to both of the pair of states at 34.3 and 35.0 keV. Angular distributions taken at 14 MeV show that the transition to the 34.3 keV level is of AJ = f 1 character, while the internal conversion data show that it is M 1 (3). Thus J" for the 254 keV state is almost certainly 3'.

The 226.2 keV state is also more strongly popu- lated in the (p,n) than in the (cr,n) reaction. The AJ = f 1 character of the strong 105.9 keV transition to the 3- state at 120.3 keV leads to J = 2 or 4 for its spin assignment with the smaller value strongly preferred. The internal conversion data of Miracle and Kern (3) indicate that the 105.9 keV transition is M1, a conclusion that is supported by their isobaric analog resonance measurements and those of Doukellis et a / . (1). We thus conclude that the 226.2 state has J" = 2-, despite the contradictory claims of Madueme and Arita (4).

The coincidence relationships that exist between the 183. 192,263,322,426,506, and 515 keV gamma rays lead conclusively to the level structure at the extreme left of Fig. 6. (The data taken at 14 MeV give a much clearer picture for these states than do those at 18 MeV.) These coincidence data and the energy measurements require levels at 43.8, 227.0, and 490.9 keV as well as those at 549.9 and 976.4 keV which have already been discussed. (For reasons to be given later, the 43.8 keV state is shown as 45.3 keV at the left of Fig. 6.) In the absence of such coincidence data, earlier workers failed to recognize that the 226 keV level was really two levels, of energies 226.2 and 227.0 keV. This failure led Miracle and Kern (3) to force the 191.9 keV transition, which is clearly M1 from their own measurements, to be regarded as an El + M2 mixture. The Ml , A J = + 1 character of the 183.3 and 263.9 keV radiations, the M1 nature of the 19 1.9 keV and the E 1 character of the 322.6 keV gamma rays lead naturally to positive parity as- signments for the 43.8,227.0, and 490.9 keV levels. These data also restrict the spins of the three states to one of the three sequences 5-4-3, 4-5-4, or 6-5-4, respectively. The last possibility is highly

VOL. 58. 1980

unlikely in the absence of what would be an M1 transition between an assumed 6+ state at 43.8 keV state and the 7+ ground state. The strength of both the 183 and 263 keV gamma rays in the (p,n) work would make 4+ and 3+ the preferred assignments for the 227.0 and 490.9 keV levels but the 5+, 4+ choice cannot be rejected. It should be noted that there may be two states close to 44 keV, a question which will be addressed when the high spin states to the right of Fig. 6 are dealt with.

The remaining levels at the left of Fig. 6 form part of the much more complex structure of low spin states discussed by others. They have been in- cluded here only because they offer some support for the high spin states discussed below.

The gamma-gamma coincidence data necessi- tate a level at 49.3 keV as first proposed by Bini et nl. (6). The photon intensity identified as feeding this level is 181 and there may well be a further 40 units of intensity associated with unidentified gamma rays. These limits and the measured photon intensity of 68 lead to a value of a, for the 49.3 keV transition in the range 1.65 to 2.25 which is to be compared with the theoretical values of 2.15 and 16.1 for MI and E2 transitions, respectively. It is thus clear that the 49.3 keV transition is M1 in character. A similar conclusion is arrived at by reworking the data of Madueme and Arita (4). The 177.0 keV state decays to the 7+ ground state. It is also connected to the 4+ state at 34.3 keV and the 49.3 keV state by MI transitions of AJ = f 1 character. These facts uniquely define J" for the 49.3 and 177.0 keV states as 6+ and 5+, respec- tively.

The 45.3 and 318.8 keV states shown at the right of Fig. 6 are required to account for the coincidence data involving the strong 255,273,3 18, and 37 1 keV transitions as well as several of the cascades ex- tending to high excitation. The 273 and 318 keV gamma rays are not in coincidence, but "see" the same set of gamma rays in their coincidence gates. Their excitation functions are identical, as one would expect for transitions from a common level, and characteristic ofan initial state of medium spin. The M 1, AJ = + 1 character of these two transitions restrict J" to 6+ or 8+ and 5+, 7+, or 9+ for the 3 18.8 and 45.3 keV states, respectively. The excitation functions would favour the 6+ choice of the first pair, leaving 5+ or 7+ as possibilities for the 45.3 keV level.

The energy of the 45.3 keV state is 1.5 keV higher than that of the 43.8 keV state discussed earlier. Although this energy separation is significantly larger than the cumulated errors ex- pected in going around the various "energy loops"

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MACH ET AL. 187

used in establishing these energies, several of the gamma-ray peaks involved appear to be too wide for single transitions. It thus must remain an open question as to whether there are one or two levels at 45 keV. Figure 6 shows them as identical with J" = 5+, the only choice common to the pair of states.

The ground state transition from the 45 keV state has not been observed. The expected intensity for such a transition would be in excess of 1.8 or 13 depending on whether it is E2 or M 1. While a peak of intensity 1.8 might have been missed in our 18 MeV experiments, it should have been seen in the 14 MeV spectra of Bini et al. (6). It is attractive to speculate that the transition is missing because of the competition fromfast M 1 transitions to either or both of the 4+ states at -35 keV. (Doukellis et al. (1) in fact reported an 11.8 keV transition of the appropriate energy, but placed it high up in their decay scheme.) For this mechanism to be valid, J" for the 45.3 keV state would have to be 5+; that for the 43.8 could still be either 4+ or 5'.

Since the (a,n) reaction transfers a large amount of angular momentum to the target nucleus, the residual nucleus is formed in a high spin state from which it deexcites by a gamma-ray cascade which carries away its excess angular momentum. Thus, in general, the spin of the initial state is higher than that of the final. This argument will be used in favour of the adoption of the higher initial spin when the angular distribution data cannot distin- guish between two choices.

The assignment of spins and parities to the high spin levels of Fig. 6 is made difficult because the internal conversion coefficients for M1 and E2 transitions in the important 500 to 800 keV range are indistinguishable. Angular distributions alone rarely yield unique spin information, since those with large negative A, coefficients can be equally well described by transitions where AJ = J, - J , = + 1 or -1 and those with large positive A, coefficients can be attributed to transitions where AJ = -2 or 0. The AJ = 0 choice is unlikely in a nucleus like 9 6 T ~ since it requires a large E2 ad- mixture and does not allow for the progression in spins characteristic of the (a,n) reaction. Finally, while the excitation functions of Fig. 2 are useful in indicating whether a transition originates in a high, medium, or low spin state, they are more able to indicate "trends in spin" rather than to lead to unique spin assignments. The discussion of high spin states which follows must be set in this con- text.

The AJ = -2 character of the 897, 926. and 995 keV gamma rays define J" as 8+, 9+, and 1 1' for the 946, 926, and 1922 keV states. The AJ = 0

nature of the 225 keV transition and the M 1, AJ = & 1 character of the 169 and 395 keV radiations lead to J" = 1 1 + and 12+ for the 2147 and 23 17 keV states. The presence of a triple cascade of AJ = + 1 transitions connecting the 946 and 2147 keV states and the AJ = - 2 cross-over transitions define J" as 9+ and 10+ for the 1447 and 1702 keV levels. The 7+ assignment for the 574 keV level follows from the AJ = & 1 character of the 525 and 371 keV transi- tions, of which the latter is known to be M1. The 13+ and 14+ assignments to the 2598 and 2642 keV states are highly probable.

The AJ = -2character of the 1013 keV transition leads to an 8+ assignment for the 1062 keV state. The AJ = + 1 behaviour of the 799, 914, 351, and 183 keV gamma rays, together with knowledge that the latter two are M1, enables one to say that the spins of the 1861, 2213, and 2396 keV levels are probably 9, 10, and 11 and that all three states have the same parity (presumably positive). The 12+ as- signment to the 3020 keV level follows from the AJ = -2 character of the 806.6 keV gamma ray.

There are a number of high energy transitions of appreciable intensity with excitation functions characteristic of 9 6 T ~ which do not appear to be in coincidence with any other gamma rays. We have chosen to include the strongest of these in Table 1 and used it to define a level at 1138.8 keV. Because there are so many low-lying states available, neither the energy nor the spin of such levels can be regarded as secure.

The coupling of a g9/, proton and a d,,, neutron should create a positive parity ground state configuration of six levels with spins ranging from 2+ to 7+. It is tempting to identify the states of energy 0.0(7+), 49.3(6+), 45.3(5+), 34.3(4+), and 254.3(3+) with this configuration but there are obvi- ously other equally acceptable choices. In the pres- ent state of knowledge of this highly complex level structure, it seems idle to speculate further.

Attempts to order the high spin states into "rota- tional bands", as has been done in Fig. 6, are not very successful. The four sequences shown are all roughly linear. However, the lines joining the levels are rather arbitrary, because transitions between "bands" appear to be just about as intense as those within bands.

Acknowledgments The authors acknowledge the assistance of other

members of the research group in obtaining the data presented. In particular, we should like to ac- knowledge the contribution of Kay Marshall Thompson whose work on 9 5 T ~ (7) gave insights into the behaviour of 9 6 T ~ . This work has been

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188 CAN. J . PHYS. VOL. 58, 1980

supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

I. G. DOUKELLIS, C. MCKLNNA, R. F I N L A Y , J . RAPAPORT, and H. J . K I M . NucI. P h y s A, 229.47 (1974).

2. B. D. K ~ R N , F. GABBARD, R . G . KRUZEK, M. R. MCPHER- SON. K. K. SLKHAVAN, and F. D. SNYDER. P h y s Rev. C , 18, 1938 (1978).

3. D. E. MIRACLL and B. D. KERN. NucI. Phys.A, 320. 353 (1979).

4 G. CH. M A D U ~ M L and K. ARITA. NucI. Phys. A, 297. 347 (1978).

5. R. A. EMIGH, J . J . KRAUSHAAR, and S . SHASTRY. N u c ~ . Phys. A, 320.335 (1979).

6. M. BINI. A. M. BIZZETI SONA. P. G . B ~ z z t r ~ , P. BLASI, A. O L M I . and N. TACCETTI. NUOVO Cimento A, 35,69(1976).

7. K. A. MARSHALL, J . V. THOMPSON, W. B. COOK, and M W. JOHNS. Can. J . Phys. 56, 1 17 (1978).

8. T . S H I B A I A, T . IT AHASHI, and T . WAKATSUKI. NucI. Phys. A, 237,382 (1975).

9 H. EJIRI. T . SHIBATA, A. SHIMIZU, and K. YAGI. J . Phys. Soc. Jpn. 33, 1515 (1972).

10. T . YAMAZAKI. NucI. Data A. 3, l(1967). l I. D. W. 0. R o c t ~ s . Nucl. Instrum. Methods, 127,253(1975).

12. L . R. MEDSKER. NucI. Data, B. 8,6(1972). 13. V. A. AGEEV, V. I. G A V R I L Y U K , V. T . KUPRYASHKIN, G.

D. LATYSHEV, I. N. LYUTYI, V. K. MAIDANYUK, Y. V. MAKOVETSKII, and A. I . FEOKTISTOV. Bull. Acad. Sci. USSR, Phys. Ser. 33. 1180(1970).

14. J . R. HUIZENGA and G. IGO. Argonne National Laboratory report. ANL-6373 (1961).

Appendix: Estimation of Attenuation Coefficients The attenuation coefficients used in the analysis

of the angular distribution data were estimated using a computer program (NELLY). The model used in this program is illustrated in Fig. 7.

The normalized population parameters for the compound nucleus, P(Jc), and the associated at- tenuation coefficients Bx(J,) were calculated for a level of spin J, in 9 7 T ~ . This nucleus is formed by the transfer of 1 units of angular momentum to a randomly oriented 93Nb target of spin J, by means of the incoming a particle. P(J,) is given by

J c + J t rrnax+Jt J c + J t 25 + 1

[ A l l P(J.1 = [ ~ = I J . - J I I ] 2Jt + / [ J,=O 1 ~ = I J , - J , ~ * T I ] 2J1 +

where T, is the transmission coefficient for a capture derived by Huizenga and Igo (14), l,,, is the maximum possible I transfer for the beam energy used, and where for simplicity we use the abbreviation

[A21 P1( J3 = [(2Jc + 1)1(2Jt + 1)1T,

The alignment parameters Bh(J,) which define the average orientation of the spin vector J, of the compound nucleus with respect to the beam axis are given by

In this expression

[A41 Uh(Jl 4 J2) = (2 J1 + 1)Il2(2 J2 + 1 ) I l 2 W ( J l A J J 2 ; J 1 J 2 )

The values of B2(Jc) and P(Jc) derived from the calculation are shown as a function of J, in the curve and histogram at the top of Fig. 7. Although the values of J, are half-integral, we have plotted P ( J c ) and B2(Jc) vs. J, - i for convenience of pres- entation. These coefficients form the starting point for calculating the attenuation which occurs as the compound nucleus deexcites by the emission of one neutron and many gamma rays to the observed levels of 9 6 T ~ .

The attenuation coefficients before and after the emission of a single particle or gamma ray are re- lated by the expression

where i and f are the initial and final states of spin Ji and Jf and j is the angular momentum carried away in the transition.

For the case of neutron emission, however, it is more convenient to use a slightly different expres- sion which takes into account the preponderance of A j = &neutrons in the decay process. In neutron emission, a given final state is fed by the initial states of spin Jf + f for s-wave and by the initial states of spin Jf + f, Jf +_ 3forp-wave neutrons. By ignoring spin changes of f and treating neutron

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MACH ET A L . 189

-- -- I W . - ____ - - - - - ATTENUATION COEFFICIENTS FOR

B2 0 6 STATES I N THE COMPOUND

I' NUCLEUS "TC

ool . ---- -- -1 RELATIVE POPULATION OF T H E

COMPOUND STATES

DECAY OF "TC - 9 6 ~ ~ BY

NEUTRON AN0 GAMMA RAY EMISSION

j GAMMA RAY EMISSION

1 0

0 0 ATTENUATION COEFFICIENTS OF

0 6 4 995 11+-9+ THE STATES IN "TC a 2

0 4

0 2

0 0

J - FIG. 7. Attenuation coefficients for states in y 6 T ~ , 21s populated in the (cr,n) reaction. The diagram also serves to illustrate

the process used in deducing these coefficients (see Appendix).

emission as if no change of spin results, the follow- by only one path, the average attenuation ing approximate expression which takes account of coefficient for any given level can be found by both s and p wave neutrons m;~y be used: computing the weighted average of the attenuation

[ A ~ I u A f i ( ~ , ) = u A i ( ~ i ) l , i = J , [(I - ~ 1 ~ ~ 0 + RUA1] associated with all possible feeding processes. Thus

where R is the fractional A j = $ intensity (-0.4 for 9 6 T ~ ) and

j := 0 [A81 u x f ( ~ , = I n u / " ( J f ) + z I,u,'(J,)

k UAO = UA(J f -+ J f )

[A71 UA' = l / 3 [ u A ( J f + 1 J f ) X Ux(Jk 3 J,)] / I f

+ ( J J ) ( J - 1 J ) where In general, agiven state may be fed by both neutron I f = I n + z I ,

1. and gamma-ray processes, each with its own frac- tional intensity. Since any one nucleus can decay is the total intensity of all branches feeding level f .

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190 CAN. J . PHYS. VOL. 58. 1980

The neutron intensity in [8] will be the value of P(J,) appropriate to the spin of the state being fed; the photon intensities, from any given spin value will be assumed to be equally divided between all possible decay modes ( A J = + I , 0 , and - 1 for states of moderate spin, AJ = - 1 , 0 for states immediately above the Yrast band and AJ = - I for Yrast states).

With these assumptions, the calculation pro- ceeds in a straightforward manner, commencing with the decay of the state of the compound nucleus J,,,,, with maximum spin. In the first step, this state may decay to any one of a group of states with the same spin, all experiencing the same attenuation. In the second stage. the calculation considers both the group of states of spin J,,,, - I which are fed by neutron emission and photons from states of J,,,,, and the group of second generation states of spin J,, - 2, J,, - 1 , and J,, are considered and so on. each group. In the third stage, groups of states of Jmas - 2 J,,,, - 1 and J,,,, are considered and so on. After an N-fold cascade, the spin J,,,, states reach the yrast level and must transfer all their intensity to J,,,,, - 1 levels. The process thus builds up more and more side feeding as it continues to states of lower and lower excitation, maintaining the high

degree of alignment characteristic of the compound nucleus in the observed states. The results are es- sentially independent of the value of N chosen (the values of a 2 obtained for calculations with N = 4 and N = 7 differed by less than 3%).

The values ofa, resulting from these calculations are presented in Fig. 7. The upper curve results from the model if one assumes that the side feeding is continued down to zero spin. This is clearly not so for 9 6 T ~ , as a glance at Fig. 6 will show. The lower attenuation curve was derived on the assumption that 66% of the intensity reaching spin 9 is trapped by the 7+ ground state, and that similar trapping occurs for the low lying 4+ states. This trapping reduces the side feeding and hence the degree of alignment of all states of spin less than 7. We have chosen to use the average of the two models, shown as the middle curve, for the calculations of Table 1. The uncertainties in the a , values calculated by this model are roughly 5% for spins above 9 and roughly half the width of the shaded area for lower spins.

As has already been indicated, it was possible to determine o and 6 for a few transitions. The attenu- ation coefficients for the values of o so measured are shown on Fig. 7; the agreement is gratifying.

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