Measurement of mean lifetimes, γ-ray angular distributions and linear polarizations for low-lying levels of 50V

ll.E.1:2.B/

Nuclear Physics A232 (1974) 200-214; Not to

MEASUREMENT AND LINEAR

North-Holland

Publishing

OF MEAN LIFETIMES, y-RAY ANGULAR POLARIZATIONS D. G. RICKEL Duke

Triangle

@

Co., Amsterdam

be reproduced by photoprint or microfilm without written permission from the publisher

FOR LOW-LYING

DISTRIBUTIONS

LEVELS

OF “V+

and N. R. ROBERSON

University,

Universities

Durham, North Carolina 27706 and Nuclear Laboratory, Durham, North Carolina

27706

and R. 0. NELSON,

J. R. WILLIAMS

and D. R. TILLEY

North Carolina State Triangle

Universities

University, Raleigh, North Carolina 27607 and Nuclear Laboratory, Durham, North Carolina 27706

Received 11 June 1974 Levels of “V were populated with the 50Ti(p, n)50V reaction at Ep = 4.50, 4.62 and 4.80 MeV. Gamma rays were measured in singles. From Doppler shift attenuation measurements mean lifetimes have been deduced for 9 levels below E, = 2 MeV. The .P’ assignments for 8 of these levels follows from y-ray angular distribution and linear polarization measurements. The transition strengths have been compared with calculations based on the wave functions of McCullen, Bayman and Zamick.

Abstract:

E

NUCLEAR REACTION 5oTi(p, ny), E = 4.50, 4.62, 4.80 MeV; measured Er, Iv, nv-coin. v(B). P..(O). DSA. 5oV levels deduced J. z. TA, 6, y-branching ratios.

1. Introduction

Several investigations of the level structure of5 ‘V have been reported in the last few years. As a result 96 levels of E, < 4.6 MeV have been established. Much of this previous work has concentrated on determinations of level excitation energies and DWBA analysis of angular distributions. Most of these levels have been assigned I-values from one or more reactions. A review of these works is given in ref. ‘). Since 5oV is a doubly odd nucleus the range of spin possibilities for a level, in most instances, is not appreciably restricted by determining the angular momentum of the transferred particle (for example, a Z, = 3 transferred proton from the 4gTi(z, d) reaction allows 0 < J < 7). Deuteron transfer reactions have been investigated for 5oV [ref. “)I and have overcome this problem to some degree by limiting the spin choice to three possibilities. With the above information, arguments based on nuclear f Work supported in part by the United States Atomic Energy Commission. 200

systematics and agreement with predicted spectroscopic factors have allowed tentative J” values for a number of the low-lying states. Gamma-ray decay systematics from recent (p, ny) studies “) are in accord with most of these assignments. At present the J” values for the first five levels as well as the 911 keV, 1331 keV and 1495 keV levels have been established. The purpose of the present work was to obtain spin-parity assignments for as many of 5‘V levels as possible via measurements of y-ray angular distributions and linear polarizations and to measure the mean lives of these levels. 2. Experimental details 2.1. THE 50Ti(p, ny)50V LIFETIME

MEASUREMENTS

Lifetimes of nine levels of 5‘V were determined with the Doppler shift attenuation method. Proton beams of 4.50,4.62 and 4.80 MeV were accelerated by the TUNL FN Van de Graaff and used to bombard an isotopically enriched “Ti foil. The target had no backing and was 1.4 mg[cm’ thick. All data were recorded in singles, and the levels of interest were populated near threshold to insure the forward recoil of the 5oV nuclei. The y-ray spectra were recorded at nine angles ranging from 0” to 145” with a 30 cm3 Ge(Li) detector placed 12.7 cm from the target. To insure that accurate relative energy shifts were measured the spectrum recorded at each angle was preceded and followed by a calibration spectrum. The count rate effects on the gain were minimized by recording the calibration spectra at the same count rate as the Doppler shift data. Gain shifts were also continuously monitored with a 137Cs source. The photopeak energies were determined from first moment calculations with a background subtraction routine. One exception to this analysis was in the instance of the 943 and 946 keV y-ray events. These two photopeaks were not completely resolved and their separate centroids were computed by fitting the line shape to two Gaussians of equal width. Only the centroid of the more intense 943 keV transition could be located accurately with this technique. The uncertainty of this centroid was chosen to be the amount that the 943 keV photopeak should be shifted by the presence of the 946 keV transition, which is approximately 10 % of their separation. The Doppler shifts were determined from a least-squares fit to the centroids of the photopeaks as a function of the cosine of the lab angle. To determine the experimental Doppler-shift attenuation factors, ratios were taken of the observed shifts to the maximum possible shifts. The expected full shift of each transition observed was computed taking into account the energy loss of the protons in the target, a changing cross section assumed proportional to (I?,-I$#, and the velocity distribution of the 5oV recoiling nuclei. Low energy (p, n) angular distribution studies on medium mass nuclei indicate that the recoil velocities are generally symmetric about 90” in the c.m. frame “). This then enables the use of VCmas the average recoil velocity for “V.

D. G. RICKEL

202

et al.

TABLE 1 Decay properties of the levels of 5oV Energy level

Transition

Ji

Jf

(keV)

Branching ratios

6 4.50 MeV

(keV) 836.1 910.2 1300.8 1331.0 1401.4

1494.8 1518.0 1561.4

1676.7

The “) b, ‘)

516.0f0.4 836 il 684.010.3 912.9kO.3 946 il 943.110.4 1013.510.3 1046.3f0.5 1082.1 f0.5 1106.9&0.3 1130.1*0.3 1162.910.3 1173.1 f0.3 1206.5&0.3

5+ 4+ 2+ 1+ 3f

1+ 2f 2+

(1, 3)+ 277 il 375.710.4 1289 +1 1321.711110.3

Doppler Relative The 946 Relative

4+ 6+ 5f 2+ 3f 2f 2+ 3f 4f 2f 2+ 3+ 2+ 3+

49 “) 51 100 61 “) 39 100 67 “) 23 10 100 8252 18k3 4912 51 A2

3+ 2+ 2+ 3+

11 “) 54 15 20

F(z) 4.62 MeV

0.08&0.40

4.80 MeV

Mean life (fs)

43&9

110&40

4015 5913

4616 50+5

110&12 75*15

0.00~0.20

83*3 Of3

0.06f0.01

5613 22t5

78%4 -515 -259 -919 52_C4 2214 2016

0.01*0.09 0.12*0.05

42f8 5213

0.00f0.20 -0.01&0.16

24&

8

5*4 10*4

74*10 270&50 345*90 t > 550 z > 220

7*5

z > 500

shift data for ED = 4.50, 4.62 and 4.80 MeV are listed. intensities at 90” in ny coincidence. keV transition is a member of a doublet. Areas were extracted by a two-Gaussian intensities at 90” from ref. 3).

fit.

The theoretical P(Z) values were calculated with the computer code FTAU ‘) which is based on the work of Blaugrund “) and the stopping-power theories of Lindhard et al. (LSS) ‘). The LSS values for electronic stopping power were used in the calculation. The F(z) values and lifetimes are listed in table 1. The total errors in the mean lives result from statistical uncertainties in the measured Doppler shifts and assumed uncertainties of 5 % for the full shift and 15 % in the electronic stopping power of the target. 2.2. THE

50Ti(p, ny)50V y-RAY

ANGULAR

DISTRIBUTIONS

The same equipment and procedure described previously was used for the angular distribution measurements. Data were taken in singles with the Ge(Li) detector placed 14.7 cm from the target. Spectra were obtained for seven angles ranging from 0” to 90”. Beam energies of 4.62 and 4.80 MeV were selected which are just above the threshold for population of the levels of interest. The data were normalized to the integrated beam current and corrected for analyzer dead time. To minimize this dead time a 0.2 cm thick lead disk was placed on the face of the Ge(Li) detec-

203

sOV

tor to attenuate X-rays coming from the target and beam stop. The angular distributions were analyzed using a variation of method II of Litherland and Ferguson “). Normally, with this method only y-ray events which are in coincidence with particles detected on the beam axis are recorded. This limits the population of the magnetic substates of the levels observed. In the present experiment the outgoing neutrons were undetected but the levels were populated near threshold and alignment would be expected since emission of neutrons with low l-values would be favored. In order to estimate the relative magnitudes of s-, p- and d-wave neutrons of appropriate energies, an optical model calculation of transmission coefficients was performed with the computer code ABACUS II “). Optical model parameters were taken from the work of Perey and Buck lo). Using these transmission coefficients the population parameters were found with a statistical model calculation coded by Gould ‘I).

10

X2

-C

I -90

I

-60

1

I

-30

0 arctan

I 30

I

60

I 90

6

Fig. 1. The upper portion of the figure shows the x2 versus arctan 6 curves, for assumed spins of 3, 4 and 5, obtained from the E, = 4.8 MeV angular distribution for the 516 keV transition to the 4+ level at 320 keV. Lower portion of figure shows calculated polarization for each trial spin (solid lines). The error bars indicate the uncertainty in the calculated polarization for mixing ratios where there are acceptable x2 minima. The hatched region is the measured polarization along with the experimental uncertainty.

-60

0

arctan

-30

30

8

60

90

Fig. 2. Plots of x2 and polarization for the 684 keVtransitionfromthe910 keVlevelatE, = 4.8 MeV. Only Jr = 4+ is a solution.

-90

6

-0.t

O(

I

e I

-60

,;/ ,/,/

I

;/

arctan

-30

3

,‘;,

/

0

1

2

6

1

30

/,.‘,

I

60

Fig. 3. Plots of x2 and polarization for the 913 keV transition from the 1301 keV level at Ef, = 4.8 MeV. Only Jr = 2+ is a solution.

P

O.!

1.(

II

IO!

X2

-60

0

arctan

-30

8

30

60

90

1 Fig. 4. Plots of x2 and polarization for the 943 keV transition from the 1331 keV level at ED = 4.8 MeV. Only .T” = 1+ is a solution.

-90

I

I

T

\

,

1

2

3

+_-I0

1~

orctan

8

0.5 ///I// /////N/N/ ///////N//N//////////

0.0

0.5

1.0

OS

1

IO

d 2 _.I

8 0

2 5oLlJ a G:

IO w

I

2 e

Fig. 5. Plots of x2 and polarization for the 1014 keV transition from the 1401 keV level at &, = 4.8 MeV. Only JT = 3+ is a solution.

P

X2

100

orctan

8

Fig. 6. Plots of x2 and polarization for the 1107 keV transition from the 1495 keV level at ED = 4. 8 MeV. Only Jw = 1.1.is a solution.

-9W

, -90 -60

/

/ 0

arctan

-30

8

I

60

1

30

90

Fig. 7. Plots of x2 and polarization for the 1130 keV transition from the 1518 keV level. Only Jr = 2+ is a solution.

P

e

206

D. G. RICKEL et al.

-90 -60

-30

0

arctan

30

60

-90 -60 -30 0 arctan

YV

8

Fig. 8. Plots of x2 and polarization for the 1173 keV transition from the 1561 keV level. Only Jr = 2+ is a solution.

I

I

30

60

6

Fig. 9. Plots of x2 and polarization for the 1207 keV transition from the 1561 keV level. An E2 transition for a spin-l assignment was included since such an assignment gives an acceptable x2. Only .I” = 2+ is a solution.

An automatic x2 search was performed with the computer code M2 to determine the optimum least-squares fit to the data for various values of spins, mixing ratios 6 and population parameters (I’,). The population parameters were restricted to within +20 % of their calculated value. A more detailed description of the fitting procedure is found in refs. lzy 13). Plots of x2 for differing combinations of spin and mixing ratio are plotted in upper sections of fig. 1 through 9 for all levels from 836 keV to 1561 keV. 2.3. THE sOTi(p, ny)50V y-RAY LINEAR

POLARIZATION

MEASUREMENTS

2.3.1. The polarinaeter. The two-crystal Compton polarimeter used in this work follows the design by Bass et al. “). Two closed-end co-axial Ge(Li) crystals each with an active volume of 30 cm3 are placed side by side with axes parallel as shown in fig. 10. Both crystals view the target and are symmetrically placed with respect to it.

207 Beam Direction

_-_-

TorgeP

a r

Y

Ge(Li)

Diode

*)A

-----

/

&

Detector

--___

. Ge(Li)

“;\‘x:‘,“’

Rotation Axis

Diode

Fig. 10. Schematic drawing of the polarimeter showing alignment of the Ge(Li) diodes and the target orientation. The polarimeter rotates 90” about the rotation axis.

The cryostat is mounted on a platform and rotates ? 45” about the detector axis (see fig. 10). The plane that is defined by the axes of the individual crystals then can rotate to a position either coincident with or perpendicular to the reaction plane. The y-ray signals from each crystal are separately amplified, and those signals associated with coincident events in the two crystals were allowed to pass through linear gates. The linear signals were then summed to produce a total energy signal. Each of the three linear pulses and a time-to-amplitude signal were processed by analogue to digital converters interfaced to the TUNL on-line computer. All events were recorded on magnetic tape for later off-line analysis. It should be noted that the electronics set a 50 keV cut-off for the y-ray events in each detector, but that it was possible to increase this threshold during the off-line analysis by setting digital windows on the events recorded on magnetic tape. The energy resolution of the individual detectors was less than 2.4 keV FWHM for a 1.33 MeV y-ray, while the resolution for the summed events was 3.5 keV. FWHM. The time resolution was 120 nsec FWHM which with the modest counting rate (2000 cts/s) gave a true to chance ratio of better than 100 to 1. 2.3.2. The polarimeter calibration. The experimental quantity determined by the polarimeter is the asymmetry between the areas of a y-ray photopeak measured with the device in the two orientations described above. The y-ray linear polarization (P) can then be related to the asymmetry (A) by the expression A = SP, where S (the polarimeter sensitivity) is a function of the geometry, the y-ray energy and the lower level threshold set on each of the detectors. This sensitivity was determined both from experimental measurements and a computer analysis. A computer code was used to compute the two probabilities, Y’I and P,, , of absorbing in one Ge(Li) crystal a linear polarized y-ray originating from the target which has been Compton scattered from the other Ge(Li) crystal. These two probabilities are distinguished by the fact that in one instance the E-vector is perpendicular to the plane defined by the axes of the two crystals and in the other instances the E-vector is parallel to this plane. The sensitivity is then defined as

D. G. RICKEL et aI.

208

In the case of a non-isotropic angular distribution, a correction must be made to the sensitivity to account for the differences in counting rate for the two orientations. The code has provisions to include the experimentally determined angular distribution

/ 400

OO

I

/ BOO

Gamma-ray Fig.

, 1200

Energy

/

/ 1600

4v(Jr

50Ti(p,n rJ5’V

‘,

2000

CkeV)

11. The calibration cnrye derived for the Ge(Li) polarimeter.

f

/

The threshold chosen was 150 keV.

& 90”

:

;Ii ,

jj I’

% -

CHANNEL NUMBER Fig. 12. Representative spectra obtained with the polarimeter of 5oV at Ep = 4.8 MeV. The upper spectrum was taken with the plane defined by the axes of the Ge(Li) diodes perpendicular to the reaction plane. The lower spectrum was obtained with the polarimeter rotated 90” from the above position.

209

SOV

in the calculation of 9, and L?,, . For this work, the polarimeter was located 13 cm from the target and in all cases the corrections to S were negligible. The code also has provision for varying the lower energy threshold for the coincidence events detected in each crystal. Experimental determinations of the sensitivity with respect to y-ray energy consisted of measurement of angular distributions and asymmetries for the pure E2 2+ -+ Of transitions in “Ti, 28Si, 24Mg, and the 3’ + 4’ transitions in lo7, logAg which are known to be E2. From the polarizations predicted by the angular distributions of these transitions and their measured asymmetries a sensitivity for each of these y-ray energies is found. Fig. 11 shows these calibration points plotted along with the sensitivity curve predicted by the computer code. A lower level threshold of 150 keV was used both for the data and the code. 2.3.3. Livlear polarization measurements of 5oV transitions. The polarimeter was placed 13 cm from the target; the detector axis was perpendicular to the beam direction. Bombarding proton energies and the target orientation were the same as for the angular distributions. Several spectra were taken at each detector orientation for each energy. Fig. 12 shows the spectra for both polarimeter orientations at EP = 4.8 MeV. Normalization was provided by the integrated beam current corrected for the analyzer dead time. Areas of the photopeaks were determined by a computer background subtraction routine that consisted of least-squares fitting each peak to a Gaussian with a linear background. Once the background was determined it was subtracted from the total area encompassing the peak. Then these areas were determined for each detector orientation and the asymmetry was found using the formula A =Y - A,-AII

.

&+AII

The symbols A, and A,, are the areas of the photopeaks for the plane of the polarimeter oriented perpendicular and parallel to the reaction plane respectively. The statistical uncertainty of Aasy is to a good approximation given by O==

1 ___. k+A,,

This error was increased by a factor of 3 to account for the uncertainty in selecting the correct low energy boundary of the photopeaks. Table 2 lists the measured asymmetries and the corresponding polarizations of the 5‘V y-rays. The bottoms of figs. l-9 show these values as shaded bands compared with the predicted polarizations (solid lines) for various combinations of initial spins and mixing ratios based on the measured angular distributions. The error flags shown with the solid lines jndicate the uncertainty in the predicted polarization due to the statistical errors of the angular distribution data.

210

D. G. RICKEL

et al.

TABLET

The y-ray asymmetries measured with the polarimeter

y-ray WV)

Asymmetry

516 684 913 943 1014 1107 1130 1173 1207

-0.185&0.024 -0.037&0.014 0.093 f0.011 -0.005~0.007 -0.112&0.014 -0.005~0.009 0.080*0.019 0.131*0.020 -0.076&0.018

Polarization

-0.49,tO.O6 -0.12&0.04 0.3410.04 -0.02+0.03 -0.47&0.06 -0.02,tO.O4 0.36f0.09 0.5910.10 -0.36&0.09

The results with Ep = 4.80 MeV are shown. 2.4. THE

(p, ny) COINCIDENCE

MEASUREMENTS

The y-ray spectra in coincidence with the neutrons was measured at 5.5 and 6.0 MeV. As a result of this measurement the 836 keV ground state transition which was not clearly seen in the singles spectra was observed. All other transitions identified as being from 5‘V were likewise seen. This investigation revealed that no new strong y-ray transitions appeared at the higher proton energies although a few weak transitions were seen that corresponded to transitions from higher excited states. It appears though that y-ray angular distributions on excited states above 1677 keV are not practical at these two proton energies. 3. Experimental results The excitation energies, J” assignments, branching ratios and mean lifetimes for the low-lying 5‘V levels are summarized in fig. 13. Table 1 presents the lifetime results and also includes the mixing and branching ratios. Only the x2 fits for E, = 4.8 MeV angular distributions are shown in the present work since the 4.62 MeV results are essentially the same. Parities of all the levels observed in this work, except possibly the 910 keV level, have been previously established as positive by DWBA analysis of stripping and pick-up reactions “14 ). It should be noted that if the parity of the initial state were negative rather than positive the polarization predicted by the y-ray angular distributions changes signs but keeps the same magnitude. The properties of the individual levels are discussed below. 3.1. THE 836 keV LEVEL

Two y-ray decay branches are observed for this level, one of 516 keV to the 4+ level and a weak decay to the ground state observed only in the n-y coincidence data. The Doppler shift, angular distribution, and linear polarization of the former transition was measured. The x2 fits are shown in fig. 1. The angular distribution limits .7

211

6

0 50

V

Fig. 13. Experimental level diagram with decay scheme. The previous work of ref. 2, established .P values for levels at 1331 and 1495 keV. For the levels at 836, 1401, and 1677 keV the relative transition rates at 90” are shown in place of the branching ratios.

to either 3 or 5. With the linear polarization results, the possible assignments are limited to 3+ with s(E2/Ml) = 5.7 or 5’ with 8(E2/Ml) = 0.08. The lifetime measurement of 110 fs restricts s(E2/Ml) to less than 0.1, therefore only the J” = 5+ curve gives a tenable solution. Additionally the J” = 3+ assignment would result in the 836 keV y-ray being an E2 transition with an enhancement of 104, an improbable occurrence. 3.2. THE 910.2 keV LEVEL

In the published works to date a level at this energy has been identified as having J” = 7+. This assignment results from the strong 1 = 3 spectroscopic strength observed with the (3He, p) reaction. This strength is predicted for a 7’ level in this region by all theoretical calculations made for 5oV. The data in the present work are inconsistent with this assigment. A 7+ assignment would require the 684 keV transition to be E2 with a strength of 4700 W.U. From fig. 2 it is evident that only spins of 4 to 6 give acceptable x2 fits. If the 910 level is assumed to have positive parity then only J” = 4+ fits the polarization data. If it were assumed to have negative parity then the solid curves would have reversed signs and neither J” = 4- or 6- would satisfy the data. On the basis of existing measurements a doublet appears to exist in this region with J” = 4+ (910 keV) and J” = 7+ (Z 911 keV).

212 3.3. THE

D. G. RICKEL

et al.

1300.8 keV LEVEL

Lifetimes, y-ray angular distributions and linear polarizations have been measured for the two y-ray decay modes of this level. The x2 analysis is summarized in fig. 3. The angular distribution of the 913 keV decay to the 2+ level limits the spin to J = 2 with a mixing ratio of either 6(E2/Ml) = - 2.7 or + 0.12. Both the linear polarization and lifetime results require s(E2/Ml) to be +0.12 .The 946 keV transition to the 3’ state was not completely resolved from the 943 keV transition centroids and areas for both of these y-rays were extracted by a two-Gaussian fit to the photopeak. The angular distribution and the linear polarization measurements resulting from the 946 transition were consistent with the 2+ assignment but had large uncertainties. 3.4. THE

1331 keV LEVEL

This level has been previously established “) as having J” = l+ due to a decay to it from a O+ isobaric analogue state. The present data based on the 943 keV y-ray transition to the 2+ level are in accord with this assignment as seen in fig. 4. Neither the angular distribution nor linear polarization measurements are helpful in establishing the mixing ratio. From its mean life of 24 fs it can be argued that the mixing ratio is close to zero. 3.5. THE

1401.4 keV LEVEL

Of the three y-ray decays observed from this level only the 1014 keV y-ray had sufficient intensity for angular distribution analysis and linear polarization measurement. It was possible though to measure lifetimes for all three decays. On the basis of fig. 5 the assignment must be 3+ with a mixing ratio s(E2/Ml) = +O.OO. 3.6. THE

1494.8 keV LEVEL

Only a transition to the 2+ level was seen. The angular distribution fits and linear polarization measurement shown in fig. 6 establishes this as a 1+ level. The mixing ratio is undetermined but is limited by the short mean life of 74 fs. This level was previously identified as 1+ since it is also fed by a O+ isobaric analogue state “). 3.7. THE

1518.0 keV LEVEL

Doppler shifts, angular distributions and linear polarizations were measured for both transitions from this level. The linear polarization measured for the 1163 keV y-ray has a large uncertainty due to difficulties in fitting the background of the photopeak. Fig. 7 shows the x2 plot and the polarization results of the 1130 keV y-ray and unambiguously determines the level to have J” = 2’ with a mixing ratio of 8(E2/Ml) = 0.06 for the 1130 keV y-ray. Since J” = 2+ the mixing ratio for the 1163 keV transition as determined from the x2 fit can have the values of 6(E2/Ml) = - 19.0, 0.0 or 6(E2/Ml) > +9.0. All three mixing ratio possibilities are also consistent with the measured polarization for this transition. The mean life for this level of 270 fs cannot be used to rule out the mixing ratios with the large E2 strength since an enhancement of 130 W.U. cannot be disallowed.

3.8. THE 1561.4 keV LEVEL

Figs. 8 and 9 show that this level has J” = 2’. The mixing ratio for the 1172 keV y-ray is ~(E2~Ml) = 0.0 and for the 1206 either ~(E2~Ml) = -0.01 or 7.1. The large mixing ratio requires an E2 strength of 170 W.U. based on the measured mean Iife for this level of 200 fs. But 6(E2/Ml) = 7.1 cannot be eliminated as a solution since this is an allowable enhancement. 3.9. THE 1677 keV LEVEL

An angular distribution was obtained for the 376 keV y-ray but spin values of 1, 2 or 3 could not be eliminated. In the polarization spectra the 376 keV peaks were barely discernable and asymmetry could not be measured. A limit on the mean life of z > 500 fs was obtained from Doppler shift measurements on the 1322 keV y-ray. For purposes of comparison to the MBZ shell model theory this level was assumed to have J” = 2’. 4. Discussion Knowledge of the spins and parities of the first twelve levels of ‘OV aIlows the comparison of their electromagnetic properties with the pre~ctions of the MBZ calculation 16). This model considers only the (f$y configurations in the calculation. The model gives a good reproduction of the observed 5oV levels up through the 1401 keV level as seen in fig. 14. It is interesting to note that the 4+ level observed at 910 keV is predicted to lie in this region. Table 3 compares the measured Ml and E2 strengths with the calculated values using MBZ wave functions. The agreement is not outstanding but in many instances the correct trends are predicted. For example, the model correctly predicts that the 910 keV 4” level should chiefly decay to the 226 keV 2270 2144 2002 -_I i21+

1677 i561 1518

2+ 2f 1+ 3* Y

1% 1331 1301

JT%-1252

911 910 836

?+-.._---I014 4+-x 5*

;:

iE

2: 8+

f 663

3*

2* ::

L-1194

716 606 E 320

;: 4+

226

5+ 6’ ?Y!c

0

Experiment

Fig. 14. Comparison

209

5’

101 too 0

2: 2:

MB2

of the energy level scheme of 5oV with theory.

D. G. RICKEL

214

et al.

TABLE3 Comparison of the measured transition strengths of 5oV with the theoretical predictions for those levels assumed to be approximately pure fs configurations using the McCullen, Bayman and Zamick wave functions Jf” (%)

Experimental Ml strength E2 strength

JE"

(&

(W.U.) 836 910 1301 1331 1401

1677

516 836 684 913 946 943 1414 1046 1082 277 376 1289 1322

5+

4+ 2+ 1+ 3+

(2)+ ‘)

1.03 0.25 “) 0.90 0.33 0.20 “) 1.58 “)

4+ 6’ 5’ 2+ 3+ 2+ 2+ 3f 4+ 3+ 2f 2f 3+

0.33 b) 0.65 0.004 0.005

(W.U.) 22.6 0.45 13.6

Theoretical Ml strength E2 strength (W.U.) (W.U.) 0.17 0.05 0.27 0.017 0.47 0.037 0.005 0.007 0.14 0.007 6.0x 1O-5 1.1 x10-5

7.4 1.2 2.3 5.3 7.7 1.9 2.7 0.37 0.087 0.10 2.5 1.4

“) 6(E2/Ml) was assumed to be zero. b, Mean lifetime of 500 fs was assumed. ‘) Jg assumed for purposes of comparison.

level. Also the model predicts that a third 2+ level should decay strongly to the second 2+ level and weakly to the first 2+ and 3+ levels, which gives some support to an assignment of J” = 2+ for the level at 1677 keV.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

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