Energy levels and γ-ray transitions in 147Pm

LE.1 : 3.A

Nuclear Physics A321 (1979) 341-353 ; © North-Holland Publishing Co ., Arrtaterrlam Not to be reproduced by photoprlnt or micro5lm without written perminion from the publisher

ENERGY LEVELS AND y-RAY TRANSITIONS IN ta'Pm TAKESHI SEO, TAKEO HAYASHI and YOKO MIYATAKE

Research Reactor Institute, Kyoto University, Kumatori-cho, Sennen-gun, Osaka, 590-04, Japan and KAZUHIKO AOKI

Himeji Institute of Technology, Himeji, Hyogo, 671-22, Japan Received 29 December 1978 (Revised 19 February 1979) Abrtrad: Gamma rays emitted in the decay of "'Nd have been studied using Ge(Li) detxtors as singles and coincidence spectrometers. Four new y-rays of 53.1, 81 .15, 149.4 and 191.24 keV have been detected and all incorporated into the decay scheme, Angular corrélation measurements for the 275-319, 275-411 and 272-408 keV cascades have yielded the following result : AZ(275-319) _ 0.006(2), A,(275-319) = 0.005(5), A2(275-411) _ -0 .013(17), A4(275-411) _ -0 .008(30), Aß (272-~08) _ -0 .283(10) and A,(272~08) = 0.015(18). From these coetïicients the E2/M1 mixing ratios of the 272 and 275 keV y-transitions have bcen determined to be 0.10(3) and 0.107(7), respectively, and the spin of the 680.43 keV level to be ~. Theoretical calculations on the intermediate coupling model for harmonic and enharmonic potential functions have been carried out and better agreement with experiment has been obtained for the enharmonic potential function .

E

RADIOACTIVITY "'Nd [from '46Nd(n, y)] ; measured Er, h, yy~oin, yy(B); "'Pm deduced levels, J, E2/M1 mixing ratios . Enriched target, Ge(Li) detectors. Intermediateooupling-model calculations with enharmonic potential functions.

I. IptrOdI1Ct10~ A number of experimental studies t-ta) have been made on the nucleus ta'pm . Nevertheless, in addition to some ambiguities, a serious inconsistency in angular correlation coefficients for the yy cascades involving the 275 keV y-transition has prevented overall theoretical investigations of this nucleus. The main purpose of the present work is to obtain a complete picture of the decay of 11 .1 d la'Nd to ta'pm by removing the above inconsistency. With careful y-ray measurements we detected four new y-rays and found the coincidence relation of the 272 and 408 keV y-rays which could disturb the angular correlation measurement on the 275-411 keV cascade in question . A new angular correlation measurement concentrated .on serarating the 408 and 411 keV y-rays yielded a result removing completely the above inconsistency and made it possible to determine the spin of the 680.43 keV level left 3a1

342

T. SEO et al.

a w z z U a w a

N H z 0

v

0 800 1600 2400

200 1000 1800 2600

400 1200 2000 2800

600 1400 2200 3000

CHANNEL NUMBER Fig. 1. Typical y-ray singles spectrum of "'Nd obtained with a l cmj Ge(Li) detector .

800 1600 2400 3200

343

unassigned so far. These experimental results are discussed on the basis of the intermediate coupling model including anharmonicity in collective potential functions. 2. Gamma-ray measurements Radioactive ' 4'Nd sources were prepared by irradiating Nd20, (enriched to 93 ~ in iaeNd) for 30 h with thermal neutrons (¢, = 8 x 10' s n ~ cm -ZSec -1) in the Kyoto University reactor. After a cooling period of about 10 d, five y-ray singles spectra were measured every seventh day with an ORTEC 1 cms Ge(Li) detector (FWHM = 0.54 keV at 100 keV) . A typical singles spectrum is shown in fig. 1 . A yy coincidence measurement was made by combining the above Ge(Li) detector and an ORTEC 58 cma Ge(Li) detector with a dual parameter data acquisition system ND4420 and 1? coincidence spectra were obtained by analyzing the coincidence events recorded on magnetic tape . From the five coincidence spectra shown in fig. 2 we found new coincidence relations of 191 .24-398.13 keV, 81 .15408.16 keV, 149.4-531 .05 keV and 53.1-541 .85 keV y-ray pairs. The coincidence relations of the 541 .85-91 .06 keV and the 272.30-408.16 keV y-ray pairs, recently reported in the reaction studies '°), were also observed in the present measurements . New y-rays of 53.1, 81 .15,149.4 and 191 .24 keV illustrated in fig. l were found in these coincidence spectra and confirmed in singles spectra. Because the 81 .15 keV peak contains a large amount of the germanium K X-ray escape component following the intense 91 .06 keV y-ray, the intensity of the 81 .15 keV y-ray was estimated from the 408 keV-gated coincidence spectrum . Results of the y-ray measurements are summarized in table 1 together with earlier data is . ie). Neither in our singles nor coincidence spectra was found any evidence of the 78, 170, 182, 232, 260, 299.7 and 312.6 keV y-rays reported earlier 1 s ). 3. Angular correlation measurements An angular correlation measurement for the 27511 keV and 272-408 keV cascades was made with a multicounter goniometer ' a) equipped with an ORTEC 60 crn3 Ge(Li) detector (FWHM = 1 .9 keV at 1 .17 MeV) and three 7 .6 cm diameter x 7.6 cm NaI(Tl) detectors. The high resolution of this Ge(Li) detector made it possible to resolve the adjacent two y-rays of 408 .16 and 410.51 keV. Liquid sources were made by dissolving irradiated samples in dilute nitric acid. The gates of the three NaI(TI) detectors were set to cover the energy region 242-302 keV and six coincidence spectra around 410 keV corresponding to six angles, 90 .0°, 112.5°, 135.0°, 157.5°, 180.0° and 202.5°, were recorded in the six memory regions of a multichannel analyzer . After a number of runs the result shown in fig. 3 was obtained. New angular correlation coefficients . for the 27208 keV cascade exhibit a large anisotropy in contrast with those for the 275-411 keV cascade . The coefficients AZ and A4 in the

T. SEO et al.

344 91

x

~

x

gate :

2Ô

keV

1100

a 200 U

a w a

w Û

xl

~

x

1200

1

10

gate : 408 keV

91 .06

275.36

100 0

200

~ 100

I

91 ~06

14`4

gate : 531 keV

15~4 . 92

0

200 100

53 .1

gate :

91 .06

542 keV

0

0

100

200

300

400

CHANNEL

500

600

700

NUMBER

Fig . 2 . Coincidence spoors obtained with 1 cm' and 58 cm' Ge(Li) detectors.

angular correlation function, W(B) = 1 +AZP2(cos6)+A4P4(cos B), are listed in table 2 after the geometrical corrections for detector sizes. Our angular correlation coefficients for the 275-411 keV cascade are consistent with the values by AlJanabi et al. t s).

345 T~erre 1

Energies and intensities of y-rays in the decay of 1 "Nd Present work

Previous works

(keV)

photons per 100 decays

53 .1 (2)"

0.0007(4)

81 .15(7)" 91 .06(3) 120.46(2) 149.4 (2)" 154.92(5)

0.0005(3) 28 (3) 0.33 (3) 0.0029(15) 0.0053(9)

191 .24(9)" 196.64(3)

0.0031(16) 0.156 (12)

272.30(4) 275.36(2)

0.012 (3) 0.67 (5)

E~

319.39(2) 398 .13(3) 408.16(5) 410 .51(3) 439.92(5) 489.30(8) 531 .05(4) 541 .85(5) 589.35(6) 594.84(6) 680.39(5) 685.89(4)

1 .68 0.79 0.014 0.096 1 .11 0.130 12 .2 0.012 0.035 0.23 0.015 0.80

(13) (6) (2) (7) (8) (10) (9) (2) (3) (2) (2) (6)

E~

(keV) 78

photons per 100 decays

ref.

0.2

Is )

26 0.37

16)

l54 170 182

0.05 0 .02 0.01

16) Is )

196.64 (4) 232 260

0.19 0.02 0.02

16)

275.374(15) 299.7 312.E 319.411(18) 398 .155(20)

0.75 0.05 0.02 1 .82 0.81

16)

410.48 (3) 439.895(22) 489.240(28) 531 .016(22)

0.13 1 .12 0.14 12.2

l6)

91 .106(20) 120.48 (5)

589.35 (4) 594.803(30) 680.52 (15) 685.902(35)

0.043 0.25 0.018 0.76

16)

Classifications 686 -. 633 489 ~ 408 91 -" 0 531 ~ 411 680 ~ 531 686 ~ 531

Is)

ls )

680 ~ 489 686 y 489

Is )

ls) ls ) 16) 16)

16) 16) 16) 16) 16) 16) 16)

680 ~ 408 686 -" 411 411 ~ 489 ~ 408 -. 411 ~ 531 ~ 489 ~ 531 --. 633 ~ 680 ~ 686 --~

91 91 0 0 91 0 0 91 91 91

686 ~

0

y

" New y-rays fast observed in coincidence spectra and confirmed in singles spectra.

Prior to this measurement, when the new 27208 keV yy cascade was not known, an angular correlation measurement wasmade by us for the 275-319 and 275-411 keV cascades with another goniometer system t7) equipped with an ORTEC 22 cma Ge(Li) détector and a 7.6 cm diameter x 7.6 cm NaI(Tl) detector. Angular correlation coefficients then obtained were AZ = 0.006(2) and A4 = 0.005(5) for the former cascade and A 2 = -0.104(11) and A4 = -0.017(23) for the latter . For many years, the small and large anisotropies for the former and the latter, respectively, were a difï-icult problem in our study ; the vanishing anisotropy of the angular correlation for the 275-319 keV cascade could not be attributed to anything but the mixing ratio of the 275 keV y-transition, the fast transition of the two cascades, because themultipolarity of the second transition of 319 keV was well established t -~)

34 6

T. SEO er a/ .

0 O O~

275 - 411

keV

cascade

272 - 408

keV cascade

0 .9

O

3

0 .8

0 .7

0 .6

90 °

120°

e

150°

180°

Result of a yy angular correlation measurement for the ~a,~ .

Fig . 3 .

275-411

and

272-408

keV cascades in

and could not lead by itself to such a small anisotropy of the 275-319 keV cascadé. Our present finding of the new 27208 keV cascade gave an answer to this problem ; the anomalous angular correlation coefficients by this earlier measurement using the T~a~ 2

Angular correlation coelFcients Ref.

4)

e)

i i) iz) 13)

present work

275-319

keV cascade

275-4I1

Az

Aa

0.0117(25) -0 .057 (16)

-0.0067(33) 0.112 (23)

0.079 (22) 0 .022 (9) 0.019 (10) 0.008 (11) 0.006 (2)

-0.038 (29) -0.009 (16) 0.011 (il) 0.005 (19) 0.005 (5)

") Values for the mixed cascade of

27511

keV cascade

Az

Az

Aa

272-408

keV cascade

Az

= 0.021(7), .!, = 0 .0013(50)

A,

(mixed)')

- 0 .048(78) 0.104(119) A z = -0.104(11), A, _ -0 .017(23)

-0.013(17)

keV and

272-408

-0 .008(30)

keV.

-0.283(10)

(mixed)')

0 .015(18)

iavp

m

347

22 cm s Ge(Li) detector which could not resolve the 408.16 and 410.51 keV y-rays were attributed to the mixing of the 275-411 and 27208 keV cascades . In spite of the small intensities of the 272.30 and 408.16 keV y-transitions the contribution of this cascade was estimated to be about 26 ~ of the coincidence counts of the mixed cascade. Weighted averages of the new angular correlation coefficients for the 275-411 and 27208 keV cascades are estimated to be t12 = -0.08(3) and X44 = 0.00(2), in good agreement with the earlier values A2 = - 0.104(11) and A4 = -0.017(23) for the mixed cascade. The angular correlation coefficients for this mixed cascade were first published by Bhati et al. 11) . But their values, AZ = 0.021(7) and A4 = 0.0013(50) ,are quite different from our present values . This difference may be due to their use of NaI(Tl) detectors whose energy resolution is too poor to make angular correlation measurements on such weak y-transitions near to other intense ones. 4. Decay scheme of "'Nd The decay scheme of l 4'Nd shown in fig. 4 is based on the present y-ray singles and coincidence measurements and includes all the new y-rays . The energies of the excited states were determined by the least squares method to get the best condition for all the values of the y-ray energies . The intensities and logft values of ß-transitions were estimated from the present y-ray intensities. The E2/M1 mixing ratio of the 319.39 keV y-transition was estimated to be Sß19) _ - 0.391(16) from the E2/M 1 mixing ratio of the 91 .06 keV y-transition S(91) = 0.086(7) [refs. Z' s)] and the angular correlation coefficient AZ(319-91) _ -0.088(5) [refs.' " 8" 'Z " '3)], where the definition of S is the same as given by AlJanabi et al. ' 3). Combining this value of Sß 19) and our angular correlation coefficient A2 (275-319) = 0.006(2), we obtained the E2/M1 mixing ratio of the 275 .36 keV y-transition as S(275) = 0.107(7). This is consistent with the value S(275) = 0.14(3) by Al-Janabi et al . i 3). The spin of the 680.43 keV level is restricted to ~, ~ or ~ because the y-transitions from this level to the -~+ 0.0 keV, ~+ 91 .10 keV and ~+ 408 .14 keV levels have large intensities indicating M1 and/or E2 multipol.arities . The ~ assignment is ruled out on the basis of our A Z and A4 coefficients ; i.e., the E2/M1 mixing ratio of the 408 .16 keV y-transition derived from the AZ coefficient, S(408) _ -2.58(11) or -0.203(15), is not consistent with the value ~S(408)~ < 0.14 from the A4 coefficient. When the experimental E2/M1 mixing ratio S(408) = 0.57(3) from reaction studies ia) is taken into consideration, ~ assignment is also rejected because the calculated AZ coefficient from this S(408) value for the ~-~-~ cascade cannot be less than - 0.236 which is higher than the experimental value of -0.283(10) . The remaining assignment of ~

348

T . SEO et al.

'6ôNd ~ » .~ d ~ 0 ~nmN~NOrir~noo rl f"1 .-I O O OD N t0 r-1 O O O O O O O " O O O O `r`r O O N 00000`r OO~U1 . f+1 f+1 O `r O O~ Ul m m OD ~O ~(1

7/2

ON~~IA O Mo~o .~ .io

1/2*

If1 N 10 O O_ O O O~ ~

~" ~O

O~ f"1 N V " N rl O~ r 01 V' N .-1 r-I

mmr'1~001 .-1 ~(1 V' Il1 ~O V' f'1 m O~ r T 1l1 1f1 ~D ~!1 N .-1 .--1

E(keV)

685 .88t0 .02 ~680 .43t0 .03 632 .9510 .05

.-. O r1 1f1 r~ O~ O ~01mMri .-1f+f f"1N

5 2*

°.~rimom,W ~o ^+ in ~,

7 2*

530 .99±0 .02 489 .2410 .03

~, v ri

3/2 +

410 .52*0 .02 ~~~408 .14t0 .04

9/2 +

mN t0 O

5/2 +

.-I

91 .1010 .02

7/2 +

0

'6; Pm Fig . 4. Decay scheme of 1 "Nd. Coincidence relations confirmed in the present work are indicated by full circles. Intensities in parentheses an gives as photon nmnbers emitted in 100 ß-decays. Spin-parity assignments an those given by Kortelaliti et aJ. i`) except the ~~*~ assignment for the 680.43 keV level determined in the present work .

is reasonable because, with an appropriate value of the E2/M1 mixing ratio for the 272.30 keV y-transition, b(272) = 0.10(3),

349

iav~

the experimental AZ and A4 coefficients can be reproduced for the ~~ cascade with S(408) = 0.57(3) . 5. Discussion The unique spin assignments of all the excited states and accurate E2/M 1 mixing ratios of many y-transitions in ta'l~n observed in the decay of t°'Nd allow us to make detailed theoretical investigations. Theoretical interpretations of this nucleus have been given on the basis of the intermediate coupling model with harmonic collective vibrations by Choudhury and O'Dwyer t9), Heyde and Brussaard z°), and others t Z . t s). Although this model has been believed to succeed in interpreting the structure of this nucleus, the E2/M1 mixing ratios of several y-transitions could not be reproduced well by this model, as seen in table 3. Moreover, negative TABLE 3

Comparison of experimental and theoretical E2/M 1 mixing ratios d Transition energy (keV)

Exp.

Calc. harmonic ')

enharmonic

91 .06 120.46 196.64 272.30 275.36 319.39 398.13 408.16 439.92

0.086(7) °) 0.050(21) °) -0 .20 (8) °) 0.10 (3) °) O.107(7) °) -0 .391(16) ") 0.30 (3) ~ 0.57 (3) `) 0.77 (10) d)

3.6 -0 .063 -0 .059 -0 .16 -0 .074 3.3 -0 .26 ~0.47 -0 .17

-0.22 0.028 -0 .38 0.22 0.091 -0 .49 0.63 0.70 -0 .76

531 .05 594.84 685 .89

< -6or4 < -0.40 (3) °) 5 -6 or 6 5 ") -0.95 (30) °)

0.17 0.20 -0.40

-6 .3 0.30 -0 .28

0.66

-0 .81

') Calculated with the same parameters as adopted by Heyde and Brussaard ~°) except that 9. = 0.5(e.)t.~ and 9a = 0.28. b) See text . `) Ref. ' `) . ") Ref. ") . °) Present work. values for the quasiparticle energy difference E(g~)-E(d~.), used in all the earlier calculations should be unacceptable on account of the experimental results by Wildenthal et al. 2t). As seen in fig. 5 the anharmonicity of the potential function for the N = 86 core calculated on the basis of a microscopic theory by Kumar and Baranger zs) may. indicate the limitation of the simple intermediate-coupling-model calculations. In order to take this anharmonicity into consideration we applied a

35 0

T. SEO er al.

Fig . 5 . Potential functions for collxtive vibration. The microscopio-theoretical calculation by Kumar and Baranger is taken from reL'Z), and the harmonic potential function is the same as used by Heyde and Brussaard ~°), C = 183 .05 MeV . Details of the enharmonic potential function used in the present intermediate-coupling-model calculation are described in text .

method developed by Leander Zs) to this nucleus. The analytical form of the potential function used in the present calculations was obtained by adjusting the parameters in the function V~~ Y) _ ~ßz + [Go + Ga

la+Gt /s cos 3y] exp ( -ßz/ßô)-Go ~Pß0 ~Pß00

to reproduce well the above calculated potential function by Kumar and Baranger as C = 140 MeV, ~o = 0.27, Go = 6 MeV, Gt = -5 MeV and G4 = 7 MeV. This is shown in fig. 5. The mass parameter was chosen as B = 286 MeV - t by fitting the first 2+ state of neighboring even nuclei with the same enharmonic potential function. The lg~, 2d.ß, 2d ß. and 3sß proton states were coupled to the enharmonic vibration with a coupling strength k = 40 MeV, by adjusting their quasiparticle energies and unoccupation amplitudes U1 to the extent allowed by the experimental

35 1 Teet .~ 4 Comparison of experimental and theoretical static moments N (n.m .) Level (keV)

~,

0.0 91 .1

}' }+

~

p.

2.58(7) °) 3.54(10) `)

Q(b) talc.

harmonic') anharmonic 2.66 2.92

2.62 3.25

exp. 0.74(20) °)

talc. harmonic') anharmonic -0 .89 - 0.75

1 .33 0.47

') Calculated with the same parameters as adopted by Heyde and Brussaard 2 °) except that

e. = o.s(a.)rrc~ and eR = 0.28. zs)

°) Ref.

.

`) Ref.'6) .

results by Wildenthal et al. 2') . After adjusting these parameters, the quasiparticle energies E~ = 0.0, 0.24, 1 .41 and 1 .63 MeV and the unoccupation amplitudes U~ = 0.64, 0.43, 0:90 and 0.90 for the 2d ß, lg~, 2dß and 3sß orbitals, respectively, were used in the present calculation ; it should be noted that our value of the quasiparticle energy difference E(g~)-E(d~) = 0.24 is positive. The calculations of level energies and wave functions were made by diagonalizing 70 x 70 matrices including 13 phonons and the four single-particle orbitals . The calculated levels are shown in fig. 6 together with those by a harmonic potential model with the same parameters as used by Heyde and Brussaard z°). The E2/M1 mixing ratios 8 and the static moments calculated with the effective values, g, = 0.5(9a)r«a 9x = 0 .28 [ref. za)] and eP = 2e, are compared with experimental values in tables 3 and 4. As seen in fig. 6, the present calculation by the anharmonic potential model can reproduce well the experimental level energies . Although the first ~ state seems to be reproduced better by the harmonic potential model, the calculated i~ state cannot be regarded as the experimental ~ (410 .52 keV) level for the following reason . The experimental branching ratio is much smaller than unity, B(E2 ; ~ 1 -. ~,)/B(E2 ; ~, -. fit) = 0 .12, and indicates that the main component of this ~t state should be 2dß + one phonon, while the ~ ~ state for the harmonic potential model contains the main component of lg~+one phonon with an amplitude of 0.74 yielding the B(E2) ratio of 6.6 which is much larger than unity. The ~ state composed mainly of 2d,t + one phonon appears as the second ~ state at about 750 keV and any harmonic potential function cannot invert the ordering of the two ~ states . On the other hand, the anharmonic potential model gives a reasonable result : the calculated ~, state is found to be composed mainly of 2d t + one phonon with an amplitude of 0.91, giving fot the B(E2) ratio the better value of 0.004, which is smaller than unity as required . As seen in tables 3 and 4, overall agreement between experiment and theory is more satisfactory for the anharmonic potential model. In spite of general success of this model the E2/M 1 mixing ratio of the 91 .06 keV y-transition could not be

352

T. S1A et al. E (keV)

I

(1NR)

(1NR) I

(g12) (d00) 5/2 91 ~~~~~ (~3/2 (90 (900) 7/2

91 5 2

(d00)

(d00)5/2

0 ~2

(g00)

(900)7/2

exp .

anharmonic

harmonic

Fig . 6 . Comparison of tûe experimental lwd scheme with those by harmonic and anharmonic potential models . Quantum-number sets (lNR) show the largest component where 1 = d(g) indicates the single particle orbital of 2ds~2(lg,is), N = phonon number and R = angular momentiun of We phonon system .

reproduced well. A careful choice of parameters, such as the unoccupation amplitudes U(d~.) and U(g.~), and the effective g, and gx factors, would give better results without major changes in the calculated values for the other transitions in the tables because these are less sensitive to those parameters . We thank Mr. S. Yamada for his help in analyzing the yy coincidence data and in constructing the computer code for the intermediate-coupling-model calculations . Thanks are also due to Mr. S. Uehara for his help in operating the angular correlation apparatus.

ta~pm

35 3

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 1 I) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26)

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