Ground state rotational bands in doubly even actinide nuclei

Nuclear Physics

A178 (1972) 41G-416;

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GROUND STATE ROTATIONAL BANDS IN DOUBLY EVEN ACTINIDE NUCLEI M. SCHMORAK,

C. E. BEMIS Jr., M. J. ZENDER t, N. B. GOVE and P. F. DITTNER

O& Ridge National Laboratory,

Oak Ridge,

Tennessee 37830 it

Received 16 August 1971 Abstract: The y-ray spectra

following the a-decay of several doubly even actinides were studied. The deduced level energies of the ground state rotational bands were compared with the collective model and the VMI model. The VMI model gave an excellent fit to the experimental levels: no phase transitions were observed in the actinide region, in contrast to the situation in the rare-earth region.

E

RADIOACTIVITY zn4U, z36U, 238Pu, 240Pu, 242Pu, 246Cm, z50Cf; measured Ey, I?. 230Th, 232Th, 234U 9 236U, 238U 240Pu 242Pu, *46Cm deduced levels. Ge(Li) dktector. ’

,

1. Introduc~on Low-lying levels of deformed doubly even nuclei exhibit remarkable regularities; they all have positive parities and the angular momenta are in order of increasing energy, Of, 2’, 4”, 6+, etc. This fact was recognized a long time ago and interpreted as a result of the collective rotational motion of nuclear matter; see e.g. Nathan et al. ‘). The level energy E BM -- AZ@+

l)+W(1+

1) 2

(1)

was believed to be an adequate description of the empirical data. Recently, however, a number of authors 2-5) suggested the variable moment of inertia (VMI) model as an alternative approach to the problem of ground state bands of doubly even nuclei. In order to establish which of these models is better in the heavy element deformed region, we have measured with high precision the y-ray energies following the r-decay of several actinide isotopes. 2. Instrumentation Radioactive sources of 234U, 236U, 23*Pu, 240Pu, 242Pu, 244Cm, 246Cm and 2 5‘Cf were investigated. Two different low-energy photon Ge(Li) detectors were used, as well as a standard TC 200 amphfier and a “Nuclear Data 2200” 4000 channel f Present address: Fresno State College, Fresno, California. +t Research sponsored by the US Atomic Energy Commission Carbide Corporation. 410

under contract

with the Union

ACTINIDE NUCLEI

411

analyzer. The y-rays of a ‘*‘Ta source were used as primary energy standards “1. The y-ray energies of 240Pu established by us were used as a secondary standard. The effects of non-linearities in the electronic system and intensity and geometry variations of the sources were investigated and found to be negligible compared to the quoted energy uncertainties. The main contribution to the uncertainty in the 8” spin level energies was the uncertainty in the peak-centroid of the 8+ + 6+ y-transition due to statistical errors (approximately 2000 counts were accumulated in these peaks). For the lower spin transitions, the number of counts per peak was in the range 104-10’. The 242Pu source was contaminated with radioactive impurities which made it more difficult to establish the peak-centroids of the ~-transitions in 238U. 3. Results The y-energies measured by us are shown in table 1. The a-branching derived from the y-intensities is shown in table 2. We have used total internal conversion coefficients calculated from the tables of Sliv and Band as described in ref. ‘). [The calculated a-branches differ by less than 5 % if conversion coefficients calculated from the tables of Hager and Seltzer “) are used.] The a-branches to 2+ states are taken from the recent compilation of M. Schmorak and Y. A. Ellis “). The a-hindrance factors lo) derived from our experiments are generally in agreement with previousiy established trends ‘). The only other known case of an a-branch to an 8+ state is in 238Pu where the hindrance factor “) is 7500. 4. Analysis of the results The energies of states belonging to ground state bands of doubly even actinides are shown in table 3. All energies, quoted to 0.1 keV or better, are derived from our measurements (table 1). The energies of higher spin states are based on Coulomb excitation results of Stephens et al. ’ ‘). The experimental level energies are compared in table 3 with the two nuclear models mentioned in the introduction. EBMis calculated from eq. (1). The deviation Eexp- EBMis given in table 3 in keV. The parameters A and B for this calculation were determined by the experimental 2’ and 4+ energies. The expression EvMI- Eexp is calculated from eq. (2)

The parameters 3, and C were calculated from the experimental 2+ and 4+ energies. It is clear from table 3 that the VMI model predicts the high-spin level energies very well in the actinide region. An additional comparison was made by least-squares fitting of the two sets of parameters to all level energies. The quantity

M. SCHMORAK

412

er al.

TABLE 1

Transition energies in eY =OTh

Transition 2+ 4+ 6+ 8+

-to+ +2+ +4+ +6+

l=Th

53 222519 120 905&12

49369& 9 112 750f15

234u

236”

43 491 f 9 99 850&10 152 719fl9 201017f30

45242& 6 104233i 5 160310& 8 212 40Oi~:100

24OPu

Tr~sition 2f -to+ 4+ +2+ 6+ +4+

44915*13 103 499135 158 8OOI!I80

42824;1r: 8 98 860&13 152 630&20

44545*

9

42852f

5

TABLE2 Alpha branches to ground state rotational Final nucleus

I”

232Th

2+ 4+ 2’ 4+ 6’ 8+ 2” 4’ 6+ 8’ 2+ 4+ 6” 2’ 4” 6’ 8+

23‘qJ

236D

238U

=*“PU

I,(%) this work

(26) 0.15 kO.02 (28.4) 0.091 *0.005 0.0024f0.0002 (1.2*0.2)x10-” (24) 0.096 kO.005 0.0012~0.0003 (2.9iO.4) x lO-s (21.1) 0.090 *0.009 0.~12~0.~ (23.6) 0.027 10.003 0.0036&0.0004

bands

I,(%) NDS “)

e+hindrance factor b,

26 0.26 28.4 0.11 0.005 8.6 x 1O-6 24 0.091 0.002

1.19 27.3 1.4 117 540 5700 1.65 90 610 8000 1.9 83 440 1.91 440 500

21.1

23.6 0.02 0.0034 $V4x10-5

ar ‘)

337 6.9 746 13.7 2.17 0.738 612 11.2 1.78 0.60 635 il.6 1.85 932 17.1 2.51

“) From a recent compilation of M. Schmorak and Y. A. Ellis g). ‘) The hindrance factors were calculated from our experimental cc-branches using the technique described in the introduction to Nuclear Data Sheets lo). ‘) The total internal conversion coefficients used for deriving the a-branching from they-intensities are calculated from the tables of Sliv and Band ‘).

ACTINIDE

NUCLEI

413

TABLE 3

Ground state band level energies (all energies in keV) o2

I 2 z32Th Es,, ‘) 49.36g9 IEVWZ%W Z&&hi

4

6

162.11918 333.75 -0.3 1.3

8

556.9’ 0.67 6

10

827.8** 1.4 23

12

14

1138.510 5.0 59

2.6 98

234* &I

9

43.4919

&UI’&~ &&BU

143.341r4 296.060a4 497.01140 0.12 0.74 0.42 2.83

9.0 77

236u &,

“1

45.2426

149.47S”

E VMI -&.r, Z&+&M

309.785r3 0.07 0.28

522.18’O 0.52 2.88

3.9 33

238fJ &rp

b,

44.915=

Z&&W&t, Et&&M

148.41437 307.214*’ 0.5 -0.2

S18.35 0.9 1.5

776.6’ 2.4 6.4

1077.81° 5.5 19

1416.825 12 44

1.5

20

24op, &x,

“)

42.824s

141.684rs

&M&W &I&BM

160Dy 86.790Lo 283.812 EeWd, Z%W%~P Z&&M lsaYb 87.730r” 286.SS2 .E,,, ‘) E;M~-ZL .&&WA

294.314*” 5003 -0.04 -2.5 0.28 4.1

0.38 2.3

581.2* -0.5 3

967.2j -1.2 19

1428.g4 0.7 62

1951.75 11 154

2515.26 43 317

585.30’ 0.18 3

970.0s2 2.6 17

1425.43 12.2 57

1935.1’O 36.4 145

2487.811 19.4 317

The quantity a2 = S[(E, ..,,-E, Es,C )2~(~E,)z]/(number of degrees of freedom). “) Present work. b, Present work up to Z = 4 in as2Th and Z = 8 in 238U, combined with ref. ‘I) “) Present work up to Z = 6 and ref. *) for Z = 8. d, Prom ref. 13). “) Prom ref. 16) up to Z = 8 and ref. 13) for higher spins.

for higher spins.

is a measure of the goodness of fit. AEi is the experimental uncertainty in the energy of level i; f is the number of degrees of freedom; for both models, f = number of experimentally determined levels minus 2. The parameters determined in the leastsquares fitting are shown in table 4. The moments of inertia 4; calculated from eq. (2) and the least-squares fitting are shown on fig. 1 as functions of spin. A smooth increase of 9 is observed for all the cases studied in the actinide region.

414

M. SCHMORAK

Ground state band parameters

et al.

TABLE4 from least-squares

fit to all level energies

232Th

A (keV) B (eV) X0 (keV-‘) C (lo6 keV3)

A B J, C

(keV) (eV) (keV_‘) (lo6 keV3)

11.580 -50.1 0.0427 0.448

7.496 -3.89 0.0665 1.18

8.941 -11.7 0.0559 0.950

8.246 -6.58 0.0603 0.93

7.268 -5.08 0.0686 0.85

24cpll

*‘Wrn “)

z54Fm b,

7.156 -3.55 0.0698 1.32

7.159 -2.79 0.0698 1.703

7.51 -2.1 0.0666 2.826

7.562 -4.42 0.0660 1.26

‘) From energies of ref. 17) and present work. b, From energies of ref. I*).

8 6.5

6.0

Fig. 1. The moment of inertia9 as function of spin J for doubly even actinides, calculated with the variable moment of inertia model by a least-square fit to all known levels of the ground state rotational band.

ACTINIDE

NUCLEI

415

5. Discussion It is clear from table 3 that the VMI model [eq. (2)] predicts the ground state band level energies very well in the actinide region, much better than eq. (1). However, for spins 12+ and 14+ in 232Th and 238U the VMI model underestimates slightly the moment of inertial. In the case of 238U, when the first three levels (2+, 4+, 6+) are used to determine the VMI model parameters, the deviation from experiment at Z = 14+ is reduced to 3.7 keV which is within the range of the experimental uncertainty. Therefore, more precise level energies are needed for 238U to establish whether the deviations from the VMI predictions are significant. For purpose of comparison, we have analyzed a number of ground state bands in the rare-earth region. Two typical examples (16’Dy and 16sYb) are shown in table 3. It is evident that significant deviations from the VMT model predictions are observed from Z = 10 or 12 or higher. The deviations for Z = 16 and higher are so large that comparison with either model is meaningless. The large and fairly sudden increase of the moment of inertia for high angular momenta states in the rare-earth region has been pointed out already by A. Johnson et al. 12*13). Th’IS increase of the moment of inertia was predicted qualitatively by Krumlinde 14). At a critical angular momentum Zp’, the neutron-pairing correlation is expected to vanish due primarily to the “Coriolis anti-pairing effect” 15). For rotational states above I:‘, the neutron part of the moment of inertia becomes rigid and depends only on the deformation. The critical angular momentum for protons in the rare-earth region is, according to Krumlinde 14), much higher than Zr’. Our experimental results suggest that the critical angular momentum Zr’ in the actinide region ( 232Th 23sU) is higher (by at least 2 or 4 units) than the corresponding Zp’ in the rare-eaith region, in agreement with the calculations of Krumlinde 14). The elucidation of the physical meaning of the parameters (shown in table 4) in the actinide region may have to wait for more extensive experimental data. 234U is perhaps an anomalous case, the value of 9. being unusually high and the value of C unusually low.

1) 0. Nathan and S. G. Nilsson, Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam, 1965) p. 601 2) S. H. Harris, Phys. Rev. 138 (1965) B509 3) M. A. J. Mariscotti, G. Scharff-Goldhaber and B. Buck, Phys. Rev. 178 (1969) 1864 4) G. Scharff-Goldhaber and A. S. Goldhaber, Phys. Rev. Lett. 24 (1970) 1349 5) M. A. J. Mariscotti, Phys. Rev. Lett. 24 (1970) 1242 6) R. C. Greenwood, R. G. Helmer and R. J. Gehrke, Nucl. Instr. 77 (1970) 141 7) Introduction to Nucl. Data Sheets B5-3 (1971) p. V 8) R. S. Hager and E. C. Seltzer, Nucl. Data Tables A4-1, 2 (1968) 9) M. Schmorak and Y. A. Ellis, Nucl. Data Sheets B4-6 (1970) 10) Introduction to Nucl. Data Sheets B5-3 (1971) p. III 11) F. S. Stephens, R. M. Diamond and I. Perlman, Coulomb excitation, ed. K. Alder and W. Winther (Academic Press, New York, 1966) p. 208

416

M. SCHMORAK

et af.

12) A. Johnson, H. Ryde and J. Sztarkier, Research Institute for physics, Stockholm, annual report, 1970 13) A. Johnson, H. Ryde and J. Sztarkier, Phys. Lett. 34B (1971) 605, and private communication 14) J. Krumlinde, Nucl. Phys. Al21 (1968) 306; A160 (1971) 471 15) B. R. Mottelson and J. G. Valatin, Phys. Rev. Lett. 5 (1960) 511 16) J. M. Jett and D. A. Lind, Nucl. Phys. A155 (1970) 182 17) L. G. Multhauf, K. G. Tirsell, R. J. Morrow and R. A. Meyer, Phys. Rev. C3 (1971) 1338 18) F. T. Porter and M. S. Freedman, private communication