Collective states of 232Th, 238U and 242Pu

I1

Nuclear Physics Al87

1.E.l: 2.A.l

(1972) 545-556;

Not to be reproduced by photoprint

COLLECTIVE

STATES

Th. W. ELZE Nuclear

Structure

Research

North-HollandPublishing

Co., Amsterdam

OF 232Th, 238U AND 242Pu

t and

Laboratory,

@

or microfilm without written permission from the publisher

J. R. HUIZENGA

University

Received 22 June (Revised 15 March

of Rochester,

Rochester,

New York tt

1971 1972)

inelastic scattering Abstract: Energy levels of 232Th, f38U and 242Pu have been studied through of 16 MeV deuterons. Inelastic scattering cross sections were measured at 90” and 125” by means of a magnetic spectrograph. In all three of the nuclei studied, the ground state rotational bands were excited up to the 8+ member. Several octupole-vibrational states were also identified were observed. in each nucleus. In 232Th and 23*U , K = Of (@-) and K = 2+ (y-) vibrations Relative reduced transition probabilities B(E2) and B(E3) were deduced from the (d, d’) cross sections. The B(E3, O+ + 3-) values agree reasonably well with results of a microscopic theory of octupole vibrations that includes Coriolis coupling between the negative-parity bands.

E

NUCLEAR REACTIONS =Th, 238U, 242Pu(d, d’), Ed = 16 MeV; measured a(E,‘, t3 = 90”, 125”); 23ZTh(d, d), Ed = 16 MeV; measured a(6). 232Th, 238U, 24aPu deduced levels, J, n, B(E2), B(E3). Enriched targets.

1. Introduction It is well known that the inelastic scattering of medium-energy projectiles predominantly excites collective nuclear states. The scattering of complex projectiles, e.g. deuterons, ‘He or a-particles, is especially well suited for a study of such states, inasmuch as compound nuclear processes contribute little to the scattering amplitude. An attractive feature of inelastic scattering processes is the direct relation between the differential cross sections observed and reduced transition probabilities. Thus, relative B(E2) and B(E3) values between the ground state and the states excited can easily be determined from such measurements. For these reasons, it was interesting to study states of some actinide nuclei, not many of which have been investigated in detail iz2). In this paper we report results of an investigation of the collective excitations of the deformed nuclei 232Th, 238U and 242Pu by means of inelastic deuteron scattering. Some preliminary results have already been discussed “). 2. Experimental

procedure and results

The measurements were performed by bombarding targets of 232Th, 238U and 242Pu with beams of 16 MeV deuterons obtained from the University of Rochester 7 Now at Institut fur Kernphysik der Universitlt Frankfurt, Frankfurt, West Germany. rt Work supported in part by grants from the United States Atomic Energy Commission and New York State Science and Technology Foundation. 545

TH. W. ELZE AND J. R. HUIZENGA

546

232Th(d,d) E, = 16MeV 0.8 -

f

Jr OS6 a b

-

w

i

40’

N Optical Mnrlnl

60’

800 1000 1200

8 CM.

Fig. 1. Angular distribution of deuterons elastically scattered from 23sTh. The dots are the experimental results, the solid curve is an optical-model calculation using the potential parameters listed.

232Th(d ,d’) 8,= 125” Ed = 16MeV

EXCITATION ENERGY IkeV)

Fig. 2. Spectrum of deuterons scattered from 232Th.

=Th,

-W,

242Pu COLLECTIVE

STATES

547

23eU( d, d') 8, = 125” Ed= 16MeV

E E

6+

%300d ~'/lsO_

% Y $jeooF

100 -

a+ EXCITATION

ENERGY

(keV)

Fig. 3. Spectrum of deuterons scattered from 23*U.

I

K

0+ 3-

>+

:

400-

242Pu(d, d’) eL= 125” Ed = 16MeV

: a d

300-

E 0. Y 2

6+ 200"'kj

F

. 100 -

o-

I i-

.

I

P

EXCITATION

ENERGY

(keV)

Fig. 4. Spectrum of deuterons scattered from 242Pu.

548

TH. W. ELZE

AND

J. R. HUIZENGA

TABLE I Levels excited in Z33Th Energy (kev)

0 48 161 334 557 713 731 776 786 885 1054 1078 1107 1149 1181 1208 1294 I329 1419 1485 1562 1618 1692 1738 1791

dajdS;I 90” @b/w)

da1d.Q 125” @b/sr)

R 90°/12Y

39447 4992 389 18 2 13 3 186 95 13 2 2 114 12 9 5

8330 1948 233 36 4 24 5 105 43 22 3 4 81 7 5 11 3 2 3 14 12 3 4 7 IO

4.74 2.56 1.67

12 12

Assignment “) previous

0+ 2+ 4+ 6+ a+ 10+r,

0+ 2+ 4+ 6+ g+ o+r*

1.77 2.21

2+“; 2+’

1.41

3-

here

3- b,

32+’ 5-

3-

(5-)

“) Levels assigned to K = O+ (b-) vibrations are marked with a double prime while K = 2” (y) vibrations are marked with a single prime. b, 2+ assignment from ref. 2); 3- assignment from ref. Is).

Emperor tandem Van de Graaff accelerator. The thorium and uranium targets were prepared by vacuum evaporation of the respective metal onto 20 pg/cm carbon backings. The plutonium target was enriched to 99.8 % 242Pu and was supplied by Oak Ridge National Laboratory. The targets ranged in thickness from 30 to 60 pg/cm2. Inelastically scattered deuterons were momentum analysed at 90” and 125” in an Enge split-pole magnetic spectrograph and detected with 50 pm Kodak NTB photographic plates. An overall energy resolution of about 8 keV was achieved. Since the elastic group and the inelastic group corresponding to the first excited 2+ level were too intense to be counted in an exposure long enough to record weaker groups, three exposures of different lengths were taken at each angle. Relative intensity normalization was accomplished by matching the intensities of the first (2+) inelastic group in the short and medium exposures and the second (4+) inelastic group in the medium and long exposures. No absolute intensities have been measured. In order to obtain

232Th, n3aU, 242Pu COLLECTIVE

STATES

549

TABLE 2 Levels excited in 238U Energy (keV)

da/d0 90” @b/sr)

da/d9 125” @b/sr)

R 90”/125”

Assignment

here

previous 0 45 149 308 520 679 731 825 930 961 998 1037 1061 1103 1126 1169 1231 1288 1375 1512 1530 1630 1647 1665 1712 1758 1774 1807

44646 6146 225 18 1 9 130 5 1 2 46 9 28 5 2 53 4 6

10 17 7 5

20

9325 2641 243 45 4 28 87 22 5 4 40 7 28

4.79 2.33 0.95

57 4 9 2 6 10 18 14 9 2 8 23 8

0.93

1.49

0.50 1.15 1.29 1.00

“) Levels assigned to K = O+ @-) vibrations are marked (y-) vibrations are marked with a single prime. ‘) 2+ level at 998 keV, 3 - level at 997.5 keV, cf. ref. 6).

“)

0+ 2+ 4+ 6+ 8+ 13512+ 2+, 3- b) 2+”

0+

2+ 4+ 6+ 8+ 135132+”

2+’ 1-

2+’

3-

3-

5-

5-

with a double

prime

while

K = 2+

differential cross sections on an absolute scale, the intensities of the elastic groups of all the individual spectra were normalized with the corresponding elastic scattering cross sections computed in a distorted-wave optical-model calculation. To test the dependability of these calculations the angular distribution of elastic deuteron scattering from 232Th was measured between 20” and 120”. As can be seen in fig. 1, the result of the calculation which employed the optical-potential parameters of ref. “) fits the shape of the experimental angular distribution over the entire range of angles rather well, thus giving added confidence in the intensity normalization using the theoretical elastic-scattering cross sections. It should also be noted that the set of optical-potential parameters used for the present work has already been successfully applied in the analysis of transfer reaction data ‘) on actinide nuclei.

550

TH. W. ELZE AND J. R. HUIZENGA TABLE3 Levels excited in 242 Pu

Energy (kev)

du/dQ 90” Qb/sr)

da/dQ 125” &b/sr)

Assignment “)

R 90”/125”

previous 0 46 148 308 519 781 833 865 927 z 992

50150 7794 306 42 3 8 178 4 9 8

10413 3763 294 53 8 32 93 3 20 3

4.82 2.07 1.04

1020 1102 1122 1204 1259 1501 1613 1638 1650 1683 1701 1776 1825

140 52 8 34

132 36 22 38 7 11 24 7 73 14 6 6 6

1.06 1.44

(ii) (5_)

0.79

(3_)

16 29 9 58 13

“) Levels assigned to K = O+ (B-)vibrations (y-) vibrations are marked with a single prime.

0+ 2+ 4+ 6+ 8+

here

1.91

Of 2+ 4+ 6’ 8’ I35-

(2+“)

are marked with a double prime while K = 2+

Spectra of deuterons inelastically scattered from 232Th, 238U and 242Pu are shown in figs. 2, 3 and 4, respectively. Differential cross sections obtained by the method described above and energies of the excited levels are listed in tables l-3. These tables also contain the spin assignments derived from both the present experiments and previously published data. Recently, the nucleus 238U has been the subject of numerous 1*286-g) investigations and its levels below 1500 keV are believed to be well understood. Thus, by mere comparison of the deuteron spectra of 232Th and 242Pu with 238U many spin-parity assignments can be readily made in 232Th and 242Pu. For example, the K = O- octupole vibrational band is immediately identified through its characteristic l--3--5intensity pattern. Cross section ratios R = da(90”)/da(125”) obtained for the strongest groups were used for spin assignments only to a limited extent. It is expected that these cross-section ratios give dependable information on the multipolarities of transitions to low-lying states, if they are excited via one-step processes. With increasing excitation energy contributions from multistep processes to the cross section become

z32Th, 23*U, *4zPu COLLECTIVE

more important

and the ratio R then depends

STATES

551

on more than one Z-value, thus losing its

angular momentum dependence. In fig. 5, the experimental energy dependence of the ratio R is shown for all of the 1 = 3 transitions observed in the present experiment. As can be seen, the quantity R decreases with increasing excitation energy while DWBA calculations result in cross-section ratios R that are nearly independent of excitation energy. Two different form factors have been used in the DWBA calculations, i.e. a complex form factor with the parameters as shown in fig. 1 and a real form factor of R depends on the form arrived at by setting W, = 0. Although the magnitude

2.0 -

--_-_--_-_--_p--_-_--_-_-0.\

a ZG 5. s 0 8 4

----____q

*

l.O-

DWBA (t=3) -real coupling

?..a i , -------____ ‘A =. b’.,. ‘0

complex coupling

0 =Th A 238~ 0

24apu I 1.0

0

I 2.0

EXCITATION ENERGY

hieV1

Fig. 5. Cross section ratios R = db(90”)/do(125”) for the 3’ states as a function of excitation energy. The heavy broken lines indicate results of DWBA calculations for I = 3 transitions in 238U empIoying complex and real form factors. The results for 232Th and 24zPn differ by less than 10 % from those shown and have been omitted in the figure.

factor used, the energy dependence does not markedly change. Since the DWBA theory accounts for direct excitations only, its inability to predict the energy dependence of R is suggestive of the presence of higher-order processes.

3. Discussion 3.1. THE NUCLEUS

of the individual nuclei

232Th

Most of the present assignments agree with results published previously tP2t ‘). The levels at 713, 776 and 885 keV are interpreted here as members of the K = O- octupole vibrational band. This interpretation is based on the intensity pattern of the inelastic deuteron groups which is very similar to the pattern observed in 238U. Further evidence for a 3 - assignment to the 776 keV level is given by the cross-section ratio R = 1.77. The 776 keV level was previously seen in Coulomb excitation and identified “) as the 2+ B-vibrational state. The discrepancy between the present results and the findings of ref. ‘) is easily explained, however. An estimate of total cross sections [ref. ’ “)I shows that in heavy-ion Coulomb excitation of actinide nuclei 2+ states are

TH. W. ELZE

552

AND

J. R. HUIZENGA

more strongly excited than 3- states of the same energy. In inelastic deuteron scattering, on the other hand, 2+ /3-vibrational states are generally found 11) to be more weakly populated than 3- octupole states. The latter observation is in agreement with our 23*U spectrum in which the 2+ /?-vibrational level is well resolved from other states. It is therefore concluded that different states may be populated in Coulomb excitation and inelastic deuteron scattering. 3.2. THE

NUCLEUS

-*U

Numerous studies it ‘# 6- “) of 23sU h ave recently been published. Spin assignments based on the present work are in excellent agreement with results “) of a high-resolution Coulomb excitation experiment. The 2+ b- and y-vibrational states at 1037 and 1061 keV, respectively, are identified on the basis of observed cross-section ratios, in keeping with the observation that beta vibrations are usually more weakly excited by inelastic deuteron scattering than y-vibrations ll). All the other assignments are readily made on the basis of intensity patterns, absolute differential cross sections and R-values. 3.3. THE

NUCLEUS

-=Pu

The only states known ‘) in 242Pu are the members of the ground state band. In addition, a O+ and 2+ state, in character similar to a b-vibration, were identified 12) at 956 and 995 keV, respectively, in a (p, t) reaction study. The Of state is unobserved in the present experiment, while a weak group found at 992 keV might correspond to the 2+ level. It is interesting to note that B-vibrations are excited by inelastic deuteron scattering in both 232Th and 238U while there is no conclusive evidence for the existence of a P-vibration in 242Pu . Spin assignments to the remaining levels are based on intensity patterns, cross-section ratios R and absolute differential cross sections.

4. Determination

of relative reduced transition probabilities

One of the objectives of the present work has been to deduce from the observed (d, d’) cross sections reduced transition probabilities B(E2) and B(E3) for the collective states. The B(EI) for an EA transition between the ground state and a rotational or vibrational state may be written B(El)f

=

$ ZeRtA+"

“fi”,.

The quantity R,A% is the nuclear radius, R,, being taken here to be 1.20 fm. Depending on the model used the p1 is a deformation parameter or a vibrational amplitude. The differential inelastic scattering cross section calculated in a macroscopic DWBA theory 13) is related to fin by

Z3zTh, 238U, =*Pu COLLECTIVE

STATES

553

Q) is the DWBA cross section calculated for the present work with the computer code DWUCK. The normalization constant N depends on the particular computer code used and is known. Hence, by inserting PI from eq. (2) into eq. (l), reduced transition probabilities can be determined from inelastic scattering. The calculations of the DWBA cross sections employed the optical-mode1 parameters “) shown in fig. 1 and a form factor containing both the first radial derivative of the optical potential and a Coulomb-excitation term 13). Calculations for all of the nuclei studied were performed by using both a complex form factor with the parameters as shown in fig. 1 and a real form factor obtained by neglecting the term with W,. All of these calculations were carried out for Q-values corresponding to excitation energies of 0 (ground state) and 1 MeV. Linear interpolation was used to find the cross sections for intermediate energies. In eq. (Z), a,(@,

TABLE 4

DWBA cross sections

for 23’%J; Q = 0

dafdiL (mb/sr~ B

I=3

1=2 real form factor

complex form factor

real form factor

complex form factor

90

71.7

125”

21.8

40.7 17.7

18.5 9.8

27.0 19.3

The magnitude of the DWBA cross sections is sensitive toward the choice of the form factor as can be seen from table 4. In this table are listed cross sections for f = 2 and 1 = 3 transfer calculated for 238U at zero Q-value. With regard to the determination of reduced transition probabilities we note that absolute B(E2) and B(E3) values extracted from the 90” measurements by using the real form factor agree with Coulomb excitation data in general to within 30 %. The B(EJ.) values extracted from the 125” spectrum, however, are systematically larger by a factor ranging from 1.3 to 2.5 depending on the excitation energy. Using the DWBA cross sections computed with the complex form factor, B(E2) values are obtained which are about twice as large as the corresponding Coulomb-excitation values. However, with the exception of the y-vibrational states of 23*U and 242Pu all of the 125” B(E2) values agree with the 90” values better than to within 15 %. For the B(E3) values we note a systematic enhancement of the 125” values with increasing excitation energy. This enhancement is directly related to the failure of the DWBA theory to account for the energy dependence of do(90”)/do(125”) as shown in fig. 5. The relative B(E2) values for the first excited 2+ states deduced from the present experiment by using the complex form factor are compared with Coulomb-excitation

554

TH. W. ELZE

AND

J. R. HUIZENGA

TABLE 5 Reduced

transition

probabilities

first 2+ states B(E2; O+ + 2+)/e2x

E (keV)

Coul. ext. b,

(4 d’)., 9 232Th 238U

48 45 46

242PU

9.4hO.2 11.7hO.2 13.3f0.4

9.1 f0.6 11.7*0.8 16.5+1.4

“) Normalized with the Coulomb-excitation “) From ref. i4).

value

104fm4

for 238U.

TABLE 6 Reduced

transition

probabilitiesy-vibrational

states

B(E2; O+ + 2+)/e’

E (keV)

Coul. ext. “)

(d, d’)., ‘) ==Th 238U

0.20%0.03 0.10*0.01 0.15*0.03

786 1061 1102

242Pll

“) From ref. z). b, Assignment uncertain. ‘) Normalized with the Coulomb-excitation

x 104fm4

0.14 0.09 b)

value for the 45 keV level of 238U from

table

5.

TABLE 7 Reduced

transition

238U

2--Pu

“) “) ‘) “)

776 1107 731 998 1169 833 1020 1650

octupole

B(E3; O+ + 3-)/e*

E (keV)

*=Th

probabilities

Cd,d’h”

(4 d’m”)

0.71 0.44 0.57 0.20 0.24 0.85 0.67 0.29

0.59 0.45 0.51 0.23 0.34 0.57 0.81 0.46

(4 d’hv 9 0.65 *0.06 0.45 30.05 0.54+0.07 0.22 +0.03 0.29+0.05 0.71&0.09 0.74&0.11 0.38+0.06

‘)

states x 106fm6

theory

other exp. “)

Coul. ext. “)

0.59 0.26 0.44 0.18 0.11 0.41 0.12 0.09

x 0.50 0.30~0.10 0.50&0.06 0.22+0.05 0.20&0.10

0.54+0.04 0.23&0.02 0.13rtO.02

From ref. Is). Taken from ref. 6, assuming lB(E3),.p.U. = 2.35 X IO4 e’ . fm’. Assignment uncertain. Normalized with the value for the 731 keV level of z38U [ref. ‘)I.

232Th, 238U, -‘Pu

COLLECTIVE

STATES

555

data i4) in table 5. Since there is excellent agreement between the values from the 90” and 125” spectra, only average B(E2) values are shown. The relative B(E2) values from our experiment have been normalized with the Coulom~excitation value 14) for 238U, A similar comparison is made for the 2’ y-vibrational states in table 6. The numbers shown here were arrived at by applying the same normalization as was used for the first excited 2+ states in table 5. In table 7, reduced transition probabilities extracted from both the 90” and 125” intensities of the 3- states, as well as averages of these values are compared with results of a microscopic-model calculation of nuclear vibrations “). This table contains also B(E3) values measured recently by Coulomb excitation “) of 238U and experimental data cited in ref. ’ “). Our results have somewhat arbitrarily been normalized with the B(E3) value of the first 3- state of 238U [ref.6)]. In general, there is reasonable agreement between our average B(E3) values and the experimental results of refs. 6‘ I’). For the lowest 3- state of 232Th and the first and second 3- states of 238U we note also good agreement with the microscopic calculations of Neergard and Vogel Is). The higher 3- states, however, show the aforementioned enhancement of B(E3) values which may be indicative of higher-order processes. All of our spectra show strong excitation of the 4+ and 6f members of the ground state rotational bands. In the presence of large p4 and p6 deformations these levels are excited predominantly in a one-step process. On the other hand, if higher-order deformations are small, the large cross sections to the 4” and 6+ levels can be explained only in terms of multiple excitations. With the aid of eq. (2) the hexadecapole deformation necessary to account for the entire experimental 4+ strength has been found to range from approximately 0.2 to 0.6 of the & deformation, depending on the form factor used in the DWBA program. This result compares with recent calculations i6) which predict the p4 moments to be of the order of 30 % of the /32 moments. The excitation of the 4+ levels via either one-step processes or higher-order processes is therefore consistent with the present analysis. The authors wish to thank J. S. Boyno for his contributions to the data collection and Ole Hansen for several suggestions on the data analysis. The support of the Nuclear Structure Research Laboratory by the National Science Foundation is gratefully acknowledged. The authors also appreciate the availability of computer time at the University of Frankfurt Computing Center.

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556

TH. W. ELZE AND J. R. HUIZENGA

6) F. K. McGowan, W. T. Mimer, R. L. Robinson and P. H. Stelson, Bull. Am. Phys. Sot. 16 (1971) 493 7) E. Eichler, N. R. Johnson, C. E. Bemis and R. 0. Sayer, Bull. Am. Phys. Sot. 16 (1971) 494; J. L. C. Ford, Jr., P. H. Stelson, R. L. Robinson, F. K. McGowan, W. T. Milner and C. E. Bemis, Bull. Am. Phys. Sot. 16 (1971) 515 8) N. Kaffrell, private communication; G. Herrmann, N. Kaffrell, N. Trautmann, R. Denig, W. Herzog, D. Hiibscher and K. L. Kratz, Proc. Int. Conf. on properties of nuclei far from the region of beta stability, Leysin, Swilzerland, 1970, p. 985 9) F. S. Stephens, B. Elbek and R. M. Diamond, Proc. Int. Conf. on reactions between complex nuclei, Asilomar, 1963, p. 303 10) K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Rev. Mod. Phys. 28 (1956) 432 11) R. Bloch, B. Elbek and P. 0. Tjom, Nucl. Phys. A91 (1967) 576; E. Veje, B. Elbek, B. Herskind and C. M. Olesen, Nucl. Phys. A109 (1968) 489 12) J. V. Maher, J. R. Erskine, A. M. Friedman, J. P. Schiffer and R. H. Siemssen, Phys. Rev. Lett. 25 (1970) 302 13) R. H. Bassel, R. M. Drisko and G. R. Satchler, Oak Ridge National Laboratory report ORNL-3240 (1962) 14) J. L. C. Ford, Jr., P. H. Stelson, C. E. Bemis, Jr., F. K. McGowan, R. L. Robinson and W. T. Mimer, Phys. Rev. Lett. 27 (1971) 1232; P. H. Stelson and L. Grodzins, Nucl. Data Al (1965) 21 15) K. Neergard and P. Vogel, Nucl. Phys. Al49 (1970) 209; Al49 (1970) 217 16) B. Nilsson, Nucl. Phys. Al29 (1969) 445