Gamma decay of the 238U shape isomer

Nuclear Physics A240 (1975) 13 -28;

@ North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

GAMMA DECAY OF THE 23*U SHAPE ISOMER t P. A. RUSSO t+, J. PEDERSEN ttt and R. VANDENBOSCH University of Washington, Seattle, Washington 98195 Received 16 September 1974 Abstract: A search for a competing y-decay branch of the spontaneously fissioning 238mU isomer is reported. The 200 nsec 238U shape isomer was produced by the (d, pn) reaction with a pulsed beam of 18 MeV deuterons incident on natural uranium targets. A y-ray line at 2.514 MeV has been observed which is attributed to the decay of the shape isomer to the 0.045 MeV 2+ rotational state of 238U. It has a half-life in agreement with that observed for the fission branch and is produced with a yield consistent with predictions of a more penetrable inner barrier. A second weaker line has been observed at 1.879 MeV corresponding in energy to the transition from the shape isomer to the first excited l- state at 0.680 MeV in 238U. The decay of this line is also consistent with the measured half-life of z3smU.

E

238U(d, pn)238mU, E = 18 MeV; measured y-decay NUCLEAR REACTIONS energies and intensities from shape isomer. Obtained isomer excitation energy EII = 2.559, deduced barrier parameters for inner and outer barriers.

1. Introduction The discovery of spontaneous fission isomerism ‘) and its subsequent interpretation as due to a doubly humped fission barrier has led to an enormous increase of our understanding of single-particle effects on nuclear deformation energies. In the actinide element region single-particle effects modulate the liquid-drop model potential energy surface to produce a second minimum in the potential energy surface at a deformation twice as large as that of the nuclear ground state. A recent experimental investigation of the 240Pu spontaneous fission isomer ‘) has shown that the rotational moment of inertia of 240mP~ is approximately twice as large as the value for the normally deformed ground state. This is direct evidence that spontaneously fissioning isomers are highly deformed metastable nuclei. Decay of the shape isomer by penetration of the outer barrier results in delayed fission. Spontaneously fissioning isomers, which are observed predominantly among the isotopes of plutonium and americium, are rare for the, low-2 actinides. Fission isomers have been identified in 236U [refs. “j”)] and 238U [refs. 4*‘)I. The isomer ratio, defined here as the cross section for delayed fission divided by the cross section + Work supported in part by the US Atomic Energy Commission. *+ Present address: Lawrence Berkeley Laboratory, Berkeley, CA 94720. t+t Permanent address: Niels Bohr Institute, Riss. 4000 Roskilde, Denmark. 13

14

P. A. RUSSO et al.

for formation of the normally deformed nucleus by the same reaction, is approximately one order of magnitude lower for each of the uranium fission isomers than the values obtained for the doubly even plutonium shape isomers “). Searches for delayed fission in other isotopes of uranium have produced negative results 3*4*“). Only one neptunium fission isomer has been observed. This is identified ‘) as 40 nsec 237mNp. The half-life is anomalously short, and the reported isomer ratio is several orders of magnitude smaller than the measured values for the plutonium isotopes. The most probable explanation for the lower yields and infrequent occurrence of delayed fission in the low-2 end of the actinide region is the existence of an alternate mode of decay which effectively competes with delayed fission for de-excitation of the low-2 actinide shape isomers. It is likely that the inner barrier of the uranium and neptunium isotopes is sufficiently penetrable that the y-branch dominates over the fission branch. De-excitation via the y-branch would occur by penetration of the inner barrier and y-decay (directly or by a cascade) to the ground state of the normally deformed nucleus. The fact that this decay mode had not been observed when the present investigation was initiated is not surprising in view of the much greater experimental difficulty in observing y-rays compared to detection of fission fragments from the decay of a short-lived, weakly populated shape isomer. There are a number of indications, both theoretical and empirical, which suggest that the inner barrier decreases in height relative to the outer barrier as the atomic number decreases. Fission barrier calculations 8, ‘) applying shell corrections to the liquid-drop barrier by the Strutinsky method show that the inner barrier is the higher of the two barriers for plutonium and higher-2 actinides and that the outer barrier is the higher for the lower-2 actinides. The systematic trend is in part the consequence of the outward shift in deformation of the liquid-drop fission barrier as 2 decreases. This theoretical result supports the existence of a competitive y-branch for the low-Z actinides. Experimental results provide additional support for the existence of a dominant y-branch resulting from a more penetrable inner barrier for the low-Z actinides. The evidence comes from the systematics of barrier heights determined by direct reaction fission excitation functions, fission fragment angular distributions from near-barrier (n, f) experiments, and fission fragment angular distributions from near-barrier photofission experiments as described below. Direct reaction fission excitation functions have been used along with thresholds for delayed and prompt fission to parameterize the fission barriers for the actinides. Fig. 1 shows the relative barrier heights obtained by Back et al. ’ “) based on fits to (t, pf) data. For the doubly even actinide elements, the inner barrier is systematically higher than the outer barrier for plutonium and higher-Z nuclei and the reverse is true for the lower-Z actinides. The appearance of strong fluctuations in the energy dependence of the fission fragment anisotropy for near-barrier (n, f) experiments with low-Z actinides and the

238mU y-DECAY

15

1 I I I I

P+ ,

*P-0

P

z=92 U

Fig. 1. Barrier parameters EA and Es from fits to (t, pf) data for doubly even actinide nuclei. Figure adapted from Back et nl. lo).

statistical behavior of the angular distributions with neutron energy for plutonium and higher-Z actinides has been interpreted by Bjornholm and Strutinsky 11) in terms of channel effects at the barrier. The arguments assume that K, the projection of total spin on the nuclear symmetry axis, is not conserved at deformations corresponding to the inner barrier. Therefore, the angular distributions for near-barrier fission of the higher-Z actinides are determined at the outer barrier. Fission fragment angular distributions for near-barrier (n, f) experiments with plutonium and higher-Z actinides indicate a statistical distribution of K-values consistent with an outer barrier low enough that when sufficient energy has been provided to exceed the higher inner barrier the excitation energy at the outer barrier is high enough to have a considerable number of channels with different K-values accessible. The strong energy dependence of the angular distributions for the low-Z actinides is explained by the selection of K-values corresponding to the limited number of open channels at the higher outer barrier. The large value of the ratio of dipole to quadrupole photoabsorption leads to a dominance of the dipole component in the angular distribution for near-barrier photofission except when the 2+ fission channel is open and the l- channel is closed. The systematic increase in quadrupole photofission with increasing Z in the doubly even actinides has been interpreted r2) as a consequence of the decrease in outer barrier height as Z increases. The lowest 2+ and 1- channels at the deformation of the inner barrier are the 2+, K = 0 rotational state and the l-, K = 0 vibration lying approximately 0.5 to 1 MeV higher in excitation energy for the reflection-symmetric shape characteristic of the inner barrier. At the deformation of the outer barrier the two states are nearly degenerate due to the predicted s. 9*r3* 14) reflection asymmetry of the nuclear shape at the outer barrier. Therefore, quadrupole photofission is expected to dominate for near-barrier photofission when the fission barrier height is determined by the inner barrier. The near absence of quadrupole photofission for

16

P. A. RUSSO et nl.

232Th and the dominance of the quadrupole component for near-barrier photofission of 240Pu is in agreement with the previously stated trends concerning the relative heights of the inner and outer barriers. The 238U nucleus has been chosen for an experimental investigation of the shape nsec [ref. “)I is convenient for the isomer y-branch. The 238mU half-life of 195+30 detection of delayed y-rays. The isomer ratio measured by delayed fission of 238mU produced by the 23*U(d, pn) reaction 15) is at least an order of magnitude smaller than the isomer ratio measured for the delayed fission of 240mP~ which has the same neutron number. This suggests that the cross section for the 238mU y-branch is ten times larger than the isomeric fission cross section of approximately 6 pb. Based on half-life systematics, the 200 nsec 238U shape isomer is expected to be the ground state in the second well i ‘. 1“). Another consideration is that 238U is a doubly even nucleus. In such a nucleus the y-de-excitations are expected to be concentrated in relatively few, strong, high-energy transitions. The y-decay of the Of shape isomer should be dominated by a transition of 2 to 3 MeV to the lowest-lying 2+ state at 0.045 MeV in normally deformed 238U. The experiment has been designed to detect a 2-3 MeV y-ray with a half-life consistent with 195f 30 nsec. 2. Experimental procedures and data analysis The major technical problem in this investigation was to achieve sufficient sensitivity to see y-rays from the decay of the shape isomer with an expected yield approximately lo4 times smaller than that for prompt fission. The principal techniques in achieving this sensitivity were use of a high resolution detector, optimization of the beam time constants, and the employment of a number of measures to reduce the sensitivity of the detector to y-rays from fission fragments. A beam of 18 MeV deuterons incident on a natural uranium foil 3.67 mg/cm2 thick was used to produce the 238U shape isomer by the (d, pn) reaction. The deuteron and proton beams were pulsed at 100 psec intervals with a pulse width of about 100 nsec. The time-averaged beam current was less than 1 nanoamp. Gamma rays were detected with a 25 cm3 true coaxial Ge(Li) detector positioned within two inches of the target. The y-rays were timed against a signal from the beam pulser oscillator. The 100 psec interval between beam bursts was a compromise between maximum duty cycle and minimum build-up of long-lived background y-ray activity. The beam was transported 6.1 m away from the detector and stopped in a lead-lined Faraday cup to reduce the y-ray background. Lead was also used for beam collimators and to line the scattering chamber and beam tubes. The remaining delayed y-ray background was dominated by the de-excitation of normal isomers in fission fragments. The uranium foil thickness permitted 85 y0 of the fragments to escape from the target. The scattering chamber was a 40.6 cm diameter hemisphere with a recess on the flat side for insertion of the Ge(Li) detector cryostat l 5*l’). The fission fragments leaving the target in directions opposite to the location of the y-ray detector settled on the

*38mU y-DECAY

17

remote hemispherical surface or further down the beam tube. Those emitted from the target in the direction of the detector settled on a lead-lined 25.4 cm diameter aluminum disc positioned in the vacuum chamber between the target and the detector recess wall. The motor driven disc made 1000 rpm in a plane approximately perpendicular to the fragment flight paths. Thus fragments which would otherwise deposit on the relatively small surface area in front of the detector were distributed over a surface area eight times larger resulting in a significant reduction in y-ray background. The effective decrease in solid angle for y-rays emitted milliseconds or longer after fission produced a 50 % reduction in y-background. Since high energy y-rays were of primary interest, a lead absorber was positioned between the target and detector to attenuate low energy y-rays. The absorber thickness was sufficient to attenuate 75 % of 0.5 MeV y-rays. The timing signal from the Ge(Li) detector was derived from a constant fraction discriminator. This resulted in a resolution of 5-8 nsec, FWHM, when timed against a coincident 6oCo y-ray dete ct e d by a plastic scintillator. An important problem in this experiment was the tailing in the time spectrum, as indicated for example by the time resolution at one one-hundredth maximum. Initially this tailing, apparently due to occasional badly shaped pulses from the detector, was unacceptable. The tailing was greatly reduced by employing pulse shape discrimination which also improved the FWHM to about 3-5 nsec. Data collection was accomplished with an on-line computer which stored both time and energy information for each y-ray, event by event. The computer was also used to monitor the positions of known lines in the energy spectrum and the position of the prompt peak in the time spectrum during the long data collection periods. The data was corrected for gain and zero shifts in the energy spectrum. Gain shifts of as much as a few tenths of a percent occurred during the typical five-day data collection periods. Separate energy spectra were generated for successive time bins. Analysis of 2-3 MeV y-rays began typically 150 nsec from the edge of the prompt peak. Spectra of events in the late time bin were subtracted as long-lived background from the spectra corresponding to early time bins. As a result, the experiment was sensitive to cross sections of 15-25 pb for 200 nsec y-rays of 3.5-1.5 MeV in the 18 MeV deuteron data. Further details of the procedures for data collection and analysis appear elsewhere ’ “). The 18 MeV deuteron experiment was performed twice. Two additional experiments were performed with the same uranium target and experimental set-up. These were carried out with beams of 13 MeV deuterons and 13 MeV protons. In both cases, the yield of the 238U shape isomer is greatly reduced from the 18 MeV deuteron yield such that these experiments are insensitive to y-rays resulting from the de-excitation of 238U by the y-branch. Each of the four experiments produced the same number of prompt fission events. Therefore any y-line common to the 18 MeV deuteron data and either the 13 MeV deuteron or 13 MeV proton data is ascribed to the de-excitation

P. A. RUSSO et 01.

18

TABLE 1

Tabulation & (MdV)

3.532 2.833 2.514 2.241 2.211 2.034 1.879 1.779 1.760 1.719 1.646 1.592 1.492 “) 1.408 1.394 1.362 1.015 0.999 0.976 0.956 0.899

of y-lines appearing in both 18 MeV deuteron experiments No. of counts in peak after background subtraction (18 MeV deuteron experiment)

31f15 47&16 143*30 45f21 193f35 106f35 66*30* 680+65 95&31 74,t33 103&25 60&30* 80+45* 156*45 375&45 156f60 2360& 100* 295f70* 5720*90* 340*45 785+100*

Where observed 13 MeV proton exp.

13 MeV deuteron exp.

x

X

X

X

X

x

X

X

X

x X

X

X

X

Lines with half-lives incompatible with 195&30 nsec have been excluded. The number of counts in a peak corresponds to integration over the time interval from 150-750 nsec after the prompt peak except where indicated by an asterisk in which cases the time interval was 150450 nsec. “) Ascribed to double escape peak of 2.514 MeV y-ray.

of a normal fission fragment isomer and eliminated as a possible candidate for the 238U y-branch. A summary of these experiments is given in table 1. For y-ray energies in excess of 2 MeV only two lines decaying with half-lives consistent with the measured half-life of 238mU appear in the data from each of the 18 MeV experiments and are absent in both the 13 MeV deuteron and 13 MeV proton data. One of these at 3.532 MeV is too high in energy to be consistent with a preliminary measurement ‘s) of the excitation energy of 238mIT. It is possible that the origin of this line is a shape isomeric state of an isotope of neptunium, although the excitation energy is larger than would be expected. The second y-ray line at 2.514 MeV is a more promising candidate for the decay of 238mU. Fig. 2 shows the line at 2.514 MeV in a background-subtracted energy spectrum of the combined data from the two 18 MeV deuteron experiments. Fig. 3 shows the decay curve for this line. The fitted half-life of 191+44 nsec is in good agreement with the 195f30 nsec half-life of 238mU, The cross section for the

=“*U

ENERGY .

,

2.40 I,

I

I,

2.45

I

I

I,

2.50

750

&leV)

* 3 s 8,

“‘U f 150 -

19

y-DECAY

2.55 2.60 s Q 8 1 ,“‘I

2.70 4 a II

2.65 I’,

+ 18 MeV d

nsec AFTER

PROMPT PEAK)

BACKGROUND-SUBTRACTED

SPECTRUM

2.514 MeV i

2.6145

MeV ‘**Pb

line

I

t

I

20

I

1,

I

I

CHANNEL

Fig. 2. Background-subtracted

I

I

c

1

2500

2400

c

1

1

3

a

2600

NUMBER

energy spectrum near 2.5 MeV for the 18 MeV deuteron ment of uranium.

E =2.514

TIME

bombard-

t&V

Wed

Fig. 3. Decay curve for the 2.514 MeV y-ray observed in the 18 MeV deuteron uranium.

bombardment

of

20

P. A. RUSSO et al.

2.514 MeV line is 90f25 pb based on a 195 nsec half-life. This is consistent with expectations for the 23*mU y-branch. The double escape peak for the 2.514 MeV y-ray is also observed, with the expected intensity, at 1.492 MeV. The 2.514 MeV line and the 1.492 MeV line do not appear in the control experiments with 13 MeV deuterons or 13 MeV protons. The high energy y-ray spectrum obtained with 13 MeV deuterons is shown in fig. 4. The identification of the 2.514 MeV y-ray with the transition from the O+ shape isomeric state to the first excited 2+ state at 0.045 MeV in 238U establishes the shape isomer excitation energy of 2.559 MeV. Decays from a state at this energy to other known low-lying 2+ and l- levels in 238U correspond to y-ray energies between 1 and 2 MeV as illustrated in the proposed decay scheme in fig. 5. Of the possible transitions, the most probable is the 1.879 MeV decay to the 1 - state at 0.680 MeV. Analysis of the low energy spectrum of the 18 MeV deuteron data reveals a weak line at 1.879 MeV which shows a decay consistent with a 200 nsec half-life. No line appears at this energy in either the 13 MeV deuteron or proton data. The cross section for the 1.879 MeV y-ray is 40+ 20 pb based on a half-life of 195 nsec. A search for the remaining lines corresponding to transitions to the higher lying lor 2+ states in 238U gives negative or inconclusive results. The cross sections for the 2.514 and 1.879 MeV lines are summarized in table 2. It is possible for a O+ state to decay by an EO transition to the ground state in competition with the E2 transition to the first excited state. Although the known first-excited Of states in the uranium region, typically at about 1 MeV of excitation,

2.35

I(

2.40

0 8 I ,I

2.45

11 1 ,I

“‘I

(MeV) 2.55

ENERGY 2.50

“aU

II

I”#

1’

2.60

b 10 n ”

2.65

18 8 3’

2.

1

+ 13 MeV d

(150-750 “set AFTER BACKGROUND-SUBTRACTED

2.514

PROMPT PEAK) SPECTRUM

MeV

2.6145

MeV 20*Pb

line

1

2500

Fig.

4.

Background-subtracted

2600 CHANNEL

2700

2600

NUMBER

energy spectrum near 2.5 MeV for the 13 MeV deuteron bombardment of uranium.

21

23*mU I/-DECAY 2.6 SHAP ‘E I SOMER LEVEL

2.4

c 4

Ot2.559

MeV

1

1.4

1.2

2+,1.224

1.0

Cl .035:

I;

I.105

2tLO60\ ::ggg **

MeV

_

2.51, Me\

P

0.6 I-,0.660

_---. -_-

___i__________________

0.6

0.4

0.2

0

2+,0.045. s 238~

LEVELS ASSIGNED ASlor 2+

Fig. 5. Proposed decay scheme for the 238U y-branch based on the assumption that the 2.514 MeV transition is the decay of the shape isomeric state to the first excited 2+ state at 0.045 MeV in normally deformed 23*U.

do decay with comparable strengths for the EO and the E2 decays, the relative energy dependence of EO and E2 decays are expected to lead to a preponderance of E2 decays for a state with more than 2 MeV of decay energy. TABLE 2

Experimental

cross sections for y-rays at 2.514 MeV and 1.879 MeV for the three reactions 238U target 18MeVd

13 MeVd

13MeVp

(r (2.514 MeV)

go*25

-22&-15

-10*12

Ocb) u (1.879 MeV) Olb)

40*20

-12f14

2&15

22

P. A. RUSSO et al.

3, Discussion

The energies and half-lives of the two y-rays in table 2 are consistent with the ydecay of a 195 nsec state at 2.559 MeV to the 2+ and l- levels in 238U at 0.045 and 0.680 MeV respectively. The excitation energy of 2.559 MeV agrees with theoretical predictions for the excitation energy of the 238U second minimum 14P19-21) and is comparable to measured excitation energies of the doubly even plutonium shape isomers. The absolute cross section for the lines is consistent with the expected yield for the 238mU y-branch. The appearance of both lines in the spectra from 18 MeV deuteron bombardments of uranium and the absence of the lines in the 13 MeV deuteron and 13 MeV proton experiments which were equal in sensitivity to y-rays from fission fragments excludes fission fragments as a possible origin of the lines. It is unlikely that an isomer as long lived as 200 nsec would occur at 2.5 MeV excitation energy in the first well. It is proposed, therefore, that the 2.514 MeV y-ray is the strongest primary transition in the y-decay of the shape isomeric state in 238U, and that the 1.879 MeV transition competes in this decay mode with approximately one half the strength of the high energy line.

Fig. 6. The ratio Z(El)/Z(E2) plotted versus E,,.For the radioactive decay data, values of Z(E2) have been corrected to the energies of the corresponding El transitions by the factor (E#J?l)~E,,(E2))“. The ratio corresponding to the present result is also adjusted by this factor.

*=“U y-DECAY

23

The ratio of the strength of the 2.514 MeV E2 transition to the 2+ state to that of the 1.879 MeV El transition to the I- state is intermediate with respect to the ratios of E2 to El strengths obtained near 4 MeV from (n, y) data ‘“) and near 1 MeV from radioactive decay data 23). This is illustrated in fig. 6 which is a plot of the observed intensity ratio, ~(El)/Z(E2), as a function of energy for the available data. The comparison with the present result, also plotted, provides additional evidence that the two lines do indeed represent primary decays of the same state. Evaluation of the 23*mU isomer ratio requires a knowledge of the total y-branch cross section. The sum of the observed cross sections for the 2.514 and 1.879 MeV lines is 130+30 pb. To this can be added estimated decay strengths to the other six known l- and 2+ states in 238U (fig . 5). These strengths have been determined assuming that the reduced widths for these lower energy El and E2 transitions are equal to those observed for the 1.879 MeV El transition and the 2.514 MeV E2 transition respectively. This adds an additional 70 + 20 fib to the observed cross sections giving 200f 50 pb for the total y-branch cross section. A possible contamination as large as 30 % of the 2.514 MeV line would lower this estimate by about 50 pb. A contamination of this order of magnitude can be expected from the double escape peak from the 3.532 MeV peak. The possibility of decays to unknown I- or 2’ states in 238U couId increase the y-branch cross section. The quantitative estimates which foIlow are based on the range of 100 pb to 250 pb for the total y-branch cross section for 238mU_The delayed fission cross section is approximately 6 pb [ref. “)I. Table 3 gives isomer ratios for the doubly even shape isomers of uranium and plutonium which have been designated 24f2 “) as ground states in the second well. The third column of table 3 lists isomer ratios for shape isomers formed by the (cr, 2n) reaction. These have been calculated ’ “) from experimental measurements of absoIute fission isomer cross sections for 236mP~ [ref. 25)], 238mP~ [ref. ““)I and 240mP~ [refs. ‘,“)] and from expe~menta1 values for the (CX,2n) spallation cross section [refs. “, ‘“)I. The isomer ratio for 238mU formed by the (d, pn) reaction has been computed using an estimate of the cross-sectionlimits for the reaction 238U(d, pn)238U with 18 MeV deuterons ’ “). The estimated limits “) are based on the measured proton spectrum from the scattering of deuterons on thorium and on the assumption that the contribution to the proton spectrum from deuteron breakup is one half to one sixth of the total proton yield ’ “). This leads to the prediction, 150 mb s o,, pn s 250 mb, for the 238U(d, pn) 238U cross section with 18 MeV deuterons. Column 4 of table 3 gives the resulting isomer ratio for 238mU. Experimental limits for the y-branch of 236mU formed by the 235U ( d, p) reaction with 11 MeV deuterons “) have been used to estimate 15) limits for the isomer ratio of 236mU. This also appears in column 4 of table 3. Relative values of the isomer ratios for 238mP~, 240mP~, 242mP~ and 244mP~ formed by (d, pn) reactions have been determined 15) from measured cross sections for the fission isomers 24) and from the experimental systematics for r,/rr [ref. ““)]_ These have been converted to absolute isomer ratios by normalizing the relative values to the 240mPu isomer ratio determined from the (a, 2n) data.

24

P. A. RUSSO et af. TABLE3 Isomer ratios for the doubly even ground state shape isomers of U and Pu

Ground state shape isomer

Dominant mode of decay

236~ 92 144

(100 nsec) 238~ 92 146

Q‘/%.~. (X W4) experimental (from a,2n)

experimental *) (from d,pn)

predicted “)

5 to 25 “)

20

5 to 25

10

2&l

2&l

3

6f3*)

6f3

8

delayed gamma emission

(200 nsec) 236Pu 94

142

(0.04 nsec) 29JiPU144

delayed

1.5&l

fission

(0.7 nsec) 24OPu 94 146 (4 nsec) 2~:pu14*

4H

(3 nsec) 244Pu 94

150

5zb2.5

(0.4 nsec) “) Pu results calculated from q/or [ref. 25)] and r,,/I’r [ref. 30)]. Results are normalized to experimental q/u,... for 240Pu. b, Calculated from ratio of level densities in wells I and II using EA and Ea values from Back ef al. lo). ‘) Based on experimental upper limit to y-branch cross section “). “) Average of two experimental values M* 6).

A general trend toward higher isomer ratios (by a factor of 2 or 3) is observed for the plutonium isomers with neutron numbers 146, 148 and 150 compared to 142 and 144. In addition, the isomer ratios for 236U and 238U are significantly higher than those for the plutonium shape isomers. These systematic differences can be explained by variations in shell effects at the fission barriers for different N- and Z-values. The inner barriers and shape isomer excitation energies for the uranium isotopes are about the same as those for the plutonium isotopes lo). However, the outer barriers for the plutonium isotopes are significantly lower, a result of a shift in the liquid-drop barrier to lower deformations with increasing Z. The second well in uranium is deeper, therefore, and more effective as a trap to increase the population of the shape isomer. To a first approximation the relative population of the ground and isomeric state wells will be proportional to the ratio of level densities at the tops of the second and first wells ’ “). These ratios have been calculated ’ “) using the level density parameters and level density formula of Gilbert and Cameron “‘). Inner and outer

238mU y-DECAY

25

barrier heights were obtained for 236U 238U, 23sPu, and 240Pu from the (t, pf) data of Back et al. lo). V a 1ues used for’the shape isomer excitation energy, E,, , of 23gU, 238Pu, and 240Pu were the averaged results of experimental measurements [refs. 6*32e““)I. The present result for E,, of 23*U was used. The calculated isomer ratios given in column 5 of table 3 agree in both absolute magnitude and in their qualitative dependence on N and 2, with the experimental isomer ratios. It is of interest to determine the partial half-lives for fission and for y-decay and from these half-lives the penetrabilities of the inner and outer barriers. For the analysis that follows we will assume that the total y-branch cross section is 250pb, including 50 pb as an estimate of the decay to unknown 1 - and 2+ levels. This leads to a partial fission half-life of 8300 nsec and a partial y-half-life of 200 nsec. The partial fission half-life is given by t.Lf

4 x lo-*’

In 2 =

-

=

nPs

PB

’

where n is the number of barrier assaults per set, PB is the penetrability of the outer barrier and ti,f is the partial half-life (in set) for fission decay of the isomer. The numerical value of 12is based on a vibrational frequency of ho,, = 1 MeV. Implicit in this expression is the expectation that once the outer barrier is penetrated the nucleus always fissions. The y-decay rate from a shape isomer is more difficult to estimate quantitatively. In a theoretical treatment of the y-branch, Lynn 34) has expressed the wave function for the shape isomeric state as a sum of two terms. One of these corresponds to a pure state in the second well (class II state). The second describes a small admixture of strengths of states in the first well (class I states). The theoretical estimates “a ““) indicate that the second term will be the dominating one. While the pure class II term leads to collective transitions of about 1 MeV, the class I admixture term gives rise to high energy transitions to low-lying states in 238U, consistent with the present experimental results. Substitution of expectation values for the matrix elements which arise from the class I admixture leads, in the limit of complete damping of the class I admixture into the class II states, to a partialhalf-life for the y-branch,

t. L!!Lt 1, Y

ho,,P*

y’

Here, D, is the compound level spacing in the first well, Zzo,, describes the frequency of assaults on the inner barrier and t, is the half life for radiation in the first well. Estimates 15*r ‘) of the quantities D, and t, together with allowance for incomplete damping expected at the low excitation energy of the shape isomer leads to ti,y = 4X 10-“/P*.

The curvature energies, ho, and ho,,

for the 238U inner and outer barriers have

26

P. A. RUSSO

et al.

POTENTIAL ENERGY (MeV)

23Q

E, =5.90-------

I 0

I 0.170

DEFORMATION

I 0.427

(/3-j&,

Fig. 7. The 238U fission barrier constructed from two inverted parabolas smoothly joined by a third parabola. Elr, ?ioA and fioB are the values deduced from the present experiment. EA and EB are obtained from the experimental results of Back et al. I”).

been calculated from the present results using the expression for penetrability of a parabolic barrier, Zn(dE)/fio - 1 P=(l+e > 7 where AE is the height of the barrier to be penetrated. The values of EA and EB are taken from the direct reaction fission data for 238U [ref. ‘“)I. The present result is used for E,,. The fission barrier for 238U parametrized by EA, EB and E,, and the resulting values of ho, and ho, are shown in fig. 7. The barrier is approximated by two inverted parabolas smoothly joined by a third parabola. The predominance of y-decay over fission decay for 238mU is more a consequence of the “thinner” inner barrier, reflected by ho, > hm,.,, than of the slightly lower value of EA relative to &. The value of ho, is somewhat larger than the value obtained from the (t, pf) data lo). However, direct reaction fission is sensitive to curvature near the top of the barrier while decay of the shape isomer involves penetration 3 MeV below the barrier. Furthermore it must be emphasized that the y-branch strength depends on the small class I admixture in the shape isomer wave function. Considerable fluctuations in this quantity from nucleus to nucleus are expected, leading to an uncertainty in ho,. 4. Conclusions

If the present interpretation

is correct the experimental results correspond to the

23s”‘U y-DECAY

27

fjrst observation of the shape isomer y-branch. Two delayed y-rays resulting from the 18 MeV deuteron bombardment of 23*U have been identified as the dominant transitions in the y-decay of the 238U shape isomer to the normally deformed 238U ground state, The identification is based on half-life measurements, total yield and the consistency of the two y-ray energies with the excitation energies of the lowest-lying 2” and l- states of 238U which are expected to receive most of the strength from this mode of decay. The suggested decay scheme also includes y-transitions which have not been observed due to the larger y-ray backgrounds at lower energies. Moreover, the results do not account for the very weak transition at 3.532 MeV. The isomer excitation energy is higher than that obtained in a preliminary 238U(n, n’)238mU threshold measurement I*>. The (n, n’) excitation function is anomalous in two respects. It has a shallower slope than is usttally obtained in reactions where two neutrons are evaporated 6 36), whereas one would expect it to be steeper both because only a single particle is evaporated and because of the lower average nuclear temperature. At higher energies it also exhibits a bump not previously observed in charged particle excitation function measurements. Therefore, further studies are required for an unambiguous explanation of the decay of the 238U shape isomeric state. The isomer ratios for 236mU [ref. ““>] and for 238mU determined from the present results for the y-branch are larger than the isomer ratios for the doubly even ground state shape isomers of plutonium. This is shown to be the consequence of a deeper second well in uranium compared to plutonium enhancing the shape isomer population for 236U and 238U compared to the doubly even plutonium shape isomers. The experimental results show that the inner barrier for 238U is more penetrable than the outer barrier and even more penetrable than predicted by the parameters obtained from fits to the direct reaction fission data. This reflects a sensitivity to the barrier penetrability at different excitation energies for the two experiments. The participation of the following people is gratefully acknowledged: W. Jacobs for numerous contributions to many aspects of the project, 5. Calarco for interest and assistance in the preliminary experiments, and R. Heffner for assistance in taking data. One of us (J.P.) wishes to thank the University of Washington for support and hospitality. References 1) S. M. Polikanov, V. A. Drum, V. A. Karnaukhov, V. L. Mikheev, A. A. Pleve, N. K. Skobelev, V. G. Subbotin, G. M. Ter-Akopyan and V. A. Fomichev, JETP (Sov. Phys.) 15 (1962) 1016 2) H. J. Specht, E. Konecny, D. Heunemann and J. Weber, Phys. Lett. 41B (1972) 43 3) N. Lark, G. Sletten, J. Pedersen and S. Bjernholm, Nucl. Phys. A139 (1969) 481 4) K. L. Wolf, R. Vandenbosch, P. A. Russo, M. K. Mehta and C. R. Rudy, Phys. Rev. Cl (1970) 2096 5) S. M. Polikanov and G. Sletten, Nucl. Phys. A151 (1970) 656 6) H. C. Britt, S. C. Burnett, B. H. Erkkila, 3. E. Lynn and W. E. Stein, Phys. Rev. C4 (1971) 1444

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