Electromagnetic properties of 55Fe

Nuclear Physics A160 (1911) 131-153;

@

North-Holland Publishing Co., Amsterdam

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

ELECTROMAGNETIC PROPERTIES OF 55Fe B. C. ROBERTSON, T. P. G. CAROLA t, D. M. SHEPPARD and W. C. OLSEN Nuclear Research Centre, Department of Physics, University of Alberta, Edmonton, Alberta, Canada?7 Received 13 August 1970 (Revised 26 October 1970) Abstract: Measurements of level positions, lifetimes, decay modes and the deduction of spins in 55Fe have been carried out using the 55Mn(p, ny)55Fe reaction. Lifetimes of 12 levels between 1.3 and 3.1 MeV excitation are reported. Spin and mixing ratio assignments are made for levels above 2.2 MeV excitation using a statistical compound nuclear calculation. The measured lifetimes are compared with recent shell-model and intermediate-coupling predictions.

E

NUCLEAR REACTION: s5Mn(p, ny); E,, = 3.60-5.50 MeV; measured a(E; Er, E., O,,), Doppler shift attenuation. 55Fe deduced levels, lifetimes, y-branching ratios, J, 6. Natural target; Ge(Li) detector.

1. Introduction Since the nucleus 55Fe can be described as a single neutron outside and two proton holes in the doubly closed 14 shell, a relatively simple shell-model treatment should reproduce much of the low-lying structure. A number of such treatments have been made le4), and of these, the calculations of Ohnuma “) seem to be the most successful, reproducing most of the known level structure as well as predicting two high spin states which have not yet been identified. Recently, however, several detailed treatments 5- ‘) of nuclei near doubly-closed shells have shown that both shell-model and collective properties are necessary to explain many of the experimental properties of even these nuclei. This, together with the evidence for a vibrational structure “) in ’ 4Fe suggests that collective effects can also be expected in 55Fe . Carola and Ohnuma ‘) have recently described the low-lying levels in 55Fe by coupling the available single-particle neutron levels to collective surface vibrations of the 54Fe core using an intermediate coupling strength. The level positions and spins of most of the levels in the energy range treated are successfully predicted. However, a more sensitive test of both models should be provided by the 55Fe electromagnetic properties. Most of this information is not at present available. This paper describes the determination of lifetimes, spins, multipole mixing ratios and branching ratios of several excited states in 55Fe. The experimental data are compared with both shell- and intermediate coupling model predictions. + Present address: Robert van de Graaff Laboratory, Princetonlaan 4, Utrecht, The Netherlands. tt This work was supported in part by the Atomic Energy Control Board of Canada. 137

138

3.

C. ROBERTSON

2. The experimental 2.1. EXPERIMENTAL

et d.

arrangement and data analysis

ARRANGEMENT

The 55Mn(p, ny)55Fe reaction (Q = -1.014 MeV) was used to populate 55Fe excited states. The proton beam, supplied by the University of Alberta 6 MV Van de Graaff generator at energies ranging from 3.60 to 5.50 MeV, was focussed to a 0.2 cm spot at the target through a series of collimators and was stopped at the target on a thick tantalum or gold backing.

.-

ol J

,

1.0

0.5

GAMMA-RAY

5 t

1.5

ENERGY (MA’)

x

8

n

ic

_I

30

2.0

GAMMA-RAY

Ei:RGV

(MA’)

Fig. 1. A typical y-ray spectrum taken at a bombarding energy of 4.35 MeV. Most of the peaks are associated with 55Fe; the major contaminant can be seen to be due to inelastic neutron scattering in the Ge(Li) detector.

2.1.1. Angular distribution experiment. Angular distributions were measured at 4.10 and 4.35 MeV. Thick targets for these measurements were prepared by mixing a small amount of natural 55Mn powder into a glue formed by dissolving polyurethane in benzene and depositing the mixture onto a 0.1 mm thick tantalum backing. Gamma rays were detected in a Ge(Li) detector with an active volume of 15 cm3 and a resofution of 3.5 keV at 1.33 MeV. The Ge(Li) detector was mounted on a rotating trolley with its front face approximately 10.5 cm from the target. Analogue singals from the detector were fed into an ADC interfaced to an SDS-920 on-line computer. Gamma-ray intensities were measured at O”,30”, 45”, 60” and 90”; each measurement was repeated at least once. A typical y-ray spectrum is shown in fig. 1. Most of the y-rays originate from ’ 5Fe, with weak contributions from the “Mn(p, p’y) and 27Al(p, p’y) reactions.

139

JSFe

2.1.2. Lifetime experiment. The lifetime measurements were performed at a proton energy of 5.50 MeV using thick evaporated 55Mn targets (4.2 mg * cme2) and painted MnO, (15 mg - cm-“) targets on a thick goId backing. The painted targets were made by depositing a slurry of sz 10 pm particles in distilled water onto the gold backing. The targets were then sintered in air at 300” C for three hours to bind the material and ensure bulk density. Absence of voids in the targets lo) was confirmed using a metallographic microscope.

IDENTIFIER) COINCIDENCE

(NEUTRON

( 7 t

ENERGY TO

n-y

TIME-OF-FLIGHT

SELECTION) COINCIDENCE

+

TO

ADC

Fig. 2. Schematic diagram of neutron detection and ny time-of-~ght systems. The fast zero-crossing discriminator (FZCD) was used to provide good timing resolution. Y-Y

I

10 -

TIME

t

,

5

0

OF FLIGHT

(ns)

Fig. 3. Neutron-gamma time-of-flight spectrum. The solid line indicates the spectrum shape for neutrons only. Neutron groups correspond to excitations in 55Fe from w 0.4 MeV to 3.1 MeV.

Gamma-rays were detected in a Ge(Li) detector (45 cm3 active volume) placed with its front face 7.6 cm from the target. A thin lead sheet (0.3 cm thick) was placed in front of the detector to absorb the low-energy radiation originating in the beam stop. Neutrons were detected in a 5.1 cm thick x (17.8 cm O.D., 2.5 cm I.D.) NE 218 neutron detector placed at 180” to the beam axis with its front face 15.8 cm from the target. The gamma flux in the neutron detector was suppressed by a 0.6 cm thick lead

140

B. C. ROBERTSON

et cd.

shield. The detected y-rays were rejected by a cross-over time discriminator method using a constant fraction pulse-height trigger (CFPHT) for good timing characteristics. Timing signals from the Ge(Li) detector were extracted using a timing filter amplifier (TFA) and a CFPHT unit (fig. 2) to obtain an overall timing resolution of M 5.5 ns. A typical neutron time-of-flight spectrum is shown in fig. 3. Logic signals for routing and gating were provided by standard coincidence circuits. Further circuits were used to select yy coincidences between the Ge(Li) detector and a 7.5 cm x 7.5 cm NaI(T1) crystal placed nearby. A 1.Oto 1.4 MeV energy window was set on the analogue pulses from the NaI crystal, which was used to detect cascade y-rays from a 6‘Co source placed between the gamma detectors. This yy coincidence spectrum was accumulated in parallel with the ny spectrum and provided a continuous calibration of the system gain. Singles spectra with good statistics were also collected at the end of each run which, together with the ny time-of-flight and time gate spectra, were used to obtain accurate random coincidence spectra.

2.2. DATA ANALYSIS

2.2.1. Angular distributions. Gamma-ray yields were obtained by summing counts over the full-energy peaks of the appropriate y-rays and normalizing to the strong 0.410 MeV y-ray from the first excited (J = +) state. The resulting angular distributions were fitted using a least-squares procedure to an even-order Legendre polynomial expansion up to order 4, and also compared with the predictions of the statistical model of Sheldon ‘I) for various spin sequences and multipolarity mixing. By measuring angular distributions just above production threshold essentially only s-wave neutrons are produced. The substate populations of the decaying level in the final nucleus can then be explicitly calculated, assuming a statistical spin distribution for the states being populated in the compound nucleus. To ensure the existence of a statistical distribution, the incident beam spread in the target must be considerably greater than the mean compound nucleus level spacing. The theoretical distributions were calculated using the computer code MANDY, originally written by Sheldon I’). The transmission coefficients needed for the MANDY calculations were obtained from the computer program written by Davison 13) using the opti ca 1-model parameters of Rosen 14) for the proton channel, of Perey and Buck 15) for the neutron channels and of Davison 13) for the alpha channel. Spins were assigned on the basis of the 0.1 % confidence limit of x2 fits. The Rose and Brink 16) SI‘gn convention for the mixing ratio 6 was adopted. Mixing ratio errors were assigned using the 0.1 % confidence limit. Branching ratios were determined from the zero-order term of the Legendre polynomial expansion of the distributions for both sets of data corresponding to proton bombarding energies of 4.20 and 4.35 MeV respectively. The absolute intensities were obtained after correction for absorption and efficiency. The relative efficiency of the 15 cm3 Ge(Li) detector was measured using a ‘%o source.

2.2.2. Lifetime analysis. Coincidence

spectra were accumulated

at o”, 90” and 120”

with respect to the beam axis. The observed Doppler-shift attenuation was calculated from the centroid position of the appropriate y-rays in the spectra. Details of the method of calculating the F(z) versus z curves have been described previously 17); in essence they are deduced from the average velocity of a de-exciting nucleus (with a given lifetime z) as it slows down in a stopping medium. The recoil velocitytime curve takes into account both electronic and nuclear stopping; a correction fat large-angle nuclear scattering is also made. The P(z) curves are in good agreement with the predictions of Blaugrund I*). The electronic stopping power for 5 5Fe ions in Mn and MnO, was estimated using the Lindhard formula “). Systematic deviations from the Lindhard prediction for electronic stopping 20) are expected to be small “) for iron projectiles in the energy range comparable to that used in this experiment. An uncertainty of 15 y0 was assigned to the total stopping power. The mean initial recoil velocity, uo, was determined from kinematics, taking into account the finite detection angle of the neutron detector and incident beam energy loss through the target.

3. Experimental 3.1. LEVEL POSITIONS

AND DECAY

results

SCHEME

The energy of levels whose lifetimes were investigated was determined from a variance-weighted average of y-ray positions in the coincidence spectra accumulated TABLE

1

Excitation energies in 55Fe Tepel et al. “) y-decay (keV) 411.5hO.3 931.2kO.3 1316.4*0.5 1408.3*0.5 1918.6&0.7 2051.6kO.6 2144.2k0.5

“) Ref. 23).

b, Ref. *2).

Fischbeck er al. b, “Co 8’ decay

Present work WV)

(keV) 411.4hO.2 931.2A0.2 1316.4kO.2 1408.4kO.l

2152.7&2

409.9 f0.7 929X11.0 1317.7hO.5 1409.6hO.7 1918.5hO.7 2051.810.9 2143.5kl.O 2211 +3 2300.9 k 1.l 2469.7h1.4 2541.610.5 2577.5 kO.5 2871.4Jr2.1 2937.812.1 2984 +3 3027.2f2.2 3076 13

142

B. C. ROBERTSON et al. TABLE 2 Branching ratios of excited states in “%‘e

Initial state (MeV)

Final state

Fischbeck et al. “)

Tepel et al. b,

Pilt ef al. ‘)

Present work

WeV)

2‘144 X:ii0 0.930 1.318

w@>

I5 2 50 33

58rl: 4 25* 3

18&2 3ztl 431-4 36&5

17+

2

2.211

1.318 1.410

(<: 20) 100

(< 20) 100

2.301

0.930 1.318 1.410

80&10 20+10

7515 15+5 (< 10)

2.470 2.542

gs. 1.318

2.578 El0 0.930 1.318

(<

10)

100 100 84&2

(100)

712 6f2 312

2.871

gs. 0.930

63 37

(100)

88&3 12&3

2.938

g.s. 1.318

55 45

100

5.5h.5 4514

2.984

0.930 1.410

< 10 (100) 65&6 35+7
3.027 ZlO 1.410 3.076 “) Ref. 22).

1.410 “) Ref. 23).

(100) ‘) Ref . “)

.

at forward and backward angles and at 90”. A small correction to the average position was made due to the use of different forward and backward angles. The resulting level positions are listed in table 1; the previous results of Fischbeck et al. “‘) and Tepel et al. 23) are included for comparison. All coincidence spectra were calibrated using the positions of the simultaneously accumulated source peaks, and precise energy determinations listed by Marion 24). The energies of levels not investigated in the lifetime studies were determined from peak positions in spectra accumulated at 90”. The results of the branching-ratio determinations are summarized in table 2 together with other available data. In general, the agreement is good. The decay of the 2.144 MeV level reported by Fischbeck et al. (100 % decay to g.s.) is tentative since

they were unable to estimate the strength of branches to the 0.930 and 1.318 MeV levels. The 2.211 MeV level appears to decay only to the 1.410 MeV level. However, it was not possible to exclude the existence of a small branch to the 1.318 MeV level because of the proximity of such a y-ray to the known y-ray of 0.892 MeV, assigned to the decay of the 2.301 MeV level. The 2.871 MeV level was found to decay 88% to the ground state and 12 “//oto the 0.903 MeV level. The branch to the 0.930 MeV level was not reported by Pilt et al. 25) b ut was observed by Fischbeck et al. 22). The 1.666 MeV y-ray was tentatively assigned to a level at 3.076 MeV, which has been reported by Sperduto and Buechner 26). However, a y-ray of this energy could also correspond to a decay from the 2.984 to the 1.318 MeV level. As the excitation energies of the two possible parent levels differ by about 90 keV, it was not possible to exclude either level as the origin of the y-ray on the basis of its excitation curve. However, by comparing the angular distribution of the 1.664 MeV y-ray with that of the 1.574 MeV y-ray, which comes from the decay of the 2.984 MeV level to the 1.410 MeV level, an indication of the 1.666 MeV y-ray origin was obtained. Whereas the 1.547 MeV y-ray angular distribution unambiguously assigns J = 4 to the initial state, the 1.666 MeV y-ray strongly favours an assignment of J = 9 to the initial state, although a spin assignment of J = 3 cannot be ruled out entirely on the basis of the 0.1 y0 confidence limit (see subsect. 3.3.5). The 1.666 MeV y-ray was therefore tentatively assigned to the decay of the 3.076 MeV level, although the presence of a decay from the 2.984 MeV level to the 1.410 MeV level can by no means be ruled out. 3.2. LIFETIME RESULTS

Gamma rays were detected in coincidence with neutrons feeding the 55Fe levels from approximately 0.4 to 3.1 MeV excitation. Typical y-ray coincidence spectra are shown in fig. 4. Extracted energy shifts of all the y-rays studied were linear in cos ~9~ well within errors. The system gain, determined from the 6oCo peak position in the yy coincidence spectra was constant within 0.2 % throughout the experiment and when compared with a determination from a single run using the high-energy y-rays from a Rd Th source. The measured attenuation factors and deduced lifetimes are listed in table 3. Several of the lifetimes were determined from two separate y-rays. The adopted lifetime for each level is an error-weighted mean of all the determinations. With the possible exception of the 2.052 MeV level lifetime measured in Mn, the individual determinations for each level agree well within their errors. A 15 % error was assigned to the determination of the initial recoil velocity for the MnO, targets due to thickness variations of up to 50 % across the face of the target. No correction to the attenuation factors due to the fraction of recoils not stopping in the target material was made, since this was in all cases less than 2 ‘A. The large energy spread of the coincident neutrons enabled cascade feeding of the 1.318 and 1.410 MeV levels. Since recoils associated with a decay from a higher

I44

B. C. ROBERTSON

et

d.

excited state have already been slowed down during the previous decay, the effect of cascade feeding is to decrease the y-ray Doppler shift. The change in the Doppler shift is proportional to the extent of slowing down while in the higher excited state and the fraction of recoils coming from the higher excited state. At a bombar~ng energy of 5.50 MeV, approximately 22 o/oof the 1.318 MeV y-rays were due to cas.

1000

0

300

325

350

CHANNEL

875

900

925

NUMBER

Fig. 4. The 1.318 and 1.919 MeVy-rays from 55Fe observed in coincidence with neutrons. The Ge(Li) detector was placed at 0”, 90” and 120” to the beam axis. The ssFe recoils are slowing down in Mn.

cades from the 2.144, 2.301 and 2.542 MeV levels, so that the attenuation factors of 0.08rtO.04 and -=c0.08 measured in Mn and MnO,, respectively, were corrected to 0.09+0.04 and -C 0.09. Fifty percent of the production of the 0.410 MeV level was due to cascades from the 2.211 MeV level. As the lifetime, and hence the average recoil velocity on decaying, of the 2.211 MeV level has not been measured, the worst possible case was assumed, i.e. the cascade recoils were fully stopped when decaying to the 1.410 MeV level, so that the F(z) values listed in table 3 are twice the uncorrected value.

145

“Fe TABLE 3

Lifetime determinations in “Fe Transition initial final state state (MeV) (MeV)

Attenuation factor F(t)

Mean life t

Adopted value

(fs)

(fs) Mn

MnO,

Mn

MnOz

1.318 -+ g.s.

0.09&-0.04

< 0.09

1.410 + g.s.

< 0.10

< 0.26

1.919 + g.s.

0.8610.07

0.86CO.15

20+-11 $0

43

0.7910.09

0.69;0.21

30+x2 -15

60+65

0.6310.09

0.8510.18

58+24

0.86rizO.06

0.80&0X

-17 2119

0.71 kO.09

0.7910.16

4P20 -16

0.57f0.10

0.6010.17

76+32 -23

+ 0.410 2.052 + gs. --f 0.410 2.144 -+ g.s. -+ 0.930

910+91o -310 >

> 320

840

910+91o

-310

> 840

25+p -8

-42

31f8

< 53 35f26

37+3* -28 84+66

55.4’6

-12

-41

2.301 --f 0.930

0.08hO.04

< 0.09

9oo+‘OQ -230

2.470 -+ g.s.

0.8.5&0.07

> 0.80

lQ+lO

< 0.11

< 0.17

2.578 -+ gs.

0.61 kO.05

0.71&0.13

2.578 --f g.s.

0.54&0.06

60*12 -10 80”” -16

2.871 -+ g.s.

0.7910.06

28,t

2.938 -+ g.s.

0.69f0.07

42+13

3.027 -+ gas.

0.87kO.07

15&

2.542 -+ 1.318

> 1000

> 1100 < 35 > 500

> 660

53f35 -26

9oo+'*O -230 IQ&10 > 660 67&

9

28f

9

double escape

3.3. ANGULAR

9

42+13

-11

-11

9

15rir

9

CORRELATIONS

Gamma-ray angular distributions were measured for the levels between 2.2 and 3.1 MeV excitation at incident proton beam energies of 4.10 and 4.35 MeV. The resulting Legendre polynomial expansion coefficients, corrected for finite detector geometry, are listed in table 4 and the J" and 6 assignments are summarized in table 5. 3.3.1. The 2.211 and 2.301 MeV lea&. The angular distribution of the 0.801 MeV y-ray transition from the 2.211 MeV level to the 1.410 MeV level (J’ = 3-) was measured at a proton energy of 4.10 MeV (fig. 5). Although the incident proton energy was 810 keV above production threshold for the 2.211 MeV level, the relatively large anisotropy (Q = - 0.34+0.03) enabled an unambiguous assignment of J = Q for this level to be made. The 2.301 MeV level was unambiguously assigned a spin of J = 8 from the angular distribution of the 1.371 MeV y-ray to the 0.930 MeV level

B. c. ROBERTSON et al.

146

TABLE4 Summary of angular distribution E,, = 4.10 MeV

Transition initial state (MeV)

final state (MeV)

Energy above threshold WV)

2.211 2.301 2.542 2.871 2.938

1.318 0.930 1.318 g.s. g.s. g.s.

810

-0.34*0.03

725 450 100 60

0.22*0.02 0.30*0.03 O.OOf0.08 -0.10*0.05

2.984 3.027

3.076

Legendre polynomial decomposition l$ = 4.35 MeV Energy above threshold (keV)

a4

-0.05 kO.03 -0.01~0.02 -0.09~0.04 0.0010.08 -0.05 10.05

975 700 350 310 270 220

g.s. 0.410 1.410 1.410

a2

a4

0.19+0.03 0.06 *O.OS 0.00~0.09 0.06&0.05 -0.70~0.11 -0.06&0.10 -0.53*0.19 -0.16*0.07 0.38hO.06

180

-0.02f0.03 0.02+0.06 0.00~0.08 0.02+0.06 0.19+0.11 -0.11*0.1(1 0.12&0.20 0.1210.07 -0.18~0.08

TABLE5 Summary of spin assignments and mixing ratio determinations Initial state

Final state

Assigned J”

(MN

Mixing ratio s

J*

WW

2.211

1.410

2.301

0.930

2.542

1.318

‘I-

2

s‘I-

2

0.21~~:~~ or 2.15+$: -0.06:8.:3 0.00*0.16 -0.60+~::~

2.578

g.s.

2.871

g.s.

2.938

gs.

2.984

1.410

3.027

g.s.

3.076

1.410

or 161> 11 or 161> 11 or --2.75~~.~:

unconstrained

unconstrained O 85+2.so . -0.70 unconstrained 0.00*0.19 -5.65

or 161> 3.7

< 6 < -0.36

147

55Fe

_

0.1 % confidence limit

-

(b) l1.0

0.5 cos2

0

I -90

I -45

I

I

I

0

45

90

arctan

8

8

Fig. 5. Angular distribution (a) and x2 plots (b) of the 0.801 keVy-ray from the 2.211 MeV level to the 1.410 MeV level (J = 3). The angular distribution shown was measured at a beam energy of 4.10 MeV.

3

20

I

I

I

I

2’542 --I- ’

100

19 18 : z

Z F Z -

17

l6

2

15

2G

14

-

lx

12 12

J=l1/2 I

1

I

cos2

1

0

0.5

8

11

-90

I

I

I

I

-45

0

45

90

arctan

8

Fig. 6. Angular distribution (a) and x2 plots (b) for the 1.224 keVy-ray from the 2.542 MeV level to the 1.318 MeV level (J = 5). The angular distribution shown was measured at a beam energy of 4.10 MeV.

148

B. C. ROBERTSON

et d.

(J” = +-). Th e sp’m assignments and mixing ratio determinations for both these levels are in very good agreement with the results of Pilt et al. “) using the same reaction at a beam energy of 3.50 MeV, indicating that it is still possible information from y-ray angular distributions well above threshold.

to obtain

useful

3.3.2. The 2.542 MeV level. The 2.542 MeV level decays entirely to the 1.318 MeV level (J” = s-). The angular distributions of the 1.224 MeV y-ray is shown in fig. 6, together with x2 fits to the theoretical distributions for various spins. The x2 analyses for both bombarding energies reject all but two possible spin assignments, J = 4 and y. An assignment of J” = 4- has been ruled out, however, in a study of the p’ decay of 55Co [ref. 22)]. If J” = $+ is assumed the measured lifetime (t > 0.66 ps) would then indicate a severely inhibited El transition (FE1 < 5 x low4 F,), so that an assignment of J = y is preferred. 3.3.3. The 2.578, 2.871 and 2.938 MeV levels. The angular distribution of the ground state decay of the 2.578 MeV level was isotropic within errors, limiting the possible spin values to J 2 3. This is in agreement with the result of Pilt et aL2’) which, together with the I, = 3 determination 2), enables an assignment of J” = $- for this level. The angular distribution of the ground state transition of the 2.871 MeV level was also found to be isotropic, limiting the spin to J 5 5. A level has been observed at 2.90 MeV excitation 27S28) with an angular momentum transfer Z, = 3 in the (p, d) pickup reaction. It has been suggested by Auble and Rapaport 29) that this is in fact the 2.871 MeV level, so that an assignment of Jn = t- for the level is indicated. The ground state transition of the 2.938 MeV level is slightly anisotropic at 4.10 MeV bombarding energy (a2 = -O.lO+O.OS). Although the spin values J = +, 3 cannot be ruled out with 0.1 % confidence they are highly unlikely; the spin of the 2.938 MeV level is most probably J = 3 or 3. Fischbeck et al. 22) have reported a level at 2.948 MeV excitation with the same decay scheme as the 2.938 MeV level (table 2). The present result is then in good agreement with their assignment of J”

=

3-

or $-.

3.3.4. The 2.984 MeV level. The primary decay of the 2.984 MeV level is via a 1.574 MeV y-ray to the 1.410 MeV level (J” = $-). The angular distribution of this y-ray (fig. 7) is strongly anisotropic and the x2 analysis yields a unique spin assignment of J = Q and 6 = 0.85t2,:::. It is unlikely that this level has positive parity as this would require a strong M2-El mixing. The resulting assignment of J” = $- appears to bz in disagreement with the 55Co /3’ decay work of Fischbeck et al. who reports no p’ decay to this level and consequently rules out J” = j-, s- and $- as possible spin assignments. However, Haupt et al. 30) observed a 1.580 MeV y-ray in coincidence with a very weak (0.09_+0.05) % branch in the /I’ decay from 55Co. If this is the 1.574 MeV y-ray observed in present work, the discrepancy is removed. 3.3.5. The 3.027 and 3.076 MeV levels. Angular distributions of the y-rays from the 3.027 MeV level to the ground state (J” = 3-) and to the 1.410 MeV level (J” = $-)

149

1

I (b) P cos2 8

I 45 orctan

90

6

Fig. 7. Angular distribution (a) and x2 plots (b) for the 1.574 MeVy-ray from the 2.984 MeV level to the 1.410 MeV level (J = 3). The angular distribution was measured at a beam energy of 4.35 MeV.

I

I

I

I

3.076

J -T-

>- 40( k u-l Z : Z -

\ Y

1.410-.--ik55Fe

,:;,I2

J=11/2

1

u 30( > I= a ;: p: 20(

7/2-

\

\ \

\ i-

(0) I

I

u

I

0.5 cos2

(b) L

0 e

v

45 arctan

90

8

Fig. 8. Angular distribution (a) and x2 plots (b) for the 1.666 MeV y-ray from the 3.076 MeV level to the 1.410 MeV level (1 = 8). The angular distribution was measured at a beam energy of 4.35 MeV.

150

B. C. ROBERTSON

et al.

were measured. Both transitions were isotropic, limiting the spin to J 5 5, consistent with an assignment of J” = 4- based on radiative neutron-capture measurements 31) andanl, = 1 momentum transfer ‘*32) o b served in stripping. The measured lifetime (z = 15 +9 fs) corresponds to a normal Ml transition (r = 0.02 r,). The angular distribution of the 1.666 MeV y-ray from the 3.076 MeV level to the 1.410 MeV level (f” = $-) is shown in fig. 8. The x2 analysis yields two possible ~signments, f = J$ or 3, the latter being less probable. No pi decay has been observed to this level 22).

4. Discussion The shell-model treatment of Ohnuma ‘) considers one neutron which may lie in the 2p+, If+ and 2p3 shells, and two proton holes in the If; shell. Proton-proton interaction energies were taken from experimental level spacings and the neutron-proton interaction energies determined from a fit of an assumed effective interaction to the 3076

(lOO)-

3027 --65+6--35c7

Cl-

1”

1


(?1/2,9/2f 3t29/Z-

45+4

5!2;7/2-

2871 -90+3

(3) (512-I _--.------

2578 -8At2-77c2--btZ-33_+2 2542 2470 -100

I

2301

’ I

(3) 512‘ 11/2;(912)

100 I

I

t

80-20--lO-

3/Z912 9/Z

2211 2144 -18+2-3rl-43+4-36t5

3

5/r.?-

2052 --23t2-77+2

I I

312-

1919 -68+3-32r3 1410

3

7/Z-

1 I

l/2-

412 -lOO$

l/2:3/2-

3/2-

=Fe

Fig. 9. Level scheme for states in 55Fe below 3.1 MeV excitation. Branching ratios listed for levels below 2.144 MeV are taken from ref. 25); &, transfer values listed are from refs. 2,32). Excitation energies are in keV.

energy levels of 56Co and “SC. Effective neutron and proton charges of 1.0 e were used to calculate E2 transition matrix elements. The intermediate coupling calculation of Carola and Ohnuma “) considers one neutron in the 2pa, lf, and 2p+ orbitals coupled with core states of up to three phonons. The contribution to the wave functions

151

55Fe

from three-phonon states is negligible for the levels below 3 MeV excitation. Collective E2 matrix elements are fixed by the deformation parameter determined from the fit to the level scheme. No effective charge is used in their calculations. The J” = q- state predicted by Ohnuma to lie at 2.79 MeV is most likely the state at 2.539 MeV, which has been given a preferred assignment of J = 9 in this experiment. Carola and Ohnuma also predict this state, with an excitation energy of 2.59 MeV. However no evidence was found in this experiment for the existence of a. TABLE 6

Comparison

Shell model a. b, t (mode)

Excited state (MeV) J*

0.930

of theoretical

Q-

106

PS

Iz-

0.95

Ps

Q-

15

fs

110

fs

44

fs

110

fs

76

fs

I1 I8

%.z-

fs

1.8

*-

2.542

Y-

13

25+9 -8

fs

31&8

fs

s5+“6 -12

fs

Ml+E2 fs

41

fs

Mi+E2 Ps

0.8

0 9()+0.70 ’ -0.23

PS

Ps

E2

E2 2.470

PS

PS

i8-

Ml 2.301

0.56

%-

Ml 2.144

PS

Ml i-E2

Ml 2.052

3.8

Experiment t

“)

E2

E2 1.919

Intermediate coupling z (mode)

lifetimes in 55Fe

Ml

Ml 1.318

and experimental

fs

193,lO

fs

0.66

Ps

Ml 1

PS

>

E2 2.578

t-

14 Ml

“) Ref. 4).

fs

31

fs

671_ 9

fs

Ml

b, Ref. 9).

level, predicted by Ohnuma to lie at 2.98 MeV. Neither model predicts the 1.410 (J” = $-) and 2.211 (J” = %-) MeV levels. The 1.410 MeV level is strongly excited in (p, d) and (jHe, a) pickup reactions 27128T 33), suggesting a predominant lf% neutron-hole configuration. The proximity of this hole state to the 1.318 MeV level (J’ = $-) would suggest strong mixing of the two states and hence a 1.318 MeV level lifetime greatly inhibited compared with the model predictions, in view of the nature of the admixed component. However the experimental decay scheme (see fig.

J” = -“is_-

152

B. C. ROBERTSON

et d.

9) indicates that there is little overlap between the two states since no level decays to both of these states. Furthermore the measured lifetime of the 1.318 MeV level is in reasonable agreement with both predictions (see table 6). A comparison of measured lifetimes and available theoretical predictions is shown in table 6. All parities have been assumed negative and calculations for both J = 3 and 3 have been included for the levels at 1.919 and 2.052 MeV. In the following discussion, the spin assignments J”(1.92) = 3- and J”(2.05) = $- of Tepel et al. ‘“) and Earle and Bartholomew 31) will be used. There is a systematic difference in the Ml strength distribution of the two models. The major difference is found in the 0.930 MeV level, where the shell model predicts a lifetime retarded by a factor of M 30 compared with the intermediate coupling calculation. This lifetime could not be accurately measured in the present experiment and is expected to be outside the range of normal Doppler-shift experiments. The other Ml widths compared show a systematically greater strength in the shell-model picture, being at least strong enough to reproduce the experimental value. The intermediate coupling Ml strength, which comes mainly from the single-particle matrix elements, is systematically too weak, with the possible exception of the 0.930 MeV level. The 1.919 and 2.052 MeV level lifetime predictions are retarded by factors of z 3 and 2 respectively, and also contain considerable E2 contributions. The predicted E2/M1 mixing ratio for both the ground state transition of the 1.919 MeV level and the decay to the first excited state of the 2.052 MeV level is x 0.4. Little experimental information is available about E2 transition strengths. Both models for 55Fe predict comparable E2 strengths “) although the effective charge of 1.0 e used by Ohnuma in this nucleus is considerably greater than the value of 0.6 e used in ‘IV by Talmi 34) to fit the experimental B(E2) and static quadrupole measurements. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

K. Ramavataram, Phys. Rev. 132 (1963) 2255 J. R. Maxwell and W. C. Parkinson, Phys. Rev. 135 (1964) B82 J. Vervier, Nucl. Phys. 78 (1966) 497 H. Ohnuma, Nucl. Phys. 88 (1966) 273 A. P. Shukla and G. E. Brown, Nucl. Phys. All2 (1968) 296 H. G. Benson and B. H. Flowers, Nucl. Phys. Al26 (1969) 332 M. B. Lewis, N. R. Roberson and D. R. Tilley, Phys. Rev. 168 (1968) 1205 W. Kreische, W. Lampert, G. Loos and D. Weltle, Phys. Lett. 29B (1969) 170 T. P. G. Carola and H. Ohnuma, to be published; T. P. G. Carola, Ph.D. thesis, University of Alberta, 1970, unpublished B. C. Robertson, Nucl. Instr. 84 (1970) 1 E. Sheldon, Rev. Mod. Phys. 35 (1963) 795 E. Sheldon and R. M. Strang, Comp. Phys. Comm. 1 (1969) 35 N. E. Davison, University of Alberta Laboratory Report (1969) no 8 L. Rosen, Proc. 2nd Int. Symp. on Polarization phenomena of nucleons, eds. P. Huber Schopper (Birkhauser Verlag, Basel, 1966) F. G. Perey and B. Buck, Nucl. Phys. 32 (1962) 353 H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306

and H.

55Fe

153

17) B. C. Robertson,

18) 19) 20) 21) 22) 23) 24) 25)

R. A. I. Bell, J. L’Ecuyer, R. D. Gill and H. J. Rose, Nucl. Phys. Al26 (1969) 431 A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 J. Lindhard, M. Scharff and H. E. Schiett, Mat. Fys. Medd. Dan. Vid. Selsk. 33 no. 14 (1963) B. Fastrup, P. Hvelplund and C. A. Soutter, Mat. Fys. Medd. Dan. Vid. Selsk. 35 no. 10 (1967) B. Fastrup, A. Borup and P. Hvelplund, Can. J. Phys. 46 (1968) 489 H. I. Fischbeck, F. T. Porter, M. S. Freedman, F. Wagner, Jr. and H. H. Bolotin, Phys. Rev. 150 (1966) 941 J. W. Tepel, J. G. Malan and J. A. M. de Villiers, Atomic Energy Board, Pelindaba, Transvaal, Republic of South Africa, to be published J. B. Marion, University of Maryland, Laboratory Report (1968) ORO-2998-58 A. A. Pilt, D. M. Sheppard, W. C. Olsen, T. P. G. Carola and P. J. Twin, Nucl. Phys. A150

(1970) 439 26) A. Sperduto

and W. W. Buechner, Phys. Rev. 134 (1964) B142 C. D. Goodman, J. B. Ball and C. B. Fulmer, Phys. Rev. 127 (1962) 574 R. Sherr, B. F. Bayman, E. Rost, M. E. Rickey and C. G. Hoot, Phys. Rev. 139 (1965) B1272 R. L. Auble and J. Rapaport, Nuclear Data sheet 3B January 1970 W. Haupt. D. Lange, H. G. Eckert and A. Flammersfeld, Z. Phys. 188 (1965) 256 E. D. Earle and G. A. Bartholomew, Bull. Am. Phys. Sot. 11 (1966) 98 32) R. H. Fulmer and A. L. McCarthy, Phys. Rev. 131 (1963) 2133 33) C. Glashausser and M. E. Rickey, Phys. Rev. 154 (1967) 1033 34) I. Talmi, Phys. Lett. 25B (1967) 313

27) 28) 29) 30) 31)