1.E.4: I 3.A
I
Nuclear Physics A104 (1967) 213--240; (~) North-Holland Publishiny Co., Amsterdam
Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher
H I N D E R E D E1 T R A N S I T I O N S I N 159Dy, 16STm, 172Lu, 173Lu A N D lS°w T. W. CONLON t, R. A. NAUMANN and A. L. McCARTHY Palmer Physical Laboratory, Princeton University, Princeton, New Jersey *t
Received 21 June 1967
Abstract: Several new isomeric states with half-lives in the range 10 ps-30 ms have been identified following the 17.5 MeV proton bombardment of the natural elements and separated isotopes of the elements Eu-Pb. The gamma rays from these states have been observed using a 8 cm3 Ge(Li) detector. The E1 isomers observed in 159Dy,~65Tm,172Lu,~80Wand 17aLuare described. The characteristics of the previously unidentified isomeric states in the first four nuclei, and of some of the intermediate states populated in the decay have been measured. The results are discussed in terms of the available states of the single-particle, Nilsson model and its extension to two-particle states and in terms of the selection rules for transitions between these states. A three-particle state is suggested to explain the high-spin isomer observed in ~59Dy.
E
NUCLEAR REACTIONS 159Tb,17nyb(p,n); 19SEr,178yb,lSlTa(p, 2n), E = 5-17.5 MeV; measured or(E; Er), p?-delay. Natural and enriched targets. RADIOACTIVITY 159Dy, Xn~Tm,tT~,~r3Lu,asoW [from (p, xn) reactions]; measured T~, E~, I s, lee; deduced levels, multipolarities, K, J, n. Ge(Li) detector.
1. Introduction A survey has been m a d e of the isomeric activity in the time range 10/~s to 30 ms p r o d u c e d by b o m b a r d m e n t of 17.5 MeV p r o t o n s o n the n a t u r a l elements E u to P b [refs. 1, z)]. The isomeric nuclei have been identified by b o m b a r d m e n t of separated isotopes a n d the characteristics of the g a m m a rays resulting from the decay of the isomeric states have been m e a s u r e d using a n 8 cm 3 lithium drifted g e r m a n i u m Ge(Li) detector. Several new short-lived states have been p r o d u c e d a n d i m p r o v e d data o b t a i n e d o n m a n y previously reported isomeric nuclei. The results presented here describe the E1 isomers observed in 159Dy, 165Tm, 172Lu ' 173LH a n d l S ° w a n d the properties of the isomeric states a n d intermediate levels p o p u l a t e d in the decay of these states. The metastable states identified i n ~59Dy, ~65Tm a n d 17ZLu had n o t been previously reported or had the decay scheme of the 180w isomer been previously established prior to this work. * Recipient of a NATO Fellowship during the period of this work. Present address: Nuclear Physics Division, AERE, Harwell, England. t* This work was supported by the U.S. Atomic Energy Commission and the Higgins Scientific Trust Fund. 213
214
T.W. CONLON et al.
The large retardations over the single-particle estimates for the E1 transitions are discussed in terms of the K-selection rule of the unified model 3) and the selection rules for transitions between intrinsic particle states described by Nilsson orbitals 4) (N, nzA); N is the total oscillator quantum number, nz the oscillator quanta along the symmetry axis of the nucleus, A the orbital angular momentum along this axis and K the total angular momentum along this axis. The quantum number Z = K - A is also used to describe the states. The selection rules of Alaga 5) for a transition of multipolarity l and parity • connecting states (KiTEi) and (KfT~f) a r e A K = IKi-Ktl < l,
rc =
R i T ~ f.
In particular if A K exceeds l, the transition is forbidden, and the quantity v -- A K - l represents the degree of forbiddenness. The selection rules governing changes in the asymptotic quantum numbers n~, A and 2; for El radiation are reproduced in table 1 from ref. s). TABLE 1
Section rules for allowed changes in the asymptotic quantum numbers Multipole E1
AK 1 0
Operator x+iy
z
AN
A nz
AA
A,S
±1
0
1
0
1 --1
1 --1
0
0
2. Experimental procedure 2.1. ELECTRONICS In this investigation the gamma-ray energy and its time of arrival following bombardment of the target by a pulsed beam, are measured. A 4096-channel, twodimensional analyser is used in these two simultaneous measurements. The array used was 256 × 16, providing 256 channels for pulse-height analysis and 16 channels for the time measurement. The energy analysis used the 4096-channel instrument as a conventional pulse-height analyser. The time measurement is accomplished by the use of a time-to-pulse-height converter in the following manner: a linear voltage ramp of chosen duration is triggered at the time of bombardment and sampled for height at the instant each gamma-ray pulse is presented to the analyser, so that each energy pulse is stored in the appropriate time channel. The pulse-height for the time channel is proportional to the height of the voltage ramp at the time of arrival of the pulse. A block diagram of the electronics used is shown in fig. la; a schematic diagram showing the approximate time relationship of the signals at various parts of the circuit is also shown in the fig. lb. A similar arrangement has been used by McCarthy et al. 6) to study isomeric activity in the range 5-1000/~s.
215
E1 TRANSITIONS
In order to avoid storing prompt events, the monostable circuit of fig. la is used to gate the analyser which is turned on only in a chosen interval between beam pulses. The duration of this interval is selected according to the half-life of the radiation investigated. Since the analyser coincidence circuit will not function with a pulse longer than a few/lsec, an auxiliary circuit is used to provide suitable pulses, 7 V high and Schematic showing the approximate time relationship of signals at various ports of the block diagram.
Block diagram of the circuits used tO measure the energies end half-lives of isomeric tronsltions.
Moln
.,FI
nplifie¢
Ge (L-i) ]
Maln
Amplifier
Amplifier Output
And
"Random" pulse~r tO measure |
i d:CI'st:;eJ Con~trol Scipes
Discriminator
~ garmg ~ monosto ble
bcope Trin~°r
~L~.
Output
Monostoble "Test" Pulse .........
I
4-'~
[
1 of 3 and 4
Coincidence
®
5----- I
HI]HI
I]
J
Linear
r-
I
I--
Voltage Ramp
Dee Quench
t I
Woveform
Mor~ostable
Signal Magnitude to Time Address of Analyser
7
ond Diode Cathode
I
Attenuo tar
J
~Hower~
Time Ronges~ used
-~uu
It
500 p.s 1.5 m s 20ms
U P't
Wove form Generators
(a)
(b)
Fig. 1 (a) Block diagram of the circuits used to measure energies and half-lives of isomeric transitions. (b) Approximate time relationship of signals at various parts of the block diagram. 4 ps wide, derived from the signals from the main amplifier, as shown in line 5 of fig. lb. The coincidence pulses are fed into the coincidence imputs on both sides of the analyser, so that each gamma-ray pulse occurring between beam bursts has an appropriate coincidence imput. At the same time, the "M" or time side of the analyser receives a coincidence imput which causes it to sample the height of a linear voltage ramp at the time the gamma-ray pulse arrives, so that the signal magnitude to the time address of the analyser is linearly proportional to the time of arrival of the gammaray pulse following the start of the ramp. Pulses are thus stored in their proper energy and time channels.
216
T.W. CONLONet
al.
A 60 Hz mercury pulser shown in the block diagram enables corrections to be made for analyser losses. The average time required to analyse each amplified pulse from the detector is about 50 ps; if the activity measured has a half-life of 100 ps or less, the count rate varies rapidly with time over a period comparable to the analysis time; hence analyser losses for the various time channels also change rapidly. The 60 Hz pulser is random with respect to the analyser gating pulse (line 4 of fig. lb), and the pulses it generates are treated in the same way as detector pulses; thus, the number of such pulses in each time channel is a measure of the live time of the analyser for each particular channel. Such procedure does, of course, also correct for any inequality in the time intervals whether it is due to acount rate losses as discussed, or non-linearities in the ramp voltage, or in the channel definition by the A D C of the analyser. The gamma counts in each time channel are normalized by dividing by the sum of counts in the pulser peak. The initial survey was carried out in three parts; each element was bombarded three times and the activity recorded over the time ranges 300/~s, 1.5 ms and 20 ms. When an isomer was observed, in the subsequent runs on this element and on separated isotopes, the time range used was about 5 to 10 times the half-life involved. The analyser gating interval was measured directly from the two monitoring oscilloscopes, and a more precise measurement was used a pulser of variable repetition rate. The interval between pulses was set so as to be equal to the length of the gating period as observed on the oscilloscopes, and the number of pulses coming in a given time, as measured by an accurate stop-watch, were counted by a scalar. The interval could in this way be measured to much better than 1 ~ , and hence the uncertainty in this measurement is not a significant source of error in the half-life determination. The uncertainty in half-life is principally determined by statistics and background subtraction, errors in which tend to smooth out since in general there are up to 16 points defining each decay over a period of 5-10 half-lives. The quoted error was estimated on the basis of consistency between independent runs which was usually about 2 ~o. Each isomeric decay was observed at least twice using natural targets, and in those cases where separated isotopes were required for identification of the isomeric nucleus, the decay products were observed three or more times. Thus, for strongly excited isomeric states the quoted half-life is probably not worse than + 2 ~o; for weaker cases the uncertainty is larger and is quoted in the text. 2.2. BEAM PULSING The pulsed beam from the Princeton University FM cyclotron in the normal operating mode has a duration of about 20 ps and a repetition rate of about 3 KHz. The pulsing system has been modified for the current work to provide intervals in which no beam is extracted of up to 100 ms [ref. 2)]. This has resulted in a loss of beam intensity such that for intervals of longer than about 20 ms, the beam intensity was too low to produce usuable activities in the geometry used. The range of half-
E1 TRANSITIONS
217
lives observable with this modification are between about 10 #s (limited by the beam pulse duration) and 20 ms. A measurement of the residual beam between beam bursts, that is during the counting interval used, showed that it was < 10- 5 of the main beam intensity, and hence all the activity recorded is due to delayed events. The absolute beam energy used was 17.5-t-0.2 MeV. 2.3. EXPERIMENTAL GEOMETRY
The general facility for charged particle reaction studies using the 17.5 MeV proton beam from the Princeton F M cyclotron has been described in refs. 7, 8);
Beam line7 / ~Target
/
~ - -~ Ge (Li)detector ~ - z ~ / <~ Cu backing plate ~ (C°ld Finger) L Aluminum Can J" ~
....
\ Beam
/ tube
/ \ /
" /I Spectrometer /IMagnet
_
\
/
_
"Y'/~ "/"/"/,'/// "~Pb bficks//~/ Scattering
[/// .-'>//Chamber Wall: V~ // / / / Inside radius:lO'' / /
// Fig. 2. Scattering chamber set-up.
the arrangement used in the current experiment is similar to that described there. A drawing showing the set-up in the 50.8 cm diam. scattering chamber is shown in fig. 2. The target is mounted with its plane at 30 ° to the beam line, and the Ge(Li) detector is positioned about 6 cm from the target on a line perpendicular to the target plane. Thus, if t is the target thickness over which isomeric activity is produced by proton reactions, then the target thickness for gamma rays reaching the detector is clearly t cos 60 ° = ½t, thus the effective target thickness is halved. The solid angle subtended by the 8 cm z area of the detector at the target which is 6 cm from it is 8/6 z = 0.22 sr. Lead bricks placed between the beam pipe and the detector mounting provided shielding from the background activity produced in the spectrometer magnet and beam tube and also served to reduce the intense group of prompt gammas reaching
218
T.W. CONLONet
al.
the detector from the carbon degraders used to reduce the beam energy, which were attached to the beam tube extending into the scattering chamber. In the initial survey, the targets used were rolled metallic foils of the natural elements of about 1 m m thickness. Enriched samples of the separated isotopes of the elements were obtained in oxide form and mixed into a semi-plastic solution of polystyrene in benzene on glass slides; after evaporation of the benzene and removal from the glass slide, the slurry target thus produced 9) was ready for use. The targets of the separated isotopes were constructed, whenever possible, to be of such a thickness so that the loss in intensity of the characteristic X-ray due to absorption, assuming uniform production of X-rays throughout the target material, was < 50 ~ ; this thickness varies for each target according to the linear absorption coefficient but is about 0.2 m m for the materials used here. 2.4. MEASUREMENT OF THE ENERGIES, RELATIVE INTENSITIES AND MULTIPOLARITIES OF THE GAMMA RAYS The lithium drifted germanium detector used was constructed by one of the authors (T.W.C.) in this laboratory 2); it has a volume of 8 cm 3 and a capacitance of 14 pfd. These figures were obtained by a measure of the depletion depth by copper staining and also by a direct measure of the detector capacitance 2). It was enclosed in a metal dewar and operated at liquid nitrogen temperature at a reverse bias of 1250 V. The thickness of the outer wall of the dewar limited the lowest-gamma-ray energy observable to about 25 keV. The combined system, detector, preamplifier and main amplifier (fig. la) has a noise width ( F W M M ) of 3.5 keY for a test pulse, 3.5 keV for a 122 keV gamma ray, 4.1 keV for a 279 keV gamma ray and 5.0 keV for a 662 keV gamma ray. The detector response to 203Hg and 137Cs sources is illustrated in fig. 3. The figures above refer to a single integration and single differentiation of 0.8 gs of the pulses in the main amplifier. In the experimental runs the detector pulses were doubly differentiated for a more rapid restoration of the baseline; this together with the small baseline shifts encountered at the beginning of the counting interval led to a typical resolution ( F W M M ) of about 5 keV for the isomeric radiation detected (which was usually =< 500 keV). Standard sources of 57Co, 2°3Hg and 137Cs in addition to the 511.0 keV annihilation radiation which appears in many spectra were used for energy calibration. Calibrations were taken at the beginning and end of each run; in all cases these two calibrations differed by less than the equivalent of 0.3 keV in 500 keV. The uncertainty in the gamma-ray energies quoted is estimated at ±0.3 keV for well defined peaks. In cases where the gamma-ray intensity was weak or the analysis required reduction of a composite peak the uncertainty is greater and is quoted. With the current resolution, it has been possible in many cases to resolve the K~ and K~ components of the X-ray produced following K-shell conversion in the isomeric nucleus. A measurement of the K~ component has been used to identify the atomic number Z of the isomeric nucleus. This also partially identifies the reaction
E1 TRANSITIONS
219
leading to this nucleus; thus (p, n) and (p, 2n) are distinguished from (p, p') and (p, pn). The K= X-ray consists of two lines K,, and K=2 whose energies are well known from X-ray spectroscopy measurements 10), however, there is some uncertainty as to the energy of the composite peak K~ = K=,+K,2 observed here. Gamma 1600
ET(keV)
From
A
Hg
2O3
Source
72.29
279.16
X - Rays K~ KB keV/ch = 0 . 2 8 5
_I Z Z "-r
Spectrum
1200
n.W 13_
800 FWHM
I--
0
= 4.1
keV-
a"'¢;
Z
400
1024
256 512 768 CHANNEL NUMBER Gamma
2400 J hl Z Z < I 0
keV/ch
Spectrum
From
A
Cs 137 Source
=1.32
Backscotter
661.6 keY
Pulser ("folded over")
1800 FWHM
W (3_
4.1 k e V - -
1200
([)
•
FWHM~
~5.3
keY
Z 0 (D
600
I
256 CHANNEL
512 NUMBER
I
J
768
Fig. 3. Detector response to Z°3Hg and 1~7Cs sources.
For this reason the K= component of the X-rays for the elements concerned has been measured in a separate experiment 2). In order to determine the multipolarity of the gamma-rays, the K-shell conversion coefficient has been measured by comparing the intensity of the X-ray with that of the
220
T. W, CONLON et al.
isomeric transition, in those cases where only a single transition is involved. This determination of relative intensity requires a knowledge of the relative efficiency of the detector for different photon energies. The isomeric decay of 18°W reported here provided an ideal means of calibration since the decay involves five gamma rays in direct cascade and the X-ray whose intensity with respect to the other transitions can be computed. This has provided a calibration from 50-500 keV as shown in fig. 4 and has the additional advantage that the calibration was taken under identical conditions to the other spectra. The calibration has been checked using a 2°3Hg source and the known intensities of the gammas from the fl+ decay of 2.2 h 178Ta. I
l--
--
I
"
I
I
RELATIVE FULL ENERGY PEAK Ge(Li) ENERGY RANGE 5 0 - 5 0 0
60
I
EFFICIENCY keV
OF
Z D >@-®~, ® F-"
20
cr" <~ >0 Z i,i
I0 O
6-
\o
ks_
LL IJJ hi >
®
I-<~
® Hg 2o3.
-J laJ rr
2
_
0
_
W 180m
1
I00
Q
~e
£
I
I
I
200
300
400
500
GAMMA RAY ENERGY IN keV Fig. 4. Relative full energy peak efficiency o f the Ge(Li) in the energy range 50-500 keV.
If B is the ratio of the X-ray intensity to that of the isomeric transition corrected for detector efficiency, it can be shown 2) that the K-shell conversion coefficient aK is given by F Y B O , ~ - ~,~)t _ 4 ( i - e - ~,~t)}, ( 1) ~K ~ [ e 5\ ~ where 1 / F is the fluorescent yield,/~x and/zr the linear absorption coeffÉcients for the X- and y-radiation and t the effective target thickness. The multipolarity is then determined by comparing ~i~ with values calculated by Sliv and Band it). 2.5. IDENTIFICATION OF THE ISOMERIC NUCLEUS The isomeric nucleus has been partially identified by measuring the energy of the K, component of the X-ray as discussed above. Final identification was accomplished
E1 TRANSITIONS
221
by bombarding separated isotopes of the target material and by measurements of the relative intensities of the activity produced at two bombarding energies. For example, if the K, energy indicated that the reaction at 17.5 keV bombarding energy on the separated isotope was (p, n) or (p, 2n) [(p, 3n) etc. is excluded energetically] then a bombardment at an energy lower than the (p, 2n) threshold (typically ~ 8 MeV) was sufficient to identify the final nucleus uniquely. 3. Results and discussion
In the figures showing the experimental data, only two energy spectra of the 16 taken are shown; the first taken shortly after irradiation and the second several halflives later. The number of counts minus background and corrected for analyser losses for each peak in the various time channels is also shown. The figures are labelled according to the target used in the excitation of the isomer; each isomer is discussed under this heading and the identity of the isomeric nucleus is stated immediately after the heading. In the discussion below reference is often made to the Nilsson states which have been identified in the nuclei of interest. We refer to a compilation of observed states in ref. 12). The reduced matrix elements [MI 2 have been calculated according to [M]2 = (T~)s.p./(T~)exp
single-particle units,
where (T~)s.p. is the Weisskopf estimate 13) and (T~)exp = T+ (1 +~), where T~ is the measured half-life and ~ the total conversion coefficient for the isomeric transition. 3.1. ERBIUM; 165Tm The proton bombardment of natural erbium leads to the production of a new isomeric state in 16STm which decays principally by an E1 transition of energy 69.3 keV and with a half-life of 80.3+__3/~s. The spectra from the bombardment of 166Er is shown in fig. 5. The fact that it is the Tm X-ray which is seen in fig. 5 plus the fact that the activity was not observed by bombardment of 167Er is sufficient to show that the reaction leading to the isomeric state is 166Er (p, 2n)I65Tm. The ratio of the X-ray intensity to that of the 67.3 keV gamma from fig. 5 is 1.9 + 0.2; using eq. (1) above, this yields a value of ~K = 0.9___0.5 which is consistent only with E1 radiation. (The theoretical values for E1 and E2 are 0.7 and 2.1, respectively.) The existence of an E1 isomer in 165Tm is not unexpected if one considers the properties of the excited states of 167Tm, 169Tm and ~71Tm. The lowest Nilsson state available to the last (69th) proton in the odd Tm isotopes is [411] ½+; this is the observed ground state of 165Tm, 167Tm, 169Tm and aTiTm. The [523] -~- and [404] ~+ intrinsic proton excitations have been identified in the last three of these isotopes.
I
-(a)-250~s
after
bombardment
(b)-
after
bombardment
8OOps
keV/ch I IO
ps/ch
69.9
X-RAY
50.3
keV
= 1.624 I 20
I 30
I 40
CHANNEL
I 50
60
240
260
Fig. 5. Energy
spectra
I
I
I
5
7
9
TIME
NUMBER and half-life
data from
\
1
3
CHANNEL
an IsEEr target.
425
[523] 7/2--
-
5/2+_-
0
[411]1/2+
[411]1/2+
Tm 165
Tmi67 Fig. 6. Location
Tm 169 of the *B6Tm isomer.
I /2+
0
Trn171
E1 TRANSITIONS
223
Fig. 6 shows the location of these states; for clarity the rotation members built on them have not been included; similarly only the ½+ and -~+ members of the ground state rotational band in each nucleus has been shown. In 171Tm ' the [523] ~ - state and ½+ rotational member of the ground state band are observed 1,) to form an isomeric pair with a half-life of 2.6 ps; this represents a hindrance of 4 x 109 over the Weisskopf estimate for the E1 transition connecting these states. Such a large hindrance is expected since the transition is K-forbidden with AK=
3.
In 169Tm the [404] -~+ state now occurs below the [523] -~- level and these two states are observed to form an isomeric pair 14). The half-life of the E1 transition observed 14) is 50 ns representing a hindrance of 105. In this case the hindrance is due to a violation of the asymptotic quantum numbers (with (Anz = 2, A A = 1 and AS
=
1).
The half-life of the [523] ~ - state in 167Tm has not been measured. In 165Tm it would seem that there are two possibilities for isomerism depending on the location of the [404] -~+ and s + member of the ground state rotational band with respect to the [523 ] ½- state. N o information is available on the excited states of 165Tm, however from the systematics of fig. 6 it seems likely that the 5+ state should lie approximately 120 keV, while the [523] ~ - state which is dropping slowly in 171,169,167Tm still lies above the ~+ rotational state (probably at about 200 keV). The 69.3 keV E1 transition observed here may thus connect the [523] ~ - state and the ~+ as indicated in fig. 6. This suggestion is supported by the fact that the E1 transition connects the same states as in the 2.6 ps 17~Tm isomer, and in fact both are hindered to the same degree of 4 X 109 single-particle units. The other possibility for an El isomer in 165Tm is the transition between the two intrinsic states [523] ~- and [404] ~+. Such transition occurs in 169Tm as discussed above and shown in fig. 6 with a very similar transition energy to that observed here (63 keV compared to 67.3 keV) but the half-life is 50 ns, - 103 times faster than that observed here. This fact would seem to exclude a similar origin for the 67.3 keV transition. The first explanation is thus more likely and if in fact it is correct it would exclude the possibility of the [404] ~+ lying at a lower energy than the [523] ~ - isomeric state since if it did lie lower it would provide an easier decay path for the proposed isomeric state (i.e. as in 169Tm), The fact that only a single g a m m a ray has been observed in the 165Tm isomeric decay is puzzling and deserves further comment. In 171mTm in addition to the 308 keV E1 transition, a weaker branch to the 7 + member of the ground state rotational band has been observed 14) with energy of 296 keV. The branching ratio is •(308 keV)/I(296 keV) = -37-.Using these figures and the typical splitting of about 15 keV between the ~-+ and ~+ rotational states, one can estimate that the branch from the suggested isomeric state in 165Tm to the ~+ rotational state would be ~ 10 ~o of the intensity of the 69.3 keV gamma. The energy
224
T.w. CONLONet
al.
of this transition would also be less than 69.3 keV, and it is possible that it has been obscured by the X-ray in fig. 5. However, the ~+ rotational state, which according to the above discussion is populated by the 69.3 keV isomeric transition, should decay to the lower members of the rotational band, namely the 2-+ and ½+. According to the systematics of fig. 6 the energy o f t h e z5 + ~ 3 + should be about 120 keV and from similar transitions in the isotopes 167, 169, 171Tin ' which are essentially pure M1 transitions, the total conversion coefficient should be about ~ = 3. Hence this transition should have ½to 3I the strength of the isomeric transition and yet it has not been observed. No explanation of this has been found. 3.2. YTTERBIUM; 173Lu AND 17~Lu
Two distinct isomeric decays are produced following the bombardment of a natural Yb target as shown in fig. 7. The 123.9 keV transition has a half-life of 87 + 3 ps and measured ~K = 0.12, consistent with only E1 radiation (~i~ theoretical = 0.15). The results in fig. 7 yield a half-life of about 400 #s and an c~K = 1.2+5 for the 67.4 keV gamma. The 123.9 keV E1 transition has been previously observed in 173Lu by Mihelich et al. 15). The isomeric level giving rise to this transition has been suggested by Valentin et al. 16) as the ~- rotational member of the [541 ] ½- state which decays by a K-forbidden transition to the 173Lu [404] ~+ ground state with A K = 3. The state is reached in the current work by the reactions lV4Yb(p ' 2n)173Lu and 173yb(p ' 2n) 173Lu"
The lowest Nilsson state available for the odd nucleon (the 71st proton) in 173Lu is [404] ~+, and this is the observed ground state. The [541] 1 - intrinsic state should occur in 173Lu as a low-lying excitation. Valentin et al. 16) have identified three levels in 173Lu which may be interpreted as members of the [541 ] ½- configuration with the ~- member lying lowest at 123.9 keV excitation. The energy of the 123.9 keV gamma ray observed here, its multipolarity El, and large measured retardation ~ 109 (IMI z = 0.9 • 10 - 9 ) support the interpretation of ref. 16). However, it must be noted that the rotational members of the [541] 1 - state have not been identified in other nuclei with 71 protons (175Lu and t 77Lu). Bombardments of separated isotopes of Yb of mass number, 171, 172, 173, 174 and 176, each enriched to about 97 ~ , were performed in order to locate the isomeric nucleus responsible for the 400 ps decay. Only 17/yb and 173yb gave positive results. Since the isomer was more strongly excited in the 173yb target, the spectra from this target are presented in fig. 8. The relative strength of the 67.4 keV gamma in the spectra from 172yb and 173yb targets together with the observation of the Lu X-ray, 53.4 keV in fig. 8, require that the activity be assigned to the 172Lu nucleus and produced by the reactions 173yb(p ' 2n)172Lu ' and 172yb(p ' n)t 72Lu; this was further established by bombarding 173yb at a reduced beam energy of about 5 MeV, which is below the 173yb(p, 2n) threshold; the activity was not observed in this run.
E1 TRANSITIONS
I0
E,WeV
. . . . . . . . . .
105
after bombardment
(o) Energy spectrum~3OOp.sec (b) (C)
700p.sec 1500h~sec
225
X-Roy
. . . . . . . .
E7 = 5 2 5 key
ET,]2&gkeV
o
T'/Z" 87p'S
,el9
~2~ sgo 674
2
g
400p. s
4
ZZ I0 3
<= 0 13_
tO 3
I0 2
oo
10
I
I
I
I
I
]0
50
50
70
90
1"
/e
I10
/ / 220 24(
4 6 8 I0 12 2 4 6 8 I0 12 14
CHANNEL NUMBER
TIME
CHANNEL
Fig. 7. Energy spectra and half-life data from a Yb target.
I05~ ~
6 7 3 keV
f Yb '~SOs
I@!
P
I?i ,
b,
T
GO X-RAY 4 .
Z O
102 l(a)~FOO~s
o-,oCDc~
o o
o
o
after
j
t
ao iL
baoba,dme0t
lb) ~ 1600p. s
o
after
~
o
114.7/xs/ch.
Ooo~
bombardment cls/ch.
I
I
I
I
I
60
80
tOO
i20
140
i60
I
t
t80
200
CHANNEL NUMBER
220
240
I 4 TIME
Fig. 8. Energy spectra and half-life data from a 17sYb target.
i 8
I
I
t2
~6
CHANNEL
226
x . w . CONLON et al.
The results shown in fig. 8 yield the more precise value of 4 3 4 _ 15 #s for the halflife. The ratio of the X-ray strength to that of the 67.4 keV g a m m a is 0.9; in this case corrections for target thickness are unreliable due to the proximity of the gamma-ray energy to the K-absorption edge of Yb, however, since the corrections all reduce the intensity of the X-ray with respect to the gamma, it is certainly true that cc~: < 0.9. The only multipole with c~K < 0.9 [ref. ~1)] is El. The 67.4 keV gamma is thus an E1 transition in 172Lu. Bjornholm et al. tv) have reported a 64 keV transition of halflife 430+ 80/is in z 72Lu which may be the same transition as discussed here; however they have not identified the isomeric level in t 72Lu.
E(keV)
E(keV)
433/.Ls L33.3
[ 4 0 4 - 52:5]
rd (M
I10.0 2 +
65.9 0-F[404 _ 633] K=0
-- 41,9
i
I
[404-5Ja]
0~ -2"
m
4
o
[ 4 0 4 • 521]
t Ta Lu
71
Fig. 9. D e c a y s c h e m e o f t h e mZLu i s o m e r i c state.
Harmatz and Handley 18) in their study of the rare-earth activities have examined the electron capture decay of 172Hf which feeds levels in ~72Lu. A weak gamma ray of energy 67.4 keV and multipolarity E1 has been observed. It seems very likely that this is identical to the transition observed to decay with a half-life of 434/~s in the present work. A partial level scheme showing only the decay mode of the level leading to the 67.4 keV g a m m a and taken from ref. as) is shown in fig. 9. It is clear that the situation is much more complicated than would have been expected from the simple g a m m a spectrum observed in the present work. However the fact that only one transition was observed here is readily explained. According to ref. ~8) the principle decay mode of the 133.3 keV state is by the 67.4 keV gamma reported in the current work; a weaker branch occurs by a 23.4 keV transition to the 2 + member of the K = 0 band at 110.0 keV. This transition was not observed in the current work since it is highly converted and also, close to the minimum
E1 TRANSITIONS
227
energy detectable with the present set-up. The 24.0 keV g a m m a from the level at 65.9 keV to the 41.9 keV state has not been seen for the same reasons. The 44.1 and 41.9 keV gammas were not observed probably due to their large conversion coefficients in the L subshells. The 91.6 keV transition should however have been seen here and from the spectra in fig. 8, one can estimate an upper limit of 1 ~ for its intensity with respect to the 67.4 keV gamma. This is consistent with the results in ref. is). 3.3. INTERPRETATION OF THE 434 #s ISOMERIC STATE The low-lying states of 172Lu can be well explained in terms of the Nilsson states available to the last odd proton and last odd neutron in 172Lu [ref. 19)]. The K of the ground state of the doubly odd nucleus should be given by the sum or difference of the K-values of the last odd neutron and odd proton, thus Kodd-oad = IKp+Knl. According to Gallagher 19) the state in which the intrinsic spins of the proton and neutron are in the triplet state I ~ p + ~ n l = 1 will in general lie lowest, although possible exceptions have been noted in this reference. Excited states of the doubly odd system are formed by the coupling of excited states available to the odd proton and odd neutron, thus Kdoublyodd(excited state) = IKp -4-K'[, K,~'ublyodd(excited state) = [Kp _+K.[. In general in the doubly odd nuclei, where several two-particle states have been identified, intrinsic excitations of the neutron lie at lower energies than the corresponding proton excitations (ref. 19), table 5) thus the low-lying, excited states are likely to be of the form K ' = IKp+K'[ with the state having ~tota~ = 1 lying lower as noted above. In fig. 9, the intrinsic two-particle states have been labelled according to the appropriate Nilsson orbital. The ground state of 172Lu is described by A = [{p[404] 7+} {n[52111-}],
K s = 4-,
since these are the lowest states available to the last proton (69th) and last neutron (101st). The lowest intrinsic excitations available for the neutron are [512] 5 - and [633] 7 - leading to the 1- state at 42 keV described by B = [{p[404]~} +
{n[512]s-}]l - ,
and the 0 + state at 66 keV described by C = [{p[404]~ +}
{n[633]~+}]0+.
These two-particle states have been suggested by H a r m a t z et al. 18). However from the compilation of states in ref. 12), the [523]~- neutron state is expected as the
228
T . w . CONLON et al.
next intrinsic neutron excitation after those discussed above. This coupled to the same proton state as in A, B and C in the form D = [{p[404]~ +}
{n[523]~-}]l-
is a possible explanation for the existence of a 1- state at 133.3 keV, which is suggested by the E1 nature of the 67.4 keV gamma. However, the state described by 4
I0
TQ K= K~ "E~keV=58,7 67.3
ro3.e
233,9
E2 2+--0 *
d
(o}~
390.7
~51.1
E2 4+~,-2 ÷
E2 6*-4-4 +
EM8-,9-) ~ B ÷
450.4
E2
P
8*---6*
~ 3 Ichs = 66keV
5103 0 n
5 102
::::::::::::::::::::::::
g
ke//chV 2 I I0
I0
I
I
I
50
I00
50
200
240
CHANNEL NUMBER Fig. 10. E n e r g y s p e c t r a f r o m a T a target.
D has Z = 0 whereas the state formed from the same particle configurations with X = 1 usually lies lower as discussed above. Such a state with 2; = 1 has not been identified. However, the configuration D is not inconsistent with the properties of the 67.4 keV gamma. Thus the E1 transition from D to C would involve only the neutron states [523]~- to [633] 7+. The reduced matrix element for the 67.4 keV transition is measured to be 1 • 10 -9 or a hindrance of 1 0 9. This large hindrance cannot be explained by a violation of the K-selection rule since A K = l = 1, however the transition is expected to be hindered since it involves the following changes in the asymptotic quantum numbers: A n z = 1, A A = 0 and AX = 1, the last being forbidden for E1 radiation according to table 1.
E1 TRANSITIONS
229
3.4. TANTALUM; ls°W
Fig. 10 shows the spectra following proton bombardment of natural Ta (99.9 % Ta 181), 5 ms and 15 ms after irradiation. The spectra are complicated and involve five gamma-rays and an X-ray, all of which decay with the same half-life of 5.53 + 0.1 ms as shown in fig. 11. On reducing the beam energy below the (p, 2n) threshold at DECAY CURVESFOR GAIMMAS OBSERVED
~" 8 X 105
MEAN TI/2: 5,53t O.Ims SCALE=I~77mS/Ch / B~=58.7+67.3keV
Ka,K 3 X-RAYS
E~;551.lkeV
--4xlO 4
--~2xI'~O ~~~ ~ -'~
-gxId
5 x IOs
~'-~o
E~= 390.7 keY
--2x103
"~q~.
2xlO
:i?,7j eV
--2x103 i
i
i
i
i
I
CT/CL
~
2 4 6 8 I0 12 14
TIME
~ ,
i
i
i
I~
2 4 6 8 1012 14
CHANNEL
Fig. 11. Half-life data from Ta.
8 MeV, no isomeric activity was recorded; this fact together with the observation of the W X-ray (K, = 58.7 keV) is sufficient to show that the isomeric nucleus is 18°W, and the reaction leading to its production is tSlTa(p, 2n)~S°W. The gamma-ray energies 103.8, 233.9, 351.1 and 450.4 keV are consistent with the expected energy differences between successive members of the K = 0, ground state rotational band of as°W up to the 8 + level. The 10 + ~ 8 + transition energy is expected to be about 520 keV, thus the fifth g a m m a observed here at 390.7 keV does not fit in with the rotational structure formed by the other gammas. It is highly likely that this g a m m a is the transition from the isomeric state to the 8 + level.
230
T, W.
et al.
CONLON
The relative efficiency curve for the Ge(Li) detector obtained for the 178Ta decay described above showed that all gammas concerned are approximately of the same intensity and that the total conversion coefficient ~ of the 390.7 keV gamma is < 0.05. In order to establish the decay scheme unambiguously, the conversion electrons associated with the gammas have been observed using a cooled, lithium-drifted, silicon detector which replaces the Ge(Li) in fig. 1. A single spectrum was taken with the analyser gated on for a 20 ms period between beam bursts as shown in fig. 12. CONVERSION
104[
.....
,\
i
z
•
EekeV
;
~
.......,-"
\
165.8 (234K)
223 235 (235 L , M )
282 (35lK)
"~ aExp. 0108 Normoti~ 0.051 0.0104 . aTh~r ~1~E2.0,108 ¢~ E2=057
L"....."" , ; \ .~
10 3
320 329 (590K) (351L)
436 (450L)
377 (450K,390L)
oo67
.031 .0103 .0106 eKE2=O]7 eKE2'.OII7 O~EI =.OIOZ
a~¢2=.oo53
;".
""\
_1". ........ ""' "" ""~..../\' \ " h
oz OD O_
z
OF
~,.,o.,..o,~" \
I o
oO
DECAY
o°,
"
._1 LJJ Z
THE
E L E C T R O N S FOLLOWING W m°m Ti/2= 5 . 5 5 m s .
]~f~" "-~.-. "~.\ "'~.-.~.._~"~.
10 2
D 0 (J
10 / ."
L
I
I
I
I
I
I
I
I
I
I
I0
20
50
40
50
60
70
80
90
I00
I10
CHANNEL
I
120
I
130
I
140
NUMBER
Fig. 12. Conversion electrons from the decay of the zs°W isomer.
In fig. 12, the 0~K/~L ratio for the conversion electrons corresponding to the 234 keV gamma is found to be 2.1___0.3 in good agreement with the theoretical value ~1) of 2.00 for an E2 transition. Having thus established the E2 nature of the 234 keV gamma, the relative intensities of the electron groups in fig. 12 have been normalized using the number of counts in the 234 K electron peak and the theoretical value of 0.108 for the ~K of the 234 keV transition. The figures thus produced are in good agreement with the assignment of E2 multipolarity to the 351 and 450 keV transitions and with E1 for the 391 keV isomeric transition. The electron groups corresponding to the 104 keV transition have not been observed due to the presence of the X-ray peak in fig. 12. However the relative intensities of the 104 keV gamma and the 234 keV, E2 gamma in fig. 10, after correcting for
E1 TRANSITIONS
231
target thickness, gave a value of 3.0-t-0.5 for the total conversion coefficient of the 104 keV gamma, which is in agreement with the theoretical value of 2.95 for an E2 assignment. The above results suggest the scheme shown in fig. 13 for the decay mode of the 5.53 ms isomer in as°w. The E1 nature of the isomeric transition and its decay to the 8 + state limit the spin and parity of the metastable state to 7 - , 8- or 9 - . An assignEkeV 1529.9 -- 1.5 MeV
5.53ms. [
E)t
ke=I y
390.7 -+ 0.3 El
1139,2
r
--,MeV
8+
4~0.4 +- 0.3
686.8
/~
Mev
/
537,7
~~'
"103.8
~
6+ +
~l?J03.8 + 0.3
--0
0.:5
4+
2+ C+
W ~8o
Fig. 13. Decay scheme of the ls°W isomeric state.
ment of 7 - must be excluded since no strong transition has been observed to the 6 + state. The reduced matrix element caluclated for the E1 isomeric transition is 2.5 • 10-13 single-particle units, a figure which strongly suggests that the E1 transition is Kforbidden. An empirical rule suggested by Rusinov z0) relating the degree of Kforbiddenness with the retardation factor in such cases is given by 1 ~ logto -iMl2
2(Ak-l),
where l is the multipolarity and IM[ 2 the reduced matrix element.
(2)
232
T.w. CONLONet al.
This relation has been found by Rusinov to work particularly well for E1 transitions in doubly even nuclei. In this case, eq. (2) yields A K = 7.3 which suggests a A K difference of 7 or 8 for the states connected by the isomeric transition and hence an assignment of K I n = 7, 7 - or 8, 8- for the isomeric state. The former has already been excluded and hence 8, 8- is suggested. This assignment is also suggested by the close similarity of the decay in question to those of the metastable 8, 8 - levels in 17aHf and 18°Hf at about 1.15 MeV excitation both of which decay principally by Kforbidden, E1 transitions to the 8 + member of the ground state rotational band with similar reduced matrix elements 14). However, in the decay of the 8, 8- state in lS°Hf a strong transition has been observed ~4) to the 6 + member of the ground state rotational band. The observing branching ratio is / ( 8 - ~ 8 +, 58 keV)
81
I ( 8 - ~ 6 +, 501 keV)
17"
The 8 - --. 8 transition has been measured to be almost pure E1 and the 8- ~ 6 + transition almost pure E3 [ref. ~4)]. Scaling the observed energies for is OHf to those observed in ~s°W according to the Weisskopf estimates the calculated branching ratio (8- ~ 8+)/(8 - --* 6 +) in lS°W is ~ 40/1. A search was made for the 8- ~ 6 +, 84.1 keV transition in the aS°W decay; no such transition has been observed and the estimated upper limit of the intensity of this with respect to the isomeric transition is 1 • 10 -5. The E3 intensity in the decay of tS0mw is thus reduced by more than 1 0 3 over that in the ls°mHf decay. Such a result is surprising in view of the similarities between the two states discussed above. Previous investigations of the transitions involved in the as°mw decay have suffered principally from poor resolution, with the result that the information gleaned from such experiments has been incomplete and in some cases confusing. Thus Softky 21) and Morozov 22) have observed only transitions of energy 0.22 and 0.35 MeV with a half-life of 5.5__+0.3 ms. Lark et al. 23) have observed roughly the same half-life and from the results of their spectrum have concluded that the isomeric level lies at about 1.5 MeV. Finally, Remaev e t al. 24) have observed gammas at 0.055, 0.1, 0.15, 0.22, 0.33 and 0.37 MeV and a conversion electron line at 70 keV which they attributed to the 0.15 MeV gamma. They have concluded that the decay is complicated but that the energies observed are similar to those seen in the decay of the metastable level in ~8°Hf and that the isomeric level is probably of a similar nature in both cases. In the present work no evidence has been found for the 0.15 MeV transition seen strongly by Remaev et al. 24); from the spectra presented in fig. 10 we estimate that the intensity of a 0.15 MeV g a m m a as < 1 - 1 0 - 3 that of the 390.7 keV gamma. A 0.134 MeV gamma is involved in the 20 ps isomeric decay 25) of 18~mTa; this corresponds within the limits of error in ref. 25) to a 0.15 MeV transition.
E1 TRANSITIONS
233
Burde e t al. 26,27) in their recent investigation of the la°mw decay have reached similar conclusions concerning the isomeric state as these described here. O F T H E Kin = 8, 8 - S T A T E A T 1.53 M e V
3.5. I N T E R P R E T A T I O N
The last odd neutron in ~79W (Z = 74, N = 105) is described by [514]½- and so the configuration of the last neutron pair in IS°W is {[514]½- [51417-}KF = 0, 0 +. keV
K I "rr
L48o
s
,4s
s s-,[
keY
KI ~
(1) KI Tr
keV
8 s-
....
o4
°s ÷
,4z 08 +
0 8+
-
06 +
0 4 +
-
-
0
-
02 + 00 + Hf
6
+
06 +
0 4 +
04
02 + 00 +
178
W
180
Fig. 14. Location of the two-particle K i n
Hf
~
180
+
02 + O0 +
8, 8- states.
The lowest intrinsic excitation available to the neutrons is [624]~ + which in 179W lies at 220 keV; and so a two particle neutron state with K I n = 8, 8 - can be formed by breaking the pair (1) and the transfer of one of the neutrons to the [62419z+ state, thus [{[5141~-}
{[624]9+}]8, 8-.
(2)
A two-particle, neutron state of the same configuration has been identified 19) in 178Hf (Z = 72, N = 106) which is an isotone of 18°W. This state occurs at 1.480 MeV in iVaHf compared to 1.530 MeV in 18°W. In 178Hf a two-particle proton state of K F = 8, 8- has also been identified 19) at 1.148 MeV. However an examination of the orbitals available to the last proton pair in ~8°W show that an 8, 8 - state cannot be formed from the available states. The 8, 8- state observed in the current work must thus be described by the configuration (2) above. For completeness the location of 8, 8- states in i78Hf, 18°Hf and 180W and their probable configurations are compared in fig. 14.
10 5
-
1145
Tb
"E?,(keV) 45.5 Dy X-RAY
J bJ
104
80,1
99.6
120.4 157.5 151.9
175 179.0
218
(.o)
Z Z "t-
Ld
03 l--Z 0 £.)
I0 ~
~..?p
keWch = 1.215
/
(a)~2OO,u.s
affer bombardment
2I|(b)~lOOO/~s
after bombardment
~o
!
i
I
I
I
f
r
I
I
P
I
I
I
I
20
40
60
80
I00
120
140
160
180
200
220
240
260
CHANNEL
NUMBER
Fig. 15. Energy spectra from a Tb target.
r-Tb Tqz =122.5+ 3~s X-Ray 45.5 keV
~oS?lo5
69JO~s/ch
\
~D \
137.3 keY
99.6keV
+\
122.3/~s
J I.d Z Z T (..) fr nl Q-
105 -
CO I-Z 0
11451keV Doubter
12o.4~
[ Izgo
\
2i8 keV cts. 4- 2
keV Double'
\
L ~ L ~ 4
6
8
I0
12
4
6
TIME
8
IO
CHANNEL
Fig. 16. Half-life data from Tb.
4
6
8
I0
E1 TRANSITIONS
235
3.6. TERBIUM; 15~Dy Fig. 15 shows the short-lived activity p r o d u c e d following b o m b a r d m e n t o f T b (which is 100 ~ 159Tb). Seven peaks, two o f which are u n r e s o l v e d doublets, plus an X - r a y are involved. Fig. 16 shows the decay o f each peak, all the g a m m a s involved having a c o m m o n half-life o f 1 2 2 . 3 _ 3 #s. T h e m e a s u r e d K , X - r a y energy 45.5 keV shows t h a t the i s o m e r is l o c a t e d in a D y nucleus, a n d hence the r e a c t i o n leading to its p r o d u c t i o n is (p, n) o r (p, 2n). T h e isomeric activity was still observed when the p r o t o n b e a m energy was r e d u c e d below the Q-value for 159Tb(p, 2n) which is a b o u t - 8 M e V ; hence the r e a c t i o n is lSgTb(p, n)lSgmDy (Q = - 1 . 2 MeV). TABLE 2 Relative intensities of the gamma-rays from lS°mDy
Borggreen
Present work
et al.
relative intensities type
gamma electron
K X-ray M1 M1 M1
183 12 17
M1 E2
48 <5
E2 E2 a) b) c) a) e)
14 5.0
192 15 14 20
relative intensities E~(keV) ~ 45 574-0.5 81 4-0.7 1004-0.4
38 4.8
1184-0.6 1384-1
14 5.6
181 4-1 2184-1.5
E
b)
e)
~totat a)
e)
7.4
9.4
1 0 . 0 10.0
9.3
0.72 1.00 1.9 1.2 0.14 0.08 0.07 0.28 0.08
0.76 1.00 1.7 1.1 0.20 0.10 0.06 0.22 0.07
0.81 1.00 1.7 1.1 0.20 0.10 0.06 0.22 0.07
0.76 1.00 1.9 0.6 1.3 1.5 0.28 0.17 0.14 0.55 0.29
0.81 1.00 1.7 1.1 0.20 0.10 0.06 0.22 0.07
Ep = 17.5 MeV. E p ~ 8 MeV. E p ~ 5 MeV. Average corrected for target thickness. = (d) × correction for detector efficiency.
T h a t all the transitions are p r o d u c e d in this r e a c t i o n is shown b y the u n c h a n g e d relative intensities o f the transitions as the b o m b a r d i n g energy is changed. T a b l e 2 shows the results at b o m b a r d i n g energies o f 17.5, 8 a n d 5 MeV. The results at 2 M e V are n o t shown because o f p o o r statistics, h o w e v e r they d o n o t differ within the associated errors f r o m the results at 5 MeV. T h e c h a n g e in relative intensity between the 17.5 M e V a n d 8 M e V results is due to the t h i c k target used (0.05 cm) a n d the decrease in effective target thickness for g a m m a - r a y a b s o r p t i o n as the p r o t o n energy a n d consequently the p r o t o n range in T b is reduced. The c o n s t a n c y o f the relative intensity m e a s u r e m e n t s at 8, 5 a n d 2 M e V s u p p o r t the association o f all g a m m a s o b s e r v e d with the d e c a y o f a single isomeric level p r o d u c e d in the r e a c t i o n 159Tb
236
T . w . CONLON et al.
(p, n)~59Dy. The fact that the measured half-lives of all the transitions agree within 3 ~ further supports this conclusion. Borggreen et al. 28) (hereafter referred to as BFHB) have reported the excitation of a 115/~s isomer in 159Dy and have suggested that the isomeric level is the previously unreported [50511! - neutron state. BFHB have excited this isomer using a pulsed beam of 10 MeV protons and observed the decay products using a N a I as g a m m a
471.0_ ~__~ _
tisp.s
_
~o,~
I I I
Kl~r
5/zs
E ( k e V ) 122.0 -+
i
I
3
I1-
3
9-
3
7-
.... i
I
g g
T
3 5-
3
3-
~g Dy 159
I(Ref. 28)
-:'-'.;;;'-: Transitions - - - --*Transitions ,wvw,. Transitions
I
Dy 159 Tr Present
Work
seen here but
not by Ref. 28 seen by Ref. 28 but not here. not seen by Ref. 28 or here.
Fig. 17. Decay scheme o f the lSgDy isomeric state.
detector and a magnetic spectrometer for conversion electron studies. The similarity in energy and relative intensity of the gammas and of the half-life observed by BFHB to the present work show that the same states are involved in both experiments. However the additional information obtained from the present experiment does not support their identification of the metastable state. In particular, all the transitions observed by BFHB have been observed in this experiment apart from the 56.8 keV gamma which BFHB show is highly converted and was too weak to be seen here. In addition, however, we do see the 137.3 keV cross-over gamma to the ground state from the 137.1 keV level and also three more gammas of the same half-life as the others have been recorded in this work; their
E1 TRANSITIONS
237
energies aIe 114.5 +0.5, 151.9___0.5 and 173 +_ 1 keV respectively. These are listed in table 2 and are shown as dashed arrows in fig. 17, where a comparison is made of the scheme suggested by B F H B and that demanded by the measurements presented in the present work. The energies and relative intensities of gammas from levels in 159Dy up to 236.1 keV from the two experiments are in good agreement with each other and with the assignment of the ground state, 56.8, 137.1 and 236.1 keV levels as the 3 - , ~ - , 7 and 9 members, respectively, of the K = ~2 ground state rotational band. However the 173 keV g a m m a labelled a in fig. 17 (II), which was observed in the work here indicates that the known level at 310 keV reported by Abdurazokov et al. 29), but not included in the scheme of BFHB, is fed by the isomeric decay. The relative intensities of the 114.5 and 120.4 keV gammas (table 2 column e) are consistent with their being in cascade as are the intensities of the weaker 151.9 and 173 keV gammas. A consistent scheme can be constructed if we consider the metastable level to lie at 471.0 keV and to decay principally ( ~ 95 ~o of the decays) by the emission of a 114.5 keV g a m m a to the level at 356.5 keV and also by the much weaker process of emission of a lowenergy gamma, about 9 keV and the 151.9 keV g a m m a in cascade to the 310 keV level. The low-energy g a m m a has not been seen in the present work which is insensitive to any E~ < 25 keV. The fact that B F H B have not observed the 114.5, 151.9 or 173 keV transitions seen here is not surprising if one considers the relative intensities of these gammas and the techniques used by these authors. Thus, the 114.5 keV g a m m a has not been resolved from the 120.4 keV g a m m a in the present work; the presence of two transitions at about 118 keV is indicated in fig. 15 by a considerable broadening of the peak. This broadening would not have been seen in the N a I spectrum of BFHB since the F W H M of this peak in their spectrum is at least 20 keV. Moreover, the relative intensities of the 114.5 and 120.4 keV gammas from table 5.4, column e show that the total conversion coefficient of the lower-energy g a m m a is about 3 times smaller than that of the 120.4 keV transition. This fact together with their separation of only 6 keV could easily have led to the 114.5 keV transition being missed in the conversion electron spectrum of BFHB. In fact, table 1 of BFHB (reproduced in part as A in table 2 here) supports this explanation. Thus, the intensity ratio of the " g a m m a " at 118 keV to the 218 keV transition in BFHB is (1) = 10 and in their conversion electron spectrum is (2) = 6.8. In the present work table 5.4 e) the intensity ratio [I(114.5)+1(120.4)]/[1(218)] is 11 in agreement with (1) but not with (2) and supporting the explanation above. The 151.9 and 173 keV transitions, both of which are of low intensity, may similarly have been obscured in the work of BFHB. BFHB, using a best fit to the energy values of the ~2 - , ~- and ~- members of the ground state K = ~ rotational band, estimate that the ~ - - member of this band would lie at 362_ 1 keV. Using a similar procedure and the energies obtained in the current work which lie consistently lower, a value of 357 + 2 keV is found which is in excellent agreement with the energy value of the 356.5 keV level. Moreover the
238
T.W. CONLON
et
al.
discrepancy between the reduced E2/M 1 branching ratios for the cases (~-~-- -~ 5 - ) / ( 1 1 - ~ 9 - ) and (z~- ~ ~ - ) / ( ~ - ~ 7 - ) , shown in table 2 of BFHB and which have been used as evidence that the ~ - - level is not a member of the K = ~ band, is reduced considerably when account is taken of the contribution of the 114.5 keV transition, not observed by BFHB, to the intensity of the 120.4 keV, 11_- ~ 29_-,branch. It would seem then that one must assign K = 3, I~ = -~-- to the 356.6 keV level and that the metastable state level lies higher in energy, probably at 471.0 keV. Using the M1 and E2 assignments of BFHB to the 120.4 and 218 keV gammas, respectively, from the observed relative intensity of the 114.5 keV transition to the 120.4 and 218 gammas shown in table 2, the total conversion coefficient of the 114.5 keV g a m m a is estimated as 0.6_+ 0.4. The large uncertainty arises from the peak shape analysis of the unresolved doublet of 114.5 and 120.4 keV transitions. The total conversion coefficient for El, M1, E2 and M2 at 114.5 keV are 11) respectively 0.23, 1.6, 1.8 and 18.5. The most likely assignment for the 114.5 keV transition is thus El. If this is the case the spin and parity of the isomeric level at 471.0 keV are thus limited to ~+, _~1_+ or _13_+. A ~9 + or ~1_+ assignment would seem to be excluded, since no transition has been seen to the 2 - member of the ground state rotational band at 236.5 keV. The assignment of the 471.0 keV level is thus suggested to be ~ + . 3.7. INTERPRETATION OF THE ~+ STATE AT 471.0 keV The ground state of 159Dy is described by the Nilsson orbital available to the last (93rd) neutron, [52113-. However, no intrinsic excitation with a spin of ~3_+ is available for the neutron in this region. A possible explanation for the occurrence of a state with such a high spin may be given in terms of a three-particle state, examples of which have recently been reported by Kristensen et al. 3o) in 177Lu and 177Hf and by E m m o t t et aL 31) in 183Re. Possible three-particle states involving particles with K-values K1, K 2 and K 3 will be fourfold degenerate corresponding to the four spins values obtainable from the couplings ]KI+_K2+_K3[. The states will be more complicated than the twoparticle states described in 17 7Lu and a80W in this section, in that they can be either three-neutron, two proton-one neutron or two neutron-one proton states. In the established three-particle state in 177Lu the state is formed by coupling the single-proton state (which is the ground state of 177Lu ) [404]~+ to the two-neutron state K I ~ = 8,8- excitation which has been observed experimentally in 178Hf: this two neutron state is described by [{ [62419+}~ [51417-}]K ~ = 8-. Only one member of the four possible states thus formed has been identified; this is the state of the form [{p[404]~+}{([62419+)([514]~-)}8-]K ~ = 23. This state is observed at 967 keV excitation in 177Lu"
E1 TRANSITIONS
239
The last proton pair in 159Dy (65, 66th protons) is described by A = [{[411]~+}{[41113+}]0 +, and the lowest lying intrinsic proton excitation is the [523]½- state. Thus the twoproton state formed by the breaking of the ground state pair A and the excitation of one of the protons to the [523]½- state leads to the two-proton configuration B = [{ [41113+}{ [523]~-}]5-, and by coupling B to the ground state of 159Dy in the form I K I + K 2 + K 3 [ , we obtain a three particle state (two proton, one neutron) with the required spin and parity C = [{ [n[521 ]3-}{([41113+)([523]~-)}5-]K ~ = 1~_+ An examination of the states available by breaking a neutron pair (91st and 92nd neutrons) and excitation to the low-lying neutron states for the 91st neutron show that there are no other possibilities for forming a KS -- -T13+ state. If C does in fact describe the isomeric state, its decay to the 11_- rotational state at 256.5 keV involves a K-forbidden transition with A K = 5 and v = A K - I = 4. The reduced matrix element calculated for the isomeric state is 1 • 10-9 or a hindrance factor of 109. This large inhibition is certainly consistent with a K-forbidden transition of v = 3 or 4 and hence consistent with the above interpretation. N o account has been taken in the above discussion of the weaker branch of the isomeric decay involving a low-energy g a m m a of about 9 keV and the 157.9 keV g a m m a to the 310 keV state. No assignment is available for this 310 keV state nor was it possible to determine the multipolarity of the 151.9 keV gamma. More information on these and the intermediate state shown by dashed lines in fig. 16 is obviously desirable in order to establish the properties of the isomeric state, especially since the present interpretation requires a three-particle state to lie at 471 keV - considerably below the energy gap due to pairing. 4. Conclusion The application of the Nilsson model has proved to provide an adequate explanation for the cause of isomerism in the five cases discussed here. A natural extension of this single-particle model to include the last two particles in even-mass nuclei has proved useful in understanding the isomeric states observed in 172Lu and ~8°W. In order to understand the high-spin isomer in 159Dy in terms of this model it is necessary to suggest a state formed by the coupling of three particles described by Nilsson orbitals in the form IKI + K 2 +K31. The small reduced matrix elements for the E1 transitions observed here can also be qualitatively understood in terms of the selection rules governing transitions between the intrinsic states of the Nilsson scheme. It is interesting to note that the
240
T.W. CONLON et al.
E 1 t r a n s i t i o n i n 159Dy, 165Tm, 172 L u a n d a v 3 L u all h a v e r e d u c e d m a t r i x e l e m e n t s of t h e o r d e r o f 10 - 9 s i n g l e - p a r t i c l e u n i t s , b u t o n l y i n t w o cases, a TaLu a n d X65Tm are t h e t r a n s i t i o n s h i n d e r e d b y t h e s a m e v i o l a t i o n o f t h e K - s e l e c t i o n r u l e w i t h A K = 3.
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