High spin properties from the study of continuum gamma rays

Revi.ota Mezicana de Fúica 39, Suplementa!
(1993) 153-161
High spin properties from the study of continuum
gamma rays
LY. LEE
Lawrence Berkelell Labomtory
Berkelell, CA 94720, USA
ABSTRACT.A quantitative analysis has been carried out on the two-dimensional energy correlation of the continuum gamma rays in 17oHf.The results indicate the existance of at least
two widths in the gamma-ray energy distribution: a narrow width of about 20 keY, most likeIy originating from decay along different discrete bands near the yrast line and a wide width
of about 200 keY from mixed states at higher excitation energy. Lifetimes of states associ.
ated with the narrow width were measured by the Doppler-shift attenuation method. The results indicate a reduction of the collectivity associated with gamma-rays with energy from 0.7
to 0.9 MeY and an enhancement of collectivity for those above 0.9 MeY. These observations
were interpreted as due to the effect of rotational damping and rotational-induced nuclear shape
change.
RESUMEN.Se llevó a cabo un análisis cuantitativo de las correlaciones en energía en dos
dimensiones de rayos gama del continuo en l7oHf. Los resultados indican la existencia de al
menos dos anchuras en las distribuciones de energía de los rayos gama: una estrecha de cerca
de 20 KeY, probablemente originada por el decaimiento entre bandas discretas diferentes cerca de
la linea Yrast, y una ancha de cerca de 200 KeY, del decaimiento de estados mezclados a energías
de excitación mayores. Yidas medias de estados asociados con la anchura estrecha, se midieron
por el método de Atenuación del Corrimiento Doppler. Los resultados indican una reducción en
la colectividad asociada con rayos gama de energía entre 0.7 y 0.9 MeY y un incremento en
la colectividad para energías mayores. Estas observaciones fueron interpretadas como debidas al
efecto de dispersión rotacional y al cambio de forma nuclear inducido por rotación.
PACS: 27.70.+q; 23.20.En; 23.20.Lv
1. INTRODUCTION
In heavy-ion fusion reactions, compound nuelei can be formed with large angular momentum and excitation energy. Typically, nuelei in the rare-earth region can have angular
momentum up to 70fi and an excitation energy of 70 MeY. These nuelei decay first by
partiele emission,which removes most of the excitation energy but little angular momentumo Gamma decay takes over when the excitation energy above the yrast line is reduced
to less than the neutron binding energy. At the early stage of the gamma-ray cascade,
the gamma-rays are from states with high spin and high excitation energy. Due to the
high level density, a large number of available gamma-decay pathways existo Therefore, in
a one-dimensional spectrum these gamma rays appear as an unresolved quasicontinuum.
At lower spin the cascades gradually converge into a few pathways near the yrast line and
discrete gamma-ray transitions are observed.
154
LY. LEE
It is known experimentally that in most nuclei the majority of continuum gamma-rays
are stretched E2 in nature [1] and that they follow rotational-like sequences where by the
gamma-ray energy increases linearly with angular momentum. In one-dimensional spectra
the maximum energy edge is from states with maximum spin. As the compound nucleus is
populated with increased angular momentllm this edge moves to higher energies. In twodimensional sprectra, the rotational-like behavior show up as an additional ridge-vallay
structure that parallels the El = E2 diagonal [2).
2. ROTATIONAL DAMPING
Theoretical calculations have shown that the level mixing in the high level density regio n
produces the effect of "rotational damping". The collective E2 decay from one state is
no longer confined to one state in the same rotational band, and the decay probability is
distributed over states with a range in excitation energy. The width of this distribution is
called the rotational damping width f ro' which has a value in the range of 100-400 keV.
The large values of the rotational damping will change the features of the ridge-valley
structure in the two-dimensional spectra. Figure 1 shows one-dimensional gated spectra
generated from a two-dimensional matrix by placing a narrow gate on one of the energies
and projecting the other energy. These spectra were calculated assuming a 60 keV spacing
between the gamma rays and f,o' values of 15, 40 and 100 keV. As shown in Fig. l(a),
which has f ro' smaller than the separation of the gamma rays, the peak is clearly visible
and the dip created by the gated transition and the region between the peaks has no
counts. As the value of f,o' approaches the separation of the gamma rays (see Fig. l(b)),
the wider peaks merge into each other and the apparent intensity of the peaks is reduced.
Finally , as shown in Fig. l(c), when f,o' is significantly greater than the gamma ray
separation, the structure of the peaks and dips corresponding to neighboring transitions
completely vanishes, the central dip is filled in and becomes wider, and its shape changes
from rectangular to Gaussian.
\Ve have performed an experiment using 18 Compton-suppressed
Ge detectors in connection with the 52 NaI elements of the Spin Spectrometer. The fusion reaction 130Te +
44Ca was used at a beam energy of 195.5 MeV and the target consisted of a 1 mg/cm2
self supporting foil. The beam was supplied by the HHIRF tandem accelerator at Oak
Ridge National Laboratory. Two dimensional gamma-ray energy correlation matrix were
produced from events where at least two Ge detectors recorded an evento A condition
requiring that at least 15 NaI detectors were in coincidence with the two Ge detectors.
This condition almost completely eliminated the gamma-rays from other reaction channels
apart from the desired channel 17oHf. More importantly this condition also restricted the
feeding to only the high spin region in 170Hf, and this enabled us to compare the gated
spectra with the total projection spectra. The two-dimensional spectra, with a total of
7 x 107 events, was then unfolded by using measured response functions to remove the
non-full-energy-peak
contributiou and by correcting for the full-energy peak efficiency of
the Ge detectors.
A one-dimensional coincidence spectrum was generated from the two-dimensional ma.
trix by placing a gate on one of the energies and projecting the other energy. A total
HIGHSPINPROPEIITIES.
..
155
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4‫סס‬oo
r
(a)
= 15 keY
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-'
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10000
Z
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z
\
r "" 40
(b)
:>
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o
keV
10000
V
o
r
(e)
10000
=
100 keV
-----
-----
o
500
600
700
800
900
Ey (keV)
FIGUREl. Spectra generated assuming rotationa! easeades with a moment of inertia of 66
Mey-l and (a) for r = 15 keY, (b) for r = 40 keY, and (e) r = 100 keY.
,,2
projeetion speetrum was also obtained by projeeting the entire matrix. To compare the
latter with the gated eoincidenee speetrum, we normalized the speetra in the regions
200 keY aboye and below the gating energy, thus avoiding the region of the dip and the
peaks in the gated speetra. Figure 2 compares a eoincidenee speetrum gated at 0.7 MeY
and the normalized total projeetion speetrum. A eomparison of the two speetra shows
several interesting features. First of al!, in the gated speetrum a dip is c1early seen but it
does not reaeh zero. Seeondly, two wel! defined peaks are observed at the edge of the dip.
Final!y, beyond the neighboring peaks, additional dips and peaks can be seen.
•
Qualitative
features of the experimental speetrum can be understood from a eomparison
with the simulated speetra in Fig. 1. The width of the peaks in the experimental seetrum
is comparable to the. width of the peaks in Fig. l(a), indieating the existenee of a narrow
width with r,O! about 15 keV. However, the main dip does not reaeh zero and the side
dips are even less obvious. These features can only be found in Fig. l(e), indieating the
coexistenee of a wider damping width. Figure 3 shows the intensity of the peak and dip as
a function of the gating energy. The intensity of the dip is larger than the intensity of the
peak, indieating also the existenee of eontributions from eomponents with a width greater
156
LY. LEE
ORMl-D\IG
91.10SM
12000
10000
...¡
ti!
Z
Z
8000
u
6000
«
:r:
'""
[f)
~
4000
::>
O
u
2000
o
400
700
1000
Ey (keV)
= 0.7 MeV shown as a solid curve, and the normalized total projection spectrum shown as a dotted curve.
FIGURE 2. Coincidence spectrum gated by E,
than the 15-20 keY width oí the peaks. It is relatively easy to make a separation into a
narrow width which produces both peak and dip and a wide component which produces
only a wide dip. From the dip intensity of the wide component f ro' can be determined form
the curve in Fig. 4. These values are shown in Fig. 5 as a function oí the gating energy.
The experimental results indicate that the value oí fro' is in the range of 150-250 keY.
Although the uncertainty is large, the data show a trend toward larger f ro' at higher energies. This variation reflects the change in f ro' at the higher spin and excitation region oí
the decay pathway. Recent calculations [31 of the rotational damping width gave values between 100 and 200 keY. These values are in good agreement with the experimental values.
3. LIFETIME OF THE CORRELATION RIDGES
The diagonal ridge structures in the 2-dimensional gamma-ray energy spectrum are most
likely associated with rotational-like cascades having an excitation energy oí less than
approximately 1 MeY aboye the yrast lineo Hence a measurement of the lifetime associated
with the ridges provides information on the collectivity of high-spin states near the yrast
lineo
Lifetime measurements
for 170Hf and 164Yb were made using the reactions
130Te(44Ca,4n) at 195 MeV and 124Sn 4Ca,4n) at 189 MeY, respectively. Targets oí
1 mg/cm2 enriched material with a gold backing sufficiently thick to stop the recoiling
nuc1ei were used for the experiments. The beams were provided by the Tandem accelerator
of the HHIRF at ORNL. The gamma rays were detected in an array of 20 Comptonsuppressed Ge detectors. The four detectors with the most forward angle with respect to
the beam direction were at 45 degree, and the four most backword angle detectors were
e
HIGH SPIN PROPERTIES...
157
60
~
~
~
~
40
-'
¡¡;
<:
'<:"
-'
20
o
600
700
800
900
1000
1100
Ey (keV)
FIGURE 3.
Experimental intensity of the peak and the dip as a function of the gating energy.
OUl.DIOG
91-1O~1l.8
120
100
~
~
~
~
-'
80
.~
Vl
60
'<:"
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-
Peak
20
O
O
FIGURE 4.
50
100
r
150
200
250
300
(keV)
Area of the peaks and dip determined from the simulated spectra.
at 135 degree. These eight detectors observed the largest Doppler shift. Therefore their
spectra provided the most sensitive ¡¡fetime measurment. Triple-coincidence data were
taken at arate of 1000 events per second, and a total of 150 million events were collected
for each experiment.
Two E,-E, correlation matrices were generated from each data set: one with coincidence events between any of the four 45 degree detectors and any other detector, and
the other with coincidence events between the four 135 degree detectors and any other
158
I.Y. LEE
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-
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o.
ff)
,
50
600
700
800
900
1000
1100
Ey (keV)
FIGURE 5.
rro'
for lhe broad widlh derived from lhe measured inlensily oC lhe valley.
detector. The Doppler shiCts were determined using the one-dimensional spectra of the 45
degree and 135 degree detectors obtained by gating on gamma rays recorded in the other
detectors. Figures 6 and 7 show the spectra for the 45 degree and the 135 degree detectors
for 164Yb and 170Hf, respectively. As expected, the spectra show a wide dip centered at
the energy of the gated gamma ray and a 20 keV wide peak at 60 keV both aboye or below
the gating energy. The peaks in the 45 degree speclra are shifted to higher energy and
shifted to lower energy in the 135 degree spectra. The energy difference between the peaks
in the 45 degree and the 135 degree sprectra was used to determine the Doppler shift.
The measured Doppler shift was converted to a fraction of the maximum shift by
dividing by an amount corresponding
to the maximun recoil velocity of 0.024 of the
velocity of light. Figures 8 and 9 show the fractional shift for 164Yb and 170Hf, respectively.
These results show that for gamma-ray energies between 0.7 and 1 MeV, the Doppler shift
increase from zero to its maximum value. This result indicates a decrease in the total time
from the formation of the compound nueleus to the emission of the continuum gammaray in this energy region. A model assuming a rotational cascade was used to calculate
the total decay time in order to compare with the experiment. The energy of the E2
transition was obtained from the moment oC inertia, the B(E2) value was obtained from
the transition quadrupole moment Q,. The lifetime of the transitio'1 was then calculated
from the energy and the B(E2) values. The three curves shown in lig. 8 correspond to
Ql = 7 eb (the accepted experimental value [41 for the 2+ ....• 0+ transition of 170Hf)
and Q, = 6 and 8 eb. The cascades were assumed to start at spin 50. This value was
determined from the average value of the measured gamma-ray multiplicity. The value
of the moment of inertia (57 ,,2/MeV) was chosen lo reproduce lhe distance belween
lhe ridges. For 164Yb, the calculalions were carried out with a maximum spin of 46 and
moment of inertia 57 ,,2/MeV). Curves are shown in Fig. 9 for Ql = 5.6, 6.6 and 7.6 eb,
where 6.6 eb corresponds to lhe accepted experimental value [41of the 2+ ....•0+ transition.
HIGH SPIN PROPERTIES. ..
159
7500
....l
¡.,¡
Z
Z
6500
<l;
;r:
u
"-rn
5500
135 deg.
~
Z
::>
O
4500
u
3500
670
720
770
820
870
920
Ey (keV)
FIGURE 6. Spectra for 16'Yb at 45 and 135 degrees gated by the 820 keV gamma-rayo Peaks at
76C and 880 keV show opposite Doppler shifts in the two spectra.
8000
....l
¡.,¡
Z
Z
7000
<l;
;r:
U
6000
::>
5000
"-rn
~
z
O
U
4000
610
660
710
760
810
860
Ey (keV)
FIGURE 7. Spectra for 170Hf at 45 and 135 degrees gated by the 760 keV gamma-rayo Peaks at
700 and 820 keV show opposite Doppler shifts in the two spectra.
The comparision of the experimental results with the model calculations indicate that
the £2 transition strength, for the gamma-rays in the continuum ridges with energy less
than 0.9 MeV, is less than that of the 2+ -+ 0+ transition. However, for both nuclei, lhe
colleclivity of the gamma-rays with energy greater than 0.9 MeV are larger than that
of the 2+ state in the same nucleus. The red uction of the collectivity at intermediate
spins has been observed for the discrete gamma-ray transitions in several nuclei in this
160
LY. LEE
120
100
<¡.,
-:r:
80
<-
60
Ul
Z
¡.:¡
U
o::
¡.:¡
o..
40
20
O
600
700
800
900
1000
1100
Ey (keV)
FIGURE 8. Comparison of lhe measured and calculaled Doppler shifls as a funclion of gamma-ray
energy for 170Hf.
120
100
<¡.,
-:r:
80
<-
60
8 eb
7 eh
6 eh
Ul
Z
¡.:¡
U
o::
¡.:¡
o..
40
20
O
600
700
800
900
1000
1100
Ey (keV)
FIGURE 9.
energy for
Comparison of lhe measured and calculaled Doppler shifls as a funclion of gamma-ray
164Yb.
mass regio n [5-9]. It has .been interpreted as a reduced quadrupole deformation or a
triaxial deformation due to rotational1y-induced
modifications of the occupation of the
strongly shape-polarizing high-j orbitals (such as the neutron i13/2 orbital) at high spin.
The increase in col1ectivity at energies greater than 0.9 MeV may also be associated with
a shape change resulting from the occupation of strongly shape-polarizing single-partide
configurations. Cranking model calculations indicate that the proton i13/2 and neutron
HIGH SPIN PROPERTIES.
..
161
j¡S¡2 orbitals become yrast at 1 = 45 and 55, respectively. The predicted Qt values of states
based on these configurations is about 7-8 eb. However, it is unlikely that the transitions
in the ridges are associated with these states beca use the observed ridge separation is
nearly constant in contrast to an expected reduction associated with a larger moment of
inertia. This ahorter elfective Iifetime is most Iikely due to faster feeding times of the more
collective states Iying aboye the near-yrast region.
4.
CONCLUSIONS
Properties of the continuum gamma-rays have been obtained from studies of two-dimensional energy correlations. A narrow and a wide correlation width have been resolved in
170Hf.The narrow component with a width of about 20 keV results from a regíon near
the yrast line. The wide component which has a width of 150-250 keV is interpreted
as gamma rays from a region of higher excitation energy where rotational damping due
to level mixing produces the wide width. Theoretical calculations have reproduced these
mesured features. Lifetimea of states associated with the ridges were measured by the
Doppler shift attenuation method. An increase in collectivity for gamma-rays with energy
aboye 0.9 MeV has been observed in 164Yb and 170Hf.This observation is understood as
a rotationally-induced occupation of high-j orbitals with larger deformation.
ACKNOWLEDGMENTS
This work was carried out in collaboration with C. Baktash, J.R. Beene, M.L. Halber,
D.C. Hensley, N.R. Johnson, F.K. McGowan, M.A. Riley, D.G. Sarantites, H. Xie, W.B.
Gao, J .D. Garrett and R. Wyss. 1 would Iike to thank B. Cederwall and P. Fallon for
their help in preparing this manuscript. Research sponsored by the U.S. Department of
Energy, under contract DE-AC03-76SF00098 (LBL), DE-AC05-840R21400 (ORNL) and
DE-FG05-88ER40407 (Vanderbilt University).
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