Colletive Mode in Nuclei: Progress in the Study
of the Gamma Decay of the Giant Dipole
Resonance
A.Bracco and O.Wieland
Dipartimento di Fisica Università di Milano Via Celoria 16, 20133 Milano and INFN sez. Milano, Italy
Abstract. The study of the gamma decay of the giant dipole resonance (GDR) has allowed to
investigate nuclear structure properties at excitation energies up to the Fermi energy. It continues
to be a useful tool to explore the basic nuclear nuclear properties at finite temperature and
angular momentum, such as nuclear shapes and thermal effects. In particular, the dependence of
the GDR width as a function of temperature and angular momentum provides information on the
evolution of the nuclear shapes and of the damping mechanisms of this collective state. This is
an interesting topic under discussion which is presently addressed with new and more exclusive
measurements. In reviewing the activity in this field selected exclusive data concerning the
extreme region of temperature and angular momentum will be presented. In particular data for
the two mass regions A=120-130 and A=180-200 will be discussed, with results based on
measurements made at the INFN laboratories LNL using the HECTOR and GARFIELD arrays.
Keywords: Giant Dipole Resonance, nuclear shapes.
PACS: 24.30.Cz, 24.60.Dr, 25.70.Gh, 21.60.Ev
INTRODUCTION
During the last years considerable efforts have been made to investigate the
properties of the giant dipole resonance built on excited states. The field has
progressively expanded resulting in significant nuclear structure and nuclear reaction
information. Among the structure and reaction effects explored with the GDR there
are, for example, the determination of the nuclear shape, the coupling to low lying
states and to quadrupole deformation, damping due to collisions and thermal shape
fluctuations, fission time scales, loss of collectivity at high temperatures, entrance
channel effects and pre-equilibrium giant dipole vibrations.
This paper focuses on the problem of the nuclear shape and of the damping
mechanisms [1] as addressed by the measurements of the GDR width. In this
connection it is important to stress that the existing investigations made in different
mass regions in the interval of temperature 1-2 MeV give results for the GDR widths
which are larger than the T=0 values and that are in general rather well reproduced by
the model predictions. The latter include the effects of thermal shape fluctuations and
assume that the collisional damping does not change with temperature. Nevertheless,
a much more stringent test to the theory in the region at the limits of temperature and
angular momentum is needed and this requires exclusive measurements to be made.
In the case of high temperatures, namely at T >2.5- 3 MeV it is not yet clear
whether or not the width becomes roughly constant with temperature as expected from
the fact that thermal shape fluctuation effects should saturate. The experimental
approach to address this question requires exclusive measurements of particles and
gamma rays to determine precisely the temperature of the compound nucleus on which
the GDR is built.
In the following sections we discuss the results of two exclusive experiments. The
first concerns the measurement of the damping width in heavy nuclei at T =1.3 MeV
where the competition with fission play an important role. The second concerns the
measurement of the GDR width at T >2.5 MeV in the mass region A=130.
PROBING THE NUCLEAR SHAPE AROUND THE FISSION
LIMIT IN 216RN
An interesting and still open question concerning the mechanism of nuclear fission
induced by fast rotation, is the nuclear shape evolution on the way to scission. This
problem can also be addressed with the study of the GDR which, as discussed before,
is sensitive to the average nuclear shape at finite temperature. Nuclear deformations
corresponding to the saddle point configurations are often expected to be very large.
The related experimental information is particularly interesting as it provides a
sensitive test of both the macroscopic methods of calculating the total nuclear energy
at high temperatures as well as the microscopic ones taking into account thermal
excitations.
The term 'fission limit' used throughout this paper applies by definition to the spin
value, say If, for which the fission-barrier penetrability from the static equilibrium
deformation equals 50%. Within a model, such a spin can be relatively easily
determined in the calculations but much less so in measurements. Calculation results
for the case of 216Rn and their comparison with experiment suggest that in the present
context If ~40 ħ, within a few ħ inaccuracy [2].
In order to obtain information about the nuclear shape evolution along the fission
path, it is possible to use at least two different approaches. One of them consists in
studying the GDR in fissioning nuclei, by measuring the GDR decay during the fission
process. From the high-energy -ray spectra in coincidence with the fission products,
in principle one may expect to obtain the information about the shape of fissioning
nuclei and thus about their shape evolution along the fission path. However, the
existing data show that this is not at all an easy task because of the presence in the
spectra of rays from the fission products [3,4].
Another approach consists in measuring the GDR decay in the fusion-evaporation
reaction by selecting very high spins around the critical spin value at which the fission
process is beginning to dominate. Such measurements are also in general very
difficult, because one has to select a very narrow spin window and at the same time to
reject the fission contaminations. This can be achieved by tagging either on the fusionevaporation products or on the -rays from specific residual nuclei.
So far, investigations of this type have provided high-energy -ray spectra through
gating on different residual nuclei (see e.g. the case of 194Hg [5]). However, the
measurements did not allow to make a spin selection in a region very close to the
fission limits.
More recent measurements performed using the fusion-evaporation reaction
18
O+198Pt at the bombarding energy of 96 MeV, populating with a rather high cross
section residual nuclei characterised by the presence of long-lived high-spin isomeric
states. The decaying 216Rn compound nucleus strongly feeds the isomeric states of
I=30 ħ in 212Rn and I=63/2 ħ in 211Rn. In addition, since only two feeding transitions to
these isomeric states were found, one expects that the fission limit in 216Rn is below or
around 40 ħ. Therefore, the selection of the GDR -decay in coincidence with delayed
-ray transitions is expected to probe mainly the compound nuclei which survive
fission, yet, with angular momenta close to the fission limit.
Lmax
7
10
33 h
37 h
39 h
41 h
45 h
6
10
5
Y [a. u.]
10
4
10
3
10
FIGURE 1 The measured fold
< M > = 5
2
10
exp. tot.
exp. tot. - isomer
exp. isomer
1
10
2
4
6
8
10
12
14
16
18
20
distribution of the reaction 18O+198Pt at
the bombarding energy of 96 MeV in
comparison with calculated fold
distributions assuming different values
of the maximum angular momentum.
Fold
The multiplicities of low energy γ rays are shown in figure 1. The measured
multiplicity around the target in coincidence with the isomeric-states is of the order of
only 5 (the average value measured in the reaction is of the order of 13–15) indicating
that the isomers are populated in the reaction and stopped in the catcher which collects
the rest of the decay.
Fig. 2 shows the measured high energy -ray spectra. Panels (a) and (b) show the
spectra in coincidence with the fold intervals 5–8 and 9–30, respectively. Panel (c)
shows the -ray spectra in coincidence with the isomer. In all plots, the continuous
grey line shows the results of a statistical model calculation performed using the
Monte Carlo version of the statistical model code CASCADE. As it can be seen, the
statistical model calculations reproduce well the measured spectra in all cases.
The GDR centroids and widths are found to be very similar in the three cases (see
caption of Fig.2). In panel (c) the thick dark line shows the calculation which
reproduces the total un-gated spectrum while the thin one shows the calculation where
the conditions of populating the 212Rn residues and of having initial spin larger than 35
ħ are required.
FIGURE 2. The high energy spectra measured in the compound fusion reaction 18O + 198Pt at 96 MeV.
Panels (a) and (b) show the spectra measured for low energy coincidence folds 5–8 and 9–30
corresponding to an average spin of 23 ħ and 29 ħ, respectively. Panel (c) shows the high energy -ray
spectrum measured in coincidence with the isomer stopped in the catcher. In all panels, the thin light
continuous lines show the results of the statistical model calculations. In panel (c) the calculations have
been done requiring 212Rn as a residue and compound nucleus with a spin higher than 35 ħ. The thick
line shows the results of the calculations where such conditions are lifted. In all three cases the GDR
centroid value is 13.2 MeV while the GDR width is 7.0,7.0 and 7.3 MeV respectively.
It should be noted that the measured values of the GDR width are found to be: (i)
larger than in the ground state nuclei (almost by factor of two); (ii) independent of the
angular momentum of the compound system. The observed discrepancy between the
T=0 value and those at finite temperature is of the same order of magnitude of that
found in lighter nuclei which was interpreted in terms of thermal shape fluctuations of
the hot nuclei. This can be seen in figure 3 where the data on the GDR width as a
function of spin for A>110 are shown.
In addition, the fact that the experimental results are independent of the angular
momentum indicates that the average deformation of the nucleus is not changing
significantly by increasing the spin. Such a scenario is theoretically confirmed by the
thermal shape calculations [6,7] which are shown with lines in figure 3.
THE DAMPING MECHANISMS AT HIGHER T
In contrast with the picture of the GDR width at T< 2MeV, which is in general well
understood, at T> 2 MeV there is the open question whether the width of the GDR
saturates or increases [11] with increasing temperature. This question has been newly
addressed particularly in relation to the problem of how well one can determine the
excitation energy of the nucleus on which the GDR is built. Up to now almost all the
performed measurements are essentially inclusive and particularly at the highest
excitation energies (E* > 100 MeV) exclusive measurements are necessary for the
understanding of this problem. Recent experiments were performed in which both
high energy rays and light charged particle (LCP) emitted in coincidence with
(heavy) evaporation residues were measured.
14
13
147
Eu T=1.3
106
Sn T=1.8
176
W T=1.5
194
Hg T=1.3
12
 [MeV]
11
10
9
8
7
6
5
0
10
20
30
40
50
60
Figure 3: The GDR width as a
function of spin obtained for
experimental GDR strength
functions is shown for the data
on 216Rn (filled circles) in
comparison with data from
literatures concerning other
nuclei in different mass regions.
< I > []
In order to evaluate the contribution of the preequilibrium emission we have chosen
two different reactions leading to the same excitation energies. The measured
reactions were the symmetric 64Ni + 68Zn at Ebeam = 300, 400 and 500 MeV ( E*= 100,
150 and 200 MeV) and the asymmetric 16O + 116Sn at Ebeam = 130 and 250 MeV
(E*=100 MeV and 200 MeV).
The experiment has been made using the GARFIELD set up combined with the 8
BaF2 detectors of the HECTOR array. The GARFIELD vacuum scattering chamber
was equipped with one of the two drift chambers of the GARFIELD apparatus
(gaseous microstrips coupled with CsI(Tl) crystals) from  = 30° to 90°, while the
BaF2 were positioned at backward angles between 125° and 160°. In the forward
direction, between 4° and 12°, two couples of PSPPACs were positioned
symmetrically with respect to the beam. Two Si(Li) detectors were positioned between
each couple of PSPPAC at the larger angles. The pulsed beam (with the repetition
period of 800 ns) was provided by the LNL TANDEM+ALPI accelerator system. The
targets were 68Zn and 116Sn with a thickness of 500g/cm2 and 450g/cm2,
respectively. The BaF2 detectors were calibrated using standard  sources and with the
reaction 2D(11B,n)12C which gives a high energy  ray of 15.1 MeV. The Garfield
apparatus was calibrated with the elastic scattered beam of the above described
reactions and the two nuclear reactions 12C+12C and 32S+64Ni at Elab= 70 MeV and 140
MeV respectively. With the system GARFIELD+HECTOR we could measure both
rays and charged particles in coincidence with residual nuclei detected in PSPPAC
detectors [12].
The main aim of the analysis was to extract the information about the temperature
and preequilibrium energy loss and therefore to gain a deeper understanding of the
evolution of the system towards thermal equilibrium. The experimental LCP kinetic
energy spectra have been analyzed using a moving source fit in which the particles are
assumed to be emitted isotropically from two different moving sources, one with
approximately the beam velocity which is responsible for the preequilibrium, and a
second with the velocity approximately similar to the compound which is responsible
for the statistical emission. The alpha-particle spectra clearly shows that the
preequilibrium emission is practically absent in the Ni-induced reactions as only an
evaporative behaviour from a source with quite standard emission parameters has been
measured. In fact, (see Fig.4 upper row) it has been obtained that only one evaporative
source with velocity Vsource(Ebeam=500 MeV)=1.9 cm/ns and Vsource(Ebeam=400
MeV)=1.7 cm/ns is needed to describe the measured spectra. This is in agreement with
standard statistical model calculations without preequilibrium contribution (PACE4)
where Vevap.source(Ebeam=500 MeV)=1.88 cm/ns and Vevap.source(Ebeam=400 MeV)=1.69
cm/ns. Therefore in the symmetric case with the highest excitation energy one can say
that the pre-equilibrium emission is negligible.
The analysis of the O-induced reaction shows (see Fig. 4 lower row) that a large
part of the cross section cannot be described by a single evaporative component only.
A second preequilibrium source has to be added to the evaporative part to fit the
spectra (work in progress [13]).
FIGURE 4. Alpha particle spectra in coincidence with evaporated residues. The upper (E lab=500MeV)
and middle (Elab=400MeV) panels show the measured (filled points) and calculated evaporation source
fit (thin line) for the Ni-induced reaction of different detection angles. The lower panel shows measured
alpha particle spectra (filled points) for the more asymmetric case of the O-induced (Elab=250MeV)
reaction for three different detection angles and the calculated evaporation source fit (thin line), which
in contrast to the symmetric reaction does not reproduce the particle spectra, due to preequilibrium
contributions.
10000
10000
statistical
model
64
68
Ni + Zn
Elab=500MeV
E*=200MeV
Yield (arb.units)
1000
statistical
model
64
68
Ni + Zn
Elab=300MeV
E*=100MeV
1000
100
100
10
10
1
0.1
1
6
10
14
18
22
E [MeV]
26
30
6
10
14
18
E [MeV]
FIGURE 5. The panels show (filled points) the measured high energy -ray spectra for 132Ce* at 200
and 100 MeV of excitation energy. The experimental  spectra are obtained in coincidence with
evaporated residues. The thin continuous line shows the result of statistical model calculations. The
calculations have been performed assuming a fully thermalized compound nucleus.
Based on the alpha particle experimental spectra we obtain the preliminary result
that the system losses a significant part of its excitation energy due to preequilibrium
emission in the case of the Elab = 250 MeV 16O + 116Sn reaction.
The analysis of the obtained -ray spectra has been performed with the statistical
model. To reproduce the -ray spectra of the reaction 64Ni+68Zn simulations based on
the CASCADE code were performed. The obtained spectra are then folded by the
experimental set-up response function calculated using the GEANT [14] libraries. We
used a single Lorentzian strength function for the GDR position and width. A sum rule
strength of 100% is assumed in all calculations. Figure 5 shows preliminary results on
the experimental measured high energy -rays and the best fitting statistical model
calculations at excitation energy of 100 and 200 MeV.
The obtained values of the widths are displayed in figure 6 together with data at
lower excitation energies [15-17] and predictions based on the thermal fluctuation
model [6,7]. It is clear from the comparison of the data with model predictions that the
increase of the width at T >2 MeV is mainly due to the compound nucleus lifetime
while the width increase due to shape fluctuation is much less rapid [18-19].
CONCLUSION AND OUTLOOK
Selected results of experiments concerning the study of the GDR built on excited
states at high spins
and
high
Preliminary data
temperature
have
been presented.
Th. Shape Fluc.
Theory + CN lifetime
FIGURE 6. The data on the GDR width obtained from the experiment with HECTOR and GARFIELD
(filled diamonds, preliminary data) are plotted as a function of temperature of the compound nucleus
130
Ce. The data at lower temperature are from literature [15-17] and the calculations are based on the
model of refs. 6 and 7. The compound nucleus lifetime is from the statistical model.
The picture emerging from the study of 216Rn around the fission barrier is that the
nucleus is nearly spherical with a small oblate deformation, similar to that found in the
Hg nuclei. The deformation of the 216Rn nucleus does not change with increasing spin
up to the fission value.
From the measurements of the GDR in the mass region A=130 and in the
temperature interval 2.5-4 MeV we have found a strong entrance channel effect in the
compound nucleus formation when we use O beam as compared with Ni beam. The
analysis of the -ray spectra for the reaction induced by O is in progress. With the
symmetric reaction 64Ni + 68Zn we show that it is possible to study the GDR in the
region E* = 100 - 200 MeV. In fact, in this case, also at the highest excitation energy
(E* ≈ 200 MeV) the system is fully thermalized and the pre-equilibrium emission is
negligible. Particle and -ray spectra are both well reproduced with the statistical
model of CN emission. In addition, the observed GDR width has a value in qualitative
good agreement with the thermal fluctuation model which reproduces the general
increase of the width with excitation energy.
The two examples here discussed show that the progress in the field of nuclear
structure at finite temperature requires new exclusive measurements of the GDR on
excited nuclei with good selection of spin and temperature but also of beam and target
combination. In connection with this, it is important to stress that the availability
radioactive beam facilities of second generation such as SPES and SPIRAL2 will
open new perspectives for investigating nuclear shapes at finite temperature for nuclei
farther away from the stability line.
ACKNOWLEDGMENTS
The work presented here could not be possible without the precious contributions
and continuous efforts of our collaborators. They are: F. Camera, G. Benzoni, S.
Leoni, B. Million, S. Brambilla, A. Giussani, A. Moroni and N. Blasi from University
of Milano and INFN; S. Barlini, V.L. Kravchuk, F. Gramigna, A. Lanchais, L.
Vannucci and P. Mastinu from LNL Legnaro; A. Maj, M. Brekiesz, M. Kmiecik, W.
Królas, W. Męczyński, J. Styczeń and M. Ziębliński from Kracow; M. Bruno, G.
Vannini and E. Geraci from Bologna; G. Casini and A. Nannini from Firenze.
Financial supports from the Polish State Committee for Scientific Research (KBN
Grant No. 2 P03B 118 22) and the Italian INFN are acknowledged.
REFERENCES
1. P. F. Bortignon, A. Bracco and R.A. Broglia, Giant Resonances: Nuclear Structure at Finite Temperature, New
York: Gordon Breach (1998).
2. M. Kmiecik et al., Phys. Rev. C70 064317 (2004).
3. R. Butsch et al., Phys. Rev. Lett. 41, 1530 (1990).
4. T. Tveter et al., Phys. Rev. Lett. 76, 1035 (1996).
5. F. Camera et al., Phys. Rev. C60, 014306 (1999).
6. D. Kusnezov et al. Phys. Rev. Lett. 81,542 (1998).
7. D. Kusnezov and W. E. Ormand, Phys. Rev. Lett. 90, 042501 (2003) and reference therein
8. M. Mattiuzzi et al. Phys. Lett. B364(1995)13
9. M.Mattiuzzi et al. Nucl. Phys. A612(1997)262
10. M.Kmiecik et al Nuclear Phys. A674(2000)29
11. M. P. Kelly et al., Phys. Rev. Lett. 82 (1999) 3404
12. F.Gramegna et al., Nucl. Phys. A389 (1997) 474
13. S.Barlini et al., work in progress, to be published
14. R. Brun et al., CERN Report No. CERN-DD/EE/84-1, unpublished (1985)
15. E.F. Garman et al. Phys. Rev. C28, 2554(1983)
16. I. Dioszegi et al. Phys. Rev. C63, 047601(2001)
17. R.K. Voijtech et al. Phys. Rev. C40, 2441(1989)
18. O. Wieland et al. J. Phys. G: Nucl. Part. Phys. 31 (2005) S1973
19 O. Wieland et al. to be published.