Spectral Structure of the Pygmy Dipole Resonance
A.P. Tonchev,1,2S.L. Hammond,3,2J.H. Kelley,4,2E. Kwan,1,2H. Lenske,5G. Rusev,1,2W. Tornow,1,2and N. Tsoneva5,6
1Duke University, Durham, North Carolina 27708-0308, USA
2Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708-0308, USA
3University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3255, USA
4North Carolina State University, Raleigh, North Carolina 27695-8202, USA
5Institut fu ¨r Theoretische Physik, Universita ¨t Gie?en, Gie?en, D-35392, Germany
6Institute for Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria
(Received 23 July 2009; published 18 February 2010)
High-sensitivity studies of E1 and M1 transitions observed in the reaction138Bað ~ ?;?0Þ at energies
below the one-neutron separation energy have been performed using the nearly monoenergetic and 100%
linearly polarized photon beams of the HI~ ?S facility. The electric dipole character of the so-called
‘‘pygmy’’ dipole resonance was experimentally verified for excitations from 4.0 to 8.6 MeV. The fine
structure of the M1 ‘‘spin-flip’’ mode was observed for the first time in N ¼ 82 nuclei.
DOI: 10.1103/PhysRevLett.104.072501PACS numbers: 21.10.Hw, 21.60.?n, 23.20.En, 24.70.+s
In stable and unstable neutron-rich nuclei a resonance-
like concentration of dipole strength is observed at excita-
tion energies around the neutron-separation energy [1–10].
This clustering of strong dipole transitions has been named
the pygmy dipole resonance (PDR). In hydrodynamic and
collective approaches, it was suggested that an oscillation
of a small portion of neutron-rich nuclear matter relative to
the rest of the nucleus is responsible for the generation of
pygmy resonances [11,12]. Further, in microscopic models
based on the quasiparticle-random-phase approximation,
relativistic (RQRPA) and nonrelativistic (QRPA), the po-
sition and the distribution of the PDR have been investi-
gated [13–16]. From the analysisof transitiondensities, the
unique behavior of the PDR mode is revealed, making it
distinct from the well-known giant dipole resonance
(GDR) . The systematic studies of the PDR over iso-
tonic and isotopic chains of nuclei indicate a correlation
between the observed total BðE1Þ strength of the PDR and
the neutron-to-proton ratio N=Z [5,8,14,15]. In addition, it
has been suggested that the PDR is independent of the type
of nucleon excess (neutron or proton) [13,15].
The existence of the PDR mode near the neutron thresh-
old has also important astrophysical implications. For ex-
ample, the reaction rate of the (?, n) and (n, ?) reactions in
explosive nucleosynthesis of certain neutron deficient
heavy nuclei may be significantly enhanced by the PDR
. Furthermore, for very neutron-rich exotic nuclei, the
PDR is an important topic of study at the new generation of
radioactive ion beam facilities .
In many cases the interpretation of the PDR excitation is
based on the assumption of negative parity for the majority
of the J ¼ 1 states. However, there has not been a system-
atic experimental verification that all the dipole states
observed in the entire PDR region are indeed 1?states.
The parity was measured directly in certain energy inter-
vals, e.g., off-axis bremsstrahlung or Compton polarimetry
. The advantage of using 100% linearly polarized
photon beams for parity identification has been recently
demonstrated [21–24], which opens new opportunities for
unveiling the character of the nuclear dipole response.
On the other hand, in heavy mass nuclei there should be
the PDR, i.e., in the low-energy tail of the GDR . A
major experimental problem is to distinguish M1 and E1
strengths, since the former is highly fragmented at these
energies . In order to unambiguously discriminate
between these different dipole excitation modes, the spin
and parity of the involved states must be known.
In the present Letter, we report first on the experimental
determination of the character of the PDR as a predomi-
nantly E1 mode of excitation. Furthermore, the fine struc-
ture of the dominant E1 and dispersed M1 strength
distributions below the particle separation energy is deter-
mined. Finally, the dynamics of the PDR as an interplay
between isoscalar and isovector excitation modes is re-
138Bað~ ?;?0Þ reaction below the neutron-separation energy
of about 8.6 MeV using the nearly monoenergetic and
100% linearly polarized photon beams of the High-
Intensity ?-Ray Source (HI~ ?S) facility .
The monoenergetic photon beams were produced by
intracavity Compton backscattering of free-electron-laser
light from electron beam bunches and collimated by a lead
collimator of length 30.5 cm with a cylindrical hole of
1.9 cm diameter. The photon flux on target exceeds
1000? eV?1s?1within an energy spread of about 3%.
After proper attenuation, the energy distribution of the
photon beam was measured with a 123% high-purity ger-
manium (HPGe) detector placed in the beam. The photon
flux was measured by Compton scattering of the beam
from a 1.0 mm thick copper plate, positioned 3 m behind
the barium target.
The target consisted of 4.2905 g of BaCO3powder
enriched to 99.68% in138Ba. It was placed into an evacu-
PRL 104, 072501 (2010)
19 FEBRUARY 2010
? 2010 The American Physical Society
ated plastic tube at the center of an array of five large-
volume HPGe detectors. These detectors were arranged
ð90?;90?; and 270?Þ, (90?, 0?, and 180?), and (135?,
0?), where ? is the polar angle of the outgoing radiation
with respect to the horizontally polarized incoming photon
beam, and ? is the azimuthal angle measured from the
polarization plane. This detector configuration allows for
unambiguous determination of E1, M1, and E2 transitions
regardless of the ground-state spin.
The photon scattering spectra at three different angles
relative to the linearly polarized HI~ ?S beam is shown in
Fig. 1. All peaks seen in these spectra represent ground-
state transitions of excited states in138Ba. The dotted lines
between the top and the center spectrum connect the
transitions present in the vertical and backward-angle in-
plane detectors, but not seen in the horizontal detectors at
90?. Hence, from the azimuthal intensity patterns for elas-
tic scattering of linearly polarized photons, one can un-
ambiguously assign pure E1 excitations to the observed
transitions [26,27]. On the other hand, the bottom spectrum
shows transitions present in the horizontal and backward-
angle detectors, but not in the vertical detectors. These
transitions correspond to pure M1 excitations.
In this way, a total of 18 measurements were carried out,
covering the entire energy region from 4.0 to 8.6 MeV.
Only transitions with phonon width greater than 1 meV
were resolved. Our measurements confirm the previous
parity assignments in one of the pioneering experiments
at HI~ ?S between 5.5–6.5 MeV  and the dipole charac-
ter of the states measured in Refs. [1,5]. However, higher
experimental sensitivity allowed us to observe 87 new
dipole states in138Ba. Most of these states are at energies
above 6.5 MeV and have relatively small strength. The
summed E1 transition strength from 4.0 to 8.6 MeV is
?BðE1Þ "¼ 0:96ð18Þe2fm2, corresponding to 1.3% of the
energy-weighted sum rule (EWSR).
Equally important are the concentrations of M1 dipole
states which have been observed for the first time in138Ba.
They are clustered around 6.5 MeV and close to the
neutron-separation energy. The summed M1 transition
strength from 4.0 to 8.6 MeV is ?BðM1Þ "¼ 2:5ð6Þ?2
contained in 19 newly observed resonances. About
Nof this strength is localized within a doorway state
at6.5MeV.The centroid energyof these states corresponds
to E ? 35A?1=3MeV.
The 100% polarized and nearly monoenergetic photon
beam allows us not only to determine unambiguously the
electromagnetic character of the transitions, but it also
enables a closer examination of the dynamics of the decay
pattern in the PDR region. First, it should be noted that no
sizable branching transitions to low-lying excited states
(greater than 2%) have been observed. This fact is con-
firmed by the microscopic calculations presented below,
suggesting that the elastic dipole transitions are due to
almost pure neutron particle-hole states decoupled from
the GDR. According to the calculated structure of thewave
functions of QRPA 1?states and corresponding proton and
neutron transition densities, theyhave been associated with
the PDR [13,15].
Second, at excitation energies close to the neutron-
separation energy, the density of complex configurations
like 2p ? 2h, 3p ? 3h, etc., becomes higher. Accordingly,
the inelastic part of the absorption cross section increases
with the energy and smoothly merges with the low-energy
tail of the GDR. The inelastic cross section was also
measured directly by the decay of the low-lying 2þstates
to the ground state, which are known to collect most of the
inelastic transitions cascading from higher excitation en-
ergies. The elastic (???), inelastic (???0), and photoab-
sorption (??¼ ???þ ???0) cross sections for the
138Bað~ ?;?0Þ reaction below the neutron-separation energy
are shown in the upper panel of Fig. 2. These cross sections
include transitions from both 1?and 1þstates. The elastic
cross section, which is due to ground-state transitions,
shows resonancelike structures and dominates the nuclear
dipole response up to the neutron-separation energy. In
contrast, the inelastic cross section which is due to statis-
tical decays, shows an exponential increase with excitation
energy. The deduced photoabsorption cross section (??) is
shown in the lower panel of Fig. 2 in comparison to
experimental data for the
GDR region . As can be seen, for certain energies
below the neutron-separation energy (Sn) the photoabsorp-
tion cross section has values larger than the extrapolation
of the tail of the GDR implies.
We have performed microscopic calculations of low-
energy electric 1?and magnetic 1þdipole states in
138Ba, respectively, within the quasiparticle-phonon model
(QPM) approach  based on density functional theory,
138Bað?;xnÞ reaction in the
FIG. 1 (color online).
reaction observed in two vertical detectors (V) positioned at (?,
?) of (90?, 90?) and (90?, 270?), one in-plane backward-angle
detector (B) positioned at (?, ?) of (135?, 0?), and two hori-
zontal detectors (H) positioned at (?, ?) of (90?, 0?) and (90?,
180?). The energy distribution of the photon beam with a
centroid at 6400 keV is shown in the top panel.
Gamma-ray spectra of the138Bað~ ?;?0Þ
PRL 104, 072501 (2010)
PHYSICAL REVIEW LETTERS
19 FEBRUARY 2010
as discussed indetail inRefs. [14,15]. In the calculations of
the M1 strength, an effective spin giromagnetic factor
(2QP) QRPA calculations lead to a sequence of 1?states
in the energy range E?¼ 6:0–8:2 MeV. The structure of
these states is strongly dominated by the 2QP neutron
configurations formed by quasiparticle states from the 3s,
2d, 1g shells and the 3p, 2f shells, respectively. The
transition densities reveal an oscillation pattern typical
for PDR modes . The wave function of the magnetic
1þstates is dominated by 2QP spin-flip states. The lowest
tion strength BðM1;g:s: ! 1þ
contains proton 2QP spin-flip components connecting the
spin-orbit partners of the 2d shell (99%) with a minor
admixture of 1h-shell contributions (0.2%). The most sig-
is given by the 1þ
state at E?¼ 6:43 MeV with
BðM1;g:s: ! 1þ
proton 2QP components result from spin flip within the
1g shell (95.1%), and again with a small admixture from
the neutron 1h shell (4.8%), respectively. A large M1
strength associated with the maximum of the spin-flip
M1 strength is found close to the neutron-separation en-
ergy at E?¼ 8:7 MeV (see as well in ) with
BðM1;g:s: ! 1þ
neutron 2QP spin-flip components in the 1h shell (94%)
and a small amount of 1g-shell proton contributions (5%).
In Fig. 3 multiphonon results for the electric and mag-
netic photoabsorption cross sections are presented in com-
parison to the present experimental data for the 1?states in
s ¼ 0:6gs
1state is found at E?¼ 4:28 MeV with a transi-
1Þ ¼ 0:5?2
N. The state vector
2Þ ¼ 2:4 ?2
N, where the most important
3¼ 8 ?2
NÞ. It essentially consists of the
138Ba at E?< 8:5 MeV. The measured elastic E1 (open
histogram) and M1 (solid histogram) cross sections, inte-
grated over 200 keV bins, are shown in the upper part of
Fig. 3. As can be seen at excitation energies below the
particle emission threshold, the E1 transitions in138Ba are
distributed in a broad, resonancelike structure. The ob-
served concentration of 1?states is characterized by the
high level density which increases steeply towards the
threshold. In this connection, the multiphonon QPM cal-
culations which account for nonharmonic effects, are im-
portant for reproducing the fragmentation pattern. The
calculations show that the 1?QRPA states are fragmented
over 130 multiphonon states below E?¼ 8:5 MeV. This
agrees very well with the number of experimentally ob-
served 1?states in this energy range. In contrast, the
magnetic dipole transitions which result from the decay
of single-particle states, are much more isolated and they
are concentrated at well specified regions. For example, a
group of 1þexcited states, located at E?¼ 6–7:5 MeV, is
connected to the dissipation and fragmentation of the 1þ
QRPA state. Above 8 MeV the 1þstates are characterized
predominantly by multiphonon configurations, incorporat-
ing only a few percent of the strength of the 1þ
(indicating the maximum of the QRPA M1 strength). In the
energy range E?¼ 6–8:5 MeV 19 1þstates with transition
strengths larger than 0:05?2
comparison, theory predicts 15 such states.
In addition, the QPM calculations predict M1 strengths
smaller than 0:05?2
excitation energies E?< 8:5 MeV. In particular, an
amount of this strength is concentrated around 4 MeV.
These excitations are closely related to the fragmentation
of the 1þ
1QRPA state. The discrepancy between the pre-
Nhave been observed. For
Nand distributed in 58 1þstates with
FIG. 2 (color online).
(???0), and total absorption cross sections (??) in138Ba below
the one-neutron-separation energy (Sn¼ 8:6 MeV) averaged
over the beam energy spread of about 3%. The actual beam
energy spread is shown as horizontal bars. Lower panel: the
present total absorption cross section (??) is combined with the
(?, xn) data from the GDR .
Upper panel: Elastic (???), inelastic
FIG. 3 (color online).
calculations (lower panel) for E1 and M1 elastic scattering cross
sections in138Ba below 9.0 MeV. The cross sections are averaged
over 0.2 MeV energy bins.
Experimental (top panel) and QPM
PRL 104, 072501 (2010)
19 FEBRUARY 2010
dicted and observed M1 strength shown in Fig. 3 below Download full-text
6 MeV can probably be attributed to local fragmentation of
the strength into states that are too weak to be detected.
Overall, as summarized in Table I, the theoretical cal-
culations are in good agreement with the present E1 and
M1 data below the particle threshold, both with respect to
the mean excitation energy, defined as hEi ¼ ?EiBi=?Bi,
total strength ?Bi, and the isovector EWSR . However,
Fig. 3 and Table I also show that the theoretical strength
This shift can be traced back to a slightly too large spacing
of the theoretical 2QP spectrum, which in turn is probably
caused by an underestimation of core polarization effects,
although up to three phonon configurations are taken into
account already. Polarization self-energies acting directly
on the quasiparticle states may be required.
A common feature of 1?and 1þstates is that both
modes are excited by almost pure 2QP QRPA states.
They serve as doorway states which decay into multicon-
figuration states with complicated multiphonon wave func-
tions, thus giving rise to fragmentation of the spectral
distributions. Therefore, the fragmentation pattern, espe-
cially above 7 MeV, is not yet described in all details.
However, the basic mechanism responsible for a more
detailed fragmentation pattern is clear: it will eventually
be accomplished by further increase of the multiphonon
configuration space used in the QPM calculations.
The comparison of E1 and M1 strengths in the whole
energy range between 4 and 8.6 MeV shown in Fig. 3 leads
to the conclusion that E1 transitions clearly dominate M1
transitions by intensity and amplitude. The ratio of elastic
M1 and E1 cross sections is only 2.7 (0.8)%. This ratio is in
very good agreement (2.0%) with the theoretical calcula-
tions based on the QPM model, and presented in the
bottom panel of Fig. 3.
In conclusion, the systematic spin and parity measure-
ments on138Ba at the HI~ ?S facility have unambiguously
verified that the observed dipole strength from 4 MeV to
the neutron-separation energy is predominantly of electric
dipole nature. The fine structure of the M1 ‘‘spin-flip’’
mode was detected as well, for the first time in N ¼ 82
nuclei. Enhanced dipole strength above the Lorentzian
extrapolation of the GDR has been directly measured for
elastic and inelastic transitions below the neutron-
separation energy and found to be related to the dominance
of electric transitions. This strength falls into two catego-
ries: elastic, originated by the skin oscillation of the excess
neutrons against the proton-neutron saturated core, and
inelastic, due to states coupled to more complicated con-
figurations than 1p ? 1h states. Combining these two
strengths, they define the gross structure of the PDR reso-
nance which exhibits a resonancelike shape distribution
with pronounced peak structure above the low-energy
extrapolation of the GDR. According to the theoretical
model, electric and magnetic transitions are found to be
mechanisms. In order to determine the pure dipole strength
associated with the neutron skin phenomenon, the mag-
netic contribution must be identified and subtracted.
We are grateful to the HI ~ ?S staff for their delivery of
excellent photon beams. This research was supported by
the DOE Grants No. DE-FG02-97ER41033, No. DE-
FG02-97ER41041, No. DE-FG02-97ER41042, No. DE-
FG52-06NA26155, and DFG Grant No. Le439/6.
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E1 and M1 parameters deduced in138Ba below the neutron-separation energy in comparison with the QPM calculations.
?BðE1Þ " ½e2fm2?
?BðM1Þ " ½?2
a4:1 MeV < E?< 8:5 MeV.
PRL 104, 072501 (2010)
19 FEBRUARY 2010