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Pygmy dipole resonance
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2014 J. Phys.: Conf. Ser. 533 012028
(http://iopscience.iop.org/1742-6596/533/1/012028)
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XX International School on Nuclear Physics, Neutron Physics and Applications (Varna2013)
IOP Publishing
Journal of Physics: Conference Series 533 (2014) 012028
doi:10.1088/1742-6596/533/1/012028
Pygmy dipole resonance
Vladimir Ponomarev
Institut f¨
ur Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, 64289 Darmstadt, Germany
E-mail: [email protected]
Abstract. The pygmy dipole resonance (PDR) is a low-energy debris of the 1¯
hω E1-strength
which is pushed by an isovector residual interaction to higher energies to form the giant dipole
resonance. It exhausts about 1% of the EWSR below the particle threshold. High energy
resolution experiments performed during the last decade reveal fine structure of the PDR
in many nuclei. We report on the studies of the PDR fine structure performed within the
Quasiparticle-Phonon model. Excited states are described by a wave function which includes
one-, two-, and three-phonon configurations, i.e. the configuration space in calculations below
the threshold is almost complete. We discuss also some particular features of the PDR excitation
in different nuclear reactions.
A low-energy dipole strength below the threshold has been observed for the first time in
experiments with tagged photons (see, e.g., [1]) in the late 70-ies. It was observed as a kind of
a bump on top of the tail of the giant dipole resonance and received the name of the “pygmy
dipole resonance” (PDR). Theoretical calculations of those days also reported substructures
at low energies [2]. With a new generation of germanium detectors it became possible in the
late 90-ies to resolve the fine structure of the PDR establishing that many dozens of 1− states
are excited in the nuclear resonance fluorescence (NRF) experiments to form the PDR [3, 4].
During the last decade the properties of the PDR have been studied within many different
theoretical approaches. In my talk I limit the presentation by only the results obtained within
the quasiparticle phonon model (QPM) [5].
From the theoretical point of view, the PDR may be considered as a low-energy debris of
the 1¯hω E1-strength which is pushed to higher energies by an isovector residual interaction
forming the giant dipole resonance (GDR) (see figure 1). As figure 2 demonstrates, while many
two-quasiparticle configurations contribute coherently to the E1 transition matrix element of a
state belonging to the GDR, we deal with a destructive interference in the case of a PDR state.
The process of the strength fragmentation in the PDR energy region is demonstrated in
figure 3 for 136 Xe. The major part of the E1 strength below the threshold is carried by a
few QRPA (or one-phonon) states (figure 3a). These states are coupled to more complex
configurations. Theoretically, to describe this process we write the wave function of excited
states as a composition of one-, two-, etc. phonon configurations and diagonalize the model
Hamiltonian to obtain the eigenstates. Calculation performed on the basis of one- and twophonon configurations is presented in figure 3b. In this calculation each 1− state carries only
a small fraction of one-phonon configurations and accordingly, its B(E1) value is much smaller
than in figure 3a. At the same time, the total B(E1) strength does not change much for the
PDR energy region. The fragmentation process continues when three-phonon configurations are
added to the wave function (figure 3c). One should keep in mind that the density of four-, five-,
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1
XX International School on Nuclear Physics, Neutron Physics and Applications (Varna2013)
IOP Publishing
Journal of Physics: Conference Series 533 (2014) 012028
doi:10.1088/1742-6596/533/1/012028
15
136
Xe
140
<1 || E1 || 0gs >, e fm
mean field
+ BCS
5
Ce
4
PDR
GDR
0
QRPA
1
2
0
1
-1
-
10
5
2
3
+
2
2
B(E1) (e fm )
10
0
-2
6
0
0
5
10
15
Ex (MeV)
20
8
10
12
14
16
6
8
E, MeV
25
10
12
14
16
E, MeV
Figure 2. Running sum of the E1 transition matrix
element for a state belonging to the GDR and PDR.
Vertical lines present contribution of different twoquasiparticle configurations to the matrix element.
Figure 1. E1-strength distribution
in 136 Xe calculated in the mean field
and QRPA approximations. Dashed
line shows 1¯
hω energy.
etc. phonon configurations is still very low below the threshold. It means that calculation in
figure 3c is performed on almost complete basis of states for this energy region.
In addition to 1− states, 1+ states are also excited by an electromagnetic probe below the
threshold. The later are either isoscalar 1+ states or the ones belonging to the tail of the M1
resonance (see figure 4).
a) Σ B(E1) =0.84e fm
2
2
136
Xe
0.04
B(E1 ) (e fm )
0.4
60
0.03
Ni
0.02
1
2
2
0.2
b) Σ B(E1) =0.90e fm
2
0.06
2
0.01
2
2
B(E1) [e fm ]
0
-
0
1
2
B(M1 ) (µ N)
0.03
0
c) Σ B(E1) =0.90e fm
2
0.04
2
1
+
0.5
0.02
0
4
0
4
5
6
7
Energy [MeV]
6
8
10
12
14
Ex (MeV)
8
Figure 4. Fragmentation of the E1 and
M1 strength in 60 Ni. Oval marks the energy
interval which is typically covered in NRF
experiments.
Figure 3. Fragmentation of the PDR in
136 Xe. Calculations are performed: a) within
the QRPA, and with coupling to b) two- and
c) two- and three-phonon configurations.
2
XX International School on Nuclear Physics, Neutron Physics and Applications (Varna2013)
IOP Publishing
Journal of Physics: Conference Series 533 (2014) 012028
doi:10.1088/1742-6596/533/1/012028
Experiment
QPM
120
80
136
Xe
40
0
120
138
Ba
2
40
-3 2
B(E1)[10 e fm ]
80
0
120
140
Ce
80
40
0
120
142
Nd
80
40
0
120
144
Sm
80
40
0
0
10
20
30
40
-3 2
50
60
2
B(E1)[10 e fm ]
Figure 6. Fragmentation in the experimentally observed distribution and within the
QPM for the N = 82 isotones.
Figure 5. Fragmentation of the PDR in Sn
isotopes.
The QPM calculations of the PDR have been performed for nuclei belonging to different
parts of the nuclei chart: Cr-Fe-Ni [6, 7, 8], Zr-Mo [9] regions, Sn isotopes [4, 10, 11], N=82
isotones [12], and Pb isotopes [13]. The model describes rather well fragmentation of the E1
strength in the PDR region (see, e.g., figures 5 and 6) when almost complete basis of complex
configurations is employed. In addition to many observed 1− states it predicts many more weak
1− states below detection limit (see left part of figure 6).
The PDR has been recently studied in (α, α0 γ) reaction [11, 14]. A good correspondence
between the levels observed in this reaction with the (γ, γ 0 ) data has been established for the
low energy part of the PDR. But no 1− levels have been detected in the (α, α0 γ) reaction at
higher excitation energy. Calculation in figure 7 also predicts that excitation of the low energy
part of the PDR by the isoscalar r3 Y1 external field which mimics (α, α0 ) reaction, is enhanced
in comparison to the excitation by the electromagnetic field. Analysis of transition densities
indicate that their tails out of nucleus are responsible for this enhancement.
The PDR has been also observed in the (p, p0 ) reaction at small scattering angles [15].
To extract information on 1− states in the energy region of overlapping levels the multipole
decomposition analysis (MDA) has been performed. The spectrum has been split into energy
bins of about 100 keV and the cross section behaviour in each of them has been fit assuming
contribution from 1− , 1+ , and 2+ levels (see figure 8 top). For 1− levels cross sections have
been calculated with the PDR and GDR wave functions. It has been found that the best χ2 fit
for the low energy part of the spectra is obtained with the PDR wave function while at higher
energies the GDR wave function gives better results (see figure 8 bottom).
A new direction in the PDR studies concerns its decay properties. In analysis of the NRF
spectra branching ratios to low-lying states are often neglected. Nevertheless, decays into them
have been observed (see, e.g., [7]).This type of studies allows not only to correct extracted from
3
XX International School on Nuclear Physics, Neutron Physics and Applications (Varna2013)
IOP Publishing
Journal of Physics: Conference Series 533 (2014) 012028
doi:10.1088/1742-6596/533/1/012028
electromagnetic
140
Ce
0.06
2
2
Bem(E1) (e fm )
0.08
0.04
0.02
isoscalar
1500
2
6
Bis(E1) (e fm )
0
1000
500
0
4
5
6
7
Ex (MeV)
8
Figure 8. Examples of the MDA fits for two
adjacent energy bins (top) and best χ2 values
in the MDA using either PDR- or GDR-type
angular distributions for excitation energies
Ex = 7 to 9 MeV (bottom).
Figure 7. Electromagnetic and isoscalar
response for 1− states in 140 Ce.
NRF data B(E1) value but also investigate coupling of doorway 1− states to some particular
complex configurations.
Acknowledgments
I thank my colleagues experimentalists for fruitful many years collaboration on this topic. This
work has been supported by the DFG through the grant SFB 634.
References
[1] Laszewski R M 1986 Phys. Rev. C 34 1114; Laszewski R M and Axel P 1979 Phys. Rev. C 19 342
[2] Soloviev V G, Stoyanov Ch and Voronov V V 1978 Nucl. Phys. A 304 503
[3] Herzberg R-D et al 1997 Phys. Lett. B 390 49
[4] Govaert K et al 1998 Phys. Rev. C 57 2229
[5] Soloviev V G 1992 Theory of Atomic Nuclei, Quasiparticles, and Phonons (IOP, London)
[6] Bauwens F et al 2000 Phys. Rev. C 62 024302
[7] Scheck M et al 2013 Phys. Rev. C 87 051304; Scheck M et al 2013 Phys. Rev. C 88 044304
[8] Pai H et al 2013 Phys. Rev. C 88 054316
[9] Romig C et al 2013 Phys. Rev. C 88 044331
¨
[10] Ozel
B et al 2009 arXiv:0901.2443
[11] Endres J et al 2010 Phys. Rev. Lett. 105 212503; Endres J et al 2012 Phys. Rev. C 85 064331
[12] Savran D et al 2008 Phys. Rev. Lett. 100 232501; Savran D et al 2011 Phys. Rev. C 84 024326
[13] Enders J et al 2003 Nucl. Phys. A 724 243
[14] Savran D et al 2006 Phys. Rev. Lett. 97 172502
[15] Tamii A et al 2011 Phys. Rev. Lett. 107 062502; Poltoratska I et al 2012 Phys. Rev. C 85 041304
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