NITheP WITS node seminar: Prof. V. Yu. Ponomarev (Technical University of Darmstadt, Germany) TITLE: "Pygmy dipole resonance in atomic nuclei"

Pygmy dipole resonance in atomic nuclei
V.Yu. Ponomarev
Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
V.Yu. Ponomarev (TU Darmstadt) 13.05.2014 1 / 31

Outline
Introduction
Quasiparticle-phonon model
Basic of pygmy resonance
Low lying E1 strength in Ni, Sn, N=82 isotones, and Pb
Excitation of pygmy in (α, α ) reaction
Excitation of pygmy in (p, p ) reaction
1−
states in (e, e ) scattering

cen-
is
ner-
ion
to
airs
ons
are
rom
rror
zing
cat-
of
by
on
phi-
ries
sses
and
bove
100
the
Z
ion
be
end
ion
tten
(5)
gen
cen-
is
ded
ely
ergy
NA dE
Figure 7 shows the analysis of the data for
uranium. It is evident that the cross section for
photo-fission must be extremely small for
quantum energies above 30 Mev. The resulting
curve of 0 (E) vs. E is given in Fig. 8 for uranium.
0'a to "cM',
7
0 20
E, Msv
30
FrG. 8. Cross section for photo-fission of uranium.
Because of approximations made in the analysis and
uncertainty of the experimental data for low x-ray energies,
this curve must be considered of only qualitative sig-
nificance.
The determination of the cross section in-
volves first drawing a smooth curve through the
experimental points, multiplying the ordinates
of this curve by a function known only roughly, ,
and then differentiating the product; It is evident
that the given data are not sufficiently precise
to determine the cross section as a function of
energy, even if the calculation of r(E) were
exact, since in this case the portion of the yield
curve which is most significant to the deter-
mination of the cross section is that below 30
Mev. The experimental points in this region are
subject to considerable Huctuation, and the true
yield curve may be appreciably different from
G.C. Baldwin and G.S. Klaiber,
Phys. Rev. 71 (1947) 3
EGDR ∝ 80 · A−1/3
MeV

R. M. Laszewski and P. Axel

Cologne, Darmstadt, Gent

QPM Hamiltonian : H = Hs.p. + Hpair + Hres
Hs.p. − Woods − Saxon,
Hpair = −G0
jj mm
a†
jma†
j−maj −m aj m
Hres = −
λµ
(κis + κiv τ1τ2)M†
λµMλµ;
M†
λµ =
jj mm
jm|iλ
Rλ(r)Yλµ|j m a†
jmaj m

I. BCS: a†
jm → α†
jm
α†
jm = uj a†
jm + vj aj ˜m αj ˜m| g.s = 0
II. QRPA: [α†
jmα†
j m ]λµ → Q†
λµ
Q†
λµi =
N,Z
jj
Xλi
jj [α†
jmα†
j m ]λµ + Yλi
jj [αjmαj m ]λµ Qλµi | g.s = 0
III. Coupling to complex conﬁgurations:
|Ψν
J =
Ji
Rν
Ji Q†
Ji +
12
Pν
12[Q†
1Q†
2]J +
123
Tν
123[Q†
1Q†
2Q†
3]J | g.s
1 (2, 3) = {λi}

Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
Q
+
0
0ν ν1
ν2
ν
ν
ν1
ν2
ν1
ν2
ν3
ν4
ν5
ν1
ν2
ν1
ν2 ν3
ν1
ν2
ν3
ν4
ν5
Pauli principle corrections: exact [Q+
λ1µ1i1
, Qλ2µ2i2
]
Large s.p. basis, easy control of truncations

0
5
10
15
0 5 10 15 20 25
Ex
(MeV)
0
5
10
B(E1)(e
2
fm
2
)
136
Xe
mean field
+ BCS
QRPA

-0.1
0
0.1
PDR
neutron
protons
-15 -10 -5 0 5 10 15
Axial distance (fm)
-0.5
0
0.5
r
2
(r)(efm
-1
)
GDR
208
Pb

B(E1, Ex ) ∼
(Ejj ≤Ex )
jj
(Xjj + Yjj ) j ||E1||j
2
Ejj = εj + εj
10 20 30
Ex
(MeV)
0
10
20
B(E1)(e
2
fm
2
)
GDR
PDR
non-collective
124
Sn

B(E1, Ex ) ∼
(Ejj ≤Ex )
jj
2
Ejj = εj + εj 0
2
4
B(E1)(e
2
fm
2
)
10 20 30
Ex
(MeV)
0
10
20 GDR
PDR
non-collective
124
Sn

B(E1, Ex ) ∼
(Ejj ≤Ex )
jj
2
Ejj = εj + εj
0
0.2
0.4
0
2
4
B(E1)(e
2
fm
2
)
10 20 30
Ex
(MeV)
0
10
20 GDR
PDR
non-collective
124
Sn

0
0.2
0.4
a)
136
XeΣ B(E1) =0.84e
2
fm
2
0
0.03
0.06B(E1)[e
2
fm
2
]
b)Σ B(E1) =0.90e
2
fm
2
4 5 6 7 8
Energy [MeV]
0
0.02
0.04 c) B(E1) =0.90e
2
fm
2
Σ

0
0.01
0.02
0.03
0.04
B(E1)(e
2
fm
2
)
4 6 8
Ex
(MeV)
0
0.5
1
B(M1)(µ
2
N
)
60
Ni
1
-
1
+
60
Ni 1
-
68
Ni

0
0.01
0.02
0.03
0.04
B(E1)(e
2
fm
2
)
4 6 8 10 12 14
Ex
(MeV)
0
0.5
1
B(M1)(µ
2
N
)
60
Ni
1
-
1
+
60
Ni 1
-
68
Ni

0
0.01
0.02
0.03
0.04
B(E1)(e
2
fm
2
)
4 6 8 10 12 14
Ex
(MeV)
0
0.5
1
B(M1)(µ
2
N
)
60
Ni
1
-
1
+
5 10 15 20
Ex
(MeV)
0
0.1
0.2
0.3
0.4
B(E1)(e
2
fm
2
)
60
Ni 1
-
68
Ni

0
0.05
0.1
4 6 8 10 12 14
Ex
(MeV)
0
0.05
0.1
B(E1)(e
2
fm
2
)
60
Ni 1
-
68
Ni

0
20
40
60
Experiment
136
Xe
0
20
40
60
138
Ba
0
20
40
60
B(E1)[10
-3
e
2
fm
2
]
140
Ce
0
20
40
60
142
Nd
0
20
40
60
2000 4000 6000 8000
E [keV]
144
Sm
QPM
136
Xe
138
Ba
140
Ce
142
Nd
2000 4000 6000 8000 10000
E [keV]
144
Sm

0.0
0.2
0.4
0.6
0.8
1.0
1.2
B(E1)[e
2
fm
2
]
1.521.461.411.371.32
N/Z
136
Xe
138
Ba
140
Ce
142
Nd
144
Sm
..
...
.Experiment
QPM
QPML
EX < 8.02 MeV
0
10
20
30
40
B(E1)[10
-3
e
2
fm
2
]
Exp.a)
0
10
20
30
40
B(E1)[10
-3
e
2
fm
2
]
2000 3000 4000 5000 6000 7000 8000 9000
Energy [keV]
2000 3000 4000 5000 6000 7000 8000 9000
QPMa)
Sn

0
40
80
120 136
Xe
Experiment
QPM
0
40
80
120 138
Ba
0
40
80
120
B(E1)[10
-3
e
2
fm
2
]
140
Ce
0
40
80
120 142
Nd
0
40
80
120
0 10 20 30 40 50 60
B(E1)[10
-3
e
2
fm
2
]
144
Sm

140
Ce

0
0.01
0.02
0.03
0.04Bem
(E1)(e
2
fm
2
)
124
Sn
electromagnetic
3 4 5 6 7 8 9
Ex
(MeV)
0
500
1000
1500
Bis
(E1)(e
2
fm
6
)
isoscalar
0
0.02
0.04
0.06
0.08
Bem
(E1)(e
2
fm
2
) 4 5 6 7 8
Ex
(MeV)
0
500
1000
1500
Bis
(E1)(e
2
fm
6
)
140
Ce
electromagnetic
isoscalar
electromagnetic: eN = −Z/A, eZ = N/A
isoscalar: eN = eZ = 1

I1(r) =
r
0
ρem
1−
i
(r)r3
dr I3(r) =
r
0
ρis
1−
i
(r)r5
dr
-0.4
-0.2
0
0.2
I1
(r)[efm]
neutrons
protons
0 5 10
r [fm]
0
20
40
I3
(r)[efm
3
]
0 5 10 15
Ex
= 7.133 MeV Ex
= 8.580 MeV

P. Papakonstantinou

20 40 60 80 100
Ee
[MeV]
10
-7
10
-6
10
-5
10
-4
dσ/dΩ[fm
2
/str]
1
-
(pygmy)
1
+
iv
1
+
is
2
-
@7.943MeV
2
-
@8.426MeV
208
Pb(e,e’), θ = 175
o

0
2
4
6
8
Γg.s.
(eV)
5 6 7 8
Ex
(MeV)
0
2
Γ2
+
1
(eV)
140
Ce (1
-
states)
0
10
20
30
40
Γg.s.
(eV)
8 10 12 14
Ex
(MeV)
0
10
Γ2
+
1
(eV)
60
Ni (1
-
states)
1−
i → 2+
1 , [1−
i ⊗ 2+
1 ]1− → 2+
1 , [λπ1
1i ⊗ λπ2
2j ]1− → 2+
1

NITheP WITS node seminar: Prof. V. Yu. Ponomarev (Technical University of Darmstadt, Germany) TITLE: "Pygmy dipole resonance in atomic nuclei"

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NITheP WITS node seminar: Prof. V. Yu. Ponomarev (Technical University of Darmstadt, Germany) TITLE: "Pygmy dipole resonance in atomic nuclei"