Upload
elizabeth-kirk
View
50
Download
3
Embed Size (px)
DESCRIPTION
PYGMY DIPOLE RESONANCE IN A SCHEMATIC MODEL. Andreea Croitoru University of Bucharest ROMANIA Bra ş ov 2014. For further information please see Prof. Virgil B ăran ’s presentation on T hursday. Collective motions in nuclei. GDR. Giant Dipole Resonance in N uclear Systems. protons. - PowerPoint PPT Presentation
Citation preview
PYGMY DIPOLE RESONANCE IN A SCHEMATIC MODEL
Andreea CroitoruUniversity of Bucharest
ROMANIA
Braşov 2014
Virgil Băran• University of Bucharest, Romania
Daniel Dumitru• University of Bucharest, Romania
Maria Colonna• Laboratori Nazionali del Sud, Catania, Italy
Massimo de Torro• Laboratori Nazionali del Sud, Catania, Italy
Virgil Băran• University of Bucharest, Romania
For further information please see Prof. Virgil Băran’s presentation on Thursday
Collective motions in nuclei
GDR
A Van der Wounde - "Electric and magnetic giant resonances in nuclei", pg 99
Giant Dipole Resonance in Nuclear Systems
])[(
4)(
22222
22
EEE
E
A
NZ
mc
eE
GDRabs
Photoreaction cross-section for Au (A=197)
MeVAEGDR3
1
80
protonsneutrons
R. A. Broglia , P. F. Bortignon, A. Bracco - Prog. Part. Nucl. Phys. (1992) 28,517
413. (1950) 5 h.Naturforsc Z. Jensen, J. ,Steinwedel A.
1046. (1948) 74 Rev. Phys.Teller, E.Goldhaber, M.
Macroscopic pictures for the Giant Dipole Resonance
Motivation • Information about the shapes of nuclei and excited states
• Information about the symmetry energy and EOS
• Influence in nucleosynthesis processes
• Relation with the neutron skin thickness
,221 1
22
A
i
A
ii
iSM r
K
m
pH
DCMpnSM HHHHH int_int_
N
ji
N
iiji
ji rrK
Nm
pp
1, 1,
22
)(22
1
2
)(
2
1
Z
ji
Z
iiji
ji rrK
Zm
pp
1, 1,
22
)(22
1
2
)(
2
1
22
22
1CMCM R
KAP
mA
22
22X
A
KNZP
mNZ
A
For
We can split
G-T macroscopic picture for GDR
therefore int int (R ) (X)n p CM
Proton sphere
Neutron sphere
pR
nR
XA
NZD
moment dipole The
np RRX
G-T macroscopic picture for GDR
pnX
,22
1 2202 X
MP
MH D
DD
3/13/10 8040 AExperimentMeVA
PROBLEMThe GDR described by
has
…but there is a problem
A
i
A
ii
iSM r
m
m
pH
1 1
220
2
22
Beyond Brink
22
20
2
2
)(
2
1X
Mm
MP
MH
DD
DD
1?
2D D
2 1/3 1/30 2
79.27 80DM A MeV Experiment Am
What if
We still can separate
G-T macroscopic picture for GDR
2 3
2 20
0
5(b )
: (b ) 32 , 1.2 ,
940MeV
sym potD
sym pot
M Am mr
with MeV r fm
m
Where the coupling parameter is related to the (potential) symmetry energy
PROBLEM
SOLVED
A
i
A
ii
iSM r
m
m
pH
1 1
220
2
22
, ,c e cN N N N Z
_ int _ int _ intc en n p CM c yH H H H H H
Considering three subsystems: neutron core,proton core, neutron in excess
we can still separate
into
But there are two problems…
A schematic model for PDR
xc
Y
2 220
2 2c c
c cc
P MH X
M
Core Hamiltonian:
2 20 2
2 2y y
yy
P MH Y
M
Pygmy Hamiltonian:
…first problem
PROBLEM
EPDR <10MeV
EGDR >15MeV
0 Both modes have energy !
5
33 3/2 2
0 0
5
3
54 ( )
3
n
p
R
e n n p np
R
N d r R R
obtained using Vlasov approach.
V. Baran et al, PRC (2013)
V. Baran et al
88, 044610
2012 85, 05160PRC 1 R
A
i
A
ii
iSM r
m
m
pH
1 1
220
2
22
,resV
?2
1
2
13
22
21 ycycres DDDDV
But what if
with
~ ; 1231
Solving the energy problem: Generalization of D-D residual
interaction
c c c ec y c
c
Z N Z ND D D X Y
A A
YCXYM
M
PX
M
M
PH cy
y
y
ycc
c
c
ccollective 222
0
2222
0
2
)(22
)(22
Core neutrons and protons sphere
Excess neutrons
Neutron sphere
Proton sphere
Core neutron sphere
Coupled modes
cX
pc nc
Yncpc,
22
21
3ycycMMC
2 21 1
2 22 2
( ( ) )
( ( ) X )
yc
cc
MX R X Y
CM
X R YC
BEHOLD :YCXY
M
M
PX
M
M
PH cy
y
y
ycc
c
c
ccollective 222
0
2222
0
2
)(22
)(22
22
22
2
222
121
1
21
2222X
M
M
PX
M
M
PH collective
122
221
22
22
21
23222
2220
2,
2,
20
22,1
)))((1(
4)(2
1
2
C
MMR yc
ycycyc
yc
A
ZNmM
A
ZNmM
ey
c
cc
12
321res
2.0 ; 62
1
2
1V
e
ycyycc
N
DDDDDD
Ni68
AGREEMENT WITH EGDR_exp=17.1 MeV, EPDR_exp=9.55 MeV (Rossi et al PRL(2013)242503)AGREEMENT WITH f2_exp=0.028 (Rossi et al PRL(2013)242503)
PREDICTS TWO NORMAL MODESX1: Xc and Y in phaseX2: Xc and Y out of phase
phase ofout Yand XC phase in Yand XC
The structure of the normal modes from Vlasov simulation (see V. Băran)
So…
• The EWSR exhausted by the pygmy mode overestimates the experimental data if Nc=Z
• But…For a more accurate picture we need microscopic self-consistent models
• A better result is obtained for a more stable core Nc>Z
• The HOSM+Vres is a useful tool in offering a microscopic description of the PDR and the GDR (centroid energy, sum rule) and a picture of nucleon vibrations in the PDR
A
ii
A
i
iSM r
K
m
pH
1
2
1
2
22
MODELSHELL OSCILLATOR HARMONIC
N
iin
Z
iip r
NRr
ZR
11
1;
1
CM Neutrons and Protons
NZCMnpCM PPPRNRZA
R
;1
N
iiN
Z
iiZ pPpP
11
;;
momenta Neutrons and Protons
NZnp P
NP
ZA
NZPRRX
11;
freedom of degrees Collective
MomentaConjugate and sCoordinate CollectiveNew
eccecc
cecc
cccc
Ne
NZc
ceynp
cc
cn
cc
c
NZnc
ne
pnp
Nc
Zcc
cccnpc
PN
PPAA
ANPRR
ZN
ZR
ZN
NY
PN
PZA
NZPR
N
NR
N
NRRRX
PN
PZA
ZNPRRX
1)(
1;
11;
11;
xc
Y
excess in neutrons
ofCM theand core ofCM thebetween distance theY
neutrons core
and protons core ofCM thebetween distance the
CX
excess in neutrons ofnumber theN
neutrons core ofnumber theN
e
c
freedom of degrees Collective
ycec
cc
cc DDYA
NZX
A
ZNX
A
NZD
DyDc
cey
c
ceyyy
ysmyi
yiyy
fNA
ZN
A
NZ
mc
e
NA
ZNDHD
c
e
DHDc
eDiE
c
edEE
20,,0
2
0,,02
140
4)(
2222
222
22
0
%1512
%5.193268
132
ye
ye
fNiN
fSnN
%5.55
%51068
132
ye
ye
fNiN
fSnN
1482 (1982) 49 PRL Bertsch,G.F. Gai, M.Alhassid, Y.
Molecular sum-rule for Pygmy Dipole Resonance
Applying the Thomas-Reiche-Kuhn sum rule 1
224m
c
eD
we obtain Dc
ey NA
ZN
XA
NZD 0|]],[,[|0
2
1,,,1 ySMyy DHDmwith and
A schematic model for PDR
A GENERALIZATION OF THE DIPOLE-DIPOLE RESIDUAL INTERACTION
ycyycc DDDDDD
321res 2
1
2
1V
ationdiagonaliza perform
modes two theof coupling the:an Hamiltoni theofpart collective The
~ ; 1231
energysymmetry theof dependenceDensity