Transcript Slide 1

Excitation and decay of Isoscalar
Giant Dipole Resonance
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Introduction on Giant Resonance
A schematic model of GR
Excitation of ISGDR in 58Ni (a, a`) reaction
Experimental details
Data Analysis
Results and discussions
Summary and conclusions
Giant Resonance: Coherent vibration of nucleons
in a nucleus.
A Schematic Model of GR:
The H0 to denote the Hamiltonian operator of a nucleon in the central potential of
the single particle shell model. In the transition of the particle from a full shell to the
one above , we must also take the particle-hole interaction into account ; the
Hamiltonian operator then be written as
The collective excitations appear just because of the mixing generated by this
particle-hole interactions V.
Nucleus
Many body system with a finite size
Vibration
Multi-pole expansion with r, Ylm, t, s
DS=0, DT=0 DS=0, DT=1 DS=0, DT=1 DS=1, DT=1 DS=1, DT=1
L=0: Monopole
ISGMR
r2Y0
L=1: Dipole
L=2: Quadrupole
ISGDR
tY0
IVGDR
r3Y1
trY1
ISGQR
IVGQR
r2Y2
L=3: Octupole
IAS
LEOR, HEOR
rY3, r3Y3
tr2Y2
IVGMR
tr2Y0
tr3Y1
GTR
t s Y0
SDR
ts rY1
ts r2Y2
IVSMGR
t s r2Y0
ts r3tY1
Isoscalar Excitation Modes of
Nuclear Resonance
Giant Resonance: Coherent vibration of nucleons
in a nucleous.
Resonances due to imcompressibility :ISGMR,
ISGDR
EISGMR 
KA
m  r2 
EISGDR 
3 K A(27 / 25) F
7
m  r2 
K nm
 2 d 2 ( E / A) 
 9 

d 2    

0
Nuclear matter
102
29.5 MeV
101
100
10-1
10-2
0
2
4
6
c.m.
8
10
12
ISGMR, ISGDR
KVI (1977)
TAMU(2000)
Large instrumental background!
励起の弱いISGDRを議論する
には不十分。
D.H. Youngblood et al.,
RIKEN Rev. 23, 159(1999)
Y.-W. Lui et al., PRC 61,
067307 (2001)
Measurement Details
• 386 MeV a @RCNP
58Ni, 90Zr, 116Sn, Sm,
208Pb
• 0-13 deg (Angular
range)
• Elastic scattering :3.5-25 deg range.
Nucleus
Angles
(degree)
Excitation
energy(MeV)
58Ni
0-13
10-35-52
90Zr
0-13
10-35
116Sn
0-13
10-35
Sm
0-13
10-35
208Pb
0-13
10-35
RCNP
Ea=386 MeV
DEa = 250 keV@FWHM
Halo free beam
~10 counts/ 1nA
@ empty target, 0degs.
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• RCNP facility
K=400 MeV ring cyclotron
Grand Raiden spectrometer
• Beam：
– 4 He++, 386 MeV
• Target:
58Ni
foil 5.8mg/cm2
GRAND RAIDEN SPECTROMETER
Instrumental Background
VDC Y-position
Typical Spectra
Excitation Energy Spectra at 0o
Angular Distribution
Excitation Energy Spectrum
Multipole decomposition analysis (MDA)
 d 2s


(c.m. , E ) 
 ddE

ex.
 d 2s


(c.m. , E ) 
 ddE

ex.
calc
 d 2s

  aL ( E )
(c.m. , E ) 
d

dE
L

L
: Exprimenta
l cross section
calc
 d 2s


(c.m. , E ) 
: DWBA cross section(unit cross section)
d

dE

L
aL ( E ) : EWSR fraction
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DWBA 計算 ・・・ Ptolemy
Folding Model
DWBA Formalism:
Transition Potential:
U (r , E )   d r '  L (r ' , E )[V (| r  r ' |, 0 (r ' ))  0 (r ' )
U (r )   d r 'V (| r  r ' |, 0 (r ' ))0 (r ' )
V (| r  r ' |,  (r ' ))
0 (r ' )
Transition density
• ISGMR G.R.Satchler, Nucl, Phys, A472 (1987) 215
 0 (r , E )  a 0 [3  r
d
] 0 ( r )
dr
2 2
a 
m A r 2  E
2
0
• ISGDR M.N.Harakeh, Phys. Rev. C23 (1981) 2329
1
d
5
d
d2
d
2
1 (r , E )  
[3r   10r   r    (r 2  4 )] 0 (r )
dr
3
dr
dr
dr
R 3
2
R2
2 6
 1
m AE (11  r 4  (25 / 3)  r 2  2 10  r 2 )
2
• Other modes Bohr-Mottelson(BM) model
d
 0 (r )
dr
l (2l  1) 2 2 2  r 2l 2 
2
2
 L (  L c) 
(l  2) 2 m AE  r l 2  2
 L (r , E )   L
58
Ni
Transverse flow
SN1987A
CONCLUSIONS
. A two component ISGDR strength distribution
has been obtained for the first time in 58Ni
ISGDR strength distribution is in excellent
agreement with recent QRPA predictions.
 The value of incompressibility of infinite nuclear
matter( Knm ) is 217 MeV as obtained from global
systematic of present study.