Damping of giant resonances in extended RPA with ground state correlations
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Damping of giant Damping of giant resonances in extended resonances in extended RPA with ground state RPA with ground state
correlationscorrelations
Kyorin UniversityKyorin University Mitsuru TohyamaMitsuru Tohyama
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ContentsContents
Time-dependent density-matrix Time-dependent density-matrix theory (TDDM) and theory (TDDM) and its small-amplitude limit (STDDM)its small-amplitude limit (STDDM) Giant quadrupole resonance in Giant quadrupole resonance in 1616OO SummarySummary
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TDDM and STDDMTDDM and STDDM
)(|)1()2()'2()'1(|)():'2'121(
)(|)1()'1(|)():'11(
2 taaaattC
taatt
TDDM is an extended TDHF and gives time evolution of and C2
Time derivatives of and C2
),,(/
),()(|]),1()'1([|)(/
3222
21
CCFtCi
CFtHaatti
BBGKY hierarchy: S. J. Wang and W. Cassing, Ann. Phys. 159(1985)328
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),(/
),(/
222
21
CFtCi
CFti
Truncation C3=0 gives TDDM equations
Applications of TDDM GQR: M. Tohyama and A. S. Umar, Phys. Lett. B549 (2002)72 Fusion: Phys. Rev. C65(2002)037601
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Ground state: A stationary solution of TDDM eqs.
0)(
0),(/
0'
)(
0),(/
''''''''''
''2''
321'213
''
'1'
213321
321
HPBC
CnFtCi
vCCv
n
CnFtni
Born term Pair correlations p-h correlation
Time independent form of TDDM
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Iterative gradient method
M. Tohyama et al., Eur. Phys. J. A 21, 217(2004)
)(
)(
)(
)(
)1(
)1(
2
1
1
22
11
NF
NF
NC
Nn
NC
Nn
C
F
n
F
C
F
n
F
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Neglect of g.s. correlations: STDDM Second RPA
X
x
X
x
db
ca
STDDM: Linearization of TDDM eqs. for and C2
a, b and d contain n and C : g.s. correlations
Application of STDDM to 2+1 in oxygen isotopes
M. Tohyama et al., Prog. Theor. Phys. 114(2005)1021
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Giant quadrupole resonance in Giant quadrupole resonance in 1616OO
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Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790
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Effective interaction: Skyrme III Effective interaction: Skyrme III Single-particle states:Single-particle states: nn and and C C : 1p: 1p3/23/2, 1p, 1p1/21/2, 1d, 1d5/25/2
xxαααα’’ : 1s: 1s1/21/2 ~ 1f~ 1f5/25/2
XXαβααβα’’ββ ’ ’ : : 1p1p3/23/2, 1p, 1p1/21/2, 1d, 1d5/25/2
Calculational details
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Strength function for r2Y20
RPA
SRPA
STDDM
Reduced strength of SKIII
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STDDM and SRPA Only in STDDM
Damping processes
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Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790
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Strength function for r2Y20
RPA
SRPASTDDM
Original strength of SKIII
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SummarySummary
STDDM based on TDDM ground state STDDM based on TDDM ground state was presented. was presented.
STDDM is an ERPA with ground-state STDDM is an ERPA with ground-state correlations.correlations.
STDDM was applied to GQR in STDDM was applied to GQR in 1616O. O. STDDM gives larger fragmentation of STDDM gives larger fragmentation of
22++ states than SRPA. states than SRPA. →→Importance of ground-state Importance of ground-state
correlationscorrelations
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Ground state of 16O
Etot(MeV) = EMF + Ecor
= -122.4 -12.5 = -134.9 < EHF= -130.8
1p1p3/23/2 1p1p1/21/2 1d1d5/25/2
nn 0.950.95 0.930.93 0.060.06
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QuadrupoleQuadrupole states in states in 1616OO
Experiment*Experiment* STDDMSTDDM
E (MeV)E (MeV) B(E2) (eB(E2) (e22fmfm44)) E (MeV)E (MeV) B(E2)B(E2)6.926.92 3636±4±4 5.05.0 7.87.8
9.859.85 0.670.67±0.27±0.27 9.4, 9.79.4, 9.7 11.811.8
11.5211.52 25.6725.67±2.83±2.83 12.012.0 17.217.2
13.1513.15 13.813.8 12.912.9 17.817.8
15.1515.15 8.18.1±4.1±4.1 15.415.4 1.81.8
16.4616.46 2.72.7±0.9±0.9 16.3, 16.716.3, 16.7 6.86.8
18.518.5 5.15.1±0.5±0.5 18.5, 19.418.5, 19.4 3.03.0
20-3020-30 2020±8±8 20-3020-30 5454
*A. Hotta et al., Phys. Rev. Lett. 33 (1974) 790.*A. Hotta et al., Phys. Rev. Lett. 33 (1974) 790.
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Relation to HFB and QRPARelation to HFB and QRPA
*'''' C
M. Tohyama and S. Takahara: Prog. Theor. Phys. 112, 499 (2004)
*'''''' X