damping of giant resonances in extended rpa with ground state correlations
DESCRIPTION
Damping of giant resonances in extended RPA with ground state correlations. Kyorin University Mitsuru Tohyama. Contents. Time-dependent density-matrix theory (TDDM) and its small-amplitude limit (STDDM) Giant quadrupole resonance in 16 O Summary. TDDM and STDDM. - PowerPoint PPT PresentationTRANSCRIPT
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
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
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
),(/
),(/
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
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
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
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
Giant quadrupole resonance in Giant quadrupole resonance in 1616OO
Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790
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
Strength function for r2Y20
RPA
SRPA
STDDM
Reduced strength of SKIII
STDDM and SRPA Only in STDDM
Damping processes
Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790
Strength function for r2Y20
RPA
SRPASTDDM
Original strength of SKIII
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
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
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.
Relation to HFB and QRPARelation to HFB and QRPA
*'''' C
M. Tohyama and S. Takahara: Prog. Theor. Phys. 112, 499 (2004)
*'''''' X