1. Kyorin University Mitsuru Tohyama
Damping of giant resonances in extended RPA with ground state correlations
Kyorin University
Mitsuru Tohyama

2. Contents Time-dependent density-matrix theory (TDDM) and
its small-amplitude limit (STDDM)
Giant quadrupole resonance in 16O
Summary

3. TDDM and STDDM
TDDM is an extended TDHF and gives time evolution of r and C2
Time derivatives of r and C2
BBGKY hierarchy: S. J. Wang and W. Cassing, Ann. Phys.
159(1985)328

4. 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

5. Time independent form of TDDM
Ground state: A stationary solution of TDDM eqs.
Born term
Pair correlations
p-h correlation

6. Iterative gradient method
M. Tohyama et al., Eur. Phys. J. A 21, 217(2004)

7. STDDM: Linearization of TDDM eqs. for dr and dC2
a, b and d contain n and C : g.s. correlations
Neglect of g.s. correlations: STDDM Second RPA
Application of STDDM to 2+1 in oxygen isotopes
M. Tohyama et al., Prog. Theor. Phys. 114(2005)1021

8. Giant quadrupole resonance in 16O

9. Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790

10. Calculational details
Effective interaction: Skyrme III
Single-particle states:
　 n and C : 1p3/2, 1p1/2, 1d5/2
xαα’ : 1s1/2 ~ 1f5/2
Xαβα’β’ : 1p3/2, 1p1/2, 1d5/2

11. Strength function for r2Y20
RPA
SRPA
STDDM
Reduced strength of SKIII

12. Damping processes
STDDM and SRPA
Only in STDDM

13. Spectrum of electrons scattered from 16O
A. Hotta et al., Phys. Rev. Lett. 33(1974)790

14. Strength function for r2Y20
RPA
STDDM
SRPA
Original strength of SKIII

15. Summary STDDM based on TDDM ground state was presented.
STDDM is an ERPA with ground-state correlations.
STDDM was applied to GQR in 16O.
STDDM gives larger fragmentation of 2+ states than SRPA.
→Importance of ground-state correlations

16. Ground state of 16O na Etot(MeV) = EMF + Ecor = -122.4 -12.5
= < EHF=
1p3/2
1p1/2
1d5/2 na
0.95
0.93
0.06

17. Quadrupole states in 16O Experiment* STDDM E (MeV) B(E2) (e2fm4) B(E2)
6.92
36±4
5.0
7.8
9.85
0.67±0.27
9.4, 9.7
11.8
11.52
25.67±2.83
12.0
17.2
13.15
13.8
12.9
17.8
15.15
8.1±4.1
15.4
1.8
16.46
2.7±0.9
16.3, 16.7
6.8
18.5
5.1±0.5
18.5, 19.4
3.0
20-30
20±8 54
*A. Hotta et al., Phys. Rev. Lett. 33 (1974) 790.

18. Relation to HFB and QRPA
M. Tohyama and S. Takahara: Prog. Theor. Phys. 112, 499 (2004)