2005. 9. 20, Varna

Sum Rules in Relativistic Nuclear Models-- Roles of Anti-nucleon Degrees of Freedom -Haruki Kurasawa (Chiba Univ.) , Toshio Suzuki (Fukui Univ. )Introduction
Main Difference Between Rel. Models and Non-Rel. Models
Anti-nucleons N
Model-independent Sum Rules
are useful for the study of their Roles.

Naïve Relativistic Correction

vF2 ~ 10 %Correction to Sum Rules comes from the fact that
the Complete Set is composed ofNucleon and Anti-nucleon Sectors.
If there is correction, we have to study
the coupling of p-h states with N-N states.
Vacuum polarization
If there is Divergence , we have to study
Renormalization.

1. Gamow-Teller Sum Rule

Model-independent

1-1 Non-Relativistic Models
1-2 Relativistic Models
1) Mean Field ApproximationNaïve Relativistic Correction2) RPA
Coupling with NN states
Renormalization of the Divergence
2. Dirac Sea Effects on Other Quantities
3. Conclusions
Challenge in the Future

1 Gamow-Teller Sum Rule
1-1

3
( Ikeda-Fujii-Fujita Sum Rule).

N>Z

1-2 Relativistic Models

Γ＝γ５γｙ τ±1) Mean Field ApproximationNaïve Relativistic Correction
A+(∞-B)β--(∞-C)
β+ＰN

ＤｉｒａｃNＰNaïve Correction

M* = M – Us ( Lorentz scalar Potential)

ββ+ｔｅｉｎｉｆＩｎ

infinite.

Pauli blocking terms give Rel. correction.

Na ï v e Reｌ(N-Z)-e . Correction
xpansionH. Kurasawa, T. Suzuki and N. V. Giai, Phys. Rev. Lett. 91, 062501 (2003),
H. Kurasawa, T. Suzuki and N. V. Giai, Phys. Rev. C68, 064311 (2003)
H. Kurasawa and T.Suzuki, Phys. Rev. C69, 014306 (2004)

GT strengths in 48Ca

14.997 / 16 = 0.937

6.3%
H.Kurasawa, T. Suzuki and N.V. Giai, Phys. Rev. C68, 064311(2003) , NL-SH

90Zr

7.7%
208 Pb 8.4%

Z.Y. Ma, B.Q. Chen N.V. Giai and T. Suzuki,Eur.Phys. J. A20, 429 (2004) , NL3

M* in finite nuclei is larger than in nuclear matter.

Relativistic correction is not negligible.
6 ～ 8 % quenchingThis means thatthe coupling of the p-h states and NN statesshould be examined.
Because1) The total strength of NN is infinite.
2) Recent Exp. has observed 12 ± 6±5 % quenching.
K. Yako et al., Phys. Lett. B615 (2005) 193

2) RPA with Renormalization in Nuclear MatterA
Π（A，B)

βNｐＮｈＰ
B

Model :NCoupling① Interaction② Renormalization

ＤｉｒａｃN① Interaction

T. Maruyama, H. Kurasawa, and T. Suzuki, nucl-th/0404074l ;Prog. Theor. Phys. 113, 355 (2005)

Excitation Energy and Strength of the GT state

NN EffectNaïve Reｌ. Correction

DivergenceComment on No-Sea Approximation∞B

Free TermPauli Blocking Terms

DivergentFermi Sea

Fermi Sea

=Dirac Sea

Dirac Sea

Dirac SeaZ. Ma, B. Chen, N.V. Giai and T. Suzuki, Eur. Phys. J. A 20, 429(2004)

No-Sea RPA
Divergence is neglected.
NL3+ g’+Vπ+Vρ
(g’ = 0.6 )９４ ％ StrengthNo-sea RPA
Ma et al.

No-sea RPA

Sum of the Energy-weighted Strengths

Ma et al.

RPA

Excitation Energy and Strength of the GT state

NN EffectNaïve Reｌ. Correction

Divergence② Renormalization method(nG. ‘t Hooft and M. Veltman, N.P.B44 (1972) 189

4)
Medium effect

Counter Terms
T. Maruyama, H. Kurasawa and T.Suzuki, to be published.
H. Kurasawa and T. Suzuki, Invited Paper , to be published.

No sea approx.

No sea approx.

No quenching2 Dirac Sea Effects on Other Quantities
RPA in the Full Spacewith Renormalization
How is the Effect of the Renormalization
important for Observables ?

It depends on Observables.

1.

No-Sea4. Dirac Sea Effects on 0+

No-Sea3. Conclusions
The renormalization is necessary .
The No-Sea Approximation is not justified sometimes.

Future Problems for Rel. Models :How do we renormalize other divergences ?
Which is a real phenomenological model, Rel. or Non-Rel. Model ?