We construct a relativistic framework which takes into pionic correlations(2p-2h) account seriously...

We construct a relativistic framework which takes into pionic correlations(2p-2h) account seriously from both interests: 1. The role of pions on nuclei. 2. The partial restoration of chiral symmetry in nuclear medium.

There are two strong motivations: 1. Ab initio calculation by Argonne-Illinois group. 2. Gamow-Teller transition strength distribution with high resolution at RCNP.

The pionic correlation(2p-2h) in the ground state produces the strong attractive forceat medium interaction range(~1 fm).

Our framework and its essential points to treat the pionic correlation explicitly. (spherical pion field ansatz)What we are doing now.(including the higher partial states of pions.)

Acknowledgments Y. O. is grateful to Prof. K. Ikeda, Prof. Y. Akaishi, Prof. A. Hosaka, Dr. T. Myo, Dr. S. Sugimoto for discussions on tensor force, pions and chiral symmetry. Y. O. is also thankful to members of RCNP theory group.

R. B. Wiringa, S. C. Pieper, J. Carlson, and V. R. Pandaripande, Phys. Rev. C62(014001)

Pion70 ~ 80 %

The ab initio calculation by Argonne-Illinois group

-50

-40

-30

-20

-10

0

Single particle level energy (MeV)

0s1/2

1s1/2

0p1/2

0p3/2

0d5/2

0d3/2

0f7/2

0f5/2

0g9/2

1p3/2

1p1/2

without pion with pion

1h-state

2h-state

1p-1h

2p-2h

0.20

0.15

0.10

0.05

0.00

Proton density (fm

-3)

43210

r (fm)

CPPRMF RMF

-300

-250

-200

-150

-100

-50

0

860840820800780760

Mass of σ ( )meson MeV

Total energy Central Potential Pion Potential Kinetic energy

280

230

180

330

380

130

80

16O

-220

-200

-180

-160

-140

-120

-100

860840820800780760

Mass of σ ( )meson MeV

280

260

300

320

340

360

380

Total Energy Central Potential Pion Potential Kinetic energy

12C

-60

-50

-40

-30

-20

-10

0

850800750700650

Mass of simga meson (MeV)

30

40

50

60

70

80

90

Total Energy Central Potentail Pion Potential Kinetic Energy

4HeRelation between pionic correlation and kinetic energy.

Particle states have a rather compact distribution comparing withthat of RMF solution without pionic correlation.

Intrinsic single particle-states are expanded in Gaussian basis.

High-momentum components are reflected in the wave function.

Very important result given by projected chiral mean field model

0.25

0.20

0.15

0.10

0.05

0.00543210

r (fm)

01s1/2-Proton 01p1/2-Neutron

01p1/2-Proton 01s1/2-Neutron

0.25

0.20

0.15

0.10

0.05

0.00543210

r (fm)

01s1/2Proton 01p1/2Neutron

01p1/2Proton 01s1/2Neutron

0.25

0.20

0.15

0.10

0.05

0.00543210

r (fm)

01s1/2Proton 01p1/2Neutron

01p1/2Proton 01s1/2Neutron

56

1

2

3

456

10

2

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

100Mass Number A

4He

12C

16O

28Si

40Ca

mσ = 777 MeV mσ = 800 MeV mσ = 840 MeV mσ = 850 MeV

56Ni A-2/3

Pionic energy systematics

Phys. Rev. C76, 014305(2007)

Nuclear radius

Interaction range

Orbital angular momentum of single-particle state

[3E]VNN (r)

[MeV]

-100

-80

-60

-40

-20

0

20 hardcore

VT

r[fm]

σ

1 2

VC

Acknowledgment to Professor K. Ikeda

Introduction of higher-spin pion field

G. E. Brown, Unified Theory of Nuclear Models and Forces, p.90(North-Holland Publishing Company, 1964).

Ground state wave function

We construct the 2p2h states using the RMF basis.

Hamiltonian

As for σ and fields, we take the mean field approximation.

p-h transition density matrix elementE. Oset, H. Toki, and W. Weise, Phys. Rep. 83, 281(1981).

Matrix element

Single-particle states given by RMF basis.

Radial parts are expanded in the Gaussian.

Energy minimization conditions

First minimization step

Second minimization step

This minimization is crucial important point in this frameworkin order to have significant wide variational space.At this step the high-momentum components are includeddue to pionic correlations.

Summary

2. The pions play the role on the origin of jj-magic structure.

3. The validity of above statement will be conformed theoretically by including the higher partial states of pions.

We should consider the relation between physical observables and high-momentum components.

As for the future subjects:

1.The pionic correlation favors to including high-momentum components due to the pseudo-scalar nature.

Example

48Ca(p, p’) Ep = 200 MeV, = 0 degree (IUCF data, analyzed by Y. Fujita.)

1. There are many tiny peaks.

Tiny peaks spread in significant wide energy region.

Ground state = | 0p-0h > +

2. High-momentum component

p1/2 + s1/2

f5/2 + d5/2

p3/2 + d3/2

f7/2 + g7/2

s1/2 + p1/2

d3/2 + p3/2

d5/2 + f5/2

28

20

We have to know the dependence of the distribution pattern on the momentum spacewhere pionic correlation works.