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 force
at 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.
The ab initio calculation by Argonne-Illinois group
Pion
70 ~ 80 %
R. B. Wiringa, S. C. Pieper, J. Carlson, and V. R. Pandaripande, Phys. Rev. C62(014001)
1p1/2
1p3/2
0g9/2
Single particle level energy (MeV)
0
0f5/2
-10
1s1/2
0f7/2
0d3/2
-20
-30
0d5/2
0p1/2
-40
0p3/2
0s1/2
-50
without pion
with pion
1h-state
1p-1h
2p-2h
2h-state
0.20
CPPRMF
RMF
-3
Proton density (fm )
0.15
0.10
0.05
0.00
0
1
2
r (fm)
3
4
4He
Relation between
pionic correlation
and kinetic energy.
16O
12C
Very important result given by projected chiral mean field model
High-momentum components are reflected in the wave function.
Particle states have a rather compact distribution comparing with
that of RMF solution without pionic correlation.
Intrinsic single particle-states are expanded in Gaussian basis.
Pionic energy systematics
Phys. Rev. C76, 014305(2007)
Introduction of higher-spin pion field
[MeV]
20 hard
core
0
VC
1
p
s+w
[3E]
VNN (r)
2
-20
r[fm]
VT
-40
-60
-80
r
p
Interaction range
Nuclear radius
-100
Acknowledgment to Professor K. Ikeda
Orbital angular momentum of single-particle state
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 s and w fields, we take the mean field approximation.
Matrix element
p-h transition density matrix element
E. Oset, H. Toki, and W. Weise, Phys. Rep. 83, 281(1981).
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 framework
in order to have significant wide variational space.
At this step the high-momentum components are included
due to pionic correlations.
Summary
1.The pionic correlation favors to including high-momentum components
due to the pseudo-scalar nature.
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.
As for the future subjects:
We should consider the relation between physical observables
and high-momentum components.
1. There are many tiny peaks.
p1/2 + s1/2
f5/2 + d5/2
Ground state = | 0p-0h > +
p3/2 + d3/2
28
20
f7/2 + g7/2
d3/2 + p3/2
s1/2 + p1/2
d5/2 + f5/2
Example
2. High-momentum component
Tiny peaks spread
in significant wide energy region.
We have to know the dependence of the
distribution pattern on the momentum space
where pionic correlation works.
p’) Ep = 200 MeV, q = 0 degree
(IUCF data, analyzed by Y. Fujita.)
48Ca(p,