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