LBL 5/21/2007 J.W. Holt 1

Medium-modified NN interactions

Jeremy W. Holt*

Nuclear Theory Group

State University of New York

* with G.E. Brown, J.D. Holt, and T.T.S. Kuo

LBL 5/21/2007 J.W. Holt 2

Medium-modified

Microscopic Foundation for density-dependent interactions

Can such interactions provide a good description of nuclear systems?

LBL 5/21/2007 J.W. Holt 3

Chiral Effective Theories

(e.g. Hidden Local Symmetry)

Double Decimation

Match T and dependence with QCD Sum Rule correlation functions

Traditional OBE potentials (e.g. Bonn, Nijmegen, etc.)

EFT with intrinsic T and dependence

QCDChiral decimation

Fermi liquid decimation

Describe in a unified wayG. Brown and M. Rho,

Phys. Rept. 396 (2004)

(1) Finite nuclei (2) Nuclear matter (3) Hot/dense matter

Low-momentum interaction

Introduce medium modifications “by hand”

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CD-Bonn potential Nijmegen potentials

0(135), ±(140) 0(135), ±(140), (549), '(958)

1(500), 2(900) (760), a00(983), a0

±(983), f0(976)

0(770), ±(770), (782) 0(767), ±(768), (782), (1020)

In-medium modifications (T = 0, 0)

Change in mass at = 0 Theory Experiment Us

, ~ 10 – 15% decrease Yes Yes 15%

~ small increase Yes Yes 0%

~ 10% decrease Yes No 7%

Assume linear scaling:0

1*

Cm

m

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),'();;,'();,'( 22 kkkkkTkkkT klow

or for 0 k'kkVk klow

0 2222

kq

kTqqVkdqqPkVkkTk

klowklow

klowklow

RG and EFT

Traditional problem: Strong short distance repulsion

(a) G-matrix

Ge

QVVG

(b) Vlow-k

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Bare NN Potentials

Universal interaction for = 2.1 fm-1

k = 2.1 fm-1 Elab = 350 MeV

Integrate out the experimentally unconstrained part of the NN interaction

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Nuclear matter

Easier than finite nuclei (only one density)

Saturation (E/A, kF, K )

Hartree-Fock (preliminary)

Ring diagram expansion (preliminary)

Fermi liquid theory [JWH et al., NPA 785 (2007) 322.]

Outline of Results

Finite nuclei

Diminishing tensor force

Beta decay of 14C

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Saturation with low momentum interactions

Fixed cutoff in Hartree-Fock approximation(no saturation)

S. Bogner et al., NPA 763 (2005) 59.

Add leading order chiral 3N force

Empirical saturation energy and density

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Tensor force with dropping masses

rmT e

rmrmrmSm

frV

3

1

)(

1

)(

1

4)(

231221

2

rmT e

rmrmrmSm

frV

3

1

)(

1

)(

1

4)(

231221

2

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Novel saturation mechanism

Hartree-Fock+

Preliminary!

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Ring diagrams (pp)

3200 )(

3

1)(

2

1tr

2

1FVFVFVed

iE ipp

VGed

i

d

iE ppipp ),(tr

22

1 01

00

+ + +

Introduce model space m ~ 3.0 fm –1

Choose vlowk = m

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Preliminary!

[fm–1]

[MeV

]

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Expand:

kkk

k kkkkk,

)0( )()(),(2

1)( nnnE f

quasiparticle interaction

Quasiparticles defined only near Fermi surface: k kF 2)(

1~

Fkk

Strongly interacting, normal Fermi systems at T = 0

Weakly interacting quasiparticles

Fermi Liquid Theory

kkkkkkkk

kk

Vnn

E

)()(),(

f

Hartree-Fock 21

)()(2

1)( 21122121

kkk

knknkkkkVkkknkTkE

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Spin & Isospin Dependence:

Dimensionless parameters: lF

l fkm

F2

2

*

lll

lll

Pgg

Pff

)(cos),(

)(cos),(

k

k

kk

kk

Correspondence between FLP and observables

13

11 F

m

m

* 0

22

13

Fm

kF *

K 0

22

16

Fm

kF *

3/16

1

1

11

F

FFg p

l

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l l

l

l

l

lG

G

lF

F0

)12/(13

)12/(1

Pauli Principle Sum Rules:

l l

l

l

l

l

l

lG

G

lF

F

lF

F0

)12/(1)12/(1)12/(13

2

),( kkF ),( kkFd ),( kkFi +

Babu-Brown induced interaction

S. Babu and G. Brown, Ann. Phys. 78 (1973) 1

)0,()0,(1

9

)0,(1

3

)0,(1

3

)0,(1 0

20

0

20

0

20

0

20 qU

qUG

G

qUG

G

qUF

F

qUF

FFi

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Full Driving Induced

l F G F’ G’ F G F’ G’ F G F’ G’

0 -0.48 0.03 0.22 0.78 -1.28 0.14 0.37 0.64 0.80 -0.12 -0.15 0.14

1 -0.34 0.26 0.27 0.17 -0.53 0.26 0.28 0.13 0.20 0.01 0.00 0.05

Largest effect is to cut down the strong attraction in F channel

Rapid convergence of iteration scheme

Full Calculation:Driving Terms (Vlow-k CD-Bonn)Fd0= -1.20 Fd1= -0.50 Gd0= 0.14 Gd1= 0.24 F'd0= 0.35 F'd1= 0.26

G'd0= 0.60 G'd1= 0.12 Unstable (negative K )

Sum Rules: 2.51 S 6.32 S

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Nijmegen I Nijmegen II CD-Bonn Expt.

m*/m 0.887 0.930 0.888

K [MeV] 136 102 136 200-300

[MeV] 18.1 20.5 17.6 25-35

gl[N] 0.682 0.452 0.685 0.20-0.26

Sl 0.20 0.16 0.27

S2 -0.04 -0.02 -0.04

How to improve?

1. Explicit three-body forces

2. In-medium modifications to NN interaction

Medium modifications equivalent to a type of 3N force

Extend Walecka mean field theory to constituent quarks

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VNI VNII VN93 VCDB Exp.

m*/m 0.721 0.763 0.696 0.682

K [MeV] 218 142 190 495 200-300

[MeV] 20.4 25.5 23.7 19.2 25-35

gl[N] 0.246 0.181 0.283 0.267 0.20-0.26

Full many-body calculations )(

**

ng

g

m

m

A

A

N

N gA = 1.25

gA* = 1.00

242

2

NN

NN

g

g

9

2

2

NN

NN

g

g

quark model

Decreasing g2NN by 20% cuts

K by 50% but changes other observables by ~ 5%

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Finite nuclei

Decreasing tensor force necessary!

1. Decay of 14C

2. 0– T=1 and 0– T=0 splitting in 16O

3. E2 and M1 moments of 6Li

Traditional many-body effects or novel scaling mechanism?

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14C

14N

0+

1+

03

01 PySx

13

11

13 DPS

01,00,12

TJTJ

2 holes in 0p-shell –

Nijmegen I

Preliminary

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• NN interactions with medium-modified mesons

• Saturation of nuclear matter and Fermi liquid parameters improved with dropping masses

Summary

• Full analysis of ring diagrams

• Look for nuclear observables where tensor force plays dominant role

• Understand the connection between medium modifications and three-body forces

Outlook