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### Nucleon correlations and neutron star physics

T.Takatsuka (Iwate) and R. Tamagaki (Kyoto)

KEK Ｗｏｒｋｓｈｏｐ on

「Short-range correlations and tensor structure

at J-PARC」 2009. 9.25

Contents

(1) Equation of state of neutron star matter

(2) Relevance of s.r.c. and tensor-coupling to the neutron (3P2+3F2) superfluidity

(3) Unique structure caused by the OPE- tensor correlation : ALS structure~π０condensation

(Ｃ１) Effects of proton high-momentum components on NS cooling due to the nucleon direct URCA process

(Ｃ２) Origin of universal s.r. repulsion in the baryon system from the confinement

(1) Equation of State(EOS) of neutron star(NS) matter

At first, we see the features of the short-range correlations (s.r.c.) in EOS of neutron matter (the main component of NSs), from the viewpoint that nuclear force has strong state-dependence.

・State dependence of T=1 int. and nn correlation

・Density dependence of E/N (EOS) and partial-wave contribution to E/N

・Effects of s.r.c. on M (mass) and R( radius) of NSs

References prior to 1993: Kunihiro, Muto, Takatsuka, Tamagaki and Tatsumi, Prog. Theor. Phys. Supplment 112(1993).

Each partial wave gives largely different contribution to E/N, but the <G>/N (total interaction energy) is close to <G(1S0)>/N.

- This comes from the cancellation in the three 3P-wave sum and also between the repulsive 3P-waves (in average) and attractive 1D2-wave.
- The s.r.c. due to the repulsive core plays a substantial role in the EOS of NS matter.
- We note the competition between repulsive core and outside attraction in 1S0 and 3P2 .

(2) Relevance of s.r.c. and tensor-coupling to nucleon superfluidity (SF)

- At low density in the crust of NS, neutrons dripped from n-rich nuclei turn

into the 1S0-type SF. This SF appears in the region of

- The 1S0 gap equation is of the well-known BCS type:
- Δ/E describes the pairing correlation near the Fermi surface and also

the s.r.c. far from the Fermi surface, which should be solved with full V.

- At moderate density in the fluid core of NS in (~0.7→ several) ,

neutrons turn into the (3P2+3F2)-type SF .

- At moderate density, protons as small component turn into the 1S0-type SF.

Here focus on the (3P2+3F2) SF coupled by the tensor force; Vcouple=although main attraction for pairing comes from the LS int.

(3) Unique structure caused by the OPE-tensor interaction (ALS ~π0 condensation)

Variational calculations have shown the new phase regarded as neutral pion condensation

A. Akmal, V.R. Pandaripande and D.G. Ravenhall,

Phys. Rev. 58C (1998), 1804.

Growth of the long-range

tensor correlation plays

a key role in the phase

transition from the low density

phase to high density phase.

In neutron matter, the transition

occurs at ρ=0.2fm -3= 1.25ρ0 .

・ The long range (OPE-dominated) part of tensor correlation is taken into account

in the ALS structure, equivalent to the

π0condensation.

・ In the ALS structure, the Fermi surface becomes cylindrical ; the axis is along kc (condensed momentum) and the side consists of the two dimensional Fermi circle.

・ After taking a new model state, there still remains tensor correlation of short range.

（Ｃ１）Ｅｆｆｅｃｔ ｏｆ proton ｈｉｇｈ-ｍｏｍｅｎｔｕｍ components ｏｎ ＮＳ ｃｏｏｌｉｎｇ ｄｕｅ ｔｏ ｎｕｃｌｅｏｎ ｄｉｒｅｃｔ ＵＲＣＡ

- Recent progress: The s.r.c. provides the high momentum components of n & p well above the Fermi surface. Especially for protons, the np-tensor correlation plays an important role.

e.g., M. Alvioli, C. Ciofi degli Atti and H. Morita,.Phys. Rev. Letters, !00 (2008),162503

- Question arises as to at what extent such high-momentum components influence NS phenomena.
- Recently it has been suggested that high momentum p components enhance the neutrino emissivity of NSs due to the nucleon direct URCA process.

Neutrino emissivity by Direct URCA

- Nucleon direct URCA (NDU) is the most efficient process as neutrino cooling of NS(among N,π-cond.,K-cond.,Y-mix.,q)

n→p＋e- + , p+e-→n+ (μ possible for μe>mμ).

“Direct” : without by-stander nucleon, the momentum conservation holds among three Fermi momenta of the degenerate fermions (kn=kp+ke ) , within the allowance of small neutrino’s energy ckν~kBT=(0.01-0.1MeV) .

- This becomes possible when proton mixing x=Z/A amounts to >~10% , depending sensitively on symmetry energy,

at densityhigher than several . (now still open) problem)

- At moderate densities (1~3) , because of x<~5%, normally NDU is forbidden, when we take the sharp Fermi surfaces slightly diffused due to finite temperature.

But, in such situation, NDU becomes possible, if some high momentum components above the Fermi surfaces exist , e.g. for protons due to the np tensor correlation.

This point has been noted recently,

e.g.L.Frankfurt, M. Sargsian

and M.Strikman, Int.J.Mod.Phys.,

Vol.23, no.20(2008),2991.

They give an estimate of enhancement factor

R, where Pnp is the probability for a proton

to have momentum k>kp, taking density

~nuclear density , Z/N=0.1 and Pnp=0.1.

At the internal temperature of NS as

kBT=(0.1-0.01) MeV, R becomes of

the order of (0.5~16).

This gives enormously large neutrino

emissivity, and provideｓa new problem in NS cooling.

.

What is the problem?

- Usually a large Δp to

suppresslarge NDU

emissivityis used,

to avoid too cooled

NSs which cannot

be observed.

- For the nucleons

well above the Fermi

surface, suppression

of SF does not work.

The curves and marks taken

from S.Tsuruta,Proc. of

IAU 2003 Symp.

(C2) Origin of universal s.r. repulsion in the baryon system from the confinement

R. Tamagaki, Prog. Theor. Phys. 119 (2008), 965 and arXiv:0801.2289. R. Tamagaki, Prog. Theor. Phys. Suppl. 174 (2008), 233.

Two motivations

(1) Necessity of universal repulsion of

3-body int. (3BI)to avoid thedramatic softening in EOS of NS matter

due to the hyperon-mixing,S.Nishizaki, Y.Yamamoto and T. Takatsuka, Prog. Theor. phys. 108(2002),703.

(2) String-junction structure of the baryon shown by recent lattice QCD calculations

T. Takahashi and H. Suganuma, Phys. Rev. D70 (2004), 074506.

Regardingthis universal nature as originating from the color degrees of freedom, we study the origin of the universal 3BI repulsion from the viewpoint of the confinementmechanism in QCD, adopting the string-junction model (SJM).

M. Imachi, S. Otsuki and F. Toyoda, Prog. Theor.Phys. 54 (1975), 280; 55 (1976), 551; 57 (1979)17.

Mass of neutron star (NS)with Y- mixed coreversus central density/ ,with use ofthe universal repulsion of 3BI, derived in the string-junction model(SJM)

This is an extension of the previous

approach to understand the origin of repulsive core in baryon-baryon interaction, based on the string-junction model.

R. Tamagaki, Bulletin of the Institute for Chemical Research,

Kyoto Univ. 60, No.2 (1982),190.

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