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~π ０ condensation

( 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 Tatsu

mi, Prog. Theor. Phys. Supplment 112(1993).

Strong state- dependence of nn correlations in neutron matter

• 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.

)2/110(~ 3

0

2/122

01

0

2

})())({()(

,)'(

)'(|)(|'''

1)(

kkkE

kE

kkSVkkdkk

Here focus on the (3P2+3F2) SF coupled by the tensor force; Vcouple=

although main attraction for pairing comes from the LS int.TV)5/66(

(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

π0 condensation.

・ In the ALS structure, the Fermi surface becomes cylindrical ; the axis is along kc (co

ndensed 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 mome

ntum 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 a

s 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 conse

rvation 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 density higher 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.

　

e e

0

0

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 provide ｓ a new proble

m in NS cooling. .

2/3

6

)/MeV( 16.0

)()(

TkPR

RkkkTkcNDU

Bnp

nepB

)/)exp((1

1)(

:used isfunction on distributi Dirac-Fermi eUsually th

,|||,,|

)(1)(1)()(22

asgiven is emmisivity neutrino

inverse), its plus (A direct URC For the

212

spins

21

21

4~1

TkEpn

BHlB

pnpnpnEEE

lBB

Biii

l

lifp

l

i

• What is the problem?

• Usually a large Δp to suppress 　 large NDU emissivity 　 is 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 the dramatic 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.

Regarding this universal nature as originating from the color degrees of freedom, we study the origin of the universal 3BI repulsion from the viewpoint of the confinement mechanism 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 core

versus central density/ ,

with use of the universal repulsion

of 3BI, derived in the string-junction

model (SJM)

0

• 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.