Magnetic susceptibility in neutron stars with hadron-quark transition

W.Z.Jiang（ Shanghai Institute of Applied Physics)

N.Van Giai(Institut de Physique Nucleaire, Orsay, France)

Motivation de Hass-van Alphen (HVA) OscillationsComposition in neutron stars & Nuclear EOSHVA Oscill. & Hadron-quark transitionBrief summary

Motivation

Strong magnetic field in neutron stars (NS) >1012G

Landau diamagnetism and HVA oscillation Uncertainty of Nuclear EOS and NS properti

es Another way Signal of Hadron-quark phase transition

Magneton and susceptibility

MBB 00

With M the magneton obtained from the spin and orbital motion

Bohr Magneton eB me 2/

B

HM

MBH

Hamitonian

Susceptibility

BM /

Paramagnetism from spin

,)2

1(

2

2

m

pzmc

eB

TB2

Landau level, orbital motion

Special case

))(exp(1ln(ln GZ

GZBM ln

1

General case

1. Consider paramagnetic and diamagnetic energy

Schrodinger equation

Dirac equation

HVA oscillation

T=0 ， it has

At strong field

Composition in neutron stars Neutron, Proton, Electron, neutrino

equilibrium and charge neutral conditions:

Nuclear EOS

Susceptibility of neutron star

HVA Oscillation

Yd

0.1, Y

u 0

.07

中子星强磁场中的H

VA

振荡和相变

A Brief Summary

Amplitude drops and Frequency increases with the drop of B

Susceptibility Hadron-quark transition

HVA Amplitude, Frequency, Wave shape

HVA oscillation modifies the field by about 6%

to appear in IJMPA 21(2006)2201

Outlook: Fermi Surface rearrangement to HVA oscillation

山川異域

風月同天

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共結來緣

May of 763 (A.D.) Nirvara bana (nie pan) 奈良 唐招提寺

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