1. INFN, Sezione di Catania
Elementary excitations
in Neutron Star matter
M. Baldo
INFN, Sezione di Catania
ECT* , March 2017

2. Schematic view of a neutron star

3. A section (schematic)
of a neutron star

4. MOTIVATIONS . Neutrino emission from the superfluid matter
. Neutrino mean free path
. Heat capacity
. Thermal and electrical conductivity

5. The physical picture of the matter
The homogeneous Neutron Star matter below the crust
is mainly composed of neutrons, protons and electrons,
in beta and chemical equilibrium and at low
temperature. Charge neutrality imposes equal number
of protons and electrons.
The matter is extremely asymmetric, with the proton
fraction ranging from 1% to 10 %
Both neutrons and protons can be superfluid

6. Possible physical effects
Neutrino emission
# A collective mode with energy linear in momentum cannot decay into
a neutrino-antineutrino pair. It is essential to know the strength function
# Vertex renormalization of the response function
Neutrino mean free path
# Scattering from the Goldstone mode or collective modes in general
Heat capacity
# Counting correctly the effective degrees of freedom
Transport coefficients
# Screening of the effective interaction by the collective modes

7. J. Kundu and S. Reddy, PRC 70, 055803 (2004)
Some references
J. Kundu and S. Reddy, PRC 70, (2004)
L.B. Leinson and A. Perez, PLB 638, (2006)
A. Sedrakian, H. Muether and P. Schuck, PRC 76, (2007)
A.W. Steiner and S. Reddy, PRC 79, (2009)
L.B. Leinson, PRC 79, (2009)
E. Kolomeitsev and D. Voskresenky, PRC 81, (2010)
M.B. and C. Ducoin, PRC 84, (2011)
N. Martin and M. Urban, PRC 90, (2014)

8. We will include neutron, proton and electron components
Questions to be answered
. How much protons and neutrons decouple ?
. How efficient is the electron screening ?
. How much neutron modes are affected by protons ?

9. Linear response
including electrons
and protons only

10. NORMAL SYSTEM. Electron screening effect.
From the proton plasmon to the sound mode
Static electron
background
Plasmon mode
With screening
Sound mode

11. Proton and electron spectral functions. Normal system
M.B. and C. Ducoin , PRC79, (2009)

12. Overview of superfluid gaps in homogeneous matter (below the crust)
We consider the region where neutron superfludity
can be neglected

13. Difficulty in the gap calculation
The pairing gap will be considered as a parameter
Final proton gap
M.B. , H.-J. Schulze, PRC 75, (2007)

14. Pairing interaction only
Spectrum
Strength function
Goldstone mode
Pair-breaking mode

15. Death and resurrection of the Goldstone mode
Including the Coulomb interaction
Death and resurrection of the Goldstone mode
Static electrons
Proton plasmons
Including electrons
“Pseudo-Goldstone” mode

16. Evolution of the spectrum. Pairing + Coulomb

18. From the pseudo-Goldstone
the sound mode
Pseudo-
Goldstone
Sound mode

19. The electron plasmon damping

20. Including the nuclear interaction and
neutrons in the normal phase
Nuclear interaction from BHF as Skyrme-like functional
monopolar approximation

21. Three components spectral function
The proton pseudo-Golstone mode persists

23. The proton sound mode persists

25. A closer comparison No np coupling With np coupling
Notice : no sound mode for the neutron gas
( attractive nn particle-hole effective interaction )

26. No np coupling
With np coupling

27. No np coupling
With np coupling
proton pair breakinh mode

28. No np coupling With np coupling Two times saturation density
Pseudo-Goldstone
Neutron zero-sound mode
No np coupling
With np coupling
Pair-breaking mode

29. Two times saturation density

33. THANKS !!

34. Position of the centroid of the peak
in the proton spectral function