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have to be calculated. Current microscopic mass tables
are based on self-consistent mean-field methods. Over
the last few years the accuracy of these models has been
significantly improved. However reliably extrapolating
these models far beyond the stability valley where they
are adjusted requires a better understanding of manybody
correlations in finite nuclei. Some neutron stars
are endowed with huge external magnetic fields of order
10 14 -10 15 G (the internal field could be even stronger).
Calculating the properties of the crustal matter in such
fields is crucially needed for modeling magnetars.
The inner crust of neutron stars, at densities above
∼4×10 11 g/cm 3 is a unique environment which cannot
be reproduced in the laboratory. Here there is believed
to be a coexistence of nuclear “clusters” with a neutron
liquid. Its structure has been studied with various models,
the state-of-the-art being self-consistent mean-field
methods. However the underlying effective forces are
still very phenomenological and should be more microscopically
founded. Transport properties of the neutron
liquid in the crust are not well understood even though
they are essential for modelling various astrophysical
phenomena such as pulsar glitches. In particular, neutrons
are predicted to be superfluid at low temperatures.
Microscopic studies in neutron matter using different
methods lead to different density dependence of the
1 S 0 pairing gap. Including the effects of spatial inhomogeneities
is even more challenging and essential for
determining the interaction between nuclear clusters
and superfluid vortices arising from the star’s rotation.
The influence of the neutron liquid on the elastic properties
of the crust has not been studied so far. However
this may be important for interpreting quasi-periodic
oscillations recently detected in the giant flares from
soft-γ repeaters which are believed to be the signature
of crust quakes triggered by huge magnetic stresses.
Although the nature of the crust-core transition has a
strong impact on neutron-star oscillations and possibly
on neutron-star cooling, it remains mysterious. Some
models predict the existence of nuclear “pastas” while
others do not. More realistic many-body simulations are
crucially needed.
Figure 6. The mass-radius relationship of compact stars for
different equations of state (from Lattimer et al., Phys. Rep.
442(2007)109).
The crust dissolves into nucleons and leptons at a
fraction of the nuclear saturation density ρ 0 . Over the last
decades progresses in nuclear many-body calculations
have been impressive. The equation of state obtained
from both diagrammatic and variational methods are
in rather good agreement. The use of phenomenological
three-body forces explains in a large part the
discrepancy between non-relativistic and relativistic
Brückner-Hartree-Fock (BHF) calculations. Despite a
consistent treatment of two-body and three-body forces
in current BHF calculations, large uncertainties remain
at high densities depending on the adopted nucleonnucleon
potential. The origin of these disparities should
be elucidated. The recent development of quantum
Monte-Carlo methods is very promising and will provide
a benchmark of equation of state calculations in the
coming decade. However other microscopic methods
will still be needed in order to understand the role of
many-body correlations.
Although the composition of dense matter above 2-3ρ 0
is essential for determining the structure and evolution
of neutron stars, it is still poorly known. In particular, the
threshold density for the appearance of hyperons is very
uncertain due the scarcity of experimental data about
hyperon-hyperon and hyperon-nucleon interactions.
Nucleon and/or hyperon superfluidity plays a key role in
the thermal evolution of neutron stars, and consequently
requires further theoretical studies. Various other species
could be present in neutron star cores, for instance pion
and kaon condensates. One of the most exciting possibilities
is certainly the presence of deconfined quarks.
So-called strange stars might even be composed only
of quarks even though they seem to be less likely than
hybrid stars. A lot of activity has recently been devoted
to the study of colour superconductivity, unveiling a
very rich phase diagram. However microscopic calculations
are hindered by the non-perturbative character
of quantum chromodynamics in the conditions prevailing
in compact stars. The discovery of a submillisecond
pulsar or a compact star with an apparent stellar radius
smaller than 11-12 km would be a strong indication in
favour of the existence of quark stars. Other observational
signatures of a phase transition to quark matter
in compact stars include for instance the spontaneous
spin-up of pulsars, γ ray bursts with late X-ray emission
and long quiescent times or a secondary shock wave in
supernova explosions.
Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010 | 139