13,130 research outputs found

### Chiral $2\pi$-exchange NN-potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local
NN-potentials generated by the two-pion exchange diagrams at two-loop order. We
give explicit expressions for the mass-spectra (or imaginary parts) of the
corresponding isoscalar and isovector central, spin-spin and tensor
NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar
central repulsion which amounts to $62.3$MeV at $r=1.0$fm. There is a
similarly strong isovector central attraction which however originates mainly
from the third order low energy constants $\bar d_j$ entering the chiral $\pi
N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram
with two second order chiral $\pi \pi NN$-vertices proportional to the low
energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction
to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results
presented here are relevant components of the chiral NN-potential at
next-to-next-to-next-to-leading order.Comment: 6 pages, 2 figure

### Twice-iterated boson-exchange scattering amplitudes

We calculate at two-loop order the complex-valued scattering amplitude
related to the twice-iterated scalar-isovector boson-exchange between nucleons.
In comparison to the once-iterated boson-exchange amplitude it shows less
dependence on the scattering angle. We calculate also the iteration of the
(static) irreducible one-loop potential with the one-boson exchange and find
similar features. Together with the irreducible three-boson exchange potentials
and the two-boson exchange potentials with vertex corrections, which are also
evaluated analytically, our results comprise all nonrelativistic contributions
from scalar-isovector boson-exchange at one- and two-loop order. The applied
methods can be straightforwardly adopted to the pseudoscalar pion with its
spin- and momentum-dependent couplings to the nucleon.Comment: 9 pages, 7 figures, to be published in Physical Review C (2006

### Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange

The third-order particle-hole ring diagrams are evaluated for a NN-contact
interaction of the Skyrme type. The pertinent four-loop coefficients in the
energy per particle $\bar E(k_f) \sim k_f^{5+2n}$ are reduced to
double-integrals over cubic expressions in euclidean polarization functions.
Dimensional regularization of divergent integrals is performed by subtracting
power-divergences and the validity of this method is checked against the known
analytical results at second-order. The complete ${\cal O}(p^2)$ NN-contact
interaction is obtained by adding two tensor terms and their third-order ring
contributions are also calculated in detail. The third-order ring energy
arising from long-range $1\pi$-exchange is computed and it is found that direct
and exchange contributions are all attractive. The very large size of the
pion-ring energy, $\bar E(k_{f0})\simeq -92\,$MeV at saturation density, is
however in no way representative for that of realistic chiral NN-potentials.
Moreover, the third-order (particle-particle and hole-hole) ladder diagrams are
evaluated with the full ${\cal O}(p^2)$ contact interaction and the simplest
three-ring contributions to the isospin-asymmetry energy $A(k_f)\sim k_f^5$ are
studied.Comment: 20 pages, 3 figure

### Chiral four-body interactions in nuclear matter

An exploratory study of chiral four-nucleon interactions in nuclear and
neutron matter is performed. The leading-order terms arising from pion-exchange
in combination with the chiral $4\pi$-vertex and the chiral NN$3\pi$-vertex are
found to be very small. Their attractive contribution to the energy per
particle stays below $0.6\,$MeV in magnitude for densities up to $\rho
=0.4\,$fm$^{-3}$. We consider also the four-nucleon interaction induced by
pion-exchange and twofold $\Delta$-isobar excitation of nucleons. For most of
the closed four-loop diagrams the occurring integrals over four Fermi spheres
can either be solved analytically or reduced to easily manageable one- or
two-parameter integrals. After summing the individually large contributions
from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at
nuclear matter saturation density $\rho_0=0.16\,$fm$^{-3}$ a moderate
contribution of $2.35\,$MeV to the energy per particle. The curve $\bar
E(\rho)$ rises rapidly with density, approximately with the third power of
$\rho$. In pure neutron matter the analogous chiral four-body interactions
lead, at the same density $\rho_n$, to a repulsive contribution that is about
half as strong. The present calculation indicates that long-range multi-nucleon
forces, in particular those provided by the strongly coupled $\pi N
\Delta$-system with its small mass-gap of $293\,$MeV, can still play an
appreciable role for the equation of state of nuclear and neutron matter.Comment: 19 pages, 15 figures, to be published in Eur. Phys. J.

### Spin-asymmetry energy of nuclear matter

We calculate the density-dependent spin-asymmetry energy $S(k_f)$ of
isospin-symmetric nuclear matter in the three-loop approximation of chiral
perturbation theory. The interaction contributions to $S(k_f)$ originate from
one-pion exchange, iterated one-pion exchange, and (irreducible) two-pion
exchange with no, single, and double virtual $\Delta$-isobar excitation. We
find that the truncation to $1\pi$-exchange and iterated $1\pi$-exchange terms
(which leads already to a good nuclear matter equation of state) is
spin-unstable, since $S(k_{f0})<0$. The inclusion of the chiral $\pi
N\Delta$-dynamics guarantees the spin-stability of nuclear matter. The
corresponding spin-asymmetry energy $S(k_f)$ stays positive within a wide range
of an undetermined short-range parameter $S_5$ (which we also estimate from
realistic NN-potentials). Our results reemphasize the important role played by
two-pion exchange with virtual $\Delta$-isobar excitation for the nuclear
matter many-body problem. Its explicit inclusion is essential in order to
obtain good bulk and single-particle properties.Comment: 11 pages, 6 figuers, accepted for publication in Physical Review

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