13,934 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

### Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

A recent work on the resummation of fermionic in-medium ladder diagrams to
all orders is extended by considering the effective range correction in the
s-wave interaction and a (spin-independent) p-wave contact-interaction. A
two-component recursion generates the in-medium T-matrix at any order when
off-shell terms spoil the factorization of multi-loop diagrams. The resummation
to all orders is achieved in the form of a geometrical series for the
particle-particle ladders, and through an arctangent-function for the combined
particle-particle and hole-hole ladders. One finds that the effective range
correction changes the results in the limit of large scattering length
considerably, with the effect that the Bertsch parameter $\xi_n$ nearly
doubles. Applications to the equation of state of neutron matter at low density
are also discussed. For the p-wave contact-interaction the resummation to all
orders is facilitated by decomposing tensorial loop-integrals with a
transversal and a longitudinal projector. The enhanced attraction provided by
the p-wave ladder series has its origin mainly in the coherent sum of Hartree
and Fock contributions.Comment: 17 pages, 7 figures, to be published in Eur. Phys. J.

### Parity-violating two-pion exchange nucleon-nucleon interaction

We calculate in chiral perturbation theory the parity-violating two-pion
exchange nucleon-nucleon potentials at leading one-loop order. At a distance of
$r= m_\pi^{-1} \simeq 1.4$fm they amount to about $\pm 16%$ of the
parity-violating $1\pi$-exchange potential. We evaluate also the
parity-violating effects arising from $2\pi$-exchange with excitation of
virtual $\Delta(1232)$-isobars. These come out to be relatively small in
comparison to those from diagrams with only nucleon intermediate states. The
reason for this opposite behavior to the parity-conserving case is the blocking
of the dominant isoscalar central channel by CP-invariance. Furthermore, we
calculate the T-matrix related to the iteration of the parity-violating
$1\pi$-exchange with the parity-conserving one. The analytical results
presented in this work can be easily implemented into calculations of
parity-violating nuclear observables.Comment: 7 pages, 3 figures, 1 table, published in: Phys. Rev. C76. 047001
(2007

### 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

### Pion-photon exchange nucleon-nucleon potentials

We calculate in chiral perturbation theory the dominant next-to-leading order
correction to the $\pi\gamma$-exchange NN-potential proportional to the large
isovector magnetic moment $\kappa_v = 4.7$ of the nucleon. The corresponding
spin-spin and tensor potentials $\widetilde V_{S,T}(r)$ in coordinate space
have a very simple analytical form. At long distances $r \simeq 2$ fm these
potentials are of similar size (but opposite in sign) as the leading order
$\pi\gamma$-exchange potentials. We consider also effects from virtual
$\Delta$-isobar excitation as well as other isospin-breaking contributions to
the $2\pi$-exchange NN-potential induced by additional one-photon exchange.Comment: 7 pages, 2 figures, to be published in Phys. Rev. C (2006) Brief
Report

### 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.

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