Effective theory of $^3$H and $^3$He - INSPIRE

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Effective theory of $^3$ H and $^3$ He

Sebastian König
(
- Ohio State U.
)
,
Harald W. Grießhammer
(
- George Washington U.
)
,
H.W. Hammer
(
- Darmstadt, Tech. Hochsch. and
- Darmstadt, EMMI
)
,
U. van Kolck
(
- Orsay, IPN and
- Arizona U.
)

Aug 20, 2015

35 pages

Published in:

J.Phys.G 43 (2016) 5, 055106

Published: Apr 12, 2016

e-Print:

1508.05085 [nucl-th]

DOI:

10.1088/0954-3899/43/5/055106

View in:

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Abstract: (IOP)

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order (LO) the spin-singlet nucleon–nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron–deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse

{}^{1}{S}_{0}

scattering lengths converges rapidly. Using a new systematic treatment of the proton–proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the

{}^{3}{\rm{H}}

–

{}^{3}\mathrm{He}

binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the LO is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting

{({E}_{B}{(}^{3}\mathrm{He})-{E}_{B}{(}^{3}{\rm{H}}))}^{\mathrm{NLO}}\quad =(-0.86\pm 0.17)\quad \mathrm{MeV}

.

Note:

37 pages, 14 figures, published version

pionless effective field theory
Coulomb interaction
unitarity limit
interaction: Coulomb
force: Coulomb
exchange: one-photon
isospin: symmetry breaking
splitting
binding energy
tritium

References(79)

Figures(20)

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