69 research outputs found
Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons
The Effective Field Theory "without pions" at next-to-leading order is used
to analyze universal bound state and scattering properties of the 3- and
4-nucleon system. Results of a variety of phase shift equivalent nuclear
potentials are presented for bound state properties of 3H and 4He, and for the
singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are
performed with the Refined Resonating Group Method and include a full treatment
of the Coulomb interaction and the leading-order 3-nucleon interaction. The
results compare favorably with data and values from AV18(+UIX) model
calculations. A new correlation between a_0(3He-n) and the 3H binding energy is
found. Furthermore, we confirm at next-to-leading order the correlations,
already found at leading-order, between the 3H binding energy and the 3H charge
radius, and the Tjon line. With the 3H binding energy as input, we get
predictions of the Effective Field Theory "without pions" at next-to-leading
order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the
4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm
0.6)fm. Including the Coulomb interaction, the splitting in binding energy
between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data
of (0.10\mp 0.03) MeV is model independently attributed to higher order charge
independence breaking interactions. We also demonstrate that different results
for the same observable stem from higher order effects, and carefully assess
that numerical uncertainties are negligible. Our results demonstrate the
convergence and usefulness of the pion-less theory at next-to-leading order in
the 4He channel. We conclude that no 4-nucleon interaction is needed to
renormalize the theory at next-to-leading order in the 4-nucleon sector.Comment: 24 pages revtex4, including 8 figures as .eps files embedded with
includegraphicx, leading-order results added, calculations include the LO
three-nucleon interaction explicitly, comment on Wigner bound added, minor
modification
On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)
In October 1924, the Physical Review, a relatively minor journal at the time,
published a remarkable two-part paper by John H. Van Vleck, working in virtual
isolation at the University of Minnesota. Van Vleck combined advanced
techniques of classical mechanics with Bohr's correspondence principle and
Einstein's quantum theory of radiation to find quantum analogues of classical
expressions for the emission, absorption, and dispersion of radiation. For
modern readers Van Vleck's paper is much easier to follow than the famous paper
by Kramers and Heisenberg on dispersion theory, which covers similar terrain
and is widely credited to have led directly to Heisenberg's "Umdeutung" paper.
This makes Van Vleck's paper extremely valuable for the reconstruction of the
genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did
not take the next step and develop matrix mechanics himself.Comment: 82 page
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