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New trial wave function for nuclear cluster structure of nuclei
A new trial wave function is proposed for nuclear physics, in which an exact
solution to the long-standing center-of-mass problem is given. In the new
approach, the widths of the single-nucleon Gaussian wave packets and the widths
of the relative Gaussian wave functions describing correlations of nucleons or
clusters are treated as variables in the explicit intrinsic wave function of
the nuclear system. As an example, this new wave function was applied to study
the typical (+) cluster system. By
removing exactly the spurious center-of-mass effect in a very simple way, the
energy curve of was obtained by the variational calculations
with the width of cluster, the width of cluster,
and the size parameter of the nucleus. They are considered as the three crucial
variational variables in describing the
(+) cluster system. This shows that the new wave
function can be a very interesting new tool for studying many-body and cluster
effects in nuclear physics.Comment: 10 pages, 2 figure
Note on differential operators, CHY integrands, and unifying relations for amplitudes
An elegant unified web for amplitudes of various theories was given by
Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar
web has also been constructed by Cheung, Shen and Wen, which relies on a set of
differential operators. In this note, by acting these differential operators on
CHY-integrands systematically, we have established the relation between these
two approaches. Thus, amplitudes for all theories which have CHY
representations, include gravity theory, Einstein-Yang-Mills theory,
Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory,
Born-Infeld theory, Dirac-Born-Infeld theory and its extension, bi-adjoint
scalar theory, theory, non-linear sigma model, as well as special
Galileon theory, have been included in the unified web rooted from gravity
theory.Comment: 20 page
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