Hyperspherical cluster model for bosons: application to sub-threshold
halo states in helium drops
- URL: http://arxiv.org/abs/2304.06679v1
- Date: Thu, 13 Apr 2023 17:18:50 GMT
- Title: Hyperspherical cluster model for bosons: application to sub-threshold
halo states in helium drops
- Authors: N.K. Timofeyuk
- Abstract summary: In the first excited state one helium atom stays far apart from the rest forming a two-body molecule or a halo.
The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the number of atoms in the drop.
The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: To describe long-range behaviour of one particle removed from a few- or a
many-body system, a hyperspherical cluster model has been developed. It has
been applied to the ground and first excited states of helium drops with five,
six, eight and ten atoms interacting via a two-body soft gaussian potential.
Convergence of the hyperspherical cluster harmonics expansion is studied for
binding energies, root-mean-squared radii and overlaps of the wave functions of
two helium drops differing by one atom. It was shown that with increasing model
space the functional form of such overlaps at large distances converges to the
correct asymptotic behaviour. The asymptotic normalization coefficients that
quantify the overlaps' amplitudes in this region are calculated. It was also
shown that in the first excited state one helium atom stays far apart from the
rest forming a two-body molecule, or a halo. The probability of finding the
halo atom in the classically-forbidden region of space depends on the
definition of the latter and on the number of atoms in the drop. The total norm
of the overlap integrals, the spectroscopic factor, represents the number of
partitions of a many-body state into a chosen state of the system with one
particle removed. The spectroscopic factors have been calculated and their sum
rules are discussed giving a further insight into the structure of helium
drops.
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