scholarly journals Non-symmetrized Hyperspherical Harmonics Method for Non-equal Mass Three-Body Systems

2018 ◽  
Vol 6 ◽  
Author(s):  
Alessia Nannini ◽  
Laura E. Marcucci
Keyword(s):  
Equal Mass ◽  
Hyperspherical Harmonics ◽  
Three Body

A COMPLETE VARIATIONAL WAVE FUNCTION FOR THE GROUND STATE OF 3H AND 3He

1966 ◽  
Vol 44 (9) ◽  
pp. 2095-2110 ◽  
Author(s):  
Marcel Banville ◽  
P. D. Kunz
Keyword(s):  
Wave Function ◽  
Coordinate System ◽  
Body Wave ◽  
Center Of Mass ◽  
Minimum Energy ◽  
Equal Mass ◽  
Radial Coordinate ◽  
Orthogonal Functions ◽  
Gaussian Shape ◽  
Three Body

The three-body wave function for particles of equal mass is expanded in a systematic way by making use of a hyperspherical coordinate system. Apart from the center-of-mass coordinates, three of the variables are the usual Euler angles describing the orientation of the plane defined by the three particles. The other three variables, which describe the shape of the triangle, are represented in terms of a radial coordinate and two angular coordinates. The kinetic energy for these last three coordinates is separable and allows one to expand the three-body wave function in a complete set of orthogonal functions based upon the angular variables. The particular symmetry of the internal part of the wave function under permutations of the three particles is easily represented in terms of the set of functions for one of the angular variables. By choosing a particular set of radial functions one can then obtain the upper limit on the binding energy for the three-body system through the Rayleigh–Ritz variational procedure. The advantage of this particular coordinate system is that all but a few of the variational parameters occur linearly in the wave function, and the minimum energy can be obtained by diagonalizing a small number of the energy matrices. The method is applied to find the lower limit to a standard spin-independent potential of Gaussian shape.

Triple approaches in the plane isosceles equal-mass three-body problem

2001 ◽  
Vol 27 (10) ◽  
pp. 678-682
Author(s):  
V. V. Orlov ◽  
A. V. Petrova ◽  
A. I. Martynova
Keyword(s):  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals Saari’s homographic conjecture for a planar equal-mass three-body problem under the Newton gravity

2012 ◽  
Vol 45 (34) ◽  
pp. 345202 ◽  
Author(s):  
Toshiaki Fujiwara ◽  
Hiroshi Fukuda ◽  
Hiroshi Ozaki ◽  
Tetsuya Taniguchi
Keyword(s):  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals New periodic orbits in the planar equal-mass three-body problem

2018 ◽  
Vol 38 (4) ◽  
pp. 2187-2206
Author(s):  
Rongchang Liu ◽  
◽  
Jiangyuan Li ◽  
Duokui Yan
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

scholarly journals Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism

2021 ◽  
Vol 9 ◽  
Author(s):  
Simone Salvatore Li Muli ◽  
Sonia Bacca ◽  
Nir Barnea
Keyword(s):  
Truncation Error ◽  
Expansion Method ◽  
Muonic Atom ◽  
Light Nuclei ◽  
Hyperspherical Harmonics ◽  
Irreducible Tensors ◽  
Nuclear Systems ◽  
Chiral Interactions ◽  
Three Body ◽  
Hyperspherical Harmonics Expansion

With the goal of using chiral interactions at various orders to explore the properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of 3H, 3He, and 4He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obtained by using the precise muonic atom data for single-nucleon radii. Having local chiral Hamiltonians at various orders implemented in our hyperspherical harmonics suites of codes opens up the possibility to test such interactions on other light-nuclei properties, such as electromagnetic reactions.

scholarly journals Stellar hardening of massive black hole binaries: the impact of the host rotation

2021 ◽  
Vol 508 (1) ◽  
pp. 1533-1542
Author(s):  
Ludovica Varisco ◽  
Elisa Bortolas ◽  
Massimo Dotti ◽  
Alberto Sesana
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Equal Mass ◽  
Stellar Systems ◽  
Massive Black Hole ◽  
Loss Cone ◽  
Black Hole Binaries ◽  
Influence Radius ◽  
Three Body ◽  
The Impact

ABSTRACT Massive black hole binaries (MBHBs) with masses of ∼104 to $\sim 10^{10} \, \mathrm{M}_{\odot {}}$ are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is ≈ 0.25 (≈ 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems.

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