Use of Asymptotically Correct Wave Function for Three-Body Rayleigh-Ritz Calculations

1969 ◽  
Vol 182 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Manuel Rotenberg ◽  
Josef Stein
Keyword(s):  
Wave Function ◽  
Three Body

QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function

2011 ◽  
Author(s):  
Tetsuo Nishikawa ◽  
Kazuhiro Tanaka ◽  
Atsushi Hosaka ◽  
Kanchan Khemchandani ◽  
Hideko Nagahiro ◽  
...  
Keyword(s):  
Wave Function ◽  
B Meson ◽  
Meson Wave Function ◽  
Sum Rule ◽  
Body Components ◽  
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.

Quality of the three - body wave function obtained with the unitary pole approximation

1972 ◽  
Vol 40 (1) ◽  
pp. 61-64 ◽  
Author(s):  
E. Hadjimichael ◽  
E. Harms ◽  
V. Newton
Keyword(s):  
Wave Function ◽  
Body Wave ◽  
Pole Approximation ◽  
Unitary Pole ◽  
Three Body

Three‐body quantum system on a line: Wave function asymptotics for increasing interactions

1991 ◽  
Vol 32 (1) ◽  
pp. 153-156 ◽  
Author(s):  
Yu. A. Kuperin ◽  
S. P. Merkuriev ◽  
E. A. Yarevsky
Keyword(s):  
Wave Function ◽  
Quantum System ◽  
Three Body

ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL

2009 ◽  
Vol 18 (07) ◽  
pp. 1561-1585 ◽  
Author(s):  
R. YARMUKHAMEDOV ◽  
M. K. UBAYDULLAEVA
Keyword(s):  
Wave Function ◽  
Configuration Space ◽  
Bound State ◽  
Wave Functions ◽  
Halo Nuclei ◽  
Asymptotic Normalization ◽  
Radial Wave ◽  
Asymptotic Expressions ◽  
Three Body ◽  
Normalization Factors

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

scholarly journals Strong decays of $${\bar{D}}^{*}K^{*}$$ molecules and the newly observed $$X_{0,1}$$ states

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Yin Huang ◽  
Jun-Xu Lu ◽  
Ju-Jun Xie ◽  
Li-Sheng Geng
Keyword(s):  
Wave Function ◽  
Decay Width ◽  
Lhcb Collaboration ◽  
The Other ◽  
Strong Decay ◽  
Compositeness Condition ◽  
Other Hand ◽  
New States ◽  
Three Body

AbstractLately, the LHCb Collaboration reported the discovery of two new states in the $$B^+\rightarrow D^+D^- K^+$$ B + → D + D - K + decay, i.e., $$X_0(2866)$$ X 0 ( 2866 ) and $$X_1(2904)$$ X 1 ( 2904 ) . In the present work, we study whether these states can be understood as $${\bar{D}}^*K^*$$ D ¯ ∗ K ∗ molecules from the perspective of their two-body strong decays into $$D^-K^+$$ D - K + via triangle diagrams and three-body decays into $${\bar{D}}^*K\pi $$ D ¯ ∗ K π . The coupling of the two states to $${\bar{D}}^*K^*$$ D ¯ ∗ K ∗ are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the $$X_0(2866)$$ X 0 ( 2866 ) state, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large $${\bar{D}}^*K^*$$ D ¯ ∗ K ∗ component in its wave function. On the other hand, the strong decay width for the $$X_1(2904)$$ X 1 ( 2904 ) state, much smaller than its experimental counterpart, effectively rules out its assignment as a $${\bar{D}}^*K^*$$ D ¯ ∗ K ∗ molecule.

ELECTRIC DIPOLE POLARIZABILITIES OF THE TRITON AND LAMBDA HYPERTRITON

2010 ◽  
Vol 19 (02) ◽  
pp. 225-242 ◽  
Author(s):  
V. F. KHARCHENKO ◽  
A. V. KHARCHENKO
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Electric Dipole ◽  
Ground State ◽  
Input Data ◽  
Low Energy ◽  
Dipole Polarizability ◽  
Order Of Magnitude ◽  
Three Body ◽  
Dipole Polarizabilities

A rigorous formalism for determining the electric dipole polarizability of a three-hadron bound complex in the case that the system has only one bound (ground) state has been elaborated. On its basis, by applying a model wave function that takes into account specific features of the structure of the three-body nuclei and using the known low-energy experimental data for the p–n, n–d, and Λ–d systems as input data, we have calculated the values of the electric dipole polarizabilities of the triton αE(3 H ) and lambda hypertriton [Formula: see text]. We have obtained for the triton polarizability the value 0.23 fm3. It follows from our study that the polarizability of the lambda hypertriton is close to 3 fm3 exceeding the polarizabilities of the ordinary three-nucleon nuclei by an order of magnitude.

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