Adiabatic approximation in atomic three-body systems

Das

2001

Pramana - J Phys

We critically review the ££ dynamics by examining £ £ and £-nucleon phenomenological potentials in the study of the bound state properties of double-£ hypernuclei ££ He, ½¼ ££ Be, ½ in the frame work of (core·£·£) three body model. An effective £AE potential is obtained by folding the phenomenological £AE potential into the density distribution of the core nuclei. The former two cases (i.e. ££ He and ½¼ ££ Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly £-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for ÃÑ Ü ¾ ¼ has been achieved. In our calculation we have made no approximation in restricting the allowed Ð-values of the interacting pairs.

Section: Two Body Potentialsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

Das

2001

Pramana - J Phys

“…It is not surprising for the following reason. Although convergence of HHE method is fairly fast for short range potentials [62], it is quite slow for long range potentials [32] and is even slower for extended systems like P s [33,34]. Since the halo wave function extends well outside typical nuclear dimensions, larger K-values are needed to reproduce the tail part of the wave function, making the convergence slow.…”

Section: Two-body Potentialsmentioning

confidence: 99%

“…This method is a powerful tool for the ab initio solution of the fewbody Schrödinger equation for a given set of interaction potentials among the constituent particles. This method has been used for bound states in atomic [23][24][25][26][27][28][29][30][31][32][33][34][35], nuclear [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and particle physics [54][55][56]. Attempts have been made to use it in scattering problems as well [57].…”

Section: Introductionmentioning

confidence: 99%

Investigation of halo structure of 6He by hyperspherical three-body method

Das

2001

Pramana - J Phys

Hyperspherical harmonics expansion method is applied to a three-body model of two neutron halo nuclei. Convergence of the expansion has been ensured. A repulsive part is introduced in the interaction between the core and the extra-core neutron, to simulate Pauli principle. Two neutron separation energy, r.m.s. radii, correlation factor and probability density distributions have been calculated for 6 He. It is found that the convergence of the two neutron separation energy is relatively slow, while other quantities reach convergence quickly.

“…In the similar manner, we can also define two other sets of Jacobi coordinates by cyclically permuting i → j → k → i twice, which correspond to j th and k th partitions respectively. In hyper-spherical variables [65][66] of the i th partition, three-body Schrődinger equation is…”

Section: Hhe Methodsmentioning

confidence: 99%

Hyperspherical three-body model calculation for the bound 3,1S-states of Coulombic systems

2015

Int. J. Mod. Phys. E

In this paper, hyperspherical three-body model formalism has been applied for the calculation energies of the low-lying bound 1,3 S (L=0)-states of neutral helium and helium like Coulombic three-body systems having nuclear charge (Z) in the range Z=2 to Z=92. The calculation of the coupling potential matrix elements of the two-body potentials has been simplified by the introduction of Raynal-Revai Coefficients (RRC). The three-body wave function in the Schrődinger equation when expanded in terms of hyperpherical harmonics (HH), leads to an infinite set of coupled differential equation (CDE). For practical reason the infinite set of CDE is truncated to a finite set and are solved by an exact numerical method known as renormalized Numerov method (RNM) to get the energy solution (E). The calculated energy is compared with the ones of the literature.