We have treated the ground state of the positronium negative ion (Ps - ) by a hyperspherical harmonics expansion method in which the centre of mass motion is properly accounted for. The resulting system of coupled differential equations has been solved by the renormalized Numerov method. We find that the convergence in the Binding Energy (BE) with respect to inclusion of higher hyperspherical partial waves is quite slow for this diffuse system. Using our exact numerical results up to a maximum of 28 for the hyper angular momentum quantum number (K u ) in an extrapolation formula based on the hyperspherical convergence theorems, we get the binding energy of the ground state of Ps - as 0.261 668 9 au.

TAPAN DAS

Ancient Indian History and Culture

R CHATTOPADHYAY

P K MUKHERJEE

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Hyperspherical harmonics expansion of the ground state of the Ps - ion

Physica Scripta

We calculate ground and several low-lying excited states of various two electron atoms using hyperspherical adiabatic approximation (HAA). Its spectracular accuracy, as compared to exact numerical results of a set of coupled differential equations, demands a better understanding of its mechanism. It is seen that factorizability of the potential matrix into a product of a common function of the global length (hyperradius) and a constant matrix, is responsible for this remarkable success. This is a result of the shape invariance condition in multidimensional supersymmetric quantum mechanics.

International Journal of Modern Physics A

Quality of hyperspherical adiabatic approximation for excited states of atomic systems

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei ΛΛ6He, ΛΛ10Be, ΛΛ14C, ΛΛ18O, ΛΛ22Ne, ΛΛ26Mg, ΛΛ30Si, ΛΛ34S, ΛΛ38Ar, ΛΛ42Ca, ΛΛ46Ti, ΛΛ50Cr, ΛΛ54Fe, ΛΛ58Ni, ΛΛ62Zn, ΛΛ66Ge, ΛΛ70Se, ΛΛ74Kr, ΛΛ78Sr, ΛΛ82Zr, ΛΛ86Mo, ΛΛ90Ru, ΛΛ94Pd, ΛΛ98Cd, ΛΛ102Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. ΛΛ6He and ΛΛ10Be) 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 Λ-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 Kmax = 20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.

Pramana - Journal of Physics

Study of Î›Î› dynamics and ground state structure of low and medium mass double Î› hypernuclei

We investigate the reliability of the adiabatic approximation in the hyperspherical harmonics formalism. It has been applied to a number of two-electron systems, both compact and loosely bound, with the interaction between the constituent particles being purely Coulombic. The results are compared with the exact ones obtained by solving the set of coupled differential equations numerically. The accuracy of this approximation for two-electron systems is compared with that for systems with nuclear interactions, and we find that the former is better. An explanation has been provided for better agreement with Coulombic systems, particularly for noncompact ones. © 1997 The American Physical Society.

Physical Review A - Atomic, Molecular, and Optical Physics

Adiabatic approximation in atomic three-body systems

Coupled differential equations resulting from an application of the hyperspherical-harmonic expansion method to a number of two-electron atoms have been solved by an exact numerical method (renormalized Numerov method). Calculations are feasible (for the available computer facility) for the inclusion of up to 20 (K=20) partial waves. Although the convergence trend is discernible, the binding energies for K=20 are far from the converged values. An application of a convergence theorem by Schneider [Phys. Lett. 40B, 439 (1972)] permits extrapolation of the results to large K values. Such converged results agree closely with an accurate multiparameter variational calculation by Pekeris [Phys. Rev. 126, 1471 (1962)]. Even though the hyperspherical-harmonic expansion is notoriously slow for the long-range Coulomb interaction, the present prescription is a highly economical and accurate method for few-electron atoms. We have applied this method to the ground states of H-, He, Li+, and Be2+, as well as to the first excited singlet state of He. © 1994 The American Physical Society.

Journal	Physica Scripta
Publisher	Royal Swedish Academy of Sciences
ISSN	0031-8949