We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.

We report a calculation of meson exchange current contribution to the charge form factor of³He by the hyper spherical harmonic expansion method with the inclusion of two-pion exchange three nucleon force. Results indicate that the charge form factor is changed appreciably in the right direction at high momentum transfer, due to the inclusion of the meson exchange current.

We present the full set of equations for the solution of the trinucleon problem by the hyperspherical harmonics expansion (HHE) method where nucleons interact via the Reid soft core (RSC) potential. The coupling potential matrix elements are expressed in terms of geometrical structure coefficients (GSC) and potential multipoles (PM). Introduction of GSC greatly simplifies the calculation of the potential matrix and makes the numerical algorithm efficient. A method for calculating all the twelve independent sets of GSC needed, by using the completeness property of the Jacobi polynomials has been presented. A convenient sum rule for each set of GSC has also been derived and precision of the calculated GSC has been checked by the sum rule. Such calculations of GSC are efficient and fast, in view of the complexity of the HHE equations.

We compare the effect of two body core on the charge form factor of³He by the hyperspherical harmonics expansion method using various 2BF potentials with the inclusion of three body force. We also include the meson exchange current contribution to the CFF for the same potentials in addition to the 3BF. The results indicate that the combined effect of 3BF and MEC (i) movesq_min² (the first diffraction minimum) appreciably to the left, amount of shift depends on the 2BF atr₁₂∼0.7 fm and (ii) enhancesF_max (the height of the secondary maximum of CFF) by an appreciable amount, the increment in general increases with the repulsive core of 2BF (r⩽0.1 fm).

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 K_max=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.

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 ⁶He. It is found that the convergence of the two neutron separation energy is relatively slow, while other quantities reach convergence quickly.

We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing²³Na atoms and some thermodynamical properties of the condensate.