We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (\(\sim \)3) to very large (\(\sim \) \(10^7\)) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter \(C_{6}\). We compare our results with those of the modified Gross–Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross–Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

We employ a hypervirial method within the few-body integro-differential equation approach to investigate cluster-structuring in a variety of hypernuclear and mesic-nuclear systems. We use this to investigate the possibility of the existence of the H-dibaryon as a stable subsystem within a larger hypernuclear system. To this end a series of alpha-cluster hypernuclei of the form (N alpha)Lambda Lambda, where N is an integer, are considered. The total system and subsystem binding energies are calculated using standard inter-cluster potentials. Despite the tighter overall binding induced by the relatively strong alpha Lambda attraction, in none of the hypernuclei considered was the Lambda Lambda subsystem found to be bound.

We investigate the quantum mechanical system of a carbon “test atom” in the proximity of a C60 molecule, both inside and outside the fullerene “cage”. Two sets of bound states are found to exist, a deeply bound set inside the cage and another weakly bound set outside it. Tunnelling between these regions is highly unlikely to happen because of the extreme height and width of the potential barrier. However, we predict that a layer of atoms could be adsorbed onto C60 by forming a quantum mechanical bound state, with the adsorbed atoms being concentrated above the “panels” of the buckyball, consistent with “bucky onions” observed experimentally. Until now analysis of such fullerene systems has been via classical mechanics, but a quantum approach reveals new insights.

The ground-state energy of the double-Λ hypernucleus ΛΛ 11 Be is calculated within the frame-work of the five-body model ααnΛΛ. The five-body nucleus is described using the Faddeev formalism for the unequal mass clusters involved and the potential harmonics expansion of the corresponding amplitudes. The resulting coupled differential equations depend only on the inter-cluster interactions, ΛΛ, Λn, Λα, nα, and αα, which are fairly well known from previous investigations of hypernuclei. The results obtained are in excellent agreement with the recent KEK-E373 experiment as well as with the theoretical results obtained within the Gaussian expansionmethod by Hiyama et al. The ΛΛnn double hypernucleus is also discussed.

We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.

The antisymmetrized molecular dynamics method is used to investigate the two-body electrodisintegration of 4He. Effects of final-state interactions are included via the Glauber multiple scattering approximation. Experimental data for the 4He longitudinal and transverse response functions are well described at high momentum transfer.

A simple method to calculate ground state energies for a typical condensates containing up to A ~ 107 atoms is presented. The method, based on the expansion of the wave function in terms of the Faddeev components, which in turn are expanded in terms of potential harmonics is numerically efficient. We obtain ground state results for condensates of 87Rb containing up to A → 108 atoms. The results agree very well with other methods in regions where the other methods are valid.

The extended antisymmetrized molecular dynamics (AMD) wave function is used to study the two-body nuclear electro-disintegration. The final-state interactions are included using the Glauber multiple scattering approximation. Non-relativistic nuclear charge and current operators are employed when calculating longitudinal and transverse nuclear response functions. It is found that the AMD model gives a very good description of experimental data for the 4He response functions.

A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates-dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density. DOI: 10.1103/PhysRevA.87.013608

Electron-induced proton knock-out process from the He-4 nucleus is investigated. Bound states of the systems are described with the angular-momentum-projected and parity-projected antisymmetrized molecular dynamics wave functions. The nuclear Hamiltonian is constructed with a semi-realistic nucleon-nucleon potential. Non-relativistic nuclear charge and current operators are employed in calculating nuclear transition amplitudes. Final-state interactions are taken into account by the use of the Glauber approximation. It is found that the antisymmetrized molecular dynamics generates a very good description of experimental data at high momentum transfer.

We present a formalism describing the bound state of a large number of bosons and apply it to study nuclei consisting of A α particles. The method has its roots in a few-body approach and is based on the expansion of the many-body Faddeev components in Potential Harmonics, and the subsequent reduction of the Faddeev equation into a two-variable, integro-differential equation. For A → ∞ this equation is transformed into a new simpler integro-differential equation, which is easy to use in calculations for A up to as large as 1000. We use both integro-differential equations to investigate the behavior of nuclei subject to the assumption that they are composed of α particles. Various α α forces were employed. For the Ali-Bodmer potential we found that the A = 5 system (i.e. 20Ne) is the most stable, while for the A = 10 system (i.e. 40Ca) the binding energy has a maximum. The formalism predicts α-decay for larger nuclei, but the value of A where this begins to happen is strongly dependent on the α α potential.

The description of nuclei as a system of alpha particles is considered using a two-variable integrodifferential equation describing A-boson systems. The method is based on the assumption that two-body forces are the dominant ones within the system. This allows the expansion of the A-body wave function in Faddeev components which in turn can be expanded in potential harmonics that result either in a coupled system of differential equations in the hyper-radius r or, when projected on the r(ij) space, in a single two-variable, integrodifferential equation that includes the two-body correlations exactly. The formalism can be readily applied to systems of up to A similar to 20. Going beyond this number one encounters increasingly difficult numerical problems stemming mainly from the structure of the kernel in the integral. However, these problems can be eliminated by transforming the equation, when A -> infinity, into a new one having a kernel which has a simple analytical form and is easy to use in calculations. We employed the transformed equation to investigate the possibility of describing nuclei consisting of A alpha particles. It was found that for the Ali-Bodmer potential the A = 5 system, i.e., the Ne-20, is the most stable while the A = 10 system, i.e., the Ca-40, the binding energy has a maximum. Various aspects concerning the formation of A alpha nuclei are discussed.

The angular-momentum-projected and parity-projected antisymmetrized molecular dynamics is used to analyse the charge and magnetic form factors of the three-nucleon systems. Non-relativistic nuclear charge and current operators with relativistic corrections are employed. The Hamiltonian of the nuclear systems is described with a semi-realistic nucleonnucleon potential. The results obtained are compared with some experimental data. It is found that the theoretical model describes experimental data very well at low momentum transfer.

We are concerned with the inverse scattering problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteristics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrödinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scattering scheme to construct profiles with certain predetermined reflection and transmission characteristics.

We present an integro-differential equation describing systems with large number of bosons. The new equation includes the two-body correlations exactly into account and the kernel has a simple analytic form. The equation has been employed to obtain results for \({A\in\{10,100\}}\) 87Rb atoms confined by an externally applied trapping potential V trap(r). Our results are in excellent agreement with those of the Potential Harmonic Expansion Method (PHEM) and the Diffusion Monte Carlo (DMC) method.

We present a two-variable integro-differential equation describing bound systems of unequal mass particles. The method is based on an extension of the two-variable integro-differential equations in the D = 3(A - 1)-dimensional space, known as IDEA, describing the bound states of A-body systems. This method has been successfully applied in the past to few-body systems with the results obtained being in good agreement to those of competing methods. In the present work we investigate whether the same is true for unequal mass particles. Therefore, we first employ the formalism to obtain binding energies for Lambda- and Lambda Lambda-nuclear systems and compare the results with some other results in the field. Secondly, we apply it to the phi- and phi phi-nuclear systems. Using phi-nucleon and phi-phi interactions, available in the literature, we found that mesic-nuclear systems could exist.

We present a two-variable integro-differential equation describing bound systems of unequal mass particles. The method is based on an extension of the two-variable integro-differential equations in the D = 3(A − 1)-dimensional space, known as IDEA, describing the bound states of A-body systems. This method has been successfully applied in the past to few-body systems with the results obtained being in good agreement to those of competing methods. In the present work we investigate whether the same is true for unequal mass particles. Therefore, we first employ the formalism to obtain binding energies for Λ- and ΛΛ-nuclear systems and compare the results with some other results in the field. Secondly, we apply it to the - and -nuclear systems. Using –nucleon and – interactions, available in the literature, we found that mesic–nuclear systems could exist.

We present a Faddeev-type coupled integrodifferential equations describing unequal mass A-particle systems. The equations are obtained by assuming an expansion of the A-particle wave function in Faddeev amplitudes which, in turn, are expanded in terms of Potential Harmonics. By projecting the resulting system on rij-space we obtained a system of coupled equations which can be used to study multi-strange hypernuclei.