Background:The meson exchange current (MEC) contribution is important in the neutron-proton bremsstrahlung process (npγ ) when the two nucleon-scattering angles are small. However, our understanding of such effects is limited, and the reason why meson exchange current effects dominate the npγ cross section has not been thoroughly investigated. Purpose: The primary focus of this investigation is to understand the origin of the MEC contribution, to identify the leading MEC amplitudes, and to comprehend why these MEC amplitudes dominate the npγ cross sections. Method: We used a new method that combines the one-boson-exchange (OBE) approach with the soft-photon approach to define 10 different npγ amplitudes. These amplitudes are used to calculate npγ cross sections at 225 MeV for nucleon laboratory scattering angles lying between 12 • and 43 • . The results of these calculations are then compared to investigate the meson exchange current effect in npγ . Results: (i) The OBE amplitude M PS npγ ,µ and the two-u-two-t special (TuTts) soft-photon amplitude M TuTts npγ ,µ predict quantitatively similar npγ cross sections. (ii) The MEC effect is found to be significant when the two nucleon-scattering angles are far from the elastic limit (45 • ), but the effect is insignificant when the nucleon angles approach the elastic limit. (iii) The origin of the MEC effect and the leading MEC amplitudes have been identified in this investigation. Furthermore, the reason is now clear why the leading MEC amplitudes dominate the npγ cross section when the nucleon-scattering angles are small. (iv) The contribution from the anomalous magnetic moments of the proton and the neutron is confirmed to be negligibly small. (v) In general, the theoretical cross sections using the amplitude M PS npγ ,µ , or the amplitude M TuTts npγ ,µ , are consistent with the triple differential cross sections recently measured at the Los Alamos National Laboratory. However, there exists an unexplained discrepancy between theory and experiment in some cases. Conclusions: The findings of this investigation have enhanced our understanding of the meson exchange current effect in npγ . The comparative amplitude method introduced can be used for other bremsstrahlung investigations.

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles shows the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode and N . The corresponding time values have been derived analytically under certain approximation and numerically for the parabolic atomic trap. The revival of the mode at time of several seconds, as a direct evidence of the effect, can occur, if the normal component is significantly suppressed. We also discuss alternative means to verify the proposed mechanism.PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Pj, 67.90.+z The progress [1][2][3][4] in trapping the low density alkaline gases and cooling them below the temperature T BEC of the Bose-Einstein condensation has initiated a search for features of the atomic coherent collective behavior specific for the trapped condensate. The theoretical predictions [5-7] made for the normal frequencies of the condensate in the traps have been successfully confirmed in the experiments [8,9] employing the resonant modulations of the trapping potential.It is worth noting that the calculations of the normal frequencies [5][6][7] are based on the Gross-Pitaevskii (GP) equation strictly valid in the limit of a number of particles N → ∞, with the average density ρ being fixed [10]. The GP equation describes the condensate in the mean field (MF) approximation. In this sense the condensate wave function Φ(x, t) obeying the time dependent GP equation is viewed as a classical field [10]. In the atomic traps [1][2][3][4] neither N can be obviously considered as infinite nor ρ is fixed (ρ ∼ N for N < 200 − 500 and ρ ∼ N 2/5 for N > 10 4 [11]). Therefore, it is important to understand how the actual quantum evolution of the collective mode deviates, if any, from that predicted by the mean field approach for finite N .In this paper we will show that, while the normal frequencies and short time evolution are determined correctly by the GP equation whenever N is only a few times larger than 1, the quantum behavior of the normal modes can deviate from the mean field one at times much longer than the time scale set by the normal frequencies. The quantum behavior is characterized by dephasing, that is by the phenomena of the collapses and the revivals of the normal mode amplitude at zero temperature. Below we will derive the corresponding quantum solution in the approximation neglecting the exchange effects. The numerical solution taking into account the full many body Hamiltonian for N = 300 in the approximation allowing N atoms to occupy two single particle levels only is presented also. It turns out that both approaches yield close values for the collapse and the revival times, respectively, with the collapse time being of the same order of magnitude as the relaxation time reported experimentally [8,9].The quantum collapses and revivals were first analyzed in Ref.[12] for a single atom in a resonant cavity. Very recently such phenomena hav...

The proton-proton bremsstrahlung (pp␥) process has been used as a tool to study the problems related to both the off-shell proton electromagnetic vertex and pseudoscalar ͑ps͒-pseudovector ͑pv͒ N coupling. We have developed an approach which can be applied to investigate the two problems together. We show that ͑i͒ the analyzing powers calculated using the on-shell p␥p vertex, with ps or pv coupling, yield very poor results for most of the cases with small proton scattering angles at 280 MeV, ͑ii͒ the calculations using the off-shell p␥p vertex and ps coupling in most cases produce cross sections which fail to fit the TRIUMF data at 200 and 280 MeV, and ͑iii͒ the data for both cross sections and analyzing powers in the energy region between 157 and 280 MeV can only be consistently described by the calculations using the off-shell p␥p vertex and pv coupling. Thus our results indicate that the off-shell p␥p vertex must be used in relativistic pp␥ calculations and the pseudovector coupling is the best choice for the N vertex. More accurate data are needed for further study of the problems.

Single-particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective timeaveraged potential. We show that the trapping is possible when the frequency of the rotations exceeds some threshold. Slightly above this threshold the weakly interacting gas of the trapped atoms acquires the properties of a quasi-one-dimensional system in the frame rotating together with the field. The role of the atom-atom interaction in changing the ideal gas solution is discussed. We show that in the limit of large numbers of particles the rotating field whose frequency is appropriately modulated can be utilized as a driving force principally for the center-of-mass motion as well as for the angular momentum Lϭ2 normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed. ͓S1050-2947͑97͒03001-1͔PACS number͑s͒: 03.75.Fi, 05.30.Jp, 32.80.Pj, 67.90.ϩz II. SINGLE-PARTICLE STATES IN THE ROTATING FRAMEIn our analysis of the behavior of a single atom trapped by the magnetic field B we follow the approximation that the atomic spin orientation is parallel to B ͓16͔. Then the effective potential energy of the atom seeking the low field is