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We shall, in the present article, con6ne our attention mainly to electric and magnetic excitations produced by bombardment with nuclear particles. A brief review of the theory of inelastic electron scattering is given in Sec. IIE.3. ). "T.Huus and J. H. Bjerregaard, Phys. Rev. ' 92, 15'79 (1953).r4B. Elbek and C. K. Bockelman (submitted for publication). 5 Recently, Coulomb excitation studies have been made employing cyclotron accelerated nitrogen ions LAlkhazov, Andreyev, Greenberg, and Lemberg, Nuclear Phys. 2, 65 (1956)j.K. Alder and A. Winther, Phys. Rev. 96, 237 (1954). McHale, and Thaler, Phys. Rev. 101, 662 {1956),and 102, 1567. A WKB approximation which yields results in essential agreement with the detailed quantal treatment has beep given

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It is found that the concept of pseudo-spin and pseudo-oscillator quantum numbers, introduced by previous authors, can be helpful in understanding the qualitative features of quasiparticle motion in rotating potentials, for the orbits with normal panty (excluding the high j orbits). In the first part of the paper, the use of pseudo-spin in static deformed potentials is briefly reviewed.

We investigate the ground and low excited states of a rotating, weakly interacting Bose-Einstein condensed gas in a harmonic trap for a given angular momentum. Analytical results in various limits, as well as numerical results are presented, and these are compared with those of previous studies. Within the mean-field approximation and for repulsive interaction between the atoms, we find that for very low values of the total angular momentum per particle, L/N → 0, where Lh is the angular momentum and N is the total number of particles, the angular momentum is carried by quadrupolar (|m| = 2) surface modes. For L/N = 1 a vortex-like state is formed and all the atoms occupy the m = 1 state. For small negative values of L/N − 1 the states with m = 0 and m = 2 become populated, and for small positive values of L/N − 1 atoms in the states with m = 5 and m = 6 carry the additional angular momentum. In the whole region 0 ≤ L/N ≤ 1 we have strong analytic and numerical evidence that the interaction energy drops linearly as a function of L/N . We have also found that an array of singly quantized vortices is formed as L/N increases. Finally we have gone beyond the mean-field approximation and have calculated the energy of the lowest state up to order N for small negative values of L/N − 1, as well as the energy of the low-lying excited states.