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1969•Progress of Theoretical PhysicsOpen access

On Collective Motion of Rotational Invariant System Composed ofN-Particles

Tetsuo Got o

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Abstract

We study collective coordinates of rotational motion by means of canonical transformation. It is shown that our Hamiltonian is equivalent to that of Tamura, Nataf and Villars [T. Tamura, Nuovo Cim. 4 (1956), 1307; R. S. Nataf, Nucl. Phys. 2 (1957), 497; F. Villars, Annual Review of Nuclear Science (Annual Review Inc.) Vol. 7 (1957), p. 185]. Further investigation is carried out and it shows that a rotation-like collective motion is introduced besides rotation as a whole of a system and even in a spherically symmetric case we have rotational levels. Our interest is focussed on collective momenta rather than collective coordinates and they are generators of GL(3).

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We study collective coordinates of rotational motion by means of canonical transformation. It is shown that our Hamiltonian is equivalent to that of Tamura, Nataf and Villars [T. Tamura, Nuovo Cim. 4 (1956), 1307; R. S. Nataf, Nucl. Phys. 2 (1957), 497; F. Villars, Annual Review of Nuclear Science (Annual Review Inc.) Vol. 7 (1957), p. 185]. Further investigation is carried out and it shows that a rotation-like collective motion is introduced besides rotation as a whole of a system and even in a spherically symmetric case we have rotational levels. Our interest is focussed on collective momenta rather than collective coordinates and they are generators of GL(3).

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Available abstract

We study collective coordinates of rotational motion by means of canonical transformation. It is shown that our Hamiltonian is equivalent to that of Tamura, Nataf and Villars [T. Tamura, Nuovo Cim. 4 (1956), 1307; R. S. Nataf, Nucl. Phys. 2 (1957), 497; F. Villars, Annual Review of Nuclear Science (Annual Review Inc.) Vol. 7 (1957), p. 185]. Further investigation is carried out and it shows that a rotation-like collective motion is introduced besides rotation as a whole of a system and even in a spherically symmetric case we have rotational levels. Our interest is focussed on collective momenta rather than collective coordinates and they are generators of GL(3).

Key concepts: Physics, Collective motion, Rotation around a fixed axis, Invariant (physics), Hamiltonian (control theory), Canonical transformation, Rotation (mathematics), Classical mechanics

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