Meaning of antiparallel proton and neutron angular momenta at low spins

Abstract

The meaning of the fact that the angular momenta of protons and neutrons are oriented in opposite directions, shown by Otsuka [Phys. Rev. Lett. 71, 1804(1993] for the angular-momentum-projected Nilsson wave functions, is reexamined using a two-rotor model. It is shown that this fact does not necessarily mean an unphysical situation that proton and neutron ellipsoids are rotating freely in opposite directions. On the contrary, it originates in a close binding of the two ellipsoids, which is accompanied by a large spreading of the relative angular momentum due to the uncertainty principle. It is also demonstrated that the elimination of the spurious center-of-mass motion does not substantially change the situation.

Angular correlation between proton and neutron rotors

“…In Ref. [1], Otsuka and we have shown that the elimination of the spurious center-of-mass motion does not substantially change the situation in a classical treatment of independent nucleon motions. By using a simple two-rotor model in 2-dimensional space, we have also given a correct interpretation of the opposite-direction correlation of the two angular momenta, as is discussed in Sec.…”

“…JJ [2] is larger than θ (1) JJ (≈θ (2) JJ ) by ∼ 0.3 radians. However, the decreasing behavior is common to all the definitions.…”

“…In Ref. [1] we have employed a model consisting of two rotors in 2-dimensional space to discuss the implication of the oppositely directed angular momenta of protons and neutrons. The Hamiltonian of the model is written as,…”

“…We are grateful to Professor Otsuka for useful discussions and continuous interest in this work. Sections 1 and 2 of this paper are reviews of a collaboration paper [1] with him.…”

“…We have recently given careful consideration to the meaning of the antiparallel proton and neutron angular momenta at low spins [1]. This fact that the total angular momenta of protons and that of neutrons are oriented in the opposite directions has first been demonstrated by Otsuka et al for the angular-momentum projected Nilsson wave functions [2,3,4].…”