Angular correlation between proton and neutron rotors
N. Tajimaa)a) Department of Applied Physics, University of Fukui, Fukui, 910-8507, Japan
Contact e-mail: tajima@quantum.apphy.u-fukui.ac.jp
I discuss first the main results from my collaboration with Professor Otsuka on the meaning of theantiparallel 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[2-4]. A question was raised immediately [5] that it might be incorrect because it would mean an
unphysical free contra-rotation of proton and neutron ellipsoids while only small-amplitude oscillations inthe scissors mode are possible from a physical point of view. (Actually, Ref. [2-4] has never described this
opposite rotations as free contra rotations.) Ref.[5] argued that the removal of the spurious center-of-mass
motion could make the angular momenta of protons and neutrons parallel. Afterwards, two papers [6,7] havecited Ref.[5] as solving the controversy.
In Ref.[1], by using a two-rotor model, we have confirmed the fact that the directions of angular momentaof protons and that of neutrons are indeed opposite to each other, but that this fact does not mean an
unphysical free contra rotation. On the contrary, it originates in a close binding of the two ellipsoids, whichis accompanied with a large spreading of the relative angular momentum due to the uncertainty principle.
We have also shown that the elimination of the spurious center-of-mass motion does not substantiallychange the situation in a classical treatment of independent nucleon motions.
Second, I would like to discuss further on the angular correlations between protons and neutrons
expressed by two rotors.
The principal intention of Ref. [2] has been to suggest the possibility that collective rotational excitations
are accompanied with a narrowing of the angle between the proton and neutron angular momenta. Namely,along a rotational band, the angle changes from 180 degree at spin zero to smaller angles at high spins, andclose to zero at band terminations. In this paper, I pay attention to the angle between the symmetry axes ofrotors as well as to the angle between the angular momenta. These two angles have different kinds ofinformation because of the quantum mechanical uncertainty in the directions of the angular momenta
relative to the principal axes of the ellipsoids, and also owing to dynamically correlated rotational motions of
the two rotors. I would like to discuss also the distributions of these angles, not only their expectation
values.
In Ref. [1], it has been stressed a close relationship between the opposite-direction correlation between
the angular momenta of protons and neutrons and the properties of the scissors mode which is the oscillationof the angle between the symmetry axes of the proton and neutron ellipsoids. I would also like to discuss
further on this point.
References[1] N. Tajima and T. Otsuka, Phys. Rev. C, 84 (2011), 064316.
[2] T. Otsuka, Phys. Rev. Lett. , 71 (1993), 1804.
[3] T. Otsuka, T. Mizusaki, and M. Honma, Nucl. Phys., A570 (1994), 265c.
[4] T. Otsuka and J.N. Ginocchio, Nucl.Phys. A577 (1994), 197c.
[5] E.R. Marshalek, Phys. Rev C, 50 (1994), R5.
[6] Y. Sun, C.-L. Wu, K., M. Guidry, and D.-H. Feng, Phys. Rev. Lett., 80 (1998), 672.
[7] D.R. Bes and O. Civitarese, Phys. Rev. C, 63 (2001), 044323.