Pseudospin in Rotating Nuclear Potentials

Abstract

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.

Consequences of a relativistic pseudospin symmetry for radial nodes and intruder levels in nuclei

“…For example, (n r s 1/2 , (n r −1)d 3/2 ) will havel = 1, (n r p 3/2 , (n r −1)f 5/2 ) will havel = 2, etc. This pseudospin symmetry has been used to explain features of deformed nuclei [3], including superdeformation [4] and identical bands [5,6] and to establish an effective shell-model coupling scheme [7]. In view of its central role in both spherical and deformed nuclei, there has been an intense effort to understand the origin of this symmetry.…”

Spin (Pseudospin) doublet in view of energy-dependent potential

“…The notion of pseudospins= 1/2 was defined [17,18] to elucidate this quasidegeneracy in view of nonrelativistic quantum mechanics.s (pseudospin) andl (pseudo-orbital angular momentum) concepts were introduced to define a pseudospin doublet with total angular momentum j =s+l . Identical bands, magnetic moment, deformation, and superdeformation in nuclei were successfully expounded by considering the pseudospin concept [19][20][21][22][23][24][25]. In spite of knowing that the pseudospin initially was a nonrelativistic concept, its relativistic characteristic was discovered [26]; Ginocchio reported that usual l of the lower part of the Dirac spinor corresponds to the pseudo-orbital angular momentum.…”

Pseudospin symmetry in nuclear structure and its supersymmetric representation

“…The pseudospin symmetry remains an important concept in the axially deformed [1,11,12,13] and even the triaxially deformed [14,15] nuclei. Based on this concept, a simple but useful pseudo-SU(3) model was proposed, and it was generalized to be the pseudo-symplectic model [16,17,18,19].…”

“…One of the pioneering quantitative studies was carried out by Bohr, Hamamoto, and Mottelson [1] in 1982 in the scheme of rotating nuclear potentials. For the large deformation, the asymptotic Nilsson quantum numbers [N, n 3 , Λ]Ω are good quantum numbers.…”

“…Based on this Nilsson Hamiltonian, Bohr, Hamamoto, and Mottelson tried to understand the origin of pseudospin symmetry in terms of the spin-orbit v ls and orbit-orbit v ll interactions. It turned out that the origin of pseudospin symmetry was connected with a special ratio between the strengths of these two interactions, i.e., v ls /v ll = 4 [1]. They found that the pseudospin symmetry is helpful to qualitatively understand the properties of quasi-particle motions in the rotating potentials.…”