Pseudospin symmetry in the relativistic harmonic oscillator

Guo, Jian-You; Fang, Xiang-Zheng; Fu-Xin, XU

doi:10.1016/j.nuclphysa.2005.04.017

Cited by 63 publications

(38 citation statements)

References 42 publications

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“…An added motivation for this article is given by the recent demonstration that the relativistic 3 + 1 HO with scalar and vector potentials can describe successfully the heavy nucleus spectrum [22]. The parameters of the HO are determined by fitting the scalar and vector potentials derived from relativistic mean-field nuclear calculations (RMF).…”

Section: Introductionmentioning

confidence: 99%

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Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

et al. 2006

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We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3 + 1 dimensions. We show how the charge conjugation and γ 5 chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

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Section: Introductionmentioning

confidence: 99%

“…[23] and can be included in a calculation like the one of Ref. [22] to improve the results. Thus, the study of all the possible eigenenergies of the 1 + 1 HO, presented in this article, considering not only the positive energy solutions already obtained for the 3 + 1 case in Ref.…”

Section: Introductionmentioning

confidence: 99%

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

et al. 2006

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“…Furthermore, some authors have investigated the spin symmetry and Pseudospin symmetry under the Dirac equation in the presence and absence of coulomb tensor interaction for some typical potentials such as the Harmonic oscillator potential [16][17][18][19][20][21][22][23][24][25], Coulomb potential [26,27], Woods-Saxon potential [28,29], Morse potential [30][31][32][33][34][35], Eckart potential [36,37], ring-shaped non-spherical harmonic oscillator [38], Pöschl-Teller potential [39][40][41][42][43], three parameter potential function as a diatomic molecule model [44], Yukawa potential [45][46][47][48][49], pseudoharmonic potential [50], Davidson potential [51], Mie-type potential [52], Deng-Fan potential [53], hyperbolic potential [54] and Tietz potential [55].…”

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confidence: 99%

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

Oyewumi

Falaye

Onate

et al. 2014

Int. J. Mod. Phys. E

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In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac equation because the spin-1/2 fermions represent the most frequent building blocks of the molecules and atoms. Motivated by the considerable interest in this equation and its relativistic symmetries (spin and pseudospin) in the presence of solvable potential model, we attempt to obtain the relativistic bound states solution of the Dirac equation with double ring-shaped Kratzer and oscillator potentials under the condition of spin and pseudospin symmetries. The solutions are reported for arbitrary quantum number in a compact form. the analytic bound state energy eigenvalues and the associated upper-and lower-spinor components of two Dirac particles have been found. Several typical numerical results of the relativistic eigenenergies have also been presented. We found that the existence or absence of the ring shaped potential potential has strong effects on the eigenstates of the Kratzer and oscillator particles with a wide band spectrum except for the pseudospin-oscillator particles where there exist a narrow band gap.

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“…On substituting equation (35) into equation (33) and using equations (34), (36) and (37), equation (33) becomes…”

Section: Spin Symmetry Solutions Of the Dirac Equation With The Rosenmentioning

confidence: 99%

Approximate Solutions of the Dirac Equation for the Rosen-Morse Potential in the Presence of the Spin-Orbit and Pseudo-Orbit Centrifugal Terms

Oyewumi¹

2012

Theoretical Concepts of Quantum Mechanics

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1 2 ) and (n − 1, ℓ + 2, j = ℓ + 3 2 ), where n, ℓ and j are the single-nucleon radial, orbital and total angular momentum quantum numbers for a single particle, respectively (Arima et al., 1969;Hecht & Adler, 1969;Ginocchio, 2004 ). The total angular momentum is given as j = ℓ + s, where ℓ = ℓ + 1 is a pseudo-angular momentum and s = 1 2 is a pseudo-spin angular momentum. Meng et al., (1998) deduced that in real nuclei, the PSS is only an approximation and the quality of approximation depends on the pseudo-centrifugal potential and pseudo-spin orbital potential. The orbital and pseudo-orbital angular momentum quantum numbers for SS ℓ and PSS ℓ refer to the upper-and lower-spinor components (for instance, F n,κ (r) and G n,κ (r), respectively. Ginocchio (1997); (1999); (2004); (2005a); (2005b) and Meng et al., (1998) showed that SS occurs when the difference between the vector potential V(r) and scalar potential S(r) in the Dirac Hamiltonian is a constant (that is, ∆(r)=V(r) − S(r)) and PSS occurs when the sum of two potential is a constant (that is, Σ(r)=V(r)+S(r)). A large number of investigations have been carried out on the SS and PSS by solving the Dirac equation with various methods (Alberto et al

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Pseudospin symmetry in the relativistic harmonic oscillator

Cited by 63 publications

References 42 publications

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

Approximate Solutions of the Dirac Equation for the Rosen-Morse Potential in the Presence of the Spin-Orbit and Pseudo-Orbit Centrifugal Terms

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