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Latest Results for Few-Body Systems

01 November 2024

• Calculable Microscopic Theory for $$^\textbf{12}$$ C( $$\alpha $$ , $$\gamma $$ ) $$^\textbf{16}$$ O Cross Section near Gamow Window II

  Abstract

  A microscopic approach to the \(^{12}\) C \((\alpha , \gamma )^{16}\) O radiative-capture reaction near the Gamow window has been proposed by Y. Suzuki, Few-Body Syst. 62, 2 (2021). The important ingredients of the approach include the following: (1) The states of \(^{12}\) C and \(^{16}\) O relevant to the reaction are described by fully microscopic 3  \(\alpha \) -particle and 4  \(\alpha \) -particle configurations. (2) The isovector electric dipole transition is accounted for through the isospin impurity of the constituent \(\alpha \) -particles. (3) The relative motion among the \(\alpha \) -particles is expanded in terms of correlated-Gaussian basis functions. A calculation of the radiative-capture cross section demands double angular-momentum projections, that is, the angular momentum of \(^{12}\) C consisting of 3 \(\alpha \) -particles and the orbital angular momentum for \(^{12}\) C \(-\alpha \) relative motion. Advancing the previous formulation based on the single angular-momentum projection, I carry out the double projection and present all the formulas needed for the cross section calculation.

• Algebraic Approach and Coherent States for the Modified Dirac Oscillator in Curved Spacetime with Spin and Pseudospin Symmetries

  Abstract

  In this paper, we study and exactly solve the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries using an algebraic approach. Moreover, we focus on the radial part of this problem and apply the Schrödinger factorization method to demonstrate that the system possesses an SU(1, 1) symmetry. From this, we derive the wave functions and their respective energy spectrum. Additionally, we compute the radial coherent states of the modified Dirac oscillator and examine their temporal evolution in the spin and pseudospin limits, respectively.

• Integral Equation Approach for a Hydrogen Atom in a Strong Magnetic Field

  Abstract

  The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwinger form. Then, we approximate the asymptotically irrelevant parts by a discrete Hilbert space basis that allows an exact analytic evaluation of the relevant Green’s operators by continued fractions. The total asymptotic Green’s operator is calculated by a complex contour integral of subsystem Green’s operators. We present a sample of numerical results for a wide range of magnetic field strengths.