Search results for "Momentum operator"

RPA in wavefunction representation

1992

The RPA is formulated in subspaces of coordinate-like and momentum-like I ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.

Angular distributions in quasi-fission reactions: Evidence for incomplete relaxation of the tilting mode

1985

Angular distributions of fission-like fragments have been measured for50Ti+208Pb and56Fe+208Pb collisions. Z-dependent asymmetries around Θincm= 90° preclude their interpretation in terms of compound nucleus fission with the transition state theory. Fits of the data with a simple ansatz for statistical angular momentum fluctuations (tilting) give evidence for an incomplete relaxation of the tilting mode in quasi fission reactions.

Erratum to: “A quark model analysis of orbital angular momentum” [Phys. Lett. B 460 (1999) 8–16]

2000

Additivity of effective quadrupole moments and angular momentum alignments in the A~130 nuclei

2007

The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and angular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.

The Ramsey method in high-precision mass spectrometry with Penning traps: Theoretical foundations

2007

Abstract This paper presents in a quantum mechanical framework a theoretical description of the interconversion of the magnetron and modified cyclotron motional modes of ions in a Penning trap due to excitation by external rf-quadrupole fields with a frequency near the true cyclotron frequency. The work aims at a correct description of the resonance line shapes that are observed in connection with more complicated excitation schemes using several excitation pulses, such as Ramsey’s method of separated oscillating fields. Quantum mechanical arguments together with the “rotating wave approximation” suggest a model Hamiltonian that permits a rigorous solution of the corresponding Heisenberg eq…

FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS

2020

We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.

Dirac operator spectrum in the linear σ model

2003

Abstract The spectrum of the Dirac operator for the linear σ Model with quarks in the large Nc approximation is presented. The spectral density can be related to the chiral condensate which is obtained using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear correaction are recovered. The spectrum beyond the low energy regime is discussed.

Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields

1997

The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.