Deformed Wave Functions Research Articles

Hadronic Paschen-Back effect in P-wave charmonia under strong magnetic fields

The Hadronic Paschen-Back effect (HPBE) is a new phenomenon induced by the interplay between finite orbital angular momenta of hadrons and external strong magnetic fields. We review the HPBE in P-wave charmonia and show its mass spectra, deformed wave functions, and mixing ratios, which are evaluated by the constituent quark models in a magnetic field and the cylindrical Gaussian expansion method.

Neutron removal from the deformed halo nucleus Ne31

Experimental data on Coulomb breakup and neutron removal indicate that 31Ne is one of the heaviest halo nuclei discovered so far. The possible ground state of 31Ne is either 3/2- coming from p-wave halo or 1/2+ from s-wave halo. In this work, we develop a treatable model to include deformed wave functions and a dynamical knockout formalism which includes the dependence on the nuclear orientation to study the neutron removal from 31Ne projectiles at energies around E=200 MeV/nucleon. A detailed account of the effects of deformation on cross sections and longitudinal momentum distributions is made. Our numerical analysis indicates a preference for the 31Ne ground state with spin parity 3/2-.

Electromagnetic transition strengths in soft deformed nuclei

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $<\Delta \vec{J}^2>$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.

Role of low-lcomponent in deformed wave functions near the continuum threshold

The structure of deformed single-particle wave functions in the vicinity of zero energy limit is studied using a schematic model with a quadrupole deformed finite square-well potential. For this purpose, we expand the single-particle wave functions in multipoles and seek for the bound state and the Gamow resonance solutions. We find that, for the ${K}^{\ensuremath{\pi}}={0}^{+}$ states, where K is the $z$-component of the orbital angular momentum, the probability of each multipole components in the deformed wave function is connected between the negative energy and the positive energy regions asymptotically, although it has a discontinuity around the threshold. This implies that the ${K}^{\ensuremath{\pi}}={0}^{+}$ resonant level exists physically unless the $l=0$ component is inherently large when extrapolated to the well bound region. The dependence of the multipole components on deformation is also discussed.

Unified description of the 2νββ decay in spherical and deformed nuclei

The Gamow-Teller double-beta decay, with two neutrinos in the final state, is calculated within the QRPA approach. Higher-order corrections to the RPA result are studied within a boson expansion formalism. The specific feature of the present paper is that the single-particle basis is obtained through angular-momentum projection from an orthogonal set of deformed wave functions. The effect of deformation on the Gamow-Teller transition amplitude, as well as on the the single β − and β + strengths distribution is obtained. The Gamow-Teller amplitude is calculated for the transitions 0 + i → 0 + f and 0 + i → 2 + f. The method is applied to the 2νββ d probability 82 34Se to 82 36Kr.

On the construction of translationally invariant deformed wave functions

Translationally invariant nuclear wave functions are constructed from deformed harmonic oscillator shell-model wave functions, with an exact projection of angular momentum quantum numbers. It is shown that the computation of matrix elements with the translationally invariant wave functions is as simple as the standard calculation, and formulae are obtained for (i) the potential energy, (ii) the kinetic energy and rms radius, and (iii) the charge form factor.

Deformed binding fields: (II). Deformed wave functions in 6Li arising from the tensor force

A Hill-Wheeler representation is used to provide variational wave functions in a calculation of the T = 0 levels of 6Li. The model Hamiltonian contains a harmonic central force as well as a tensor interaction. It is found that the lowest levels with J = 1, 2 and 3 may be generated from a single intrinsic function with approximately the same stationary values of the variational parameters for each level and thus form a kind of collective band. The level scheme indicates that the vector effects of the tensor force have been taken into account. It appears that the α-particle core is soft towards deformation caused by the 1p nucleons.