Coriolis Coupling Model Research Articles

Level Spectra of Odd Isotopes of Ga, As, Br, and Rb in the Coriolis Coupling Model with a Residual Interaction of the Pairing Type

Low-lying positive- and negative-parity states of odd isotopes of Ga, As, Br, and Rb in the mass region bounded by $30lZl38$ and $40\ensuremath{\le}N\ensuremath{\le}48$ have been calculated in the Coriolis coupling model with the incorporation of a residual interaction of the pairing type in calculating the intrinsic states. The single-particle energy levels and wave functions are first computed in a deformed well with a spin-orbit strength of $\ensuremath{-}0.26\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ and for a well-flattening parameter $D$ between $\ensuremath{-}0.035\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$ and $\ensuremath{-}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$. These values are consistent with the observed location of the $1{f}_{\frac{5}{2}}$, $2{p}_{\frac{3}{2}}$, and $2{p}_{\frac{1}{2}}$ states in ${\mathrm{Sc}}^{41}$ and ${\mathrm{Sc}}^{49}$. The deformation $\ensuremath{\beta}$ has been restricted to a range around $\ensuremath{\beta}=\ifmmode\pm\else\textpm\fi{}0.2$ which is consistent with the observed $B(E2)$ value to the first excited ${2}^{+}$ state of neighboring even-even nuclei, assuming a rotational character for this state. Using the orbitals in the deformed well as vacuum states, new particle states are calculated for a residual interaction of the pairing type, using a pairing-force strength consistent with the observed odd-even mass difference and the Bardeen-Cooper-Schrieffer (BCS) variational formalism. The complete variational calculation has been carried out for the ground, the particle, and the core excited states with due consideration of the blocking effect. This procedure, which differs from the usual quasiparticle treatment, ensures that the particle and core excited states are orthonormal to each other and to the ground state and that the average particle number is conserved in each configuration. Band-head energies and the unperturbed bands built on them are calculated, using these new renormalized single-particle states and the moment of inertia obtained from the excitation energy of the first excited ${2}^{+}$ state of neighboring even-even nuclei, assuming a rotational character for this state. Using the same moment of inertia and the computed wave functions of the deformed well, the Coriolis coupling matrix elements between these bands are calculated. The inclusion of the residual interaction introduces multiplicative into the Coriolis coupling strength which results in a reduction of its magnitude for off-diagonal terms. These overlap factors have been calculated from the BCS wave functions. Thus we have used no arbitrary free parameters in the computation. The final spectra of the negative- and positive-parity states are obtained by a diagonalization procedure, using, respectively, the bands built on the 10 Nilsson states in the $1f\ensuremath{-}2p$ shell and on the 15 Nilsson states in the $1g\ensuremath{-}2d\ensuremath{-}3s$ shell. The model can correctly account for (i) the observed ground-state spins for all nuclei in this region, (ii) the large number of negative-parity states with spins $\ensuremath{\le}{\frac{7}{2}}^{\ensuremath{-}}$ below 1-MeV excitation energy, and (iii) the occurrence of several low-lying positive-parity states, in particular a low-lying ${\frac{9}{2}}^{+}$, ${\frac{5}{2}}^{+}$ doublet.

Decay ofNi57and Excited Levels inCo57

The decay of ${\mathrm{Ni}}^{57}$ has been investigated in order to obtain detailed information about the level structure of the odd-even ${\mathrm{Co}}^{57}$. Lithium-drifted germanium detectors as well as standard scintillation-spectrometry techniques have been used. The levels at 1.46, 1.59, 1.75, and 2.62 MeV have been established with direct de-excitation to the ${\mathrm{Co}}^{57}$ ground state, in addition to the already known levels at energies of 1.37, 1.497, and 1.9 MeV. It has been confirmed that the 1.497-MeV level is the only one which decays by a (0.127-1.37)-MeV cascade of gamma rays. The various gamma-gamma coincidence studies have been performed; and based on these results, and on the ratios of electron capture to ${\ensuremath{\beta}}^{+}$ decay, a decay scheme of ${\mathrm{Ni}}^{57}$ is proposed, and the results discussed in the light of the Coriolis coupling model. The half-life of the 1.497-MeV level has been measured as (0.60\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec and an upper limit for the half-life of the 1.37-MeV level is given as \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ sec.

Coriolis-Coupling Model Prediction of Moments and Transition Rates for Deformed Odd Nuclei in the1f72Shell

The magnetic dipole and electric quadrupole moments and reduced transition probabilities have been computed for the Coriolis-coupling model using the wave functions obtained in an earlier paper. These wave functions were obtained from a linear combination of the ten rotational bands based on the ten available single-particle and core excited states in the $1f\ensuremath{-}2p$ shell, and the corresponding eigenvalues were consistent with the observed level spectra of the odd nuclei in the $1{f}_{\frac{7}{2}}$ shell. The moments and transition rates predicted here are also in good agreement with experiment. Thus, the observed magnetic moments can no longer be considered as evidence supporting the validity of solely the spherical shell model for these nuclei. Contributions to the magnetic moment from single-particle terms and from cross terms between the bands are found to be important and have been included. The observed inhibition of the $M1$ transitions (which are allowed in the collective model) is a consequence of the strong band mixing which results in strong cancellation between the contributions from the direct and the cross terms. The good agreement between the predicted and observed values of the quadrupole moments and $B(E2)$ values has been achieved using the free proton charge of unity and neutron charge of zero. The contribution to the quadrupole moment from the single-particle term is found to be important, and on occasion constitutes as much as 50% of the total quadrupole moment. Furthermore, the collective spectroscopic quadrupole moment, with proper inclusion of the contribution from different bands, in some cases has a different sign from the intrinsic quadrupole moment. Proper inclusion of the contributions to the quadrupole moment from different bands and of the single-particle term leads to the important result that odd nuclei may yet have a very small quadrupole moment despite having large deformations.