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Register a new userCan one identify the intrinsic structure of the yrast states in $^{48}$Cr after the backbending?
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The backbending phenomenon in $^{48}$Cr has been investigated using the recently developed Projected Configuration Interaction (PCI) method, in which the deformed intrinsic states are directly associated with shell model (SM) wavefunctions. Two previous explanations, (i) $K=0$ band crossing, and (ii) $K=2$ band crossing have been reinvestigated using PCI, and it was found that both explanations can successfully reproduce the experimental backbending. The PCI wavefunctions in the pictures of $K=0$ band crossing and $K=2$ band crossing are highly overlapped. We conclude that there are no unique intrinsic states associated with the yrast states after backbending in $^{48}$Cr.
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We present a novel and simple algorithm in the variation after projection (VAP) approach for the non-yrast nuclear states. It is for the first time that the yrast state and non-yrast states can be varied on the same footing. The orthogonality among the calculated states is automatically fulfilled by solving the Hill-Wheeler equation. This avoids the complexity of the frequently used Gram-Schmidt orthogonalization, as adopted by the excited VAMPIR method. Thanks to the Cauchys interlacing theorem in the matrix theory, the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. Once such minimization is converged, all the calculated energies and the corresponding states can be obtained, simultaneously. The present VAP calculations are performed with time-odd Hartree-Fock Slater determinants. It is shown that the calculated VAP energies (both yrast and non-yrast) are very close to the corresponding ones from the full shell model calculations. It looks the present algorithm is not limited to the VAP, but should be universal, i.e., one can do the variation with different forms of the many-body wavefunctions to calculate the excited states in different quantum many-body systems.
The yrast lines in Kr isotopes with $N=42$, 44, and 46 are investigated in a beyond mean field framework with both prolate-oblate coexistence and quasiparticle alignment taken into account. Quasiparticle orbitals with high-$j$ and low-$Omega$ on the oblate side are shown to be responsible for the sharp backbending observed in $^{82}$Kr, by driving the yrast shape from prolate to oblate. This suggests that quasiparticle alignment may not be neglected in the investigation of the shape evolution along the yrast line.
Projection is noninvertible. This means two different vectors may have the same projected components. In nuclear case, one may take the intrinsic state as a vector, and take the nuclear wave function as the projected component obtained by projecting the former onto good quantum numbers. This immediately comes to the conclusion that, for a given nuclear state in the laboratory frame of reference, the corresponding intrinsic state in the intrinsic frame of reference can not be uniquely determined. In this letter, I will show this interesting phenomenon explicitly based on the improved variation after projection(VAP) method. First of all, it is found that, the form of the trial VAP wavefunction with spin $J$ can be greatly simplified by adopting just one projected state rather than previously adopting all $(2J+1)$ spin-projected states for each selected Slater determinant. This is crucial in the calculations of high-spin states with arbitrary intrinsic Slater determinants. Based on this simplified VAP, the present calculations show that orthogonal intrinsic states (differed by $K$) may have almost the same projected wavefunctions, indicating the uncertainty of the nuclear intrinsic states. This is quite different from the traditional concept of intrinsic state which is expected to be unique.
Low spin states in the self-conjugate even-even nucleus 48-Cr were investigated using the MINIBALL gamma-ray spectrometer. At the FN tandem accelerator in Cologne the 46-Ti(3-He,n) reaction was used for the measurement of gamma-gamma coincidences for an excitation function from 7 to 12 MeV beam energy. 17 excited states were observed, nine for the first time by means of gamma-ray spectroscopy, and new spin assignments were made. No excited states apart from the ground band were observed below 3.4 MeV.
Isotopical dependence of spin-orbit splitting discovered by us in spectra of heavy nuclei close to doubly magic ones is checked in polarization effects arising in charge exchange (p,n) reaction between the A=48 isobarical states.
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