Shape Isomeric States Research Articles

Shape isomeric states effects on the giant monopole resonances in even-even molybdenum isotopes

Shape isomeric states effects on the giant monopole resonances in even-even molybdenum isotopes

Shape isomers in Pt, Hg and Pb isotopes with {hbox {N}}le 126

Deformation-energy surfaces of 54 even-even isotopes of Pt, Hg and Pb nuclei with neutron numbers up to 126 are investigated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop macroscopic energy and shell plus pairing-energy corrections obtained from a Yukawa-folded mean-field potential at the desired deformation. A new, rapidly converging Fourier shape parametrization is used to describe nuclear shapes. The stability of shape isomeric states with respect to non-axial and higher-order deformations is investigated.

Effects of the γ -soft isomeric states on the giant monopole resonances in even-even cadmium isotopes Cd110,112,114,116

The shape evolutions of the even-even cadmium isotopes $^{110--116}\mathrm{Cd}$ are investigated in this work. The giant monopole resonances built on different shape isomeric states are studied using the quasiparticle random phase approximation, which is implemented with a finite amplitude method. We find the local minima corresponding to the prolate, oblate, and triaxial-deformed isomeric states in the even-even cadmium isotopes. Their responses to external monopole perturbations are quite different. Larger deformation tends to make the energy of the giant monopole resonance to shift lower. It is well known that the density functional models have some difficulties in predicting the right positions of the monopole resonances in cadmium isotopes: the centroid energies always seem too large compared to the experimental results. Our calculations show the giant monopole resonances built on the $\ensuremath{\gamma}$ soft isomeric states in the cadmium isotopes have centroid energies even lower than the experimental measurements. Therefore, if the isomeric branching of these $\ensuremath{\gamma}$ soft isomeric states turns out to be prominent, isomer mixing may be a good explanation to the longstanding puzzle.

Pygmy dipole resonance built on the shape-isomeric state inNi68

The pygmy dipole resonance (PDR) of $^{68}\mathrm{Ni}$ was measured by Wieland et al. [Phys. Rev. Lett. 102, 092502 (2009)] through virtual photon scattering and Rossi et al. [Phys. Rev. Lett. 111, 242503 (2013)] through a photoneutron reaction. However, the PDR peaks are observed at different positions: 11 and 9.55(17) MeV respectively. Our calculation based on the deformed relativistic random phase approximation suggests that the discrepancy between these two measurements might be induced by the effect of the shape-coexistence isomeric state in $^{68}\mathrm{Ni}$.

On possible shape isomers in the Pt-Ra region of nuclei

.A certain number of yet unknown super- and hyper-deformed shape isomeric states are predicted in even-even nuclei of the region between Pt and Ra, using the macroscopic-microscopic model based on the Lublin Strasbourg Drop for the macroscopic energy and shell plus pairing corrections evaluated through the Yukawa-folded mean-field potential for the microscopic part. A new, rapidly converging shape parametrization is used to describe the vast range of nuclear deformations between the ground and the fission isomeric states up to near the scission configuration. Quadrupole moments are evaluated in the local minima and turn out to be in good agreement with the experimental data wherever available.

Shape coexistence and α-decay chains of 293Lv

Two recently observed 293Lv (Z = 116) α-decay chains [Eur. Phys. J. A 48, 62 (2012)] are investigated in the framework of covariant density functional theory with PC-PK1, where the pairing correlations are treated by the Bardeen-Cooper-Schrieffer method with a density-independent zerorange force. From the calculated potential energy curves, it is found that two minima always occur, with one having an almost spherical shape and the other exhibiting a large deformed prolate shape. Originating from the ground state and the shape-isomeric state of 293Lv, the two observed α-decay chains are constructed and the calculated Qα values are found to be in good agreement with the data.

Global Calculation of Nuclear Shape Isomers

To determine which nuclei may exhibit shape isomerism, we use a well-benchmarked macroscopic-microscopic model to calculate potential-energy surfaces as functions of spheroidal (epsilon{2}), hexadecapole (epsilon{4}), and axial-asymmetry (gamma) shape coordinates for 7206 nuclei from A=31 to A=290. We analyze these and identify the deformations and energies of all minima deeper than 0.2 MeV. These minima may correspond to characteristic experimentally observable shape-isomeric states. Shape isomers mainly occur in the A=80 region, the A=100 region, and in an extended region centered around (208)Pb. We compare our model to experimental results for Kr isotopes. Moreover, in a plot versus N and Z we show for each of the 7206 nuclei the calculated number of minima. The results reveal one fairly unexplored region of shape isomerism, which is experimentally accessible, namely the region northeast of (82)(208)Pb.

Mean-Field Theoretical Structure of He and Be Isotopes

The structures of He and Be even-even isotopes are investigated using an axially symmetric Hartree-Fock approach with a Skyrme-IIIls mean field potential. In these simple HF calculations, He and Be isotopes appear to be prolate in their ground states and Be isotopes have oblate shape isomeric states. It is also shown that there exists a level crossing when the nuclear shape changes from the prolate state to the oblate state. The single neutron levels of Be isotopes exhibit a neutron magic number 6 instead of 8 and show that the level inversion between 1/2- and 1/2+ levels occurs only for a largely deformed isotope. Protons are bound stronger in the isotope with more neutrons while neutron levels are somewhat insensitive to the number of neutrons and thus the nuclear size and also the neutron skin become larger as the neutron number increases. In these simple calculations with Skyrme-IIIls interaction no system with a clear indication of neutron halo was found among He and Be isotopes. Instead of it we have found 8He+2n, 2n+8He+2n, and 16Be+2n like chain structures with clusters of two correlated neutrons. It is also shown that 8He and 14Be in their ground states are below the neutron drip line in which all nucleons are bound with negative energy and that 16Be in its ground state is beyond the neutron drip line with two neutrons in positive energy levels.

Decay of1+States as a New Probe of the Structure of0+Shape Isomers

The nuclides 98Mo and 100Mo have been studied in photon-scattering experiments by using bremsstrahlung produced from electron beams with kinetic energies from 3.2 to 3.8 MeV. Six electromagnetic dipole transitions in 98Mo and 19 in 100Mo were observed for the first time in the energy range from 2 to 4 MeV. A specific feature in the two nuclides is the de-excitation of one state with spin J = 1 to the 0+ ground state as well as to the first excited 0+ state, which cannot be explained in standard models. We present a model that allows us to deduce the mixing coefficients for the two 0+ shape-isomeric states from the experimental ratio of the transition strengths from the J = 1 state to the 0+ ground state and to the 0+ excited state.

Hartree-Fock+BCS Approach to Unstable Nuclei with the Skyrme Force

We reanalyze the results of our extensive Hartree-Fock + BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2 <= Z <= 114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration formulae suitable for Cartesian mesh representation and elucidate the features of each formula and the differences from a method based on the Fourier transformation.

Search for highly deformed shape isomers in 28Si, 24Mg and 20Ne linked by successive alpha decays

Measurements of the 12C( 16O, 20Neα)α, 12C( 16O,αα) 20Ne, 12C( 16O, 8Be) 20Ne and 12C( 16O, 16Oα) 8Be reactions have been performed at E c.m. = 27.0 MeV. For decays proceeding through resonant states in the intermediate 24Mg nucleus, angular correlation measurements have enabled spin assignments to be made and the dominant entrance channel angular momentum to be determined. The results are inconsistent with recent similar experiments which were interpreted as arising from successive α-decays from deformed shape isomeric states in 28Si and 24Mg.

Generator coordinate method calculation of the E2 decay lifetime of shape isomers in the actinide region.

We apply the generator coordinate method in a fully microscopic calculation of the {ital E}2 decay lifetime of the shape isomeric states of {sup 236}U, {sup 238}U, and {sup 240}Pu. The basis states have been generated by constrained Hartree-Fock Bardeen-Cooper-Schrieffer calculations with the SkM{sup {asterisk}} force. Triaxial quadrupole deformations have been included. Implications upon the decay lifetime of the quasidegeneracy of the isomeric state and the one-phonon excitation in the first well are examined. {copyright} {ital 1996 The American Physical Society.}

The 8Be + 20Ne molecular resonances in the 12C + 16O collision

Excitation functions of the 12C(16O, 8Be)20Ne reaction leading to some low-lying states in 20Ne have been studied at Ec.m. = 22∼29 MeV. Some new resonances are identified with fluctuation analysis, and their spin and parity are determined. If we plot them on a Ec.m. vs. J(J + 1) plane together with resonances reported previously in the same reaction channel, they seem to constitute a rotational band which coincides with the elastic band of the 8Be + 20Ne system rather than with that of the 12C + 16O system. Furthermore these resonances are found to persist in having almost negligible correlation in energy with those identified in the 12C + 16O channels. A resonance at Ec.m. = 26.9 MeV which has been proposed by Eswaran et al. as a superdeformed shape isomeric state is not identified in the present data.

Intermediate structure and the shape isomer in 233Th

With a neutron-capture experiment the s-wave resonances in 233Th between 50 eV and 4.2 keV were investigated for delayed γ-γ coincidences. At least two intermediate structures are found in the distribution of the relative delayed γ-yield R at about 1 and 2 keV incident neutron energy confirmed by statistical tests. We interpret them as being due to the population of a shape-isomeric state via class-II states admixed to the resonances. From the derived class-II spacing DII and the gross shape of the structures the isomeric ground-state energy EII as well as the coupling width Γ↓ may then be estimated. These results are compatible with the decay of a shape isomer with a half life between 1 and 100 ns. They also would suggest that the height of the inner potential barrier EA is less than or of the order of the neutron binding energy, and that the inner barrier is relatively thin.

Structural connection of highly deformed shape isomeric states in 28Si, 24Mg, and 20Ne by alpha-alpha coincidence studies in 12C(16O, alpha )24Mg*--> alpha +20Ne*

Alpha-alpha coincidence measurements have been made in the reaction $^{12}\mathrm{C}$${(}^{16}$O,\ensuremath{\alpha}${)}^{24}$${\mathrm{Mg}}^{\mathrm{*}}$\ensuremath{\rightarrow}\ensuremath{\alpha}${+}^{20}$${\mathrm{Ne}}^{\mathrm{*}}$ at the bombarding energy of E${(}^{16}$O)=63 MeV corresponding to the resonance in the $^{12}\mathrm{C}$${+}^{16}$O system at ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=26.9 MeV leading to the compound nuclear state at 43.7 MeV in $^{28}\mathrm{Si}$. The coincidence alphas are detected, one at 0\ifmmode^\circ\else\textdegree\fi{} to the beam and the other at 20\ifmmode^\circ\else\textdegree\fi{} to 80\ifmmode^\circ\else\textdegree\fi{} in steps of 10\ifmmode^\circ\else\textdegree\fi{}. The spins of the states in $^{24}\mathrm{Mg}$ at 20.2 and 21.4 MeV are fed strongly at this resonance are inferred to be J\ensuremath{\ge}8 from the branching of these states to the states in the ground state band of $^{20}\mathrm{Ne}$. From the result it is deduced that these states of $^{24}\mathrm{Mg}$ do not correspond to the near Coulomb barrier resonances in the $^{12}\mathrm{C}$${+}^{12}$C system. In addition, the coincidence measurements also lead to the result that the states of $^{24}\mathrm{Mg}$ in the 20--22 MeV region fed at the resonance preferentially decay to the eight-particle--four-hole states of $^{20}\mathrm{Ne}$ near 7.2 MeV. These results establish the structural connection of highly deformed shape isomeric states in the region of \ensuremath{\epsilon}=1.17 to 1.35 and \ensuremath{\gamma}=50\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{} in $^{28}\mathrm{Si}$, $^{24}\mathrm{Mg}$, and $^{20}\mathrm{Ne}$ expected from the Nilsson-Strutinsky calculations of Leander and Larsson.

Comment on "Evidence for superdeformed shape isomeric states in 28Si at excitations above 40 MeV through observations of selective particle decays of 16O+12C resonances in 8Be and alpha channels"

A recent study of the $^{12}\mathrm{C}$${(}^{16}$O${,}^{8}$Be${)}^{20}$Ne and $^{12}\mathrm{C}$${(}^{16}$O,\ensuremath{\alpha}${)}^{24}$Mg reactions has led, through cross channel correlation analysis, to the identification of two superdeformed shape isomeric states in $^{28}\mathrm{Si}$ at excitation energies of 43.7 and 46.2 MeV. We suggest that both these states may have \ensuremath{\alpha}-\ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{16}$O-\ensuremath{\alpha} nuclear molecule structure. Our suggestion is supported theoretically by cranked cluster model calculations and experimentally by previous studies of the $^{12}\mathrm{C}$${(}^{12}$C,\ensuremath{\alpha}\ensuremath{\alpha}${)}^{16}$O reaction, $^{12}\mathrm{C}$${+}^{12}$C scattering, and the $^{12}\mathrm{C}$${(}^{20}$Ne${,}^{12}$${\mathrm{C}}^{12}$C${)}^{8}$Be transfer reaction.

Reply to "Comment on 'Evidence for superdeformed shape isomeric states in 28Si at excitations above 40 MeV through observations of selective particle decays of 16O+12C resonances in 8Be and alpha channels' "

Our recent study of the $^{12}\mathrm{C}$${(}^{16}$O${,}^{8}$Be${)}^{20}$Ne and $^{12}\mathrm{C}$${(}^{16}$O,\ensuremath{\alpha}${)}^{24}$Mg reactions has led to the identification of two superdeformed shape isomeric states in $^{28}\mathrm{Si}$ at excitation energies of 43.7 and 46.2 MeV. We conjectured from this study that these resonances have structures which correspond to the secondary minimum with deformation parameters \ensuremath{\epsilon}=1.35 and \ensuremath{\gamma}=60\ifmmode^\circ\else\textdegree\fi{} according to Nilsson-Strutinsky calculations. We give arguments to show that this conjecture is more appropriate and consistent with the presently available evidence.

Evidence for superdeformed shape isomeric states in 28Si at excitations above 40 MeV through observations of selective particle decays of 16O+12C resonances in 8Be and alpha channels.

Excitation functions of the reactions $^{12}\mathrm{C}$${(}^{16}$O${,}^{8}$Be${)}^{20}$Ne and $^{12}\mathrm{C}$${(}^{16}$O${,}^{4}$He${)}^{24}$Mg leading to several states have been measured in the range ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=25.7--38.6 MeV. From cross channel correlation analysis two intermediate resonance structures at ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=26.9 and 29.5 MeV corresponding to excitation energies of 43.7 and 46.2 MeV in $^{28}\mathrm{Si}$ have been identified. Angular distribution measurements for $^{12}\mathrm{C}$${(}^{16}$O${,}^{4}$He${)}^{24}$${\mathrm{Mg}}_{\mathrm{g}.\mathrm{s}.}$ have also been made at the lower resonance at ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=26.9 MeV which enable spin assignment of ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${14}^{+}$ to this resonance. Striking observation of preferential $^{8}\mathrm{Be}$ decay of both the resonances to the 8-particle--4-hole states in $^{20}\mathrm{Ne}$ is interpreted as evidence for the resonances to be highly deformed shape isomeric configurations in $^{28}\mathrm{Si}$ expected from deformed shell-model calculations.

Shape coexistence in the neutron deficient Pb isotopes and the configuration-constrained shell correction approach

Calculations of shape-isomeric states in neutron deficient lead isotopes have been performed using the configuration-constrained shell correction method with a Woods-Saxon average potential and a monopole pairing interaction. This approach enables us to decompose the ground state potential energy surface in separate parts characterized uniquely by the number of occupied intruder orbitals. The calculations reproduce the positions of the excited 0+ intruder states. The isotope196Pb is discussed in detail.

Evidence for long-lived isomeric states in neutron-deficient 236Am and 236Bk nuclei

A 5.76 MeV alpha-particle group has been observed in Am and Bk sources separated from a CERN W target. The data are interpreted due to the production of long-lived isomeric states in 236Am and 236Bk which decay to 236Pu. The possibility of high spin states as well as of shape isomeric states is raised.