Band head spin assignment of superdeformed bands in 86Zr

Two parameter expressions for rotational spectra viz. variable moment of inertia (VMI), ab formula and three parameter Harris ω² expansion are used to assign the band head spins (I₀) of four rotational superdeformed bands in ⁸⁶Zr. The least-squares fitting method is employed to obtain the band head spins of these four bands in the A~80 mass region. Model parameters are extracted by fitting of intraband γ-ray energies, so as to obtain a minimum root-mean-square (rms) deviation between the calculated and the observed transition energies. The calculated transition energies are found to depend sensitively on the assigned spins. Whenever an accurate band head spin is assigned, the calculated transition energies are in agreement with the experimental transition energies. The dynamic moment of inertia is also extracted and its variation with rotational frequency is investigated. Since a better agreement of band head spin with experimental results is found using the VMI model, it is a more powerful tool than the ab formula and Harris ω² expansion.     

Band head spin assignment of superdeformed bands in Hg isotopes through power index formula

The power index formula has been used to obtain the band head spin(I_0) of all the superdeformed(SD) bands in Hg isotopes. A least squares fitting approach is used. The root mean square deviations between the determined and the observed transition energies are calculated by extracting the model parameters using the power index formula. Whenever definite spins are available, the determined and the observed transition energies are in accordance with each other. The computed values of dynamic moment of inertia J~((2)) obtained by using the power index formula and its deviation with the rotational frequency is also studied. Excellent agreement is shown between the calculated and the experimental results for J~((2)) versus the rotational frequency. Hence, the power index formula works very well for all the SD bands in Hg isotopes expect for ~(195)Hg(2, 3, 4).     

Study for Superdeformed Bands in A～190 Region with Quantum Group Uqp(u2) Model

superdeformed bands in the A～190 region are systematically analyzed by using the twoparameter expansion of quantum group U_qp(u₂) Model. The calculated results of E2 transition γ ray energies are in agreement with experimental data. According to three different methods for the spin assignment of rotational bands, the spin values of the band head I₀ of the yrast SD bands in ¹⁹⁴Hg(1) and ¹⁹⁴Pb(1) are assigned. Furthermore, the physical meaning of the nuclear softness is discussed, and these nuclear softness values of a signature partner are almost equal.     

Aligned rotation of octupole-vibrational states in deformed nuclei

Analysis of level energies in aligned octupole bands in even-even deformed nuclei using the VMI-model expressed in terms of the rotational angular momentumR, show that almost complete alignment is reached at low spin values. It is shown that the alignment is almost spin independant. Using the ground-state band VMI-parameters only a renormalization of the alignment parameter 〈J _⊥〉 is enough to reproduce the level energies of the NPB's.     

Systematic study of rotational energy formulae for superdeformed bands in La and Ce isotopes

The experimental rotational spectra of superdeformed(SD) bands of ~(130)La, ~(131)Ce(1,2), ~(132)Ce(1,2,3) and133 Ce(1,2,3) in the A～130 mass region are systematically analyzed with the four parameter formula, power index formula, nuclear softness formula, and VMI model. It is observed that out of all the formulae, the four parameter formula suits best for the study of the ~(130)La, ~(131)Ce(1,2), ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. The four parameter formula works efficiently in determining the band head spin of the ~(130)La, ~(131)Ce(1,2) ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. Good agreement is seen between the calculated and observed transition energies whenever the accurate spin is assigned. In ~(132)Ce(1), the power index formula is found to work better than the other three formulae. The dynamic moment of inertia is also calculated for all the formulae and its variation with the rotational frequency is investigated.     

Simple model calculations of spin and quantized aligment for the A ∼ 60–90 superdeformed mass region

We have used a simple model based on the rotational energy formula E(I, K) to study the structure of the superdeformed (SD) mass region 60–90. The higher order inertial parameters A and B of such model were determined by using the Marquardt method of nonlinear least-squares routines to fit the proposed transition energies with their observed values. A good agreement between the calculated and corresponding experimental transition energies of the SD bands is obtained which supports our proposed model. In addition, the frequency dependence of the dynamic, θ⁽²⁾, and static, θ⁽¹⁾, moments of inertia is used to determine the lowest spin (I_f) and the K-value of the considered SD bands; namely, ⁵⁸Ni(b1), ⁵⁸Cu, ⁵⁹Cu(b1), ⁶¹Zn, ⁶²Zn, ⁶⁵Zn, ⁶⁸Zn, ⁸⁴Zr, ⁸⁶Zr(b1), ⁸⁸Mo(b1, b2, b3) and ⁸⁹Tc. As a result of the identity exist among some of the considered SD bands, we have studied the incremental alignment and also the angular momentum alignment.     

Identification of Bandhead Spin and Identical Bands for Odd-A Nuclei in $A\sim190$ Superdeformed Mass Region

The dynamical moment of inertia is estimated with its even-power expansion of the rotational frequency and in accordance we determine the intermediate spins of the superdeformed (SD) rotational bands. Using Marquardt method of nonlinear least-squares routines, we determine the expansion coefficients by fitting the proposed dynamical moment of inertia with its recent experimental data of the SD nuclei in the A=190 mass region. The comparison between our theoretical and available experimental data for the dynamic moment of inertia and spin shows good agreements. Also, we have calculated the static moment of inertia at three alternative values of spin. The value of spin at which the two moments of inertia are nearly equals is to be regarded as a bandhead spin of the corresponding band. These studies are carried out for eighteen bands of odd-A nuclei of the superdeformed region 190, namely ¹⁸⁹Hg(b1), ¹⁹¹Hg(b1, b2, b3, b4), ¹⁹³Hg(b2, b3, b5), ¹⁹⁵Hg(b1, b2, b3, b4), ¹⁹³Tl(b1, b2, b3, b5), ¹⁸⁹Tl(b1), and ¹⁹⁷Bi(b1). We also notice the occurrence of identical SD bands with near identical transition energies among the considered SD bands.     

The rotational quasi-continuum in specific configurations: high-K states and superdeformation

The analysis of the fluctuations of the counts of unresolved γ-γ energy spectra can extend our knowledge of the rotational motion at high angular momentum and excitation energy above the yrast band. Detailed studies of the rotational quasi-continuum built on specific intrinsic nuclear configurations are here discussed. First, the validity of the K-selection rules in the quasi-continuum region is investigated in the case of the normal deformed nucleus ¹⁶³Er. The γ cascades feeding into low-K and high-K bands are analyzed studying variance and covariance of the spectrum fluctuations. Low-K bands are found to be fed by a much larger effective number of cascades than high-K bands, while the covariance between pairs of gated spectra shows that the cascades feeding into low-K bands are different from those feeding into high-K bands. These findings suggest a persistence of K-selection rules in the region of excitation energy and angular momentum probed by the rotational decay of ¹⁶³Er. As a second case, the existence of a rotational quasi-continuum in the super deformed well of ¹⁴³Eu is discussed. An intense bump of rotationally correlated transitions is observed to develop as function of fold in the high spin region of gated spectra. Fold distribution, angular anisotropies, moment of inertia and life time show that the bump consists of fully damped super deformed transitions. This gives experimental evidence of damped rotational motion up to several MeV excitation energy above the super deformed yrast line.     

Rotational bands from shell-model Hamiltonians

Shell-model Hamiltonians with eigenstates forming rotational bands are considered. Such states have eigenvalues proportional to J(J+ 1) and can be projected from a Slater determinant of deformed orbitals. The latter are linear combinations of single-nucleon wave functions of j-orbits in a major shell. Conditions on matrix elements and single-nucleon energies are obtained in terms of the deformation parameters. An actual effective interaction is constructed yielding exact ground-state rotational bands for ²⁰Ne and ²⁴Mg which gives reasonable agreement with energies of other sd shell nuclei. Unlike the case of SU(3) symmetry, spin-orbit interaction and different single-nucleon energies can be accommodated and the procedure is not confined to oscillator major shells. Other welcome departures of our effective interaction from the SU(3) picture are the absence of rotational spectra in oxygen isotopes and that the ²⁴Mg ground-state band is projected from a Nilsson-type deformed state with axial symmetry.     

Untersuchung der Anregungen von186Re nach der (n, γ)-Reaktion

Prompt and delayedγ-γ-coincidences were measured after slow neutron capture in¹⁸⁵Re by use of Ge(Li)-detectors. New isomers were found at 99.4 keV (T_1/2=27±7ns) and at ≈330keV (T_1/2=17.4±0.7 ns). The evaluation of coincidence data established 10 rotational bands with band heads below 700 keV. The level scheme is discussed in detail: Nilsson assignments are proposed for the band configurations, and calculations of Coriolis mixing andγ-transition probabilities are presented which reproduce the experimental level energies and transition intensities very satisfactorily.     

New Method for Spin Assignment of Superdeformed Rotational Bands

A new method for spin assignment of superdeformed rotational bands is proposed and it turns out to be more efficient than other methods used before. The application is made to superdeformed bands in A～190 and A～150 mass regions. By analyzing the standard deviation of the fixed gamma-ray energies of an SD band in different methods, the advantage of the present method over the other methods is presented. This method brings then a comprehensive interpretation of the methods used in spin assignment.     

Microscopic study of electromagnetic properties and band spectra of neutron deficient ~(133,135,137)Sm

A microscopic high spin study of neutron deficient and normally deformed ~(133,135,137)Sm has been carried out in projected shell model framework.The theoretical results have been obtained for the spins,parities and energy values of yrast and excited bands.Besides this,the band spectra,band head energies,moment of inertia and electromagnetic transition strengths are also Predicted in these isotoPes.The calculations successfully give a deeper understanding of the mechanism of the formation of yrast and excited bands from the single and multi-quasi particle configurations.The results on moment of inertia predict an alignment of a pair of protons in the proton(1 h_(11/2))~2 orbitals in the yrast ground state bands of ~(133-137)Sm due to the crossing of one quasiparticle bands by multi-quasiparticle bands at higher spins.The discussion in the present work is based on the deformed single particle scheme.Any future experimental confirmation or refutation of our predictions will be a valuable information which can help to understand the deformed single particle structure in these odd mass neutron deficient ~(133-137)Sm.     

Microscopic insight into the quasi-particle structure of odd-mass terbium isotopes

The present work has been focussed on the application of Projected Shell Model to study the negative parity rotational band structure up to the high spin states of the neutron-rich odd mass Terbium isotopes with neutron numbers ranging from 90 to 98. The structure evolution in these nuclei has been made on the basis of various nuclear structure properties like energy spectra, transition energies, wave functions and electromagnetic transition probabilities (B(E2) and B(M1)). Besides, the occurrence of back bending has also been reported in the present work.     

Lifetime measurement of the ((11/2)−) isomer in 125Cs

A new rotational band has been observed in ¹⁶⁷Lu by ¹⁵²Sm (¹⁹F,4n)reaction at the HI-13 tandem accelerator of CIAE in Beijing. The high spin transition energies of the new band are almost identical to the triaxial superdeformed bands recently discovered in ¹⁶³Lu and ¹⁶⁵Lu. This new band is predicted as a triaxial superdeformed band by total routhian surface calculations. Received: 6 October 1997     

Collective structures and smooth band termination in109Sn

Six rotational bands up to energies E _x =24.7 MeV and spinsj ^π=(79/2^?) have been identified in¹⁰⁹Sn using the GAMMASPHEREγ-detector array. Four of the bands show smoothly decreasing dynamic moments of inertia at rotational frequencies?ω>0.6 MeV. The bands arise at medium spins from a coupling of a valence d_5/2, g_7/2 or h_11/2 neutron to the deformed 2p2h proton excitation of the Z=50 core¹⁰⁸Sn. At very high?ω these bands show the typical behaviour of smoothly terminating bands, i.e. a gradual alignment of the angular momenta of the valence particles and holes corresponding to a transition from high collectivity to noncollective states.     

Collective structures and smooth band termination in 109Sn

Six rotational bands up to energies E _x = 24.7 MeV and spins J^π=(79/2^?) have been identified in ¹⁰⁹Sn using the GAMMASPHERE γ-detector array. Four of the bands show smoothly decreasing dynamic moments of inertia at rotational frequencies ?ω > 0.6 MeV. The bands arise at medium spins from a coupling of a valence d_5/2, g_7/2 or h_11/2 neutron to the deformed 2p2h proton excitation of the Z=50 core ¹⁰⁸Sn. At very high ?ω these bands show the typical behaviour of smoothly terminating bands, i.e. a gradual alignment of the angular momenta of the valence particles and holes corresponding to a transition from high collectivity to noncollective states.     

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

The positive-parity yrast bands of ^{79, 81, 83, 85, 87, 89}Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.     

New perspective in the use of soft rotor formula for K = 2 γ-band

The use of soft rotor formula (SRF) for the level energies of K?=?2 γ-band for the shape transitional even Z even N nuclei in the medium mass region is illustrated. With proper treatment, we obtained positive values of the moment of inertia and softness parameter, as opposed to negative values reported in literature. The moments of inertia of the γ-band are almost equal to the ground state band values. The systematic dependence of the softness parameter on energy ratio R _4/2 is studied. The effect of the odd–even spin staggering on these parameters is studied in detail. In deformed nuclei, the same parameters for odd and even spin members yield fair energy values.     

Superfluid-to-normal phase transition and extreme regularity of superdeformed bands

We derive an exact semiclassical expression for the second inertial parameter B for superfluid and normal phases. Interpolation between these limiting values shows that the function B(I) changes sign at the spin I _c that is critical for the rotational spectrum. The quantity B proves to be a sensitive measure of the change in static pairing correlations. The superfluid-to-normal transition reveals itself in a specific variation of the ratio B/A versus the spin I with a plateau characteristic of the normal phase. We find this dependence to be universal for normal deformed and superdeformed bands. A long plateau with a small value of B/A ～ A ^?8/3 explains the extreme regularity of superdeformed bands.