E2 Transition Rates Research Articles

The SU(3) structure of rotational states in heavy deformed nuclei

The SU(3) coupling scheme provides an informative basis for the expansion of shell-model wave functions and their interpretation in collective-model terms. We show in this paper that it is possible, using the coupled-rotor-vibrator model, to infer averages of the distributions of SU(3) representation labels in heavy rotational nuclei by direct interpretation of physically observed E2 transition rates and quadrupole moments. We find that the distributions of SU(3) representation labels have nearly constant average values for states belonging to some well-defined rotational bands. These are bands of states having B(E2) values and quadrupole moments that follow the predictions of the rotor model. Such bands are interpreted as soft SU(3) bands in parallel with the concept of a soft rotor band with vibrational-shape fluctuations. The concept of a soft SU(3) band and its implications for beta-vibrational excited bands is developed. The average SU(3) representation labels inferred from experiment are interpreted by calculating those implied by the Nilsson model. An analysis of the SU(3) content of Nilsson wave functions also leads to two remarkable predictions. The first is that, in the asymptotic limit, the Nilsson model implies intrinsic states for a rotor band that are beta rigid. The second is that, although the intrinsic Nilsson state is axially symmetric, it generates a sequence of K = 0,2,4, … bands.

Electric quadrupole transition rates for even parity levels of Si I

Non-relativistic Hartree-Fock radial wavefunctions have been used to provide ab initio estimates of E2 transition rates from levels of the 3p2 configuration to those of the 3p4f configuration in Si I. Where it is possible to make comparison with experimental data the results are in reasonable qualitative accord with recent multiphoton ionization observations.

Electromagnetic properties of some odd-odd nuclei in the A≈ 100 region and IBFFM description of 106Ag

Electromagnetic properties of odd-odd transitional nuclei with A≈ 100 are investigated experimentally and theoretically. Nanosecond isomers are studied in-beam by means of delayed γγ-coincidences and the generalized centroid-shift method. The reactions 98Mo+30MeV 7Li and 92,94Mo+ 50 MeV 12C are utilized. Following half-lives are determined: T 1 2 (547.2 keV in 102Rh) = 0.25±0.07ns, T 1 2 (243.1 keV in 102Rh) = 0.30±0.10ns, T 1 2 (181.1 keV in 99Tc) = 3.8 ± 0.3ns, T 1 2 (2902.0keV in 104Cd) = 0.6±0.1 ns, T 1 2 (118.7keV in 103Pd) =0.8±0.2 ns, T 1 2 (131.1 keV in 105Cd) = 1.5 ±0.3 ns, T 1 2 (211.8 keV in 104Ag) = 1.4±0.1 ns, T 1 2 (181.0 keV in 102Ag) = 3.5±0.2 ns. Additionally, several upper limits of level lifetimes are derived. The systematics of E1, M1 and E2 transition rates in 100,102,104Rh and 102,104,106Ag is presented and discussed. Fast M1 transitions within the 2qp π g ̃ 9 2 ν h ̃ 1 2 band appear to be associated with the strong coupling of the π g ̃ 9 2 proton and the rotational alignment of the h ̃ 11 2 neutron. Extensive IBFFM calculations of level energies and electromagnetic properties of 106Ag as a typical case demonstrate that this model could account for the complex structural pattern of this type of nuclei. NUCLEAR REACTIONS 98Mo( 7Li, 3n), ( 7Li2nα), E=30 MeV; 92,94Mo( 12C, pn), 94Mo( 12C, 2n), ( 12C, 2pn), E = 50 MeV; measured E γ , I γ , γγ( t). 102Rh, 99Tc, 102,104Ag, 104Cd,

Is the confining potential weaker than linear in heavy quark-antiquark system?

By using a dipole moment sum rule, we find that there is a relation between the hyperfine splitting, fine splitting, E1 transition rates and the scalar part of the quark—antiquark potential S( r) in the heavy quarkonium. Assuming S( r) = ar s , s>0, a>0, the latest data seem to indicate a weaker confining potential ( s<1), but can not completely exclude the linear confinement ( s = 1).

Exotic N=82 nuclei 153Lu and 154Hf and filling of the pi h11/2 subshell.

Microsecond isomers in the very proton-rich N=82 nuclei $^{153}\mathrm{Lu}$ and $^{154}\mathrm{Hf}$ have been identified by \ensuremath{\gamma}-ray spectroscopy following mass analysis of $^{102}\mathrm{Pd}$ +245 MeV $^{54}\mathrm{Fe}$ reaction products using the Daresbury Recoil Separator. The decays of the isomers, interpreted as (\ensuremath{\pi}${h}_{11/2}$${)}^{n}$ states, are characterized. Examination of reduced E2 transition rates between (\ensuremath{\pi}${h}_{11/2}$${)}^{n}$ states in the N=82 isotones indicates that the half-filling of the \ensuremath{\pi}${h}_{11/2}$ subshell occurs just below Z=71.

Low-spin and isomeric states in 198Pb

Low- and medium-spin states in 198Pb are studied using the reaction 198(3He, 3n) at laboratory energy 27.5 MeV. The in-beam measurements comprise γ-ray singles, γ-RF timing, γ-ray angular distributions and γ-γ coincidences. Seven new levels are located and assigned spins and parities. The previously reported lifetimes are unambiguously assigned: T1/2(5−) = 50.4 ± 0.5 ns, T1/2(7−) = 4.19 ± 0.10 μs and T1/2(9−) = 240 ± 15 ns. The corresponding transition rates B(λ) are deduced. The new non-yrast levels are compared to the existing systematics. A tentative excited (collective) band structure is proposed and compared to a similar one in 196Pb. Systematic trends in E1, E2 and E3 transition rates in light Pb isotopes are discussed.

Broken SU(3) symmetry applied to rotational nuclei: Cylindrical intrinsic states in the interacting boson model.

An interacting cylindrical boson model, describing rotating cylindrical intrinsic states, is utilized to study the bandhead states of the rotational bands in rare-earth nuclei. The three fundamental quasispin (\ensuremath{\Lambda}) bosons, ${p}_{s}$ (\ensuremath{\Lambda}=0) and ${p}_{\ensuremath{\lambda}}$ (\ensuremath{\Lambda}=(1/2), are introduced and used to solve Hamiltonians with cylindrically broken SU(3) symmetry. This approach, simply incorporated into the interacting boson model SU(3) rotational limit, gives some new results in four areas of interest: changes in order of the strict SU(3) bandhead sequences, explanations for observed low-lying ${0}^{+}$ rotational bands not accounted for in the pure SU(3) limit, certain bandhead mixing effects, and analytical expressions for E2 transition rates between bandhead states. We also obtain further insights into the interacting boson model SU(4) sp\ifmmode\bar\else\textasciimacron\fi{} boson model of Chen and Arima. We illustrate with new results for $^{156}\mathrm{Gd}$, $^{168}\mathrm{Yb}$, and $^{168}\mathrm{a}$ sequence of well-studied nuclei having increasing interacting boson approximation valence boson number.

Absolute E0, E1 and E2 transition rates in even-even nuclei obtained in thermal neutron capture

Subnanosecond lifetimes have been measured in deformed and transitional even-even nuclei. Strong evidence is reported for spin-related octupole vibrational admixtures in 2QP band members in 168Er. The 0+ level in 172Yb is a candidate for a mixed symmetry state. Forbidden transitions in the 0(6) nuclei 196Pt and 124Te are considered.

Shell-model predictions for electromagnetic properties of N=50 nuclei.

Predictions for E2, M1, and M4 transition rates and moments, together with examples of transition-charge densities, are presented for states of N=50 nuclei. These predictions are based on one-body spectroscopic amplitudes obtained from the wave functions of a new N=50 shell-model calculation which incorporates the 0${f}_{5/2}$, 1${p}_{3/2}$, 1${p}_{1/2}$, and 0${g}_{9/2}$ single-particle orbits and an empirically determined effective Hamiltonian for this space. The predictions are compared with experimental data, first in order to evaluate how well the model space, as applied by this Hamiltonian, accounts for observations, and then to assess the importance of configurations excluded from the model space and to determine the values of the operator renormalizations (effective charges and effective g factors) which optimally map the theoretical results onto the corresponding experimental values.

The nuclear spectroscopy and structure of 223Ra

The level structure of 223Ra is reinterpreted in terms of 3 2 ±, 5 2 ±, and 1 2 ± parity-doub The non-adiabatic rigid reflection-asymmetric rotor model reproduces the main features of the experimental data assuming the presence of octupole deformation β 3 ∼- 0.1. In particular, the experimental E1 transition rates are accounted for by the calculated permanent collective electricdipole moment.

Multiplet structure and core-related effects on transition rates in87Y and neighbouringA? 90 nuclei

Bombarding a85Rb target by 27 MeVα-particles the following half-lives of excited states in different nuclei have been determined by means of the generalized controid shift method: in87Y,T 1/2(2827.1 keV)=0.75±0.10 ns,T 1/2(2675.9 keV)=0.25±0.10 ns,T 1/2(3595.3 keV)=0.5±0.2 ns andT 1/2(2986.9, 3094.4 keV)<0.1 ns; in88Y,T 1/2(232.1 keV)=0.8±0.1 ns and in85Rb,T 1/2(151.2 keV)=0.6±0.1 ns. In87Y, the members of the doublet (vg 2/−29 )8+ (πp1/2) are identified. E2 transition rates 21/2+⇒ 17/2+ in odd A≈ 90 nuclei are shown to represent essentially core transitions. Evidence for the existence of seniority-five configurations is found.

Intrinsic operators and wave functions for the interacting boson model.

We use the eigenstate of the shape operators in second quantized form to give a geometrical interpretation to each boson excitation in the interacting boson model. For well-deformed systems a method is presented by which the intrinsic components of any boson number preserving operator can be calculated in second quantized form and to leading order in the boson number. In this way vibrational and rotational modes are identified and the corresponding excitation energies and moments of inertia are calculated to leading order in the boson number. The intrinsic components of the E2 transition operator are also calculated. Using these results several E2 transition rates are calculated to leading order in the boson number.

36S(t,p gamma )38S reaction.

The $^{36}\mathrm{S}$(t,p\ensuremath{\gamma}${)\mathrm{}}^{38}$S reaction was used to populate levels in $^{38}\mathrm{S}$ up to 3-MeV excitation. A definite ${2}^{+}$ assignment to the 1292-keV first-excited state was obtained from a (t,p\ensuremath{\gamma}) angular correlation. Doppler shift information provided lower limits of 0.45 and 0.2 ps for the mean lifetimes of the 1291\ensuremath{\rightarrow}0 and 2825\ensuremath{\rightarrow}1291 transitions. Evidence for a possible new level at 2805 keV was obtained from p-\ensuremath{\gamma} coincidence data. The known level spectrum of $^{38}\mathrm{S}$ is compared to predictions of a shell-model interaction utilizing the full sdpf model space. The E2 and M1 transition rates predicted by this calculation are also presented.

Quarkonium spectroscopy with vacuum polarization correction

The quarkonium spectroscopy has been studied by considering a non-relativistic potential which includes the QCD vacuum polarization corrections. The potential consists of a short-range 2-loop QCD potential matched to a Martin-type power law potential for large distances. The Poggio-Schnitzer correction to the leptonic decay width has also been included. The energy levels, leptonic decay widths and E1 transition rates ofψ and γ families have been calculated and have been found to be in good agreement with experimental results. The toponium spectroscopy has also been studied for the range ofM, values suggested by the recent jet events observed by the UA1 collaboration. The contribution of the decay through a virtualZ 0 has also been included in the calculation. The potential seems to provide a very good non-relativistic description of the quarkonium systems.

A mixed symmetry or quasineutron pair interpretation of the Kpi=03+level in172Yb

The half-life of the 1405 keV level in 172Yb has been measured as T12/=0.42(6) ns by the generalised centroid-shift method. The E2 transition rate to the 2+01+ level is extremely low with B(E2)=2.6*10-3 Wu whereas the E0 transition matrix element is rho (E0)=0.014. The authors discuss the alternative interpretations of the level either as a mixed symmetry state with the appropriate choice of parameters within IBM-2 or as having a structure dominated by a quasineutron pair excitation (n7/2+(633)-n7/2+(633)) and (n1/2-(521)-n1/2-(521)).

Relativistic Effects and the Confining Force in Heavy Quarkonia

Mass spectra, leptonic-decay rates and E1-transition rates of the charmonium and the bb system are investigated by using the instantaneous BS equation with flavor-independent confining forces. The cutoff in the transverse part of the gluon propagator is examined by considering the 4th-order quark-pair potential, and determined to be 1.5mq. In the case of the effective-vector confining potential, only rough models can be constructed even if one assumes the long-range tensor and/ or spin-spin forces. It is contrarily shown that the mass spectra are reproduced very well by the effective-scalar confining potential. Renormalized leptonic decay widths corrected by the hard-gluon contribution are consistent with the experiments in this model. E1-transition rates of ψ′→γχj are also consistent with the experimental values.

Application of a number-conserving boson expansion theory to Ginocchio's SO(8) model.

A boson expansion theory based on a number-conserving quasiparticle approach is applied to Ginocchio's SO(8) fermion model. Energy spectra and E2 transition rates calculated by using this new boson mapping are presented and compared against the exact fermion values. A comparison with other boson approaches is also given.

A soluble γ-unstable hamiltonian

A simple five-dimensional hamiltonian for the nuclear shape is solved analytically for any value of a parameter whose variation describes vibration about a spherical equilibrium at one extreme and a rigid non-spherical but γ-unstable nucleus at the other. Spectra and E2 transition rates are compared with results from the interacting boson model.

Multi-quasiparticle induced prolate-oblate transitions in rapidly rotating N = 88,90 nuclei

Calculations have been performed to explain in a uniform way three recently measured phenomena in the N = 88–90 region: the quenching of signature-splitting in π h 11 2 bands, the reduction of E2 transition rates after the first backbend, and the loss of collective band structure in the I = 30–40 ℏ range. The model incorporates the tendency of high- j quasiparticles to drive the nucleus to triaxial shapes.

E1 transition probabilities within the [formula omitted] parity-doublet bands in 225Ra

The accuracy of the description of the K π = 1 2 ± bands in 225Ra as parity-doublet bands is tested by using the E1 transition rates connecting them. As expected, the δK = 0 E1 strength is considerably larger than that found in heavier actinides, where reflection-asymmetric shapes do not occur. The deduced ΔK = 1 E1 strength is smaller but is nevertheless surprisingly large for a reflection-asymmetric shape and remains to be explained.