The IBA-1 is reviewed with particular emphasis on the symmetry structure that arises naturally from its inherently algebraic approach. The formulation of the model, in both its algebraic and its numerical aspects, is presented and the basic character of its predictions is discussed and compared with nuclear data. The limitations of the model, and efforts to ameliorate these by appropriate extensions, are also reviewed in some detail. An effort is made to provide a simple, transparent understanding of the basic physics by clarifying the relation of the mathematical structure to underlying physical ideas, and to provide guidance in understanding and carrying out practical calculations.

The interacting boson approximation

The isomeric cross-section ratio sigma/sub m//(sigma/sub m/+sigma/sub g/) for the formation of /sup 73//sup m//sup ,//sup g/Se was determined in the /sup 70/Ge(..cap alpha..,n) reaction over the energy range of 13--27 MeV, in the /sup nat/Ge(/sup 3/He,xn) process over 13--24 MeV, in the /sup 75/As(p,3n) reaction over 25--45 MeV, and in the /sup 75/As(d,4n) reaction over 28--56 MeV. Measurements were done radiochemically using the ''stacked-foil'' technique. In (..cap alpha..,n) and (/sup 3/He,xn) processes the ratio is relatively high at low incident particle energies but decreases with increasing energy. In (p,3n) and (d,4n) reactions, on the other hand, it is practically constant. Statistical model calculations taking into account precompound emission were carried out on the four processes investigated in this work as well as on the /sup 74/Se(n,2n) reaction reported in the literature. The total cross section (sigma/sub m/+sigma/sub g/) is described well by the calculation. The calculated isomeric cross-section ratio depends strongly on the input level scheme of the product nucleus. In general, however, the statistical model, under a suitable set of global assumptions, can reproduce the isomeric cross-section ratio in all the five nuclear processes.

Isomeric cross-section ratio for the formation of 73m,gSe in various nuclear processes.

https://www3.nd.edu/~sfrauend/A100tidaldata/ru/systNPA593,21(95).pdf

Search for nuclei exhibiting the U(5) dynamical symmetry

Nuclear Data Sheets for A = 84

A detailed study of very neutron deficient nuclei with $Z\ensuremath{\simeq}40$ (Sr,Zr) and $N\ensuremath{\simeq}40$ has been carried out. Total potential energy surfaces taking into account both quadrupole and hexadecapole deformation have been calculated for the Zr ($Z=40$) nuclei, starting from the Nilsson model. Also oddmass nuclei have subsequently been studied when coupling the odd particle to the deformed even-even core. After extensive band mixing calculations for the $_{38}^{79}\mathrm{Sr}_{41}$ nucleus, comparison to the existing experimental data [energy spectra for positive and negative parity ${\frac{5}{2}}^{+}$ [422] and ${\frac{3}{2}}^{\ensuremath{-}}$ [301] bands; static moments $\ensuremath{\mu}$, $Q$; mixing ratios $\ensuremath{\delta}(\frac{E2}{M1})$ and branching ratios] has been carried out. We have also concentrated on the excited state properties of even-even Sr nuclei within the framework of the interacting boson model. A critical analysis of the interacting boson model parameters, as obtained from calculations in nearby nuclei, i.e., $_{34}\mathrm{Se}$, $_{36}\mathrm{Kr}$ is carried out, especially for the behavior of $\ensuremath{\kappa}$, ${\ensuremath{\chi}}_{\ensuremath{\pi}}$ and ${\ensuremath{\chi}}_{v}$.[NUCLEAR STRUCTURE Total potential energy surface calculations for even-even Zr nuclei ($36\ensuremath{\le}N\ensuremath{\le}60$). Band-mixing calculations for the adjacent odd-mass nucleus ($_{38}^{79}\mathrm{Sr}_{41}$). Band-state properties: [$\ensuremath{\mu},Q,\ensuremath{\delta}(\frac{E2}{M1})$, branching ratios]. Excited states in even-even Sr nuclei with $40\ensuremath{\le}N\ensuremath{\le}48$ in the interacting-boson model (IBA-2). Discussion of IBA-2 parameters. Calculation of quadrupole moments $Q({2}_{1}^{+})$, nuclear radii and isomer shifts.]

Evidence for very large deformation in neutron deficient nuclei with Z ≃ 40

$^{84}\mathrm{Sr}$ has been investigated by means of conventional in-beam gamma-ray spectroscopy with the reactions $^{76}\mathrm{Ge}$($^{12}\mathrm{C}$,$4n$) and $^{81}\mathrm{Br}$($^{6}\mathrm{Li}$,$3n$). Lifetimes of 10 levels have been measured by the recoil distance Doppler shift technique. Four positive and at least two negative parity bands have been found. The energies of the ground state band and quasigamma band as well as the $E2$ transition strengths are compared with theoretical values obtained from the proton-neutron interacting boson model. A relatively long lived ${8}^{+}$ state has been found, to which we assign the ${(\ensuremath{\nu}{g}_{\frac{9}{2}})}^{\ensuremath{-}2}$ configuration.NUCLEAR REACTIONS $^{76}\mathrm{Ge}$($^{12}\mathrm{C}$,$4n\ensuremath{\gamma}$), $E=48\ensuremath{-}60$ MeV; $^{81}\mathrm{Br}$($^{6}\mathrm{Li}$,$3n\ensuremath{\gamma}$), $E=19\ensuremath{-}32$ MeV, measured ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$, $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence, $\ensuremath{\gamma}$ angular distribution, recoil distance Doppler shift; $^{84}\mathrm{Sr}$ deduced levels, $J$, $\ensuremath{\pi}$, $\ensuremath{\tau}$. Enriched targets, Ge(Li) detectors.

High spin states of /sup 84/Sr

The decay scheme of $^{83}\mathrm{Rb}$ was studied by gamma-ray spectroscopy with the $^{81}\mathrm{Br}(\ensuremath{\alpha}, 2n)^{83}\mathrm{Rb}$, $^{70}\mathrm{Zn}(^{16}\mathrm{O}, p2n)^{83}\mathrm{Rb}$, $^{74}\mathrm{Ge}(^{12}\mathrm{C}, p2n)^{83}\mathrm{Rb}$, and $^{80}\mathrm{Se}(^{6}\mathrm{Li}, 3n)^{83}\mathrm{Rb}$ reactions. New energy levels and spins and parities were established. A stretched spin band built on the isomeric $\frac{9}{{2}^{+}}$ level at 42.3 keV, a $\frac{5}{{2}^{\ensuremath{-}}}$ ground state quasirotational band, and a three-quasiparticle band were found.NUCLEAR REACTIONS $^{81}\mathrm{Br}(\ensuremath{\alpha}, 2n)$, ${E}_{\ensuremath{\alpha}}=19\ensuremath{-}25$ MeV, $^{80}\mathrm{Se}(^{6}\mathrm{Li}, 3n)$, ${E}_{^{6}\mathrm{Li}}=23\ensuremath{-}29$ MeV, measured ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$-coincidence, $\ensuremath{\gamma}$-angular distribution, $^{70}\mathrm{Zn}(^{16}\mathrm{O}, p2n)^{83}\mathrm{Rb}$, ${E}_{^{16}\mathrm{O}}=52$ MeV, $^{74}\mathrm{Ge}(^{12}\mathrm{C}, p2n)^{83}\mathrm{Rb}$, ${E}_{^{12}\mathrm{C}}=35\ensuremath{-}49$ MeV, measured ${E}_{\ensuremath{\gamma}}$, $^{83}\mathrm{Rb}$ deduced levels, $J$, $\ensuremath{\pi}$. Enriched targets, Ge(Li).

High-spin states of /sup 83/Rb

73Se has been investigated by the reaction70Ge(α, nγ). Gamma excitation functions (Eα=10–16 MeV), gamma angular distributions (Eα=18 MeV) and gamma-gamma coincidences (Eα=15 MeV)) have been taken. A level scheme has been established, spins and partities have been assigned. States of a rotational band on the 151.2 keV (5/2−) state and an anomalous band have been identified.

High spin states in73Se observed by the reaction70Ge(α,nγ)

79Se has been investigated by the reaction76Ge(α, nγ). Gamma excitation functions (Eα=10−15 MeV), gamma angular distributions and gamma-gamma coincidences (both at (Eα=12 MeV), have been taken. A level scheme has been established, spins and partities have been assigned. The results are compared with rotational bands in neighbouring odd Se isotopes.

79 Se investigated by the reaction 76 Ge( α, nγ)

BAND STRUCTURE IN 84Sr

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