Octupole Transition Research Articles

Recurrence relations for multipole radial integrals in the semiclassical Coulomb approximation.

It is shown that in the semiclassical (WKB) Coulomb approximation the radial integrals for multipole transitions in nonhydrogenic atoms obey simple recurrence relations. As a result, any such integral can be analytically expressed in terms of Anger functions plus an algebraic part proportional to sin\ensuremath{\pi}s, where s=\ensuremath{\nu}'-\ensuremath{\nu} is the difference between the effective principal quantum numbers of the states involved. We retrieve, in particular, various formulas established previously for dipole, quadrupole, and octupole transitions.

Measurement of Reduced Electric Octupole Transition Probabilities, B(E3; 01??..31), for 118,120,122Sn

Values of reduced electric octupole transition probabilities, B(E3; ot -31), for the nuclides llB,120,122Sn have been determined using Coulomb excitation with 12C projectiles. The results are in good agreement with shell-model calculations made without introducing effective charges but involving core excitations. Values for B(E2; ot -2t) are also presented.

Enhanced octupole collectivity at double subshell closure in the96Zr region

A value of 84 ± 44 ps has been established for the half-life of the first 3− state of96Zr, using the centroid shift method. It is shown that the corresponding large electric octupole transition strength is in accordance with systematics, suggesting largest octupole collectivity when both the 1g9/2 Proton and 1h11/2 neutron orbitals are nearly empty due to the Z=40, N=56 double subshell closure.

High-resolution inelastic electron scattering fromO17

Excited states of $^{17}\mathrm{O}$ up to an excitation energy of 15 MeV have been studied by high-resolution electron scattering for momentum transfers between 0.8 and 2.6 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Previous electron-scattering measurements in this excitation region were confined to momentum transfers below 1.1 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ and were of lower resolution. Form factors were measured and reduced transition probabilities determined for most excited states below 9.5 MeV. The present data are interpreted within the framework of weak-coupling models to facilitate a simple description of the observed spectrum. Particular emphasis is placed upon understanding states that are excited strongly by electric quadrupole or octupole transitions. Spins and parities have been assigned for several levels that have very narrow widths and, hence, are not amenable to partial-wave analyses involving the $^{16}$O+n and $^{13}$C+\ensuremath{\alpha} reactions. Levels at 5.87 MeV (${(3/2}^{+}$), 6.86 MeV (${(5/2}^{+}$), 7.58 MeV (${(7/2}^{+}$), and 8.47 MeV (${(9/2}^{+}$) are suggested as candidates for predominantly 5p-4h members of a ${K}^{\ensuremath{\pi}}$${=(3/2}^{+}$ rotational band. A narrow state (\ensuremath{\Gamma}\ensuremath{\le}20 keV) at 12.22\ifmmode\pm\else\textpm\fi{}0.02 MeV was observed for the first time and the existence of narrow states at 8.90\ifmmode\pm\else\textpm\fi{}0.02 and 14.72\ifmmode\pm\else\textpm\fi{}0.02 MeV was confirmed.

Low energy octupole resonance in 46Ti studied by inelastic proton scattering at 65 MeV.

The level structure of the low-energy octupole resonance in /sup 46/Ti has been studied by inelastic scattering using a 65 MeV polarized proton beam. The excitation strength and distribution of the 2/sup +/, 3/sup -/, and 4/sup +/ states below E/sub x/approx.8.0 MeV have been determined. The energy weighted sum rule fractions of 10.8%, 11.7%, and 1.98% are found to be exhausted for the quadrupole, octupole, and hexadecapole transitions, respectively. No clear bump of the low-energy octupole resonance strength isolated from the first 3/sup -/ states has been observed. All the 3/sup -/ states dispersed in the region of E/sub x/ = 3--8 MeV seem to form one bump in /sup 46/Ti. It is suggested that the fragmentation of a collective 3/sup -/ state is due to the coupling effect of the octupole excitation with the static deformation of the /sup 46/Ti ground state, being in qualitative agreement with a random phase approximation calculation.

Selectivity of directional correlations of gamma rays from oriented nuclear states at moderately high spins

Calculations are presented for pure-multipole cascades from an aligned initial state of moderately high spin. viz., 10. Pairs of detectors at vertices of an octant in space are used, and the question of selecting a particular assignment of spins and multipolarities from all others is investigated. It is found that for representative conditions of degree of alignment of initial state and quality of data, most of the cascades composed of combinations of dipole, quadrupole and octupole transitions can be distinguished from each other, even including in many cases the order of nonbasic transitions. The number of different cascades considered is 49. Also considered are cases simulating ultrahigh-precision data in order to illustrate principles, as well as quite low-precision data. Considered too, are cases of no alignment of initial spin, as well as the other extreme of only m = 0. A concise review of the results of the general theory of directional correlation of gamma rays from oriented initial states is given.

74,76,78,80,82Se by inelastic scattering of 64.8 MeV protons.

The inelastic scattering of 64.8 MeV protons has been studied on the stable even $^{74\mathrm{\ensuremath{-}}82}\mathrm{Se}$ isotopes. The inelastically scattered protons were momentum analyzed in a magnetic spectrograph with a resulting energy resolution of approximately 20 keV. Levels up to the excitation energy of about 5 MeV were investigated. Many new levels were observed for the isotopes studied. The angular distributions obtained were compared with the predictions of distorted-wave Born approximation and coupled-channels calculations and a number of new spin assignments were proposed. Several ${4}^{+}$ states with comparable strengths were found at about ${E}_{x}$=2.0--5.0 MeV, showing large fragmentation of octupole and hexadecapole transition strengths, in contrast to the case of Zn isotopes. The distributions of the transition strengths for the ${2}^{+}$, ${3}^{\mathrm{\ensuremath{-}}}$, and ${4}^{+}$ states were compared with the theoretical calculations based on the random-phase-approximation model for spherical nuclei.

Microscopic approach to magnetic excitations in IBM-2

Starting from the collective SD subspace of the shell model, we construct boson images of the hamiltonian and the M1 and M3 operators by using the OAI method. In the magnetic operators one-boson as well as two-boson terms are considered. Energy spectra and g-factors of 130,134Ba are well reproduced by this method. Relatively strong magnetic dipole and octupole transitions at E x ∼ 2 MeV are predicted. The M1 and M3 electron scattering form factors are calculated. It turns out that the magnetic dipole operator is mainly a one-body operator in boson space, whereas the magnetic octupole operator contains important two-boson terms, which give sizeable contributions to the excitation strengths. These two-boson terms tend to diminish the F-spin selectivity of M3 excitations.

Analysis of elastic and inelastic scattering of 162 MeV pions fromC13by an optical potential and a collective model

Data for elastic scattering of ..pi../sup +/ and ..pi../sup -/ from /sup 13/C at T/sub ..pi../ = 162 MeV between theta/sub lab/ = 22/sup 0/ and 105/sup 0/ were analyzed by an optical model. Good fits were obtained with neutron and proton ground state densities of three-parameter Fermi shape having the same rms radius. Inelastic data for the quadrupole transitions to the (3/2)/sup -/ (3.68 MeV) and (5/2)/sup -/ (7.55 MeV) states and the octupole transition to a proposed (5/2)/sup +/, (7/2)/sup +/ doublet (11.82 MeV) were analyzed using a collective model. The extracted strengths for the neutron and proton parts of the transitions are compared to the results of electron scattering and ..gamma..-ray studies.

Isoscalar octupole transition rates in50Ti,52Cr and208Pb from model-independent analyses of 104 MeV α-particle scattering

Experimental differential cross sections for 104 MeV alpha -particle scattering have been analysed using a method recently proposed for model-independent analyses. Reliable values of isoscalar (O+-31-) octupole transition rates in 50Ti, 52Cr and 208Pb are presented and compared with electromagnetic rates.

Octupole modes of oscillation via analyzing power measurements

Measurements of the analyzing power in the two-nucleon transfer reactions /sup 70,72/Ge(t,p) have been carried out. This is a region where a shape transition has been previously proposed. Contrary to recent ( p,t) results, no strong interference effects between direct and two-step processes leading to the 2/sup +//sub 1/ states have been observed. However, a marked difference has been revealed for the 3/sup -//sub 1/ octupole transition. A microscopic interpretation of this effect is proposed.

Octupole states inCu63and the weak-coupling picture

A high-resolution experiment of proton inelastic scattering by $^{63}\mathrm{Cu}$ at ${E}_{p}=40$ MeV has resolved three octupole states at ${E}_{x}=3.81, 3.84, \mathrm{and} 3.89$ MeV for the first time, thus showing the existence of seven strong octupole states in $^{63}\mathrm{Cu}$. This finding is direct evidence that the traditional simple weak-coupling model in terms of one quartet $2{p}_{\frac{3}{2}}\ensuremath{\bigotimes}{3}_{1}^{\ensuremath{-}}$ is inadequate for the octupole core-excited states in $^{63}\mathrm{Cu}$. This is not evidence, however, that the weak-coupling picture in general is incorrect for the octupole states in $^{63}\mathrm{Cu}$. It is shown that to be consistent with the present experimental data, the weak-coupling picture for the octupole states requires a ground-state wave function substantially different from the ground-state wave function of the conventional particle-core-coupling model.NUCLEAR REACTIONS $^{63}\mathrm{Cu}$($p$,${p}^{\ensuremath{'}}$), ${E}_{p}=40$ MeV, strong octupole transitions, resolved new levels. Measured differential cross sections. Discussion in terms of the weak-coupling picture for the octupole states.

Generalized oscillator strength for the transition [formula omitted]1B 2u ← [formula omitted]1A 1g in benzene at initial kinetic energies 400 eV and 500 eV

Generalized oscillator strengths, ƒ, for the transition A 1B 2u ← X 1A 1g in benzene, determined by electron impact methods, are reported as a function of the momentum change. At scattering angles down to 2.5° helium was used as the comparison gas. Determinations are also reported at θ = 0° using mercury as the comparison gas. The oscillator strength curve has both a minimum and a maximum due to the superposition of electric dipole and octupole transitions. The band envelope is studied and is shown to remain unchanged in shape but is shifted by hν 6 ≈ 0.065 eV with increasing angle due to the shift from electric dipole to octupole scattering.

Electric dipole and quadrupole ground state transitions inBa138fromBa138(γ,γ) andBa138(γ,γ′)

Twelve ground state transitions up to about 5 MeV have been observed by the resonant scattering of bremsstrahlung from natural barium. Six of the first seven lines are from ${2}^{+}$ states in $^{138}\mathrm{Ba}$ as evidenced by the angular distribution measurements and the correspondence of the energies with known levels in $^{138}\mathrm{Ba}$. Presumably these arise from proton configurations. Of the remaining five lines four have distributions expected for spin 1 levels. The linear polarization of the scattered radiation for the first of these, at 4027 keV, suggests a negative parity. It is likely that this state is derived from the superposition of the one phonon quadrupole and octupole transitions in $^{138}\mathrm{Ba}$. Comparison with the results of other studies indicates that the other three lines are from neutron particle-hole states in $^{138}\mathrm{Ba}$. Widths in terms of the ground state branching ratios and the partial widths for decays to the ground state are given for the identified levels.NUCLEAR REACTIONS $^{138}\mathrm{Ba}$ ($\ensuremath{\gamma},\ensuremath{\gamma}$), ($\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}}$); bremsstrahlung $E=1.5\ensuremath{-}5.1$ MeV; measured $\ensuremath{\sigma}$ (96\ifmmode^\circ\else\textdegree\fi{}) and $\ensuremath{\sigma}$ (126\ifmmode^\circ\else\textdegree\fi{}), $\mathrm{LP}$; deduced $J$, $\ensuremath{\pi}$, $\ensuremath{\Gamma}$. Natural targets.

Nuclear matter sizes and isoscalar octupole transition rates of204,206,208Pb from 104 MeV ?-particle scattering

Differential cross sections for elastic and inelastic scattering of 104 MeVα-particles from204,206,208Pb were measured with high angular accuracy. The experimental results were analysed on the basis of a semimicroscopic folding model in order to determine the matter distributions at the nuclear surface and the transition densities. Using phenomenological parametrizations of the densities the analyses of elastic scattering yield rms radii of 〈r 2〉1/2=5.55±0.06 (204Pb), 5.57±0.06 (206Pb), 5.63±0.05 (208Pb) fm. Various sensitivities affecting the results were studied. From the inelastic cross sections for the 3 1 − -states octupole transition probabilities and transition radii were derived by using different methods proposed in literature.

Upper and lower bounds for the quadrupole moment and octupole strength of the first excited 3− state in 208Pb

Abstract The types of configuration necessary to describe the observed static quadrupole moment of an excited J π = 3 − state and its octupole transition rate to the ground state are investigated for the first excited 3 − state of 208 Pb. It is done by calculating the range of B (E3) values and quadrupole moments that simultaneously exist within a variety of configuration spaces. The spaces investigated include those of the TDA and RPA particle-hole models and models in which particle-hole excitations are coupled to a 2 + phonon. It is shown that it would be extremely difficult for any of the models considered to explain the observed properties of the above state.

Multipole Deformations in 19F and in the Neon Isotopes and Electric Multipole Strength in 19F from Inelastic Scattering of 30 MeV Protons

Cross sections were measured for inelastic scattering of 30 MeV protons from 19F, 20Ne, 21Ne, and22Ne. The cross sections of the ground state rotational band in these nuclei were analyzed in the coupled channels formalism and yield further evidence for a large hexadecapole deformation in 19F (β4 = 0.14 ± 0.04) and in 20Ne (β4 = 0.28 ± 0.05) in good agreement with several recent proton inelastic scattering experiments. These calculations show also that the Y4 moment is small or close to zero in 21Ne and 22Ne (β4 ≤ 0.05). The analysis of the available 19F cross section in the DWBA formalism shows evidence for a large and significant octupole transition strength for the 1.35 MeV (5/2−) (3.6 W.u.), the 5.43 MeV (7/2−) state (6.70 W.u.), and the 5.63 MeV (5/2−) state (3.60 W.u.). The measured transition strengths are generally in disagreement with recent low energy (α, α′) or (d, d′) results but also with the earlier Coulomb excitation measurements. Thus, we confirm that a major discrepancy still exists between inelastic scattering and Coulomb excitation of the octupole transition strength to several states in 19F but mainly to the 1.35 MeV (5/2−) state as was already pointed out some time ago from a low energy inelastic proton scattering experiment. On a mesuré les sections efficaces pour la diffusion inélastique de protons de 30 MeV excitant les noyaux 19F, 20Ne, 21Ne et 22Ne.

Simple two-level model of the hole-vibration quadruplet in 39K

The 3 2 − (3.02) , 5 2 − (3.88) , 7 2 − (2.82, 4.13) and 9 2 − (3.60 MeV) levels in 39K are described in a simple two-level model consisting of (i) a d 3 2 −1 proton hole coupled to the 3 − vibration in 40Ca and (ii) the dominating two-hole, one-particle shell-model configuration. Reasonable agreement with experimental energies and electric octupole transition strengths is obtained.

Quantitative tests of mixed crystal excition theory. I. Naphthalene monomer 1B 2u and 3B 1u spectra

A quantitative, computer processed spectroscopic study, using photon counting, on the first excited triplet and singlet states of dilute isotopic mixed crystals of naphthalene at 2 K is presented for C 10H 8; 1-DC 10H 7; 2-DC 10H 7; 1,4-D 2C 10H 6; 1,4,5-D 3C 10H 5; 1,4,5,8-D 4C 10H 4; 1,2,4,5,8-D 5C 10H 3; a β-D 4C 10H 4 and a β 2-D 6C 10H 2 as guests in C 10D 8 host crystals (and, for comparison, also for the same guests in a durene host crystal). The guest—host relative polarization Rashba formula has been verified quantitatively, and, as an added bonus, the elusive polarization ratio of the pure naphthalene crystal singlet Davydov components has been found to be 80 ± 20 ( b/a), which is in poor agreement with the transition octupole—transition octupole model. The experimental guest energies and their concomitant quasiresonance shifts for bound singlet states (as well as the occurrences of unbound states) are in excellent quantitative agreement (about 1 cm −1) with those calculated using a Green's function formalism based on the ideal mixed crystal approximation and on a restricted Frenkel type dispersion relation derived from resonance pairs. The same Green's function also accounts quantitatively (within 10%) for the guest singlet state exciton localizations (guest excitation amplitudes). The triplet exciton state reveals an orientational site splitting (about 0.7 cm −1) for the 0—0 transition of the I-DC 10H 7 guest in C 10D 8 host. The order of the α and β substituted deuteronaphthalenes in the triplet state is reversed from that of the singlet state. The last two observations are related to the different nature of the lowest Π-Π * singlet and triplet states of naphthalene.

A new satellite in the L-X-ray emission spectrum of tungsten-74

Using a 40 cm curved mica crystal spectrograph of the transmission type, the existence of a high frequency satellite at λ = 1268.84 X.U. in the L-emission spectrum of tungsten has been established for the first time. Based on the multiple ionisation theory, the satellite has been assigned to the transition L 2M 4 → M 4 2. According to the satellite nomenclature scheme proposed by Nigam and Mathur, this satellite would be designated Lβ 14. Kaufman's observation of a line at 1270.2 X.U. and its assignment to the octupole transition has been critically examined.