Strong-coupling Model Research Articles

Measurement and interpretation of electromagnetic transitions in 51V

Angular correlation measurements in the 180° geometry for the 48Ti(α, pγ) 51V reaction were used to determine the γ-ray decay properties of states in 51V at 0.32, 0.93, 1.61, 1.81, 2.41, 2.55, 2.68 and 2.70 MeV. Coulomb excitation measurements with 32S ions, using a thick 51V target and a Ge(Li) detector, were used to deduce the B(M1) and B( E2) reduced transition probabilities for the decays of the 0.32, 0.93, 1.61 and 1.81 MeV states. For these states the M1 transitions are found to be retarded by factors ranging from about 400 to over 10000, while the E2 transitions are enhanced by about an order of magnitude relative to the Weisskopf estimate. Shell-model calculations were performed for 51V considering all basic three proton states in the f-p shell and assuming a 48Ca core. Kuo and Brown two-body matrix elements were used. Remarkably good agreement is obtained between the calculated and measured transition rates, supporting the shell-model predictions of a high-configuration purity for the six levels of the basic f 7 2 3 multiplet. By contrast, the B(M1) values predicted by the strong Coriolis coupling model of Scholz and Malik strongly disagree with the measured values, generally being two or three orders of magnitude too large. We conclude that the spherical shell model provides an excellent description of the low-lying states in 51V and, contrary to Scholz and Malik, we find no evidence for deformation in this nucleus.

Decoupling Parameter in Light Nuclei

The approximate-projection method of Das Gupta and Van-Ginneken is extended to include the calculation of the decoupling parameter for $K=\frac{1}{2}$ bands. The method is tested on the first positive- and negative-parity bands of $^{19}\mathrm{F}$ and is found to give good results even when the strong-coupling model seems to fail. The validity of the formula for the decoupling parameter given by the strong-coupling model is explored.

Beta and gamma vibrational bands in 152Sm and 154Gd

Relative intensities of gamma transitions in 152Sm, 152Gd and 154Gd were measured using a Ge(Li) detector. Several new gamma transitions were observed. Angular correlation experiments were performed to determine the multipole mixing ratios of transitions from the gamma vibrational band to the ground state band in 154Gd. It is found that neither the beta nor the gamma band transition strengths in 152Sm and 154Gd can be accounted for by a single parameter band-mixing theory, nor can agreement be found by considering mixing between the beta and the gamma band. Transition rates from the negative parity levels also disagree with predictions of the strong coupling model including first order corrections.

Energy Levels inV47,49,51andMn51,53,55from (He3,d) Reactions

The ${\mathrm{Ti}}^{46,48,50}({\mathrm{He}}^{3}, d){\mathrm{V}}^{47,49,51}$ and ${\mathrm{Cr}}^{50,52,54}({\mathrm{He}}^{3}, d){\mathrm{Mn}}^{51,53,55}$ reactions are studied with high resolution at 10- and 9.5-MeV incident energies, respectively. The $l$ values and spectroscopic factors are extracted by means of the distorted-wave Born-approximation calculations. A systematic study of the ${p}_{\frac{3}{2}}$ centroid energies, of the ${d}_{\frac{3}{2}}$ and ${s}_{\frac{1}{2}}$ proton hole states, and of the splitting of the ${p}_{\frac{3}{2}}$ spectroscopic strength is presented. These quantities, and also the individual energy spectra, are compared with the expectations of the shell model and the Coriolis strong-coupling model. It is concluded that the shell model adequately describes these nuclei, while the Coriolis strong-coupling model fails to explain the observed splitting of the ${p}_{\frac{3}{2}}$ spectroscopic strength.

The lifetimes of the first excited states in 21Ne and 21Na

The lifetimes of the J π = 5 2 + mirror states at E x = 350.5 ± 1.0 keV and 332 ± 1 keV in 21Ne and 21Na, respectively, have been measured with the recoil-distance method. The two nuclei were produced by 20Ne bombardment of a 2H gas target. The results are τ = 22 ± 3 ps and 14 ± 3 ps for the states in 21Ne and 21Na, respectively. The measured lifetimes compare well with those calculated in the strong-coupling model taking into account band mixing.

The dynamical group of the SU(3)-symmetric strong coupling theory

Starting from the Hamiltonians, the complete infinite sets of isobaric states for two SU(3)-symmetric strong coupling models (with scalar and pseudoscalar mesons) are determined using the idea of the dynamical group. The physically meaningful unitary irreducible representations of the dynamical groups SU(3) · T 8 and [SU(3) ⊗ SU(2)] · T 24 follow from the minimization requirement on the potential energy part of the Hamiltonians in the strong coupling limit. The composition of these infinite dimensional representations in terms of representations of the symmetry groups SU(3) and SU(3) ⊗ SU(2) has been obtained.

A Study of the 3·00 MeV Level of 27Al via 24Mg(a, p?)27Al

It is at present considered (Thankappan 1966) that the weak-coupling- model is more appropriate to the 27 Al nucleus than the strong-coupling (Nilsson) model, which has been applied with some success to 25Mg, 25Al, and other lighter nuclei in the 2s-1d shell (Gove 1960). Thankappan (1966) has interpreted the low-lying J = ~, ~, ~, ~, and ~ levels as a multiplet formed by the coupling of a IdG/, proton hole to the first excited (2+) state of 28Si. This model is able to fit simultaneously the level positions and many of the ,,-ray transition rates. The proton inelastic scattering cross sections (Crawley and Garvey 1965) are also in better agreement with this model than with the strong-coupling model. The 3�00 MeV level has for some time been regarded as the low-lying J1r = ;+ state predicted by Thankappan's excited-core model, but the experimental evidence is somewhat contradictory. Towle and Gilboy (1962) claimed an unambiguous assignment of J = ~ from inelastic neutron scattering; the ,,-ray correlation results of Lawergren (1964) are consistent with this assignment. Wakatsuki and Kern (1966) used ,,-ray correlation methods to make a firm assignment of J = i, but it is not obvious that the data used to exclude a J = ; assignment were. free of contributions from the 2� 98 MeV level. In addition, those authors made the dubious assumption that the reaction proceeds through an isolated level of the compound nucleus, and the mixing ratio obtained for the 3�00 to 0 transition is inconsistent with a recent lifetime measurement (Broude, Smulders, and Sharpey-Schafer 1967). Sheppard and van dar Leun (1967), using a Ge(Li) ,,-ray spectrometer, have measured gamma.-gamma correlations in the 26Mg(p,'Y'Y)27Al reaction and claim a definite assignment of J =;. Gove et al. (1967a, 1967b) have performed a D.W.B.A. analysis of the angular distributions in the 28Si(d,3He)27Al reaction using a magnetic spectrograph to resolve the 2�98 and 3�00 MeV levels; they conclude that the 3�00 MeV level has J = I or~. This raises the possibility that the 3�00 MeV "level" is, in fact, a doublet, one member of which has J =; and the other, populated in the (d, SHe) reaction, J = I or~.

Untersuchung der Beschreibungsmöglichkeit des Selen 77 als deformierter Kern

Some aspects of Selen 77 are discussed in the framework of the NILSSON model. The magnetic moment of the 248 keV state give hint fore the existence of a quadrupole force. The large quadrupole moment and the large COULOMB excitation- and (d,d′) -cross sections of some levels indicate collective features. The strong coupling model explains very well the ratio of the reduced B (E2) transition probability. The NILSSON model predicts the spin and the parity of the ground state and gives a better description of the lifetime of the 248 keV level than the spherical shell model. The magnetic moment of the ground state and the 248 keV state are explained by means of a spinpolarisation. The agreement of several values of the decoupling constant is fairly good. On the whole the description of Se77 by the NILSSON model appears to be comparable to the modest success of this model in some rare earth nuclei.

Cutkosky-Leon Bootstrap Model and the Strong-Coupling Model

The static $\ensuremath{\pi}\ensuremath{-}N$ bootstrap model based on the Bethe-Salpeter equation is applied to the study of the mass spectrum and the meson coupling constants when isobars heavier than $N_{3,3}^{}{}_{}{}^{*}$ are included. By assuming $I=J$, we have obtained the solutions for two models which are constructed by adding, up to $I=J=\frac{7}{2}$, the isobars $N_{2I,2J}^{}{}_{}{}^{*}$ to those of the familiar model of the $N\ensuremath{-}N_{3,3}^{}{}_{}{}^{*}$. We discover also that this Bethe-Salpeter bootstrap model (or Cutkosky-Leon model) contains a solution which is identical to that from the strong-coupling model for the case of charge-symmetric pseudoscalar-meson theory; in this solution there are an infinite number of degenerate isobars with their isospin equal to their spin. Also included in the table of results is the $\mathrm{SU}(4)$ prediction for the various coupling constants when heavier isobars are included. The $\mathrm{SU}(4)$ model contains in addition to the pions the $\ensuremath{\rho}$ and $\ensuremath{\eta}$ mesons. We notice that the results of bootstrapping and $\mathrm{SU}(4)$ are similar and that the deviations between them are less than 50%. It is also noticed that the heavier isobars act in the bootstrap model like a small perturbation on the low-lying isobar states.

The series of hyperon resonances in the static bootstrap model

The Dashen-Frautschi off-the-mass-shell bootstrap technique is used to the calculation of strong form factors in the static model. It is proved that these form factors are analytic functions with analytic properties prescribed by the S-matrix theory and fulfil the unitarity condition if and only if a series of hyperons with I = J ± 1 2 exists and if certain relations among masses and among coupling constants of these hyperons are fulfilled. The mass spectrum for this series is found. The results obtained in this method are compared with those predicted by the Lie-group structure describing the strong coupling model. The hyperon resonance with I = 2 and J = 3 2 + is discussed in some detail and theoretical predictions derived here are compared with experimental data. The agreement is satisfactory.

Elastic and inelastic scattering of 50 MeV protons by 12C and 16O

Measurements are reported of the differential cross sections for the elastic scattering of 49.48 MeV protons by 12C and 16O, and the inelastic scattering leading to the 4.43 and 7.67 MeV levels of 12C. The results for 12C, together with values for polarization, are fitted by the optical model, and the parameters compared with revised fits of the 30.3 and 40 MeV data. The radius and the diffuseness of the spin-orbit potential are found to be smaller than the values for the central potential. The 12C elastic and 4.43 MeV inelastic data are fitted with a strong coupling model. Preliminary optical model parameters are given for the 16O data. It is evident from the present studies that there is a need for more measurements of polarization and differential cross sections at larger angles and of the total reaction cross section, in order to provide an adequate test of the applicability of the optical model.

Electromagnetic form factors in the bootstrap theory

It is shown that form factors calculated within the framework of the Dashen-Frautschi off-the-mass-shell bootsrap method have the same analytical properties as those prescribed by the S-matrix theory, i.e. only unitary cuts are present. The discontinuity calculated along these cuts satisfies the unitarity condition only when certain relations among various coupling constants are fulfilled. Using these relations, the ratios among the isovector magnetic moment of the nucleon, magnetic dipole of the Δ → N + γ transition and isovector magnetic moment of the Δ-resonance are calculated. The results are the same as those following from on the mass-shell bootstrap method and from the Lie group methods of the strong-coupling model.

Energy transfer processes in monochromatically excited iodine

Measurements of energy transfer rates in monochromatically excited iodine are used to test various theories of vibrational relaxation. The efficiency of vibrational energy transfer is observed to be greatest when the mean duration of the collision is equal to the period of vibration. An explanation for this is given in terms of a time-dependent perturbation theory due to SCHWINGER. Most of the energy transfer models developed for ultrasonic data (viz. : complete LANDAU-TELLER, COTTRELLREAM, SCHWARTZ-SLAWSKY-HERZFELD, RAPP et al.) reproduce this behavior, but the simple LANDAU-TELLER and MILLIKAN-WHITE theories do not.The magnitude of the transition probabilities derived from these models is in only fair agreement with experiment. The problem lies in that calculated values of P01 approach unity as ΔE approaches кT, and P(n, n ± 1) is customarily taken as (n + 1 /2 ± 1 /2) P01 . In order to conserve probability, a strong-coupling model will be required, such as has been proposed by RAPP and SHARP or SHULER and ZWANZIG.Inclusion of an attractive term in the intermolecular potential contributes a factor of two to three in collision efficiency, but does not alter the dependence on collision times. Three methods of carrying out the BOLTZMANN averaging are compared, namely, steepest-descents approximation, numerical averaging of transition probabilities, and numerical averaging of the rale expressions. These three methods yield essentially consistent results. The observed ratio of Δn = 1 to Δn = 2 efficiencies is given to good accuracy by the square of the exact matrix elements of the intermolecular potential.Several calculations of pure rotational and rotation-vibration energy transfer are also reported.

The exciton model in molecular spectroscopy

The molecular exciton model has received its most extensive development and application in the field of molecular crystals1'2. More recently, numerous applications to non-crystalline molecular composite systems have been made, including van der Waals and hydrogen-bonded dimers, trimers, and higher order aggregates. Another type of composite system has also been investigated, namely the composite molecule consisting of covalently bonded molecular units, with intrinsic individual unsaturated electronic systems so isolated by single bonds that but little or insignificant electronic overlap between units may occur. It is now well established that in molecular aggregates and in composite molecules, exciton effects may be observed if sufficiently strong electronic transitions exist in the component sub-units. The result of exciton splitting of excited states in the composite molecule may be the appearance of strong spectral shifts or splittings (which may be of the order of 2000 cm—1) of the absorption bands for the component molecules. At the same time, as a consequence of the exciton splitting of the excited state manifold, an enhancement of triplet state excitation may result. The purpose of this paper is to present a summary of the various type cases for molecular dimers, trimers and double and triple molecules in the description of the molecular exciton strong-coupling model. Then it will be shown by new experimental examples that, even in those cases where no significant exciton effect is observable in the singlet—singlet absorption spectrum for the composite molecule (intermediate and weak coupling cases), the enhancement of lowest triplet state excitation may still be conspicuous and significant. The ideas which are summarized in this paper have a curious history. Long ago, Kautsky and Merkel3 demonstrated experimentally that aggregation of dyes facilitated their action as photophysical sensitizers in photochemical reactions, at the same time diminishing their fluorescence efficiency. Kautsky attributed these easily demonstrated effects to enhancement of metastable state excitation in the aggregate dye. There is no doubt today that the metastable state he described is the lowest triplet state of the molecules studied. However, he did not distinguish between intrinsic and enhanced metastable (triplet) state excitation, so his interpretations were largely overlooked. Forster in l946 used the quasi-classical vector model to

Structure of excited states in 29P

The structure of the nucleus 29P has been studied in terms of both the strong coupling model and the weak coupling model. The energy levels, spins, parities and proton and gamma emission widths have been calculated using the wave functions obtained above. These theoretical values are compared with the experimental results on 29P. The predictions of the Nilsson model with the oblate deformation η = −3 show good over-all agreement with the experiments. The vibrational model, in which a proton is coupled with the core 28Si, is found not to be in quantitative accord with some properties of 29P.

A measurement of the beta-branching ratio of Lu 176m

The β-branching ratio of 3.7 h Lu 176m to the 0 + (ground) and 2 + (88 keV) levels in Hf 176 has been measured by β-γ coincidence techniques using a Gerholm-type β-γ coincidence spectrometer. The intensities of the inner and ground state groups are 37±12% and 63±12%, respectively. Using a previously reported Q β − = 1314 keV, the experimental relative reduced transition probability calculated is 0.34 −0.08 +0.30. Because the I π = 1 − for this isomer has been previously determined experimentally, the branching ratio establishes the K-quantum of the isomer as K = 0, assuming the validity of the K-intensity rules of the strong coupling model. The I π K=1−0 assignment of the isomer therefore indicates that Lu 176m has an anomalous K = 0 rotational band in which the odd spin band is displaced below the even spin band.

Studies of Decay Schemes in the Osmium-Iridium Region. III. Decay of 15.8-HourIr186

The decay of 15.8-h ${\mathrm{Ir}}^{186}$ was studied with a double-focusing electron spectrometer, a lens spectrometer, and scintillation spectrometers. Several coincidence experiments were also performed. About two-thirds of the 101 transitions observed could be fitted into a level scheme for ${\mathrm{Os}}^{186}$ consisting of a ground-state ($K=0$) band, a $K=2$ (gamma-vibrational) band, and several other levels. The positron spectrum shows at least two branches; the branch with the highest end-point energy (1.94\ifmmode\pm\else\textpm\fi{}0.02 MeV) populates the $I=6$, $K=0$, state at 0.869 MeV. The total positron intensity is (2.5\ifmmode\pm\else\textpm\fi{}0.7)%. The most probable spin assignment for ${\mathrm{Ir}}^{186}$ (15.8-h) is 7. Energies of the collective levels of ${\mathrm{Os}}^{186}$, and relative transition probabilities, are discussed in the framework of the existing knowledge of other even-$A$ osmium isotopes, and are compared with the predictions of the band-mixed strong coupling model and of various versions of the asymmetric rotor model. An appendix gives data accumulated during the course of this work on transitions following the decay of ${\mathrm{Ir}}^{185}$ and of ${\mathrm{Ir}}^{187}$.

Lifetimes of 4+ and 2+ States in the Rotational NucleiDy160,Dy162,Er166,Er168, andHf180

Lifetimes of the 2+ and 4+ states of the ground-state rotational band were measured for five even-even rare-earth nuclei using delayed coincidence techniques. The half-lives obtained are presented in the following table in units of ${10}^{\ensuremath{-}10}$ sec. The ratios $\frac{B(E2;4\ensuremath{\rightarrow}2)}{B(E2;2\ensuremath{\rightarrow}0)}$ are calculated from these lifetimes using theoretical values for the internal conversion coefficients. In all cases this ratio is in excellent agreement with the value 10/7 predicted by the strong coupling model for rotational nuclei.A measurement of the lifetime of the 2.50-MeV 4+ state of ${\mathrm{Ni}}^{60}$ is also reported. A limit of ${\ensuremath{\tau}}_{m}l5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ sec was obtained for this state.

On the Collective Motion in Even-Even Deformed Nuclei

By beginning with a spherically symmetric j-j coupling shell model Hamiltonian with a general effective two-body interaction, formulas for various empirical parameters characterizing the collective motion in even-even deformed nuclei are given with explicit reference to the effective interaction. An assumption made in this paper is the adiabatic approximation which is the same as that underlying Bohr's strong coupling model or its modified ones. Characteristics of various collective modes described in these “phenomenological models” are investigated and the physical implication underlying the models is made clear. Throughout this paper discussions are made in a general form as much as possible and, to make the understanding of our results easier, simple estimates based on the so-called “Pairing plus Quadrupole Force” are made for each case.

Coupling of Angular Momenta in Two-Particle States in Deformed Even-Even Nuclei

The recent suggestion that low-lying intrinsic states in deformed nuclei are basically two-particle excitations is considered in more detail. The result of the strong-coupling model that the two-particle states are doubly degenerate with spins $\ensuremath{\Omega}=|{\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\Omega}}_{2}|$ is re-emphasized. It is suggested on the basis of experimental evidence that the degeneracy of the two states of each configuration is removed largely by residual spin-dependent forces, analogous to the splitting observed in deformed odd-odd nuclei. Coupling rules are given for the lower-lying state of each configuration based on this assumption. As an example of the application of the coupling rules to actual nuclei the decay schemes of the two ${\mathrm{Ta}}^{178}$ isomers to levels in ${\mathrm{Hf}}^{178}$ are considered in detail.