Isoscalar Transition Research Articles

Isospin decomposition of 0+ ? 2+ and 0+ ? 3? transition matrix elements by Coulomb nuclear interference observed in inelastic ?-scattering from the even Zr isotopes

Coulomb-nuclear interference in inelastic scattering of 35.4 MeVα-particles from the stable even Zr isotopes was studied. In the framework of a collective DWBA analysis isoscalar and electromagnetic transition rates for low lying 2+ and 3− states were derived. The experimentalB (E2) values are in good agreement with results obtained by purely electromagnetic methods. The deducedMn/Mp ratios of the 21+ levels exhibit a surprisingly large increase with increasing neutron number.

Transverse isoscalar excitations in 24Mg by 180 degrees electron scattering.

Transverse electron scattering form factors have been measured for isoscalar transitions to T=0 levels in $^{24}\mathrm{Mg}$ at 1.37 MeV (${J}^{\ensuremath{\pi}}$${=2}^{+}$), 5.24 MeV (${3}^{+}$), 6.01 MeV (${4}^{+}$), and for the unresolved T=0 doublet at 4.12 MeV (${4}^{+}$) and 4.24 MeV (${2}^{+}$). Because of the large longitudinal form factors for these transitions, sometimes exceeding the transverse form factor by more than a factor of ${10}^{4}$, it was necessary to observe electrons scattered at 180\ifmmode^\circ\else\textdegree\fi{} so that longitudinal scattering was minimized. Several incident energies from 80.1 to 200.5 MeV were used to span effective momentum transfers from 0.84 to 2.07 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Results are compared with predictions calculated using Dirac wave functions for the nuclear bound states in a Woods-Saxon potential well.

Alpha-particle scattering from Ni isotopes at 25 MeV

Differential cross sections have been measured for both elastic and inelastic scattering of 25 MeV alpha particles from 58,60,62,64Ni nuclei. An increasing neutron skin thickness in the isotopic sequence from 58Ni to 64Ni has been found. The angular distributions of excited states have been analysed by the coupled-channel (CC) approximation, in the context of the vibrational model. The analysis reveals enhanced hexadecapole (0+ to 4+) transitions in 58,60,64Ni. Deformation parameters for the excited states have been deduced. Isoscalar transition rates have been extracted and compared with electromagnetic transition rates.

Inelastic alpha-scattering from the stable even germanium isotopes

Scattering of 31.5 MeV α-particles from the stable even Ge isotopes has been studied with an energy resolution of 15–20 keV FWHM. Angular distributions were measured for excitation energies of up to 5.2 MeV. Most of the levels are well described by collective DWBA calculations with vibrational model form factors. An implicit folding procedure was used to derive isoscalar transition rates. The distribution of the isoscalar multipole strength reveals an increasing fragmentation with increasing neutron number. A detailed comparison with the spectroscopic results of a recent (p, p′) study is made.

Search for short-lived axions in a nuclear isoscalar transition

Axions, if existing, can cause a strong signal of positron-electron pairs in isoscalar M1 transitions in competition with gamma-ray emission. We searched for such a signal in the 3.59 MeV transition in 10B with a fourfold Mini-Orange spectrometer. No axion events were found within two percent of the prediction for the standard axion- to γ-ray branching ratio.

Alpha scattering from 92Zr and 94Zr

Scattering of 35.4 MeV α particles from 92Zr and 94Zr has been studied with an energy resolution of 25–30 keV. Angular distributions were measured from 10 to 45 degrees for an E x range of up to 6.1 MeV and 4.4 MeV for 92Zr and 94Zr, respectively. Several new spin assignments have been made by comparing angular distributions with collective DWBA calculations. An implicit folding procedure was used to derive isoscalar transition rates, which for E x > 2.5 MeV were previously unknown. Most of the levels are well described by a vibrational model form factor.

Inelastic α-scattering from 90Zr and 96Zr

The 90Zr and 96Zr(α, α') reactions have been studied at 35.4 MeV with an energy resolution of 35–50 keV. Angular distributions were measured between 10 and 50 degrees for an E x range of 1.5 to 6.0 MeV. Spin assignments have been made on the basis of the shapes of the differential cross sections and by comparison with collective DWBA calculations. For 96Zr discrepancies in spin assignments have been removed for several levels. Within the framework of the vibrational model isoscalar transition rates have been derived.

Monopole and Quadrupole Giant Resonances in Rotating Triaxially Deformed Nuclei. II: A Microscopic Description of the Isoscalar and Isovector Modes

Microscopic calculations are performed for the isoscalar and isovector monopole and quadrupole giant resonances built on high-spin yrast states. The results of the calculation show that the shapes of the strength functions for both the isoscalar and isovector vibrations are determined mainly by the deformation parameters of the mean field. The effects of rotation on the isoscalar and isovector quadrupole modes are found to be quite different: The rotation-splittings of the former become significant at very high-spins, while those of the latter remain small. It is also demonstrated that the. transformation of the strength functions from the rotating frame into the laboratory frame is crucial to accurately evaluate the rotation­ splittings of the quadrupole modes.

Neutron-proton differences in the excitation of 104Ru from high-resolution polarized deuteron scattering

The low-excitation spectrum of 104Ru, which provides strong evidence for a triaxial shape of the nucleus, has been investigated by high-resolution inelastic scattering of 23 MeV polarized deuterons. The 2 + 2−4 + 1 doublet with an energy separation of only 4.6 keV has been resolved using the Q3D magnetic spectrograph. From the coupled-channel analysis of the data, isoscalar transition moments are obtained which yield by comparison with the electromagnetic properties the neutron moments of the transitions. For the excitation of the 2 + 1 and 2 + 2 states we find substantial differences between corresponding proton and neutron moments.

Multipole collectivity in 168Er from inelastic scattering.

The structure of the low-lying states of $^{168}\mathrm{Er}$ has been investigated by use of inelastic scattering. Differential cross sections for the elastic and inelastic scattering of 36 MeV \ensuremath{\alpha} particles and 16 MeV deuterons from $^{168}\mathrm{Er}$ have been measured. Isoscalar transition strengths for l=2, 3, and 4 excitation have been extracted by a coupled-channels distorted wave calculation involving collective model form factors. A number of known levels corresponding to the ground state band, \ensuremath{\gamma} band, and octupole bands were seen. Results for the ${2}^{+}$, ${4}^{+}$, ${6}^{+}$, and ${8}^{+}$ states in the ground state band and ${2}^{+}$, ${4}^{+}$, and ${6}^{+}$ states in the \ensuremath{\gamma} band imply the importance of the hexadecapole (${\ensuremath{\beta}}_{4}$) and the hexacontatetrapole (${\ensuremath{\beta}}_{6}$) shape components. The octupole states at 1431, 1633, and 1913 keV are excited with isoscalar strengths equal to 0.046, 0.058, and 0.023 ${e}^{2}$${\mathrm{b}}^{3}$, respectively, which are comparable with the corresponding B(E3) strengths known from Coulomb excitation of the 1431 and 1633 keV states. The octupole states at 2269, 2324, and 2486 keV with isoscalar E3 transition strengths 0.055, 0.022, and 0.018 ${e}^{2}$${\mathrm{b}}^{3}$, respectively, are newly identified. For quadrupole excitation the results agree in several ways with predictions of the interacting boson approximation model and the geometrical models and for octupole states there is a good agreement with theoretical results of Neergaaumlrd and Vogel.

Isoscalar excitations of7Li

Inelastic scattering of 35 MeV alpha particles from7Li was used to induce the five known inelastic excitations. A collective coupled channel analysis yielded deformations for each transition and isoscalar quadrupole reduced transition rates were determined for each. The strong-coupling rotational model was found to agree closely with the results for the states associated with the ground state band, but the higher states are excited mainly by a two-step mechanism.

A-particle scattering from Ni isotopes at Eα = 172.5 MeV

Differential cross sections have been measured for the elastic and inelastic scattering of 172.5 MeV α-particles from 58,60,62,64Ni nuclei. The analysis of the experimental data of elastic scattering in terms of optical potentials indicates an increasing neutron skin thickness in the isotopic sequence from 58Ni to 64Ni. Coupled-channel analyses based on the anharmonic vibrational model approach determine the values of the dynamic deformation parameters for the most strongly excited states rather precisely and reveal enhanced hexadecapole (0 + → 4 + 1) transitions. Using an implicit folding-model procedure with a correction for the density dependence of the effective α N interaction, isoscalar transition rates are extracted and compared to electromagnetic results.

Octupole vibrational states in the even-mass barium isotopes

A low-lying state of 132, 134, 136, 138Ba, strongly excited in the scattering of 20 MeV α-particles at 175°, is identified as the first 3 − octupole vibrational state in each case. Angular distribution measurements for α-particle scattering to this state and the well-known first 2 + state in 132, 134, 136, 138Ba are in agreement with harmonic-vibration coupled-channel predictions. Deformation parameters are obtained, and the deduced isoscalar transition rates are compared with measured electromagnetic transition rates. The first 3 − states of 132, 134, 136, 138Ba are found to be at excitation energies of 2.070, 2.251, 2.529 and 2.879 MeV, respectively. A state in 130Ba at an excitation energy of 1.948 MeV is tentatively identified as the first octupole-vibrational state in this nucleus.

Isospin composition of giant resonances and asymmetries in pi + compared to pi - inelastic scattering.

A fully microscopic calculation for pion inelastic excitation of giant resonances in which random phase approximation transition densities are used is presented for the first time. The mixing of isoscalar and isovector modes is incorporated in the random phase approximation calculations and its effect on \ensuremath{\sigma}(${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$) vs \ensuremath{\sigma}(${\ensuremath{\pi}}^{+}$) is discussed. Comparison with existing data is made and reasonable agreement is achieved.

Octupole vibrational states in the even-mass barium isotopes

A low-lying state of 132, 134, 136, 138Ba, strongly excited in the scattering of 20 MeV α-particles at 175°, is identified as the first 3− octupole vibrational state in each case. Angular distribution measurements for α-particle scattering to this state and the well-known first 2+ state in 132, 134, 136, 138Ba are in agreement with harmonic-vibration coupled-channel predictions. Deformation parameters are obtained, and the deduced isoscalar transition rates are compared with measured electromagnetic transition rates. The first 3− states of 132, 134, 136, 138Ba are found to be at excitation energies of 2.070, 2.251, 2.529 and 2.879 MeV, respectively. A state in 130Ba at an excitation energy of 1.948 MeV is tentatively identified as the first octupole-vibrational state in this nucleus.

The 14C(α, α') 14C and 13C(d, p) 14C reactions

The isoscalar transition rates and neutron-stripping probabilities to states of 14C have been measured using the 35 MeV 14C(α, α') 14C and 17.7 MeV 13C(d, p) 14C reactions. States showing great charge asymmetries in pion scattering at 8.32 MeV (2 +) and 11.7 MeV (4 −) were examined in detail. Isoscalar transition rates B(02) were determined to be 168, 96 and 74 fm 4 for the 7.01, 8.32 and 10.45 MeV 2 + states, with identical single-neutron spectroscopic factors of 0.065, from the (d, p) data, for the lowest two states.

The density dependence of the effective alpha-nucleon force and isoscalar transition rates of nuclei

Effects of the density-dependence of theα-particle-bound nucleon effective interaction on single-folding models of inelasticα-particle scattering are studied, in particular in view of corrections of the isoscalar transitions rates extracted by implicit folding procedures. Thel-dependent corrections factorsC l are calculated and tubulated for applications.

Dirac single-particle wave functions in inelastic electron scattering

We formulate inelastic electron scattering using Dirac single-particle wave functions to describe the nuclear states. The lower components of these wave functions are much larger than those obtained assuming a free space relation with the upper component taken to be a Schr\"odinger single-particle wave function. We note that the impulse approximation to the nuclear current operator is ambiguous in the present case. However, one of the two possible forms yields an explicitly conserved current in the single particle limit. We identify an inelastic amplitude which is linear in the lower components and is therefore very sensitive to the "relativity" of the bound nucleons. This amplitude is found to be dominant for transverse isoscalar transitions.

STRETCHED EXCITATIONS AS A MEANS TO STUDY THE SPIN MODES OF THE NUCLEUS WITH ELECTROMAGNETIC AND HADRONIC PROBES

Excitation of spin transitions using electromagnetic and hadronic probes is discussed. Spectroscopic strengths are deduced from studies of (e,e'), (p,p'), (π,π') and (p,n) for selected states. The missing isovector and isoscalar strengths imply the existence of other important quenching mechanisms since the Δ-N-1 mechanism does not contribute to high spin excitations or to isoscalar transitions. The stretched states are used as benchmarks to test the nucleon-nucleon tensor force in proton scattering and the pion-nucleon spin orbit force in pion scattering. The results are in striking agreement with predictions of the DWIA model.

Isoscalar transition rates and an implicit double folding model using density-dependent forces

A generalization of the Satchler theorem, regarding the radial moments of single folded potentials to the case of a double-folding model is obtained. A proper accounting of the density-dependence of the nucleon-nucleon force is shown to remove the long standing disparity between the isoscalar transition rates deduced from alpha inelastic scattering to those obtained from electromagnetic transitions. The strong l dependence of the disparity is accounted for.