Isospin Mixing Research Articles

Microscopic Studies of Electric Dipole Resonances in 1p Shell Nuclei

Recent data on total and partial photonuclear cross sections in the GDR region of the nuclei 6Li to 16O are compared with theoretical predictions, mostly from shell model and continum shell model studies. The influence of the size of the configuration space, of the adopted residual interaction and of the continuous spectrum on the isovector E1 response is discussed to some detail. The observed trends of the localization, the shape and width, the isospin and the configurational structure of the GDR with increasing 1p shell occupation are related to the microscopic structure of the nuclear ground state. Particular attention is given to the partial (γ, Ni) disintegration channels. Complex-particle emission and isospin mixing in the nuclear states are discussed for a few cases. An attempt is made to bring some systematics also in the evidence on excited-state giant resonances through the 1p shell region. The photonuclear GDR is compared with other giant multipole excitations, mostly for the example of the 14C nucleus.

Resonant absorption and the isospin mixing of the second [formula omitted] state of 9Be

The second T = 3 2 state of 9Be at E x = 16.98 MeV, a narrow state amidst many broad T = 1 2 states, was resonantly excited in the reaction 9Be(γ, X) with monoenergetic γ rays of variable energy produced in the 7Li(d, γ) 9Be reaction at E d = 361 keV. Analyses of the transmission dips, measured with 9Be absorbers of lengths ranging from L = 80 to 488 mm, yield a total width of Γ = 520 ± 90 eV and a radiative width of Γ γ0 = 16.6 ± 1.2 eV. Measurements of thick-target yield curves of the 7Li(d, γ) 9Be resonance at E d = 361 keV yield a total width Γ = 470 ± 60 eV for the same level and a resonance strength S = 7.6 ± l.3 eV. These results, together with literature data, give information on the isospin mixing of this highly excited T = 3 2 9 Be state.

Width of the second T=(3/2) state in 9Be.

A total width ${\ensuremath{\Gamma}}_{\mathrm{c}.\mathrm{m}.=303\ifmmode\pm\else\textpm\fi{}30}$ eV was found for the ${J}^{\ensuremath{\pi}}$, T${=(1/2)}^{\mathrm{\ensuremath{-}}}$,(3/2) level at 16.98 MeV in $^{9}\mathrm{Be}$ by employing high resolution beams of our 450 kV electrostatic accelerator. Partial widths of selected decay channels are given. A comparison with existing data of the lowest T=(3/2) level in the same nucleus as well as the ones in the mirror nucleus $^{9}\mathrm{B}$ is made. The results are discussed in terms of isospin mixing.

Isospin mixing in compound nuclear reactions: A study in the 11B(p, n) 11C system at Ep = 14.3 MeV

The elastic enhancement factor in charge-exchange reactions proceeding via the compound nucleus, predicted to attain the value of 2 in the weak isospin mixing regime by Harney, Weidenmüller and Richter five years ago, is tested here in the system 11B(p, n) 11C at 〈 E p〉 = 14.3 MeV. Both the DWBA and Hauser-Feshbach calculations employed in the analysis are used in a way which physically simulates a two coupled-channels model. Our results show an enhancement factor larger than 1 indicating that isospin is mainly conserved in this reaction.

Isospin mixing during the decay of the giant dipole resonance: A case-study in 28Si

The magnitude of the isospin mixing in the initial 1p-1h doorway state and in the underlying compound states of the 28Si giant dipole resonance is estimated from (γ, p), (γ, α) and (γ, n) cross sections. From the mixing coefficients, mixing widths of about 40 keV and 25 keV are deduced for the 1p-1h state and for the compound states respectively. This seems to indicate that the isospin mixing widths are roughly independent of the complexity and lifetime of the state involved.

Measurement of isospin mixing in 4He and its implications for charge-symmetry breaking.

..pi..-/sup 4/He inelastic cross sections have been measured at T/sub ..pi../ = 180 MeV. In the region of the J/sup ..pi../ = 1/sup -/ states (E/sub x/approx. =23 to 30 MeV) the ..pi../sup +//..pi../sup -/ cross-section ratio R/sub ..pi../ was found to be 1.05 +- 0.08 at theta/sub lab/ = 30/sup 0/. Such a small deviation from 1.0 implies that isospin mixing between the T = 0 and T = 1 states in /sup 4/He is quite weak, in striking contrast to the strong isospin mixing deduced from the large ratio of photonucleon cross sections, R/sub ..gamma../ = sigma(..gamma..,p)/sigma(..gamma..,n)approx. =1.7. Thus the conclusion drawn from the photonucleon work, that there is a large charge-symmetry-breaking nuclear force in /sup 4/He, needs to be reexamined.

Breaking of isospin symmetry in compound-nucleus reactions

The authors present an analysis of all extant data on isospin mixing in statistical compound-nucleus reactions. The analysis is based on a generalization of the Hauser-Feshbach formula allowing for isospin mixing. The strength of the mixing is described by a single parameter $z$. The theory is applicable when all compound-nucleus resonances overlap strongly. It is derived from a statistical theory of nuclear reactions allowing for the mixing of two classes of states. The parameter $z$ comprises both internal mixing (via the Coulomb interaction) and external mixing (via the channels). The theory contains both the static criterion (Coulomb matrix elements compared with spacings) and the dynamical criterion (spreading widths compared with decay widths) for isospin symmetry breaking. The theory yields the dependence on $z$ of observables like average cross sections, and auto- and cross-correlation functions. The data show that isospin symmetry breaking is neither so weak as to be altogether negligible, nor so strong as to reduce our theory to a Hauser-Feshbach formalism without any reference to the isospin quantum number. The authors argue in favor of a parametrization of isospin symmetry breaking in the data in terms of a spreading width rather than a Coulomb matrix element. They find that internal mixing dominates, and that the associated spreading width is nearly independent of mass number and excitation energy.

Pion absorption on 3He at T pi =62.5 and 82.8 MeV.

Pion absorption in $^{3}\mathrm{He}$ was studied at ${T}_{\ensuremath{\pi}}$=62.5 and 82.8 MeV using nucleon-nucleon coincidences. For ${\ensuremath{\pi}}^{+}$ absorption on proton-neutron pairs the differential cross section is the same as that for ${\ensuremath{\pi}}^{+}$+d\ensuremath{\rightarrow}p+p except for an increase by a factor of about 1.5. For ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ absorption on the proton-proton pair, the differential cross section is asymmetric about 90\ifmmode^\circ\else\textdegree\fi{}, indicating possible isospin mixing. The total cross sections ${\ensuremath{\sigma}}_{\mathrm{pn}({\ensuremath{\pi}}^{+})}$ are 10.2\ifmmode\pm\else\textpm\fi{}0.9 mb and 13.5\ifmmode\pm\else\textpm\fi{}1.3 mb at 62.5 and 82.8 MeV and for ${\ensuremath{\sigma}}_{\mathrm{pp}({\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}})}$ are 0.70\ifmmode\pm\else\textpm\fi{}0.07 mb and 0.92\ifmmode\pm\else\textpm\fi{}0.10 mb at 62.5 and 82.8 MeV. The three-body absorption cross sections for ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ are found to be comparable to each other and show no strong energy dependence. The three-body absorption cross section ${\ensuremath{\sigma}}_{3}$(${\ensuremath{\pi}}^{+}$) is 6.7\ifmmode\pm\else\textpm\fi{}2.5 mb and 5.7\ifmmode\pm\else\textpm\fi{}2.3 mb and for ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$, ${\ensuremath{\sigma}}_{3}$(${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$) is 8.7\ifmmode\pm\else\textpm\fi{}1.4 mb and 6.5\ifmmode\pm\else\textpm\fi{}2.0 mb at 62.5 and 82.8 MeV, respectively.

Neutrino neutral current isoscalar excitations in 12C-isospin mixing, II

The neutrino-neutral current isoscalar excitation of 12 C* (1 + ; T = 0; 12.71 MeV) is investigated systematically to examine the specific roles of the various pieces of the neutral current. An effective Hamiltonian for the (isoscalar) neutrino-nucleus neutral current interaction is derived, with in the context of the standard electroweak theory. The hadronic part of the neutral current interaction is found to be vectorial. Numerical results for the isoscalar total cross sections are found to satisfy the Primakoff inequality. The T = 1 admixture into the 12 C* (1 + ; T = 0; 12.71 MeV) from the 12 C* (1 + ; T = 1; 15.1 MeV) is taken into account. It is found that the isospin admixtures makes the total cross sections for the neutrino and antineutrino excitation of the 1 + ; 12.71 MeV in 12 C different. The asymmetry R is thus a direct measure of T = 1 admixture. When the T = 1 admixture is large (0.2), the Primakoff inequality is disturbed. Further effects of isospin mixing on the total cross sections are discussed.

Λ and Σ hypernuclei

The present status of structure calculations for p-shell Λ hypernuclei, including the phenomenological determination of ΛN effective interaction matrix elements, is briefly reviewed. For Σ hypernuclei the Nijmegen potential model D is used for guidance in constructing ΣN effective interactions. The structure of Σ 12Be and Σ 12C, including isospin mixing in the latter case, is discussed, and a comparison is made with experimental data.

The E2 strength distribution in 6Li studied by the (e,d 0) reaction

Angular distributions have been measured for the 6Li(e, d 0) reaction in the excitation energy range 10–28 MeV. The differential cross sections are decomposed into E1 and E2 components on the basis of a simple cluster model. The E2 strength deduced using a virtual photon spectrum is spread over the entire energy region studied. This strength reflects isoscalar E2 excitations in 6Li. The E1 strength, which results from isospin mixing, shows no significant structure.

Calculated isospin-mixing corrections to Fermi β-decays in 1s0d-shell nuclei with emphasis on A = 34

Corrections to the Fermi matrix element due to analogue symmetry breaking are evaluated for the superallowed β-decays of 22Mg, 34Cl, and 34Ar by considering the effects of Coulomb and other isospin-nonconserving potentials. Analogue symmetry breaking is calculated within the shell-model formalism by considering: (i) the deviations from unity of the radial overlap between the proton and neutron single-particle wave functions, and (ii) isospin mixing between states within the 0d 5 2 0d 3 2 0d 1 2 shell. The radial-overlap corrections for several cases of interest in the sd shell are evaluated with single-particle wave functions obtained from a self-consistent Hartree-Fock calculation. The sd-shell isospin-mixing corrections are calculated with an isospin-non-conserving potential which reproduces the experimental isobaric mass shifts. Comparisons with previous calculations are made. The Fermi matrix elements for the isospin-forbidden (β-decays of 34Cl and 34Ar to excited 0 + states are also calculated.

∑ Hypernuclei

The issues of ∑-hypernuclear level widths, isospin mixing in ∑ hypernuclei, and the ∑-nuclear spin-orbit coupling are discussed in the light of recent observations of ∑-hypernuclear levels in K − initiated reactions on 12C and 16O.

Quantitative evidence of weak isospin mixing in the low-lying isobaric analog resonances in 209Bi

Abstract The excitation functions of 208 Pb ( p , p 0 ) 208 Pb have been measured in the energy range E p = 14.2 to 17.4 MeV in 50 keV steps at θ lab = 120°, 140° and 160°. The isobaric analog resonances of the parent states in 209 Pb up to E x = 2.5 MeV and the optical-model background were fit simultaneously at all energies and angles. The spreading widths and the values of a parameter β 2 , which measures the isospin purity of the IAR, were determined for the g 9 2 , i 11 2 , j 15 2 , d 5 2 , and s 1 2 resonances. An average value of the isospin purity of β 2 = 66% was found.

Formula omitted] reaction in the giant resonance region

The energy spectra of α-particles and the (e, α) cross section for 24Mg were measured with electrons in the energy region from 14 to 30 MeV to investigate α-particle emission from the giant resonance. The ( γ, α 0) and ( γ, α) cross sections for 24Mg were deduced from energy spectra and the (e, α) cross section using the virtual photon technique. E1 and E2 components were obtained from the analysis of angular distributions. A peak of 20 MeV seen in the (γ, n), (γ, p) and absorption cross sections is not observed in the (γ, α) cross section. The cross sections are explained by the statistical model with isospin mixing in the measured energy region, except around 20 MeV.

Medium corrections to inelastic π+/ π− cross section ratios

We show that an effective δ-N interaction, constrained by elastic pion scattering and by the observed π +/gp − ratios for proton knock-out near the 3−3 resonance, modifies isospin mixing coefficients extracted from the π +/π − cross section ratio to nuclear particle-hole states.

Isospin mixing in the decay of theT>giant dipole state

The magnitude of the isospin mixing in the decay of the ${T}_{>}$ giant dipole resonance has been estimated, using the ($\ensuremath{\gamma}$, n) and ($\ensuremath{\gamma}$,p) cross sections available for the medium-weight nuclei $^{60}\mathrm{Ni}$, $^{88}\mathrm{Sr}$, $^{89}\mathrm{Y}$, $^{90}\mathrm{Zr}$, and $^{92}\mathrm{Mo}$. The deduced values show a fair correspondence with the existing data for mixing between compound states. From these results the mean mixing Coulomb matrix elements between compound states could also be derived.

Resonances

Abstract T = 3 2 resonances in 21Ne have been studied in measurements of the total neutron cross section of 20Ne using the 190 m neutron time-of-flight facility of the Karlsruhe Isochronous Cyclotron. The high time-of-flight resolution of 6.6 ps/m enabled the study of sharp T = 3 2 resonances in 21Ne with an effective energy resolution of up to 4000. Five T = case3 2 levels have been observed as sharp resonances allowing the precise determination of total width Λ, partial decay with Λno and resonance energy ER. The c.m. resonance parameters of the first T = 3 2 state in 21Ne are ER = 2098.6 ± 0.3 keV, Λ = 2.2 ± 0.5 keV and Λno = 0.21 ± 0.05 keV. Upper limits for the partial decay widths are deduced for those T = 3 2 levels which do not appear as resonance anomalies. A search for additional T = 3 2 states was undertaken. The resonance energies are discussed in the framework of the isbobaric mass multiplet equation. The decay widths are compared with shell-model predictions of isospin mixing and the systematics of isospin-non-conserving particle decays.

Magnetic multipole excitations inC12by inelastic electron scattering

Magnetic excitations in $^{12}\mathrm{C}$ have been measured by inelastic electron scattering at backward scattering angles for momentum transfers between $q=0.5 \mathrm{and} 3.3$ ${\mathrm{fm}}^{\ensuremath{-}1}$. Data for $M1$, $M2$, $M3$, and $M4$ transitions are compared to shell model calculations. In general, the excitation energies are reasonably predicted, as are the momentum transfer dependences of the form factors. However, the form factor magnitudes often exceed measurements by factors of more than 2. Candidates for ${2}^{\ensuremath{-}}$ states are seen at excitation energies of 18.2 and 22.7 MeV. It is shown how structure effects may reduce estimates of isospin mixing matrix elements from ($\ensuremath{\pi}$,${\ensuremath{\pi}}^{\ensuremath{'}}$) ratios.

Sound wave propagation in a two-component fermi liquid

We investigate the stability of the sound wave propagation in a two-component (protons and neutrons) Fermi liquid based on the time-dependent Hartree-Fock equation in configuration space. The two types of sound modes appear, which are known as plasmons and phonons. Because of the Coulomb repulsion between protons the plasma mode tends to be stabler than the phonon mode. The isospin mixing caused by the Coulomb interaction cannot be neglected for the excitation modes with wavelength of the order of nuclear size.