Isospin Selection Rules Research Articles

Gamma-transition strengths of T = 1 states in 10B

The 1.74 ( J π = 0 1 +, T = 1) and 5.16 (2 2 +, 1) MeV states in 10B have been studied through the reaction 6Li(α, γ) 10B. The lifetimes τ m = 7 ± 3 and < 6 fs, respectively, have been obtained with the DSA method. The γ-ray decay scheme of the 5.16 MeV state has been revised and the ambiguous isoscalar E2 branch to the 1.74 MeV state has been clarified and shown to have an intensity of (0.7 ± 0.2)%. The angular distributions of γ-rays from the 5.16 MeV state have been measured and mixing ratios determined. The Ml transition 1.74(0 +, 1) → 0.72(1 +, 0) MeV is compared with the analogue β-decay from the ground state of 10C(0 +, 1) to the 0.72 MeV state and is discussed in terms of shell-model calculations. The E2 strength of the 5.16(2 +, 1) → 1.74(0 + 1) MeV isoscalar transition is compared with its analogues in the neighbouring T = 1 nuclei 10B and 10C in the light of isospin selection rules.

Isospin splitting in the giant dipole resonance in 46Ti

The photoneutron cross section, 46Ti(γ, n), has been studied in the photon energy range 12 to 25 MeV. Comparison of this cross section with the 46Ti(γ, p) cross section shows evidence for isospin splitting of the giant dipole resonance. A detailed calculation for the (γ, n) and (γ, p) cross sections assuming a statistical decay process and taking into account the isospin selection rules and the predictions of Goulard and Fallieros for the energy separation and relative strengths of the two isospin components of the giant dipole resonsnce, agrees with the experimental results. The possibility of deformation splitting of the 46Ti GDR is also discussed.

Relativistic invariant approach to the parity violation in np→d γ capture

It is shown that the consistent relativistic invariant approach to the parity violation in np→d γ capture of thermal neutrons leads to results which differ essentially from those of the nonrelativistic approach. In particular the isospin selection rule established earlier for the photon circular polarization is charged due to the contribution of “relativistic” parity violating components of the deuteron and np-scattering wave function.

Comparison of the ReactionsC12(π+, p)C11andC12(p, d)C11near the Same Momentum Transfer

Observed transitions in the reaction /sup 12/C(..pi../sup +/, p) /sup 11/C at 49.3 MeV confirm the importance of multistep processes in the reaction mechanism. The relative intensitu of the transitions is nearly the same as in the reaction /sup 12/C(p, d) /sup 11/C at 700 MeV, except for an apparent isospin selection rule. Transitions to low-lying states in /sup 10/C via the reaction /sup 12/C(..pi../sup +/, d) have also been observed.

Isoscalar and isovector E2 transition matrix elements in the mass A=26 system

In the decay of the second excited 2+, T=1 state at 3160 keV in 26Al a new 5+or-2% branch to the 01+, T=1 level was found. The E2 strength of this transition is compared with its analogues in the neighbouring nuclei 26Mg and 26Si in the light of isospin selection rules. An exceptionally large reduced isovector matrix element is obtained.

Alpha capture to the giant dipole resonances of 42Ca, 44Ca and 52Cr

Differential cross sections for the 38 Ar(α, γ 0) 42 Ca, 40 Ar(α, γ 0, 1) 44 Ca and 48 Ti(α, γ 0, 1) 52 Cr reactions were measured at 90° to the beam direction in 50 or 100 keV steps over the bombarding energy ranges 6.0–15.0 MeV, 5.5–11.1 MeV and 6.0–12.0 MeV respectively. Gamma-ray angular distributions were measured at forty bombarding energies. These show that the ( α, γ 0) reaction proceeds through 1 − levels and to a lesser extent 2 + levels, whereas the ( α, γ 1) reaction most probably proceeds through 1 − and 3 − levels. It is deduced that 〈 Γ〉/〈 D〉 ≦ 1 for the 40Ar( α, γ) 44Ca. reaction whereas the fine structure observed in the 48Ti( α, γ) 52Cr reaction is probably due to fluctuations. From a comparison with other data it is shown that the (α, γ) reaction is most probably statistical in nature. Using Hauser-Feshbach theory it is deduced that the 36Ar( α, γ) 40Ca. reaction is inhibited by isospin selection rules and an estimate is made of isospin mixing in the 40Ca giant dipole resonance. The 38 Ar(α, γ) 2 42 Ca and 40 Ar(α, γ) 44 Ca data are considered with respect to theories of isosopin splitting of the giant dipole resonance.

Alpha decay of isobaric analogue states in24Mg and28Si

Theα-decay of isobaric analogue states (which are forbidden by isospin selection rules) excited in24Mg and28Si through preton capture by23Na atE p=677 and 739 keV and by27Al atE p=295, 327 and 405 keV, respectively, have been studied using solid state track detectors. The ratio ofα-decay widths of the two resonance states in24Mg to the state at 1.632 MeV (2+) in20Ne yields the value 0.065 for the mixing parametere and the value 4.01 keV for the Coulomb matrix element responsible for the isospin mixing in24Mg. In28Si the measurement of theα-decay widths of the three resonance states resulted in the determination of the proton, gamma and alpha partial widths which comprise the total width of the resonance states. Limits have been set for the value of the two mixing parameters involved in this case. Upper limits of 16 and 39 keV have been obtained for the Coulomb matrix elements responsible for the isospin mixing in28Si.

Dispersion theory of parity non-conservation in pion-nucleon scattering at low energies

We examine the possibility for testing the weak parity non-conserving (pnc) interaction in pion-nucleon scattering at low energies. We start out analysis by assuming the existence of a pnc πNN coupling which conserves time reversal invariance and has the isospin selection rule ΔI = 1, and the existence of fixed- t dispersion relations obeyed by the pnc invariant amplitudes. By using the nonrelativistic expansion, we then derive dispersion relations for the partial-wave amplitudes. We calculate parity-odd observables in π −p → π −p and in π −p → π 0n, e.g., the up-down asymmetry α in the total cross section for a polarized target and the longitudinal polarization P of the recoil nucleon. In the conventional Cabibbo model for the weak interaction P and α are found to be of order 10 −7 to 10 −8. We have also examined the t-channel pnc ϱ-exchange process which has the isospin selection rule ΔI = 0, 2 and found it to contribute dominantly to P in the charge-exchange channel π −p → π 0n.

Experimental study of the energy spectrum of theπ+inK+→π+π0π0decay

A sample of 5635 ${\ensuremath{\pi}}^{+}$ with kinetic energies between 8 and 50 MeV was obtained from ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decays in the ANL-Michigan 40-in. heavy liquid bubble chamber filled with propane. For these the energy dependence was well described by a linear spectrum of the form ${|M|}^{2}=1+g[\frac{({s}_{3}\ensuremath{-}{s}_{0})}{{m}_{\ensuremath{\pi}+}^{2}}]$, where $g=0.602\ifmmode\pm\else\textpm\fi{}0.021$. No evidence was found for a quadratic term significantly different from 0. When the five conventional test quantities for the isospin selection rules were formed using the value of $g$ from this experiment and current world averages for the other $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay parameters, it was found that there was significant evidence for $|\ensuremath{\Delta}I|=\frac{3}{2}$ amplitudes into both $I=2$ and $I=1$ final states. These experimental values are in good agreement with theoretical predictions for them obtained in models which satisfy the current-algebra relation at the soft-pion points and include $|\ensuremath{\Delta}I|=\frac{3}{2}$ as well as $|\ensuremath{\Delta}I|=\frac{1}{2}$ amplitudes.

Neutral currents in thermal np capture

We present a calculation of the circular polarization P γ and asymmetry A γ of gamma radiation in thermal neutron-proton capture with a tested numerical accuracy of 1%. The effect of neutral currents is discussed on the example of the Weinberg-Salam model of weak interaction. It is also shown that a one percent contribution of the 3S 1 scattering state to the regular np capture cross section destroys the favourable isospin selection rule in the polarization.

Theory of the pseudoscalar interaction in the two-nucleon systems

We discuss in general terms both covariant and non-covariant formulations of the pseudoscalar interactions in the two-nucleon (NN) and pion-nucleon ( πN) systems. We derived the equations allowing one to evaluate the 2 π exchange contribution to the NN scattering amplitudes and non-relativistic potentials from the knowledge of the corresponding pseudoscalar amplitudes in the πN system. Dynamical descriptions of odd-parity effects are then discussed in connection with weak interaction models based on the current-current form of the weak Hamiltonian. We present calculations of NN potentials due to 2π exchange contributions including πN and ππ rescattering effects in the strong vertices only. We consider two mechanisms: the first induced by the vertex N + N → π and the second by N + N → 2π (p-wave). Restricting ourselves to on-shell nucleons, the first contributes to potentials with isospin selection rule ΔT = 1 and the second to potentials ΔT = 0, 1, 2, the ΔT = 1 part corresponding in the factorization approximation to G-parity odd effects and the others to the familiar ϱ-exchange and triangle diagram mechanisms. It is shown that 2 π exchange effects are not intrinsically small, as they appear in a significant way in components where 1 π effects do not contribute. It is also suggested on the basis of a deviation of single-particle potentials, obtained by taking nuclear matter averages of our two-body potentials, that 2 π effects provide for 50% ∼10% enhancements in the magnitudes of the familiar π- and zero-width ϱ-exchange contributions.

Isospin conservation and pre-equilibrium decay in (p, ṕ) reactions on neutron rich tin isotopes

Energy spectra for protons emitted in (p, p') reactions on 118Sn, 120Sn and 124Sn have been studied as a function of emission angle at incident energies of 14.0 and 17.8 MeV. These data confirm the importance of isospin selection rules in such reaction systems. While it is not possible to make any definite statements about the mechanism of the reactions populating the higher isospin intermediate states, it is possible to obtain a consistent description of the observed spectra in terms of two pre-equilibrium decay components, one each for the T > and T < states in the composite system. Small T < evaporation peaks for the 118Sn and 120Sn systems may be present. While this explanation is critically dependent on the validity of the extended Griffin model used in the analysis, it is a direct consequence of the inclusion of isospin in the model using techniques adopted from equilibrium calculations. The high energy protons, which have forward-peaked angular distributions, are attributed to pre-equilibrium decay of the T < states and are predicted to be emitted fairly early in the equilibration process. The model also predicts that T > state pre-equilibrium decay should occur primarily toward the end of equilibration and identifies such processes with the low energy, isotropically emitted protons observed in the data. However, the enhanced rate of proton emission from the T > composite states may result in a breakdown of the fundamental statistical assumption of equal population for all n-exciton T > states. On the basis of the statistical model analyses performed it is estimated that 40–80% of the T > states undergo proton emission before isospin mixing occurs and that virtually none of them reach statistical equilibrium.

Isospin and the Bohr Independence Hypothesis

The influence of isospin on statistical nuclear decay at approximately 20 MeV is investigated for two composite systems $^{66}\mathrm{Zn}$ and $^{64}\mathrm{Zn}$ by measurement of the cross sections and the energy spectra of protons and \ensuremath{\alpha} particles emitted from the two composite systems. The composite system $^{66}\mathrm{Zn}$ was formed at an excitation energy of 19.7 MeV in the $^{65}\mathrm{Cu}+p$ and $^{62}\mathrm{Ni}+\ensuremath{\alpha}$ reactions, while the composite system $^{64}\mathrm{Zn}$ was formed at an excitation energy of 19.5 MeV in the $^{63}\mathrm{Cu}+p$ and $^{60}\mathrm{Ni}+\ensuremath{\alpha}$ reactions. In both systems the experimental cross-section ratio $\frac{\ensuremath{\sigma}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})\ensuremath{\sigma}(p,{p}^{\ensuremath{'}})}{\ensuremath{\sigma}(\ensuremath{\alpha},p)\ensuremath{\sigma}(p,\ensuremath{\alpha})}$ exceeded the value of approximately unity predicted by the Bohr independence hypothesis and the statistical theory of compound-nuclear decay including angular momentum. The cross-section ratios were 2.2 \ifmmode\pm\else\textpm\fi{} 0.2 and 1.3 \ifmmode\pm\else\textpm\fi{} 0.1 for the $^{66}\mathrm{Zn}$ and $^{64}\mathrm{Zn}$ composite systems, respectively. The major part of the deviation of these ratios from unity in both the composite systems is ascribed to an isospin selection rule acting in the ${T}_{g}$ states of both composite systems which causes these states to decay preferentially by proton emission. Other factors which might enhance these ratios, such as direct reactions and reduced moments of inertia, are considered and are found to change the above ratios by a relatively small amount.

Selection Rules in the Weak Interactions and Their Relation to Hadronic Mesons

In the framework of a model of weak interactions developed in a previous work, we consider selection rules in weak interactions. The isospin selection rules |ΔI| = 1 and |ΔI| = 1/2 are consequences of our model. We classify the hadronic vector and axialvector mesons into first and second class mesons similar to S. Weinberg's classification of first and second class currents, thus giving physical meaning to notions of first and second class currents. We derive the conclusion that the existence of second class currents depends on the following points: Existence of “second class” mesons. As a candidate we cite B meson: IGJP = 1+1+, m = 1220 Mev. Existence of vector (axialvector) mesons with isospin 2. Existence of neutral leptonic currents. Here the ω and φ mesons would give the main contributions. We discuss the relation of the electromagnetic currents of the hadrons to the vector part of the neutral weak currents of the hadrons. We assume these two currents to be the same and conclude from this that the possible existence of the isotensor electromagnetic currents which have been investigated by several authors in recent years is directly related to the possible existence of |ΔI| = 2 weak processes or to the possible existence of mesons with isospin 2. This assumption leads to an “extended” C. V. C. in the sense that the isospin relation between the electromagnetic and weak currents is not limited to the isovector but extended to the isoscalar and isotensor.

Veneziano Amplitude forπNScattering

A crossing-symmetric Regge-behaved amplitude for $\ensuremath{\pi}N$ scattering is constructed with a minimum number of Veneziano terms from $\ensuremath{\rho}$, ${\ensuremath{\rho}}^{\ensuremath{'}}$, ${P}^{\ensuremath{'}}$, and ${P}^{\ensuremath{'}\ensuremath{'}}$ trajectories in the $t$ channel and ${N}_{\ensuremath{\alpha}}$, ${N}_{\ensuremath{\gamma}}$, and ${\ensuremath{\Delta}}_{\ensuremath{\delta}}$ trajectories in the $s$ and $u$ channels. The parameters are determined from low-energy $\ensuremath{\pi}N$ resonances, isospin selection rules, and $\ensuremath{\rho}$ universality. The model fits the high-energy charge-exchange differential cross sections in the forward direction, and also predicts polarization in reasonable agreement with experimental values. The resulting backward elastic differential cross sections are discussed.

Calculation of the electrodisintegration cross section of4He

In the framework of a previously discussed translationally invariant particle hole model theT=1 part of the differential electrodisintegration cross section of4He is calculated. A comparison with a recent measurement of this reaction gives fairly quantitative agreement, but it is suggested that in the region below 26 MeV excitation energy besides the 2−T=1 state the 2−T=0 state presumably gives an appreciable contribution to the cross section thus indicating that the usually observed isospin selection rule does not work in this case.

34Ar and T = 1 states in 34Cl from two-nucleon pick-up reactions

The reactions 36Ar(p, t) 34Ar, 36Ar(p, 3He) 34Cl and 36Ar(d, α) 34Cl have been used to study energy levels in 34Ar and 34Cl. Excitation energies and J π values have been established for states up to 8 MeV in 34Ar, and many of their T = 1 analogues have been identified in 34Cl. These results exemplify the usefulness of the spin and isospin selection rules inherent in two-nucleon transfer reactions. The results are discussed in terms of the mass-34 T = 1 multiplet and the J-dependence of their Coulomb displacement energies.

ηAsymmetry withoutCNonconservation?

Interference asymmetry should be greatly reduced in situations where isospin selection rules forbid the occurrence of I=2 background.Received 7 October 1968DOI:https://doi.org/10.1103/PhysRev.178.2486©1969 American Physical Society

Remarks on Isospin Selection Rules andCP-Nonconserving Phases in Glashow's Theory

Remarks on Isospin Selection Rules and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>-Nonconserving Phases in Glashow's Theory

The effect of the isospin selection rule on dipole transitions in 24Mg and 28Si

We have estimated absolute γ-ray transition rates for levels found as resonanced in (p, γ) reactions on 23Na and 27Al and identified 37 (in 24Mg) and 54 (in 28Si) cases of dipole radiation between levels with known J, π and T quantum numbers. Forbidden E1 transitions between levels with ΔT = 0 are indeed retarded with respect to the allowed ΔT = 1 transitions. However, the existence of these forbidden transitions indicates a small amount of isospin admixture in the high-lying T = 0 levels. The average rate of forbidden E1 transitions is similar to that in lighter nuclei, while the average rate of allowed is 2 ≈ 15 times slower here than in lighter nuclei. We suggest that this is a consequence of the increased level density in the heavier nuclei and the presence of isospin mixtures among the radiating levels.