Isospin Rotation Research Articles

Beta decays ofNe18andNe19and their relation to parity mixing inF18andF19

We have studied transitions weakly fed in the ${\ensuremath{\beta}}^{+}$ decays of $^{18}\mathrm{Ne}$ and $^{19}\mathrm{Ne}$. The $^{18}\mathrm{Ne}$ activity was produced by bombarding natural ${\mathrm{O}}_{2}$ gas with 12.0 MeV $^{3}\mathrm{He}$ ions. $\ensuremath{\gamma}$-ray groups with energies of 659, 1042, 1081, and 1700 keV were observed with relative intensities of 1.72\ifmmode\pm\else\textpm\fi{}0.05, 100.0, (2.89\ifmmode\pm\else\textpm\fi{}0.26)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}2}$, and 0.687\ifmmode\pm\else\textpm\fi{}0.013, respectively. These intensities correspond to relative branching ratios of 100.0, (2.70\ifmmode\pm\else\textpm\fi{}0.36)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}2}$, and 2.45\ifmmode\pm\else\textpm\fi{}0.05 for ${\ensuremath{\beta}}^{+}$ transitions to the 1042, 1081, and 1700 keV levels, respectively. Normalizing to previous data we obtain $\mathrm{ft}$ of 1247\ifmmode\pm\else\textpm\fi{}11, 2971\ifmmode\pm\else\textpm\fi{}87, (1.03\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}${10}^{7}$, and (3.00\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ see for the transitions to the ground state, 1042, 1081, and 1700 keV levels, respectively. The difference in excitation energies of the ${0}^{\ensuremath{-}}$ and ${0}^{+}$ states is found to be 39.20\ifmmode\pm\else\textpm\fi{}0.11 keV. The $^{19}\mathrm{Ne}$ activity was produced by bombarding S${\mathrm{F}}_{6}$ gas by 6.4 MeV protons. A branching ratio of (1.20\ifmmode\pm\else\textpm\fi{}0.20)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ was obtained for the transition to the 110 keV level which corresponds to an $\mathrm{ft}$ value of (1.15\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}${10}^{7}$ sec. Transitions to the 1554 keV level were observed in a 9.2% Ge(Li) detector operated in the singles mode. A branching ratio of (2.34\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ was obtained which corresponds to an $\mathrm{ft}$ value of (5.01\ifmmode\pm\else\textpm\fi{}0.47)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ sec. The $^{18}\mathrm{Ne}$(${0}^{+}$; 1)\ensuremath{\rightarrow}$^{18}\mathrm{F}$(1081 keV ${0}^{\ensuremath{-}}$; 0) and $^{19}\mathrm{Ne}$(${\mathrm{\textonehalf{}}}^{+}$; \textonehalf{})\ensuremath{\rightarrow}$^{19}\mathrm{F}$ (110 keV ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$; \textonehalf{}) first-forbidden ${\ensuremath{\beta}}^{+}$ branches are analogs of the previously measured parity mixing of the 1042 keV (${0}^{+}$; 1) and 1081 (${0}^{\ensuremath{-}}$; 1) keV levels of $^{18}\mathrm{F}$ and of the ground (${\mathrm{\textonehalf{}}}^{+}$; \textonehalf{}) and 110 keV (${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$; \textonehalf{}) levels of $^{19}\mathrm{F}$, respectively. We show that the strong exchange-current corrections to the axial charge operator dominating these $\ensuremath{\beta}$ transitions involve an operator identical, apart from an isospin rotation, to that mediating the pion-exchange contribution to the parity nonconserving $\mathrm{NN}$ force. These exchange current contributions can be extracted from the $\ensuremath{\beta}$-decay rates in a manner nearly independent of nuclear structure assumptions. Thus, in these cases, the usual structure uncertainties that obscure the connection between the $\ensuremath{\Delta}S=0$ weak hadronic interaction and nuclear observables can largely be circumvented. The $\mathrm{ft}$ we obtain for the transitions to the 1081 keV and 110 keV levels of $^{18}\mathrm{F}$ and $^{19}\mathrm{F}$ suggest that the strengths of the $I=1$ and $I=0$ components of the parity nonconserving $\mathrm{NN}$ force are close to the best values of Desplanques, Donoghue, and Holstein. Except for a recent structure calculation employing complete $2h\ensuremath{\omega}$ and $1h\ensuremath{\omega}$ bases for the positive and negative parity states in $^{18}\mathrm{F}$, the $\ensuremath{\beta}$ decay and parity nonconserving matrix elements predicted in typical shell model studies are approximately three times larger than experiment. This and other evidence suggests that the softening of the nuclear Fermi surface by $2h\ensuremath{\omega}$ configurations is an essential, but missing, feature of most nuclear structure calculations of parity nonconserving matrix elements. We conclude by presenting shell model studies of the electromagnetic properties of low-lying states in $^{18}\mathrm{F}$, $^{19}\mathrm{F}$/$^{19}\mathrm{Ne}$, and $^{21}\mathrm{Ne}$/$^{21}\mathrm{Na}$ as well as the matrix elements for the operators that arise in a general meson-exchange parity nonconserving potential.RADIOACTIVITY $^{18}\mathrm{Ne}$, $^{19}\mathrm{Ne}$; measured $I\ensuremath{\gamma}$; deduced $\mathrm{ft}$. Compared to shell model calculations. Discussed connection of forbidden decays to parity mixing in $^{18}\mathrm{F}$ and $^{19}\mathrm{F}$.

Parity Nonconservation inF18and Meson-Exchange Contributions to the Axial Charge Operator

A simple relationship between the one-body and exchange-current contributions to the axial charge operator may allow a separation of these amplitudes in the $\ensuremath{\beta}$-decay transition $^{18}\mathrm{Ne}({J}^{\ensuremath{\pi}}I={0}^{+}1)\ensuremath{\rightarrow}^{18}\mathrm{F}({J}^{\ensuremath{\pi}}I={0}^{\ensuremath{-}}0)$. Since the exchange-current operator is related by isospin rotation to the pion-exchange component of the parity-nonconserving nucleon-nucleon potential, this suggests that the parity-nonconserving pion coupling can be extracted, with minimal dependence on nuclear models, from circular-polarization measurements for the analog $\ensuremath{\gamma}$ decay in $^{18}\mathrm{F}$.

Analytical theory of pion single and double charge exchange in resonance region. I. Geometrical limit

We derive analytical formulas for angular distributions $\ensuremath{\sigma}(\ensuremath{\theta})$ of pion single and double charge exchange to analog states. The result is based on the eikonal approximation and assumes that the interactions are invariant under isospin rotations. The theory reproduces semiquantitatively the results of exact coupled channel, lowest order optical model calculations and explicates the dependence of $\ensuremath{\sigma}(\ensuremath{\theta})$ on the structure of the nuclear target. The $\ensuremath{\sigma}(\ensuremath{\theta})$ for single charge exchange is proportional to the square of the ratio of the valence neutron density $\ensuremath{\Delta}\ensuremath{\rho}(R)$ to the total density $\ensuremath{\rho}(\overline{R})$. The theory predicts $\overline{R}$ as a function of energy and mass number $A$; for pion kinetic energy ${T}_{\ensuremath{\pi}}\ensuremath{\simeq}180$ MeV, $\ensuremath{\rho}(\overline{R})\ensuremath{\simeq}0.1\ensuremath{-}0.2$ of central density. The $\ensuremath{\sigma}(\ensuremath{\theta})$ for double charge exchange is proportional to ${[\frac{\ensuremath{\Delta}\ensuremath{\rho}(\overline{R})}{\ensuremath{\rho}(\overline{R})}]}^{4}$. The strong dependence of $\ensuremath{\sigma}(\ensuremath{\theta})$ on $\frac{\ensuremath{\Delta}\ensuremath{\rho}}{\ensuremath{\rho}}$ suggests that the single and double charge exchange reactions may develop into a sensitive probe of the neutron halo. The dependence of $\ensuremath{\sigma}(\ensuremath{\theta})$ on the diffuseness of $\ensuremath{\rho}$ and $\ensuremath{\Delta}\ensuremath{\rho}$ is also evaluated. Assuming that the neutron and proton densities are proportional, the relative $A$ dependence of $\ensuremath{\sigma}(\ensuremath{\theta})$ for single and double charge exchange is calculated. The result is in qualitative agreement with recent measurements for single charge exchange and predicts that a similar set of measurements for double charge exchange may be feasible. Realistic densities are used to calculate the magnitude of $\ensuremath{\sigma}(\ensuremath{\theta})$. Large enhancements are found in this case, but $\ensuremath{\sigma}(\ensuremath{\theta})$ falls below the preliminary data by as much as a factor of 4. Difficulties in reproducing the observed angular distribution of the $^{18}\mathrm{O}({\ensuremath{\pi}}^{+}, {\ensuremath{\pi}}^{\ensuremath{-}})^{18}\mathrm{Ne}$ reaction are similar to those of other theories. The extent of discrepancy suggests the occurrence of strong modifications of the pion-nucleon interaction in the nuclear medium.NUCLEAR REACTIONS Pion single and double charge exchange; analytical formulas for angular distributions.

General bounds on the isovector coupling constants of the weak neutral current

We show that experimental data on inclusive neutrino reactions can be used to obtain general bounds on the coupling constants of the isovector part of the hadronic weak neutral current provided this isovector current is related to the charged current by isospin rotation. These bounds are free from the assumption of a specific model for the neutral current as well as any dynamical assumption on the hadronic structure functions. We derive upper bounds on the coupling constants which involve only the cross sections for isospin-averaged nucleon target as well as lower bounds which require a knowledge of the cross sections for proton and neutron separately.

A non-linear realisation ofSU(3)?SU(3)

A non-linearSU(3)⊗SU(3) invariant Lagrangian is constructed. The non-linear transformations are required to be linear only on the subgroup of isospin rotations and strangeness gauges: π,K, η and scalarκ-mesons appear as goldstone bosons; masses of vector- and axialvector, as well as strange and non-strange, Yang-Mills fields are split. Results predicted by thisSU(3)⊗SU(3) invariant Lagrangian are similar to those obtained previously by Ward-identity techniques, however, no assumption on symmetry-breaking has to be made. TheKl3-formfactors are discussed.

On a theorem by carruthers

Carruthers' theorem states that self-conjugate isospin multiplets with half-integral isospin cannot exist. It is shown that this theorem can be derived from invariance under Lorentz transformations, CTP, and isospin rotations without using any other assumptions.

Zur Theorie der „seltsamen“ Teilchen

The strange particles can be represented within the framework of the nonlinear spinor theory by taking into account the degeneracy with respect to isospin and parity of the groundstate "vacuum". Use is made of the mathematical analogy between the theory of superconductivity and the theory of elementary particles, and in a first approximation a fourfold degeneracy of the groundstate is assumed. Each auf the four states is considered as a mixture of states of similar symmetry. The GREEN-functions of the type (Ωα | TX (x) X̄(x′) | Ωβ) are considered as invariant under the proper LoRENTz-group, CPT and PG, applied on the field operators or the states Ωα> separately; but as invariant under isospin rotation, P or CT or G, only if the transformation is applied on the fieldoperators and the states Ωα> simultaneously. Parity is represented in a manner discussed in an earlier paper by one of the authors. Only stationary states of strangeness 1 can be considered in this approximation. The fourfold degeneracy of the K-meson is reduced to an additional symmetry which may be connected later with the existence of electromagnetic charge. The results of the calculations may be interpreted by describing the strange particles as composed of ordinary particles and a “spurion” taken from the groundstate “vacuum”. The “spurion” carries an isospin 1/2 and a parity. The masseigenvalues and the parity of the particles are calculated by means of a slightly improved version of the TAMM-DANCOFF-method. The theoretical masseigenvalues agree qualitatively with the observed masses. The calculated relative parities of the strange particles may later be checked by experiments. Besides the known particles of strangeness 1, the theory yields other eigenstates which are probably highly unstable since they could disintegrate into more stable particles by means of strong or electromagnetic interactions.

Isospin und Parität in der nichtlinearen Spinortheorie

The isospin transformation properties and the space reflection symmetry in a nonlinear field theory of elementary particles, as proposed by HEISENBERG and coworkers, are studied. In section I it is shown that the nonlinear equation for a 4-component spinor operator ψ is equivalent to the equation for a 4-component WEYL- isospinor operator χ. In this WEYL representation of the theory the PAULI-GÜRSEY transformations and the TOUSCHEK transformation can be replaced by the conventional forms of the isospin rotations and the gauge transformation of the first kind, respectively. In section II an attempt is made to introduce parity in a rigorous manner using the invariance of the equation under l-Inversion l→ —l. Some important aspects of symmetry operations which involve transformations of parameters, are discussed. By virtue of the parity symmetry a DIRAC notation may be introduced, and the nonlinear equation then corresponds to a TOUSCHEK invariant equation of the DIRAC type with nonlinear vector- and axialvector terms of equal strength. The existence of particles with finite mass suggests a degeneracy of the ground state “world” with respect to parity. In section III and IV the TAMM—DANcoFF-method is applied for an estimate of the masses of nucleons and bosons with spin and isospin zero or one, using the simpler WEYL representation with and without consideration of the parity symmetry, respectively.