Isospin Symmetry Violation Research Articles

Isobar excitation in parity-nonconserving proton-proton scattering.

A parity violating (PV) meson exchange model is applied in the coupled channels formalism to study the effect of isobar excitation on PV [ital pp] scattering. The meson-mixing model used to calculate PV forbids the mixing of [ital S]=0 mesons in particular pions, as well as isospin symmetry violation, so only the [ital pa][sub 1] contribution is considered in isobar excitation. We find a significant contribution to [ital [bar A]][sub [ital L]] from the PV mixing of the states [sup 3][ital P][sub 2] and [sup 1][ital D][sub 2] already at relatively low energies versus one (vector) meson exchange which gives predominantly [sup 3][ital P][sub 0-][sup 1][ital S][sub 0] mixing. At the energy of 230 MeV, where a forthcoming TRIUMF experiment aims to extract the parity violating [rho][ital pp] coupling, our calculated effect from this source alone is of the same order as from the conventional single [rho] exchange.

Are the low-lying isovector 1 + states scissors vibrations?

At the Technische Hochschule in Darmstadt the group of Richter and coworkers found in 1983/84 in deformed rare earth nuclei low-lying isovector 1 + states. Such states have been predicted in the generalized Bohr-Mottelson model and in the interacting boson model no. 2 (IBA2). In the generalized Bohr-Mottelson model one allows for proton and neutron quadrupole deformations separately. If one includes only static proton and neutron deformations the generalized Bohr-Mottelson model reduces to the two rotor model. It describes the excitation energy of these states in good agreement with the data but overestimates the magnetic dipole transition probabilities by a factor 5. In the interacting boson model (IBA2) where only the outermost nucleons participate in the excitation the magnetic dipole transition probability is only overestimated by a factor 2. The too large collectivity in both models results from the fact that they concentrate the whole strength of the scissors vibrations into one state. A microscopic description is needed to describe the spreading of the scissors strength over several states. For a microscopic determination of these scissors states one uses the Quasi-particle Random Phase Approximation (QRPA). But this approach has a serious difficulty. Since one rotates for the calculation the nucleus into the intrinsic system the state corresponding to the rotation of the whole nucleus is a spurious state. The usual procedure to remove this spuriosity is to use the Thouless theorem which says that a spurious state created by an operator which commutes with the total hamiltonian (here the total angular momentum, corresponding to a rotation of the whole system) produces the spurious state if applied to the ground state. It says further the energy of this spurious state lies at zero excitation energy (it is degenerate with the ground state) and is orthogonal to all physical states. Thus the usual approach is to vary the quadrupole-quadrupole force strength so that a state lies at zero excitation energy and to identify that with the spuríous state. This procedure assumes that a total angular momentum commutes with a total hamiltonian. But this is not the case since the total hamiltonian contains a deformed Saxon-Woods potential. Thus one has to take care explicitly that the spurious state is removed. This we do in our approach by introducing Lagrange multipliers for each excited states and requesting that these states are orthogonal to the spurious state which is explicitly constructed by applying the total angular momentum operator to the ground state. To reduce the number of free parameters in the hamiltonian we take the Saxon-Woods potential for the deformed nuclei from the literature (with minor adjustments) and determine the proton-proton, neutron-neutron and the proton-neutron quadrupole force constant by requesting that the hamiltonian commutes with the total angular momentum in the (QRPA) ground state. This yields equations fixing all three coupling constants for the quadrupole-quadrupole force allowing even for isospin symmetry violation. The spin-spin force is taken from the Reid soft core potential. A possible spin-quadrupole force has been taken from the work of Soloviev but it turns out that this is not important. The calculation shows that the strength of the scissors vibrations are spread over many states. The main 1 + state at around 3 MeV has an overlap of the order of 14 % of the scissors state. 50% of that state are spread over the physical states up to an excitation energy of 6 MeV. The rest is distributed over higher lying states. The expectation value of the many-body hamiltonian in the scissors vibrational state shows roughly an excitation energy of 7 MeV above the ground state. The results also support the experimental findings that these states are mainly orbital excitations. States are not very collective. Normally only a proton and neutron particle-hole pair are with a large amplitude participating in forming these states. But those protons and neutrons which are excited perform scissors type vibrations.

Apparent violation of isospin symmetry in the 3H(3He,2H)4He reaction.

Angular distributions of the vector analyzing powers for the $^{3}\mathrm{H}$${(}^{3}$He${,}^{2}$H${)}^{4}$He reaction have been measured over the incident energy range 18--33 MeV. The measurements centered about 18 MeV display a deviation from the antisymmetric shape expected from isospin symmetry. Concentrating on the explanation of the 90\ifmmode^\circ\else\textdegree\fi{} analyzing powers, we report the results of a distorted-wave Born approximation (DWBA) analysis which includes the direct and exchange processes and the spin-orbit potential. It is shown that the anomalous behavior of the 90\ifmmode^\circ\else\textdegree\fi{} vector analyzing powers can be largely explained by the effect of a single F-wave potential resonance which leads to the magnification of the short-range differences between the $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ wave functions.

On testing vector boson self couplings in e+e−→ W+W−

We deduce bounds on the vector boson self couplings g ZWW , κ and κ z which can be obtained from measurements of the total cross section and angular distribution in e + e −→ W + W −. The three-dimensional parameter space is restricted to a two-dimensional subspace, g ZWW , κ by allowing for only those deviations from the standard model which are consistent with no intrinsic violation of global weak isospin symmetry, SU(2) WI, by the vector boson self couplings.

Nucleon-nucleon interactions and quarks I: General considerations with numerical results in the 1S0 channel

In this paper, we discuss a general development of a quark-model description of nucleon-nucleon (NN) interactions, assuming that quarks are Dirac particles and nucleons are specified approximately by flavor SU(6) wave functions. The down (d) quark is differentiated from the up (u) quark allowing isospin symmetry violating effects. As a simple model calculation, we include effects due to one-gluon exchange (which dictates the short-range behavior of NN forces), one-pion exchange (which gives rise to the Yukawa tail in NN forces), single sigma-exchange (which mocks up to the intermediate attraction in an economical manner), and one-photon exchange (which contributes to isospin symmetry violations). To avoid introduction of additional shape parameters, we adopt a double-sphere geometry with an adjustable isolated nucleon radius. All quark-interchange effects are explicitly evaluated and Pauli blocking is incorporated. Numerical results in the 1 S 0 p− p, n− p, and n− n channels are described and discussed. In particular, it is found that the simple one-boson exchange model (at the quark level) provides a reasonable description of the 1 S 0 phase shifts for 10 MeV ≤ T CM ≤ 150 MeV with T CM the center-of-mass [CM] kinetic energy. It is also found that, with the nonzero up-down quark mass difference as determined by an overall fit to the observed baryon mass splittings, isospin-symmetry violating effects arising from quark interchange are of marginal numerical importance for a nucleon radius R of 0.8 fm and become fairly sizable for R = 1.0 fm. It turns out that, for R = 0.8 fm, the predicted a nn with a nn the low-energy scattering lengths in the 1 S 0 n- n channel is in good agreement with a recent experimental result of Gabioud et al. and the observed large charge dependent effect as given by | a np | − | a nn | can also be understood.

Isospin-symmetry violation in theπ−Ninteraction and the U(1) problem

We examine the effect of the dipole introduced by Kogut and Susskind in explaining the U(1) problem on the isospin-symmetry violation of the ..pi../sup 0/--nucleon coupling. The effect is quite essential for the violation. We discuss also the eta ..-->.. 3..pi.. problem. It is shown that the effect of the dipole in this case is not large enough to explain the experimental data, contrary to our prior expectation. (AIP)

Apparent violation of isospin symmetry in the reaction 2H(α, t) 3He near threshold

The differential cross section of the 2H(α, t) 3He reaction has been measured between θ c.m. = 17° and 152° at an incident α-energy of 48.25 MeV. This represents a test of the Barshay-Temmer theorem, which requires symmetry of the angular distributions about 90°. Earlier experiments have found no asymmetry at lower incident α-energies and deviations of up to 10% at higher incident energies. We find deviations from symmetry as large as 20% at some angles.

Corrections to the ft-values of 0 + → 0 + superallowed β-decays

The second-forbidden corrections to superallowed Fermi β-decays are determined by expectation values rather than matrix elements between states of different structure. They partly cancel the corrections arising from violation of isospin symmetry. Within the limits of experimental uncertainty, ( t) corr has the same value for all the decays except that of 26Al.

The linked-cluster expansion for the transition amplitude for deuteron stripping reaction: W. F. Junkin and F. Villars. Laboratory for Nuclear Science, M.I.T., Cambridge, Massachusetts

At the Technische Hochschule in Darmstadt the group of Richter and coworkers found in 1983/84 in deformed rare earth nuclei low-lying isovector 1+ states. Such states have been predicted in the generalized Bohr-Mottelson model and in the interacting boson model no. 2 (IBA2). In the generalized Bohr-Mottelson model one allows for proton and neutron quadrupole deformations separately. If one includes only static proton and neutron deformations the generalized Bohr-Mottelson model reduces to the two rotor model. It describes the excitation energy of these states in good agreement with the data but overestimates the magnetic dipole transition probabilities by a factor 5. In the interacting boson model (IBA2) where only the outermost nucleons participate in the excitation the magnetic dipole transition probability is only overestimated by a factor 2. The too large collectivity in both models results from the fact that they concentrate the whole strength of the scissors vibrations into one state. A microscopic description is needed to describe the spreading of the scissors strength over several states. For a microscopic determination of these scissors states one uses the Quasi-particle Random Phase Approximation (QRPA). But this approach has a serious difficulty. Since one rotates for the calculation the nucleus into the intrinsic system the state corresponding to the rotation of the whole nucleus is a spurious state. The usual procedure to remove this spuriosity is to use the Thouless theorem which says that a spurious state created by an operator which commutes with the total hamiltonian (here the total angular momentum, corresponding to a rotation of the whole system) produces the spurious state if applied to the ground state. It says further the energy of this spurious state lies at zero excitation energy (it is degenerate with the ground state) and is orthogonal to all physical states. Thus the usual approach is to vary the quadrupole-quadrupole force strength so that a state lies at zero excitation energy and to identify that with the spuríous state. This procedure assumes that a total angular momentum commutes with a total hamiltonian. But this is not the case since the total hamiltonian contains a deformed Saxon-Woods potential. Thus one has to take care explicitly that the spurious state is removed. This we do in our approach by introducing Lagrange multipliers for each excited states and requesting that these states are orthogonal to the spurious state which is explicitly constructed by applying the total angular momentum operator to the ground state. To reduce the number of free parameters in the hamiltonian we take the Saxon-Woods potential for the deformed nuclei from the literature (with minor adjustments) and determine the proton-proton, neutron-neutron and the proton-neutron quadrupole force constant by requesting that the hamiltonian commutes with the total angular momentum in the (QRPA) ground state. This yields equations fixing all three coupling constants for the quadrupole-quadrupole force allowing even for isospin symmetry violation. The spin-spin force is taken from the Reid soft core potential. A possible spin-quadrupole force has been taken from the work of Soloviev but it turns out that this is not important. The calculation shows that the strength of the scissors vibrations are spread over many states. The main 1+ state at around 3 MeV has an overlap of the order of 14 % of the scissors state. 50% of that state are spread over the physical states up to an excitation energy of 6 MeV. The rest is distributed over higher lying states. The expectation value of the many-body hamiltonian in the scissors vibrational state shows roughly an excitation energy of 7 MeV above the ground state. The results also support the experimental findings that these states are mainly orbital excitations. States are not very collective. Normally only a proton and neutron particle-hole pair are with a large amplitude participating in forming these states. But those protons and neutrons which are excited perform scissors type vibrations.