Neutron Asymmetry Research Articles

Chiral configuration mixing and deep-inelastic scattering of polarized leptons by polarized nucleons

In the quark model, a large SU(3) \ensuremath{\bigotimes} SU(3) configuration mixing appears at ${P}_{z}=\ensuremath{\infty}$ as a relativistic effect due to the high internal velocities for quarks inside hadrons. This mixing describes the relative alignment between the nucleon helicity and the helicities of the quarks. Since the quark-parton model is understood in a frame where the nucleon has a large momentum, we propose to take into account this large mixing in the calculation of the spin-dependent effects in deep-inelastic scattering of a polarized lepton (electron or muon) by a polarized nucleon. The scaling of the spatial wave function is ensured by the Lorentz contraction. Unlike a previous quark-parton model calculation by Gourdin, we take into account the configuration mixing in the estimation of the singlet contribution to the asymmetries. We express our results in terms of the SU(3) \ensuremath{\bigotimes} SU(3) mixing parameters. Assuming that the nucleon is a superposition of irreducible SU(3) \ensuremath{\bigotimes} SU(3) representations allowed by the quark model, we can express the singlet contribution in terms of the $F$, $D$ couplings of the low-lying octet axial-vector matrix elements. The neutron asymmetry appears to be proportional to the deviation of $\frac{F}{D}$ from the SU(6) value $\frac{2}{3}$. As expected, the Bjorken sum rule for the difference between the proton and neutron asymmetries is satisfied. In our specific model, where the spin part of the wave function at rest is expressed in terms of free Dirac spinors, we have $\frac{F}{D}=\frac{2}{3}$, so that we predict a large positive proton asymmetry and a null asymmetry for the neutron, ${A}^{p}=\frac{1}{3}|\frac{{G}_{A}}{{G}_{V}}|$, ${A}^{n}=0$.

Neutron emission in muon capture by 40Ca

The neutron spectrum and asymmetry have been calculated for 40Ca with different wave functions for the bound proton and the emitted neutron. The asymmetry is shown to be very sensitive to the behaviour of the wave functions near the nuclear surface while the spectrum is mostly sensitive to the strength of the real part of the neutron optical potential.

Neutron Asymmetries and Energy Spectra from Muon Capture in Si, S, and Ca

Neutron Asymmetries and Energy Spectra from Muon Capture in Si, S, and Ca

Spectrum and asymmetry of neutrons emitted after polarized muon capture by 16O and 40Ca

The emitted neutron intensity and asymmetry are calculated taking account of first-order momentum-dependent terms with pure shell-model and multi-hole-multi-particle configuration mixing nuclear wave functions. The final-state interaction between the residual nucleus and the emitted neutron is taken into account by means of an optical potential with surface and volume absorption. The calculated intensity and asymmetry are for 40Ca, in agreement with measurements; because of the final-state interaction, large asymmetries are obtained for 25–30 MeV neutron energies. Second class currents, if they exist, would also affect the asymmetry and the intensity.

Neutron spectrum and asymmetry of the angular distribution in muon capture on 4He Nucleus

The neutron channel in muon capture by 4He is considered. The dependence of the energy spectrum and asymmetry of the angular distribution in the reaction μ -+ 4He → 3H+n+ ν on relativistic terms of the muon-nucleon Hamiltonian and final state interaction is investigated. It is shown that the above mentioned factors are decisive in the description of the high energy part of the spectrum and asymmetry.

The neutron channel in muon capture on 4He

The neutron channel in muon capture on 4He is calculated. It is shown that asymmetry of the neutron angular distribution when polarized muons are captured is essentially due to the relativistic terms in the muon-nucleon Hamiltonian. Those terms also contribute significantly to the capture rate. The final-state interaction changes the neutron energy spectrum and asymmetry of angular distribution.

Streuung polarisierter neutronen der energie 2.7 bis 2.9 MeV an kohlenstoff

Abstract The asymmetry of neutrons (2.7–2.9 MeV) emitted from the reaction 2H(d, n)3He at 50°lab and scattered by carbon at 50°lab was measured. The result of the present experiment indicates that the analysing power of 12C in this energy region is influenced by the 7 2 + and 5 2 − states at 7.49 and 7.55 MeV of the 13C nucleus. The anomaly in the asymmetry of neutrons near Ed = 100 keV reported earlier is caused by the property of the analyser and is not a property of the source reaction.

Relativistic corrections to the asymmetry of high-energy neutrons emitted in polarized muon capture by nuclei

We have studied the effects of relativistic corrections on neutron asymmetry in polarized μ-capture by light nuclei ( 12C 28Si 32S 40Ca). By describing the nucleus by the Fermi-gas model, for which the relativistic problem can be treated exactly, we have shown that relativistic corrections up to the (inverse nucleon mass) −2 (and only) contribute appreciably. Next, using the harmonic-oscillator shell model for the nucleus, we have shown that the M −2 corrections do increase significantly the asymmetry that gets positive, increasing with energy and in qualitative agreement with recent experiments. The asymmetry turns out to be rather insensitive to both spin-orbit coupling and final-state interaction. On the contrary, the neutron spectrum depends strongly on the final-state interaction; when included (even in a very crude way), the calculated spectrum fits closely the experiments.

The μ-capture mechanism in light complex nuclei

The μ-capture process resulting in the emission of a single neutron is treated as a double two-body process in the giant-dipole-resonance model: μ−+(A, Z)=(A, Z−1)+ν, (A, Z−1)=(A−1,Z−1)+n. The kinematics of the process is studied taking into account the recoil of the (A, Z−1) nucleus. It is found that there exist situations where there is an instantaneous zero-degree angular separation between the neutron and the (A−1,Z−1) nucleus at the time of decay of the (A, Z−1) nucleus. It is conjectured that this might destroy some delicate information about the μ-capture mechanism like asymmetry and polarization, which otherwise might have been carried by the neutrons. In addition to the widths of the fine structure of the neutron asymmetry spectrum and the neutron asymmetry, the Doppler broadening of the (A−1,Z−1) levels, in particular the 6.322 MeV level of15N, is discussed. The predictions of the direct model are systematically compared with those of the giant dipole resonance and with the experimental results.

Neutron Asymmetry in Polarized Nuclear Muon Capture

A general theoretical framework for neutron emissions due to nuclear muon capture is given in terms of relativistic and nonrelativistic kinematics, which can be applied to the cases where the energies of the final nuclear states belong to the continuous spectrum as well as the discrete one. The consequences of chiral invariance and conserved-vector-current (CVC) theory are taken into account in the formulation. The formulas obtained are compared with conventional ones. In particular, the pioneering work due to Primakoff is re-examined from this general framework. The difference between the CVC theory with the impulse approximation and the nuclear CVC theory is discussed. In the limit of small momentum of the emitted neutrino, the present formalism is related to the conventional $\ensuremath{\beta}$-decay formalism. The effect of nuclear collective motions on neutron asymmetry is discussed without assuming any detailed nuclear models.

Spectrum and asymmetry of high energy neutrons emitted in the absorption of polarized muons

The rate of production and the asymmetry of neutrons emitted directly with the capture of polarized muons have been expressed in terms of single-nucleon integrals. This expression takes account of momentum-dependent terms to first order in the muon capture Hamiltonian and is suitable for calculations involving general neutron wave functions. When plane waves in nuclear matter are assumed for the neutron wave function, the calculated intensities and asymmetries are in agreement with recent experiments on silicon, sulfur and calcium. The momentum-dependent terms strongly affect the asymmetry but not the intensity, whereas the nuclear model seems to affect the intensity but not the asymmetry.

Spectrum and Asymmetry of Direct Neutrons from Muon Capture in Calcium

The energy spectrum and asymmetry of neutrons emitted directly on the capture of polarized muons by $^{40}\mathrm{Ca}$ have been calculated in a simple nuclear shell model, taking account of terms proportional to the nucleon momentum. The energy spectrum is within the error brackets of recent experiments with the nucleon-momentum terms making a small contribution. The asymmetry coefficient is strongly affected by the inclusion of the momentum-dependent terms and is found to change sign and increase in magnitude with increasing energy, in qualitative agreement with recent experiments.

Asymmetry of Neutrons from Muon Caputre in Silicon, Sulfur, and Calcium

We have measured the asymmetry in the angular distribution of neutrons emitted following the capture of negative muons in silicon, sulfur, and calcium. The asymmetries, normalized to 100% muon polarization, varied from near zero for low neutron energies to +0.32\ifmmode\pm\else\textpm\fi{}0.05, +0.30\ifmmode\pm\else\textpm\fi{}0.08, and +0.20\ifmmode\pm\else\textpm\fi{}0.08 for energies greater than 15.6 MeV for silicon, sulfur, and calcium, respectively, in disagreement with the results of most other recent experiments.

Relativistic Effects in Muon Capture by Complex Nuclei

Relativistic contributions to muon capture by complex nuclei are considered. For the total rate calculated for a Fermi gas in the closure approximation these contributions increase the rate by about 15% for elements between Ca and Pb. The neutron asymmetry (with respect to the muon spin direction) near the top of the neutron spectrum is decreased in magnitude from a value of about -0.4 to about -0.1 by these contributions. A calculation using the Fermi-gas model for $N=Z$ indicates that the neutron asymmetry has a magnitude less than 0.15 for all neutron energies, a result which is in disagreement with experiment.

Systematics of Fission Asymmetry with Respect to Nuclear Charge and Neutron Contents

Swiatecki's asymmetry formula was applied to charge and neutron asymmetry in fission. The constants involved were determined from the average proton and neutron contents of fragments from the thermal neutron fission of ${\mathrm{U}}^{235}$ and ${\mathrm{Pu}}^{239}$. The average proton and neutron contents were then deduced from the asymmetry equations for the fragments of the compound nuclei ${\mathrm{Th}}^{233}$, ${\mathrm{U}}^{234}$, ${\mathrm{U}}^{238}$, ${\mathrm{U}}^{239}$, ${\mathrm{Cm}}^{242}$, and ${\mathrm{Cf}}^{252}$. The relationship between the average charge and mass of the light and heavy fragments leads to two almost parallel straight lines, which almost coincide with the ${Z}_{p}$ versus $A$ lines for ${\mathrm{U}}^{235}(n, F)$, implying that the relationship between the most probable values of fragment charge and mass is independent of the fissioning nucleus; in other words, this relationship is almost universal. The average charge and mass of the light fragments vary within much wider limits in comparison to the heavy-fragment charge and mass which vary in a much narrower range, signifying that the fission process is more selective with respect to the heavy-fragment composition. A neutron added to the original nucleus goes preferentially (90%) into the heavy fragment and transfers some charge (15% of one charge unit) from the light to the heavy fragment; whereas, a proton added to the original nucleus goes into the light fragment and transfers from the heavy to the light fragment a little more charge (10% of one charge unit) as well as a substantial amount (1.25 units) of neutrons. These effects are perfectly additive with respect to both the number of neutrons and/or protons added (or subtracted), and permit one to predict the average charge and neutron contents of the two fragments for any fissile nuclide, if these quantities are known for any other reference nuclide.

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co59(p,n) reaction forEp ∼ 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni59 nucleus were also determined.

Neutron Asymmetry From Mu Capture in Magnesium

It has previously been pointed out that a measurement of the angular distribution of neutrons emitted after the capture of polarized mu /sup -/ mesons by complex nuclei may give information on the nature of the coupling constants in the process mu /sup -/ + p yields n + v. A spatial asymmetry with respect to the mu spin direction would also be evidence for parity nonconservation in the reaction. The neutron asymmetry was measured by processing the negative muons stopped in a magnesium target through 90 deg by a constant magnetic field which was reversed every 30 min. (W.D.M.)

Hyperfine Splitting Effects in the Capture of Polarizedμ−Mesons

We investigate the effect of the hyperfine splitting of $\ensuremath{\mu}$-mesic atom ground states on the neutron asymmetry from muon capture in hydrogen, in deuterium, and in complex nuclei with spin which are treated by a one-particle model. It is shown that this can provide more information on the capture interaction than the neutron asymmetry from spinless nuclei. Muon polarizations and gyromagnetic ratios in the hyperfine states are also discussed.

P−nAsymmetries at 143 Mev

The asymmetry of neutrons produced by bombardment of C, Al, Cu, and Pb by 143-Mev polarized protons, at angles 20 to 70 , was measured. The asymmetry is almost independent of target element but is incongistent with that from a free p-n collision. The mechanism for the process is discussed. (auth)

Capture of μ-mesons in deuterium

The neutron spectrum, the neutron asymmetry with respect to muon spin direction, and the neutron polarization are calculated as functions of neutron energy for μ-meson capture in deuterium. The total capture rate and the dependence of the rate on the hyperfine state of the mesic atom are given and compared to approximate expressions. The dependence of the observations on the amount of Fermi or Gamow-Teller coupling and on the presence of an effective pseudoscalar coupling is displayed.