Cohen-Kurath Wave Functions Research Articles

Quadrupole moment of the proton rich β-emitting nucleus 12N

Abstract The quadrupole moment of the β -emitter 12 N( I π =1 + , T 1/2 =11 ms) has been measured to be Q ( 12 N)=+9.8±0.9 mb by use of a modified β -NMR method. The present result is 3 times smaller than the value which was deduced from the photoproduction cross-section of pions on 12 C, while it is twice the shell-model prediction based on the Cohen-Kurath wave functions in the Woods-Saxon potential.

Large basis shell model analysis of 14N( gamma, pi +)14Cg.s. reaction.

The {sup 14}N({gamma},{pi}{sup +}){sup 14}C{sub g.s.} cross section at {ital E}{sub {gamma}}=173 MeV has been calculated using shell model wave functions determined in complete (0+2){h_bar}{omega} and (0+2+4){h_bar}{omega} shell model spaces. Using the (0+2+4){h_bar}{omega} shell model wave functions yields an improvement over older results obtained with Cohen-Kurath wave functions by a factor of 2, but still overpredicts the back-angle data. When correlated with analyses of inelastic electron and proton scattering from {sup 14}N, the present results indicate the need for an improved shell model calculation and possibly an improved description of the elementary pion production process in nuclei. {copyright} {ital 1996 The American Physical Society.}

A test for the Cohen-Kurath wave functions in (p, d)-reactions

The experimental data for (p, d)-reactions on the 1p-shell nuclei atEp −33 MeV are used to test the Cohen and Kurath wave functions and the intermediate coupling. The experimental excitation energies and their order for all law transitions of the 1p-shell nuclei are compared with the theoretical predictions of Cohen and Kurath. The integrated cross-sections σ(0–90‡) for these transitions are also compared with their theoretical predictions for one-neutron pick-up. The good agreement between these data indicates a success for the Cohen-Kurath wave functions and for their model of calculations.

Electromagnetic and weak constraints on the ground state wave functions of 13C and 13N

The nuclear wave functions of the A = 13 ground state isodoublet system are analysed by constraining them (within the 1p shell) to fit the best available electromagnetic and weak data. It is found that the wave functions are dominated by only two basis states of the possible five, with a greater degree of configuration mixing than that predicted by Cohen-Kurath. The use of these phenomenological wave functions to study 13C( γ, π −) 13N g.s. at low energies gives better agreement with data than using Cohen-Kurath wave functions but a factor of three enhancement still persists.

Pion photoproduction on 14N at 173 MeV photon energy

The reaction 14 N(γ, π +) 14 C g.s. has been measured at a photon energy of 173 MeV and various pion angles at the Mainz microtron via the (e, π) reaction. Single differential cross sections were extracted using the virtual-photon theory. We have compared our data with momentum-space DWIA calculations using Blomqvist-Laget operators and pion wave functions distorted by an optical potential of Stricker, McManus and Carr. In a comparison with the Cohen-Kurath shell model and phenomenological A= 14 wave functions we show that the Cohen-Kurath wave functions overestimate the data up to a factor of 4, while a wave function recently proposed by Huffman et al. gives very good agreement. The analysis rise to new speculations on the forbidden 14C beta decay.

Recoil polarization of [formula omitted] in neutrino neutral current interactions

We report the results of the average recoil polarization of 12 C ∗ (1 +; T=1; 15.1 MeV) excited in neutrino neutral current interactions in 12C. Cohen-Kurath wave functions are used to obtain the numerical values of the recoil polarization. It is found to be insensitive to the choice of the nuclear wave functions.

Investigation of electromagnetic form factors for light nuclei

Abstract Transverse form factors for electron scattering from 6 Li and 9 Be have been calculated with the Cohen-Kurath wave functions, by using the phenomenological magnetic form factors of bound nucleons. The effects of meson exchange currents on the EM form factors were also investigated.

The average polarization of 12B in the muon capture reaction

We studied the new experimental data on the average polarization of the recoil 12B in the muon capture on 12C measured by the Tokyo group. We obtained gp/ g A = 9.6 −2.7 +2.4, with our formalism of muon capture including exchange current effects, contributions from excited states of the daughter nucleus and nuclear finite size, and using the Op-shell wave function of Hauge and Maripuu and the Sussex interaction for the core polarization. The same value of gp/ g A is obtained with the Cohen-Kurath wave function.

Investigation of nucleon recoil in the photopion production

Effects of the nucleon motion have been investigated in the photoproduction of positive pions from13C, by using the CGLN amplitude and the Cohen-Kurath wave function.

Electron scattering from 13C

Transverse form factors for elastic and inelastic electron scattering from 13C have been calculated with Cohen-Kurath wave functions, by introducing an alteration into the nucleon form factor in nuclei. The results show good agreement with the data. We have concluded that the Cohen-Kurath wave function can reproduce the experimental results of photopion production and electron scattering from 13C in the momentum transfer, q ⪅ 2 fm −1.

Spin-flip probability inC12(p→, p→′)C*12at 397 MeV

Measurements of the spin-flip probability for states in $^{12}\mathrm{C}$ excited by 397 MeV protons are presented. These data are compared with distorted-wave Born approximation and plane-wave calculations using Cohen-Kurath wave functions as well as simpler transition densities. The results are discussed in terms of the implications for nuclear structure as well as the nucleon-nucleon effective interaction.NUCLEAR REACTIONS $^{12}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p}, {\stackrel{\ensuremath{\rightarrow}}{p}}^{\ensuremath{'}})$,, spin-flip probability; DWBA, nucleon-nucleon effective interaction.

Inelastic electron scattering from 10B

Electron scattering form factors were measured for six transitions in 10B in the momentum transfer range 0.61 to 1.81 fm −1. Ground state radiative widths were extracted by means of the generalized Helm model for the levels at 1.74 MeV (M3), 5.17 MeV (M1 + M3), 6.03 MeV (C2 + C4), 7.48 MeV (M1), 8.07 MeV (C2) and 8.9 MeV (M1 + M3 or M2). The transverse form factors for the 1.74 and 5.17 MeV levels agree well with predictions based on Cohen-Kurath wave functions. The longitudinal form factor for the 6.03 MeV state shows effects due to the deformation of 10B and is in good agreement with the deformed Hartree-Fock shell model prediction of Bouten and Bouten. Estimates are presented for the ratios of radiative pion capture rates leading to analogue states in 10Be.

Effects of core polarization and exchange currents on the form factors of magnetic transitions in 12C

We have studied the form factor of the magnetic dipole excitation to the 15.1 MeV, 1 + state in 12C, taking into account the effects of core polarization and exchange currents. It is shown by using the Cohen-Kurath wave functions that the core polarization contributions, from both central and tensor interactions, are important and enhance significantly the second maximum of the magnetic form factor, while the effects of the exchange currents are shown to be small.

The decay of theT=1 isospin triplet inA=12 systems

A complete theoretical study is carried out of the beta decays of the12B and12N ground states to the12C ground state. We calculated the form factor coefficientsFKLsN(ke, m, n, ρ) using the Cohen-Kurath wave functions. In particular, we obtained reasonable values for the form factor coefficientsAF1010 andvF1110 whose ratio contains the influence of the weak magnetism coupling constant. It is shown that in this way the measurements of the shape factors presented by Wu and coworkers can be explained. In addition, it is demonstrated that the contribution of the term proportional to (WR)2 cannot be completely neglected because of the large end point energyW0. From our value ofvF1110 we have derived the radiative widthΓγ(M1) of the isobaric analogγ transition from the excited state12C* to the ground state of12C. The result is in good agreement with the experimental data.

Configuration mixing and total muon capture rates

We modify the Primakoff closure approximation to get independence on the mean neutrino energy and energy weighted sum rules are used for the corrective terms. A near model - independent discussion is then possible, and the total rates are shown to be a very sensitive tool to investigate configuration mixing of the target. Wild discrepancies with experiment would arise if the limit of pure jj or LS couplings are used for 12C, whereas the Cohen-Kurath wave function gives a very good result.

Strength of theC10→B10(2155 keV)βBranch

A search for the $\ensuremath{\beta}$ decay of $^{10}\mathrm{C}$ to the 2155-keV level in $^{10}\mathrm{B}$ has been made in order to test the independent-particle-model predictions using mixed wave functions for the lowest two ${J}^{\ensuremath{\pi}}={1}^{+}$ levels in $^{10}\mathrm{B}$. In contrast to a previously reported value of 6.4\ifmmode\pm\else\textpm\fi{}2.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ per $^{10}\mathrm{C}$ decay for this branch, our results limit the strength to \ensuremath{\le}8\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ with 90% confidence, and to \ensuremath{\le}4\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ with 50% confidence. Comparison of this result with the strength of the $M1$ transition between the 2155- and 1740-keV levels in $^{10}\mathrm{B}$ shows that the ratio of orbital to spin contributions to the $M1$ matrix element exceeds 3.5. When the Cohen-Kurath wave functions for the first two ${J}^{\ensuremath{\pi}}={1}^{+}$ levels in $^{10}\mathrm{B}$ are mixed in order to fit the strength of the 2155\ensuremath{\rightarrow} 1740-keV $M1$ transition, the predicted $\ensuremath{\beta}$ branch to the 2155-keV level is at least 3 times as strong as the present experimental upper limit.

Radiative pion capture in 12C

Transition rates for the reaction π − (at rest) + 12 C (ground) → γ + 12 B (even parity) have been computed in the impulse approximation with Cohen-Kurath wave functions for the nuclear states involved. The two available experiments disagree by a factor of 5 in the ground-state transition rate. The calculated rates agree closely with the results of Bistirlich et al.

Beta decay of 10C

The decay of 10C is studied using a Ge(Li) detector with a view to determining the branching ratio to the if J π = 1 + 2.15 MeV state of 10B. This branch isfound to be of (6.4 ± 2.0) × 10 −3% corresponding to log ft = 4.8 ± 0.15. Comparison with the speed of the analogue M1 transition between the 2.15 and 1.74 MeV states of 10B shows that the contributions to the Ml matrix element from the spin and orbital operators are approximately equal and are of the same sign. This disagrees strongly with the predictions of the Cohen-Kurath wave functions; the possibility is explored, following Warburton et al. that better wave functions for the first two J π = 1 + states of 10B (the one studied here and that at 0.72 MeV) may be given by appropriate linear combinations of the Cohen-Kurath wave functions. Good agreement with the beta decay and its M1 analogue is indeed found for a mixture close to that found by Warburton et al. to satisfy certain other transitions involving the J π = 1 + states.