12C Resonance Research Articles

A new measurement of the 429 keV 15N(p, αλ) 12C resonance. Applications of the very narrow width found to 15N and 1H depth location : II. Applications

The unexpectedly narrow width Γ p = 120 eV or Γ N 15 = 1.8 keV of this resonance opens quite new possibilities for its use in 15N or 1H depth location and for hydrogen adsorption studies using 15N beams. Resonance depth profiling of 15N is possible with much better near-surface depth resolution than thought until recently. In 1H resonance depth profiling the indeep background originating from the surface contamination peak is also much smaller than previously assumed. These features are illustrated by 15N self-diffusion experiments in NbN films and by 15N adsorption experiments on copper single crystals in ultrahigh vacuum. The strong effect of Doppler broadening on the actual ultimate near-surface depth resolution of hydrogen depth profiling with 15N beams is discussed as well as the use of this resonance for the direct measurement, based on the Doppler effect, of the vibration speed distribution of hydrogen atoms adsorbed on clean surfaces.

Hydrogen determination by means of the1H(19F, αγ)16 O and1H(15N, αγ)12C resonance reactions

Hydrogen surface contamination and depth profiles can be measured by the resonant nuclear reactions1H(19F, αγ)16O and1H(15N, αγ)12C. The method was applied to study hydrogen-implanted silicon, amorphous silicon layers and silicon oxide films produced by anodic oxidation.

Electromagnetic properties of the 12C+ 12C and 16O+ 16O quasimolecules in the generator coordinate method

Energies, widths, quadrupole moments and rms radii of 12C+ 12C and 16O+ 16O quasimolecular states, as well as E2 transitions between them, are calculated with antisymmetric wave functions. A good agreement with available experimental data is obtained. The radiative capture reactions 12C( 12C, γ 0–2) 24Mg are also studied. Although a single-channel model does not allow a quantitative comparison with the experimental cross sections, our results suggest a molecular intepretation for several observed 12C+ 12C resonances.

Alignment and resonances in 12C+ 12C inelastic scattering

Using the out-of-plane γ-ray particle coincidence method we have measured the spin alignment P zz of excited 12C(2 +) nuclei from 12C+ 12C inelastic scattering in the energy range 16 MeV ⩽ E cm ⩽ 33 MeV. P zz varies strongly as a function of energy and angle. The correlation of resonant structures in the cross section with maxima of the alignment is particularly clear in mutual inelastic scattering and in θ cm = 90° single inelastic scattering.

A new measurement of the 429 keV 15N(p,αγ) 12C resonance. Applications of the very narrow width fouNd to 15N and 1H depth location : I. Resonance width measurement

High precision nuclear reaction resonance width measurement techniques were applied to the 429 keV resonance in 15 N(p, αγ) 12 C yielding a result which may be stated at present as: Γ=120±30) eV. Work is in progress to improve precision further. The measurements were performed using a 2 MV Van de Graaff equipped with both slit and capacitive pick-off plate feedback stabilization and fitted with an automatic energy scanning system. Energy resolutions as low as ∼40 eV fwhm were reached. Thick, nearly stoichiometric niobium nitride targets highly enriched in 15N were prepared on silicon backings by reactive sputtering in a 15N 2 and argon mixture. The measurements were carried out using a ∼1μA beam, at room temperature, in 10 −6 Torr liquid nitrogen trapped vacuum. The characterization of the targets as well as the fitting procedures used to extract Γ from the thick target yield curves (including Doppler effects) are presented.

Defect trapping of hydrogen in iron studied by the 1H( 15N, αγ) 12C reaction

Since the solubility of hydrogen is defect-free iron is very low (<0.1 atom ppm) at ambient conditions one needs a rather sensitive method for profiling the local enrichment of hydrogen in iron and steel. Consequently, using the principles of low level techniques the detection limit of the 1H( 15N, αγ) 12C resonance reaction was lowered to ⩾10 atom ppm. It was still not possible to detect hydrogen at room temperature in annealed pure iron. But, in cold-worked iron and martensitic steel which were electrolytically charged with high hydrogen activity, contents of between 10 2 and 10 4 atoms ppm were measured in the first 0.5 μm below the surface. Pure iron modified in the subsurface region by ion implantation could retain up to 10 5 atom ppm in the bombarded area. After He implantation the hydrogen was probably trapped at internal surfaces of the He bubbles, after Ce implantation chemically at the site of the impurity atoms. Subsequent to bombardment with Au which has no affinity to hydrogen the maximum hydrogen concentration was found between the surface and the maximum of the gold distribution.

A semimicroscopic model of nuclear vibrations with separable forces and the giant dipole resonance of 12C

In the generalized ph basis generated for the realistic nuclear ground state, the nuclear hamiltonian is approximated by an expression containing the separable effective forces and terms which can be estimated from the spectroscopic data. The model hamiltonian obtained is used to describe normal nuclear vibrations. The application of this approach in the shell-model theory of nuclear reactions is discussed. The S-matrix for nucleon-nucleus scattering is calculated explicitly. The 12C photodisintegration calculation is made as a test example.

The theory of electron-scattering coincidence experiments

A general expression for the electron-scattering coincidence cross section for the reaction A 1( e, e′ X) A 2 with a nuclear target is derived in the one-photon exchange approximation. The result is exact to lowest order in α, the fine-structure constant. It is expressed in terms of four kinematic factors involving the electron scattering variables in the laboratory frame, and four combinations of transition matrix elements of the nuclear current operator expressed in the center-of-momentum (COM) frame. The nuclear matrix elements are decomposed into transition amplitudes of definite angular momentum using a helicity analysis. General expressions for the angular distribution of particle X in the COM frame are then derived. The analysis is independent of the detailed structure of the nucleus and particle X and depends only on general symmetry considerations and the existence of a local electromagnetic current operator for the hadronic target. A unitary transformation from the helicity basis for the final particle X and A 2 to an LS coupling basis is relevant if X is massive and a finite number of total angular momenta J are involved in the reaction. Tables of angular correlation coefficients are given for the case where the initial nucleus A 1 has J 1 π = 0 +. They constitute one of the most useful results of this paper. Connection is made in the “static limit,” and with the assumption that the reaction proceeds through a finite number of Breit-Wigner resonances with a corresponding factorization of the electroproduction transition matrix elements, to the familiar electromagnetic transition multipole moments involving excitation of a nuclear state J π . The relation to previous work by de Forest and by Drechsel and Überall is discussed. Analytic expressions for the coincidence cross sections are given for spin-zero systems and some very simple, basic models of nuclear “giant resonance” excitations. It is hoped that they will be useful in obtaining insight into the coincidence cross section and in planning future experiments. Finally, a reanalysis of the recent Stanford data of Calarco et al. on 12 C(e, e′ p 0) 11 B( 3 2 − ) in the vicinity of the giant dipole resonance in 12C is carried out using a very simple nuclear model but retaining all the terms in the coincidence cross section, some of which were previously neglected.

Coexistence of molecular and shape resonances in 12C + 12C

The structure observed in 12C + 12C excitation functions is interpreted in terms of the double resonance and doorway mechanisms, which generate bands of shape and molecular resonances, respectively.

Study of isovector resonances with pion charge exchange

Studies with the pion charge exchange reactions ( π ±, π 0) at 164 MeV using the π 0 spectrometer are yielding new results on the existence and systematic features of isovector resonances in nuclei. These experiments possess an unusually high signal/background ratio for isovector resonances of low-multipolarity. Results obtained to date are: (1) Observation and angular distribution measurement of the giant dipole resonances in nuclei 12C, 40Ca, 90Zr and 120Sn; (2) Observation and angular distribution measurements in the (π −, π 0) reaction on 90Zr and 120Sn of large signals possessing the expected angular distribution shapes and magnitudes for the isovector monopole resonance. Excitation energies are near the hydrodynamical model values 170 A − 1 3 MeV . Differential cross sections are approximately 0.7 J 2(qR) mb/sr. An overview of this experimental program, with emphasis on new results, and how they correlate with existing knowledge on the isovector resonances, is given.

Resonances in 12C + 13C at Ec.m. = 9.4 and 10.3 MeV observed in the total fusion cross section

The 12C + 13C total fusion cross section has been measured from E c.m. = 8.8 to 10.9 MeV to search for evidence of two resonances previously reported at 9.4 and 10.3 MeV on the basis of elastic scattering data. Enhancements of about 6 % are observed in the total fusion cross section at E c.m. = 9.35 + 0.05 and 10.21±0.05 MeV. If the previously assigned resonance parameters are correct, the observed resonant contribution to the fusion cross section at 10.3 MeV is too large to be consistent with the non-resonant absorption of ∼ 80 % predicted from available optical-model parameters. It is concluded that these two resonances in 12C+ 13C are comparable to the strongest resonances observed in 12C + 12C and 12C + 16O. The apparent weakness of 12C+ 13C resonances in measured reaction cross sections is expected on the basis of simple angular momentum considerations.

The theory of electron-scattering coincidence experiments: W. E. Kleppinger and J. D. Walecka. Institute of Theoretical Physics, Department of Physics, Stanford University, Stanford, California

Abstract A general expression for the electron-scattering coincidence cross section for the reaction A1(e, e′ X) A2 with a nuclear target is derived in the one-photon exchange approximation. The result is exact to lowest order in α, the fine-structure constant. It is expressed in terms of four kinematic factors involving the electron scattering variables in the laboratory frame, and four combinations of transition matrix elements of the nuclear current operator expressed in the center-of-momentum (COM) frame. The nuclear matrix elements are decomposed into transition amplitudes of definite angular momentum using a helicity analysis. General expressions for the angular distribution of particle X in the COM frame are then derived. The analysis is independent of the detailed structure of the nucleus and particle X and depends only on general symmetry considerations and the existence of a local electromagnetic current operator for the hadronic target. A unitary transformation from the helicity basis for the final particle X and A2 to an LS coupling basis is relevant if X is massive and a finite number of total angular momenta J are involved in the reaction. Tables of angular correlation coefficients are given for the case where the initial nucleus A1 has J1π = 0+. They constitute one of the most useful results of this paper. Connection is made in the “static limit,” and with the assumption that the reaction proceeds through a finite number of Breit-Wigner resonances with a corresponding factorization of the electroproduction transition matrix elements, to the familiar electromagnetic transition multipole moments involving excitation of a nuclear state Jπ. The relation to previous work by de Forest and by Drechsel and Uberall is discussed. Analytic expressions for the coincidence cross sections are given for spin-zero systems and some very simple, basic models of nuclear “giant resonance” excitations. It is hoped that they will be useful in obtaining insight into the coincidence cross section and in planning future experiments. Finally, a reanalysis of the recent Stanford data of Calarco et al. on 12 C (e, e′ p 0 ) 11 B ( 3 2 − ) in the vicinity of the giant dipole resonance in 12C is carried out using a very simple nuclear model but retaining all the terms in the coincidence cross section, some of which were previously neglected.

A list-mode study of bremsstrahlung spectra near the 12C(p,p) resonance and the time delays

Bremsstrahlung spectra in coincidence with scattered protons have been measured at four incident proton energies near the 12C(p,p) 1734 keV resonance. All coincidence events taken with two NaI and four Si detectors were stored on magnetic tape and the real coincidence events were selected by the off-line analysis. By simultaneously taking the bremsstrahlung spectra in coincidence with protons scattered at the center-of-mass angles of 158.9° and 90°, reliable values of the phase difference and the time delay between the incident and scattered protons have been obtained.

Decay of giant resonances in12C nucleus

Decay properties of (J−T= 1) resonances are calculated on the basis of the wave functions of the shell model with intermediate coupling. The results are compared with experimental data on the photodisintegration and radiative capture of pions.

Low energy spectrum and giant multipole resonances of12C (I)

In a consistent shell model approach excitation energies and electromagnetic transitions are calculated for the low energy part of the12C spectrum up to the giant resonance region within a (1p1h+2p2h) configuration space. Comparison with available experimental data shows that almost the complete spectrum up to 40MeV can be described consistently. Thereby it is found that whereas the low lying collective states remain nearly unchanged by the inclusion of (2p2h) configurations, the spreading widths of all (2ℏω) giant resonances are influenced drastically. For serious discrepancies in a few levels (4p4h) configurations or mesonic and baryonic degrees of freedom might be responsible.

Spectroscopic amplitudes for complex cluster systems

By expanding the Bargmann-Segal integral transform of nomi and overlap kernels in appropriately SU(3) coupled Bargmann space functions, the calculation of norm and overlap matrix elements in a cluster model basis is reduced to purely algebraic techniques involving the algebra of SU(3) recoupling transformations. This technique has been further developed to make calculations possible for systems of two heavy fragments other than closed-shell nuclei. In one application of the method, analytic expressions are given for the norms of binary fragment systems in which a light fragment of mass number ƒ, ƒ ⩽ 4, is combined with a heavy fragment of mass number A-ƒ, with A-ƒ ⩽ 24 . The A-ƒ fragment nuclei with different p- and sd-shell structure illustrate somewhat different problems in the recoupling technique. In a second application, spectroscopic amplitudes are calculated for the most important open channels of the 12C+ 12C resonances. Eigenvalues and eigenvectors of the antisymmetrizer are evaluated in a “molecular basis” of the 12C + 12C system, in which each 12C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations of 0 +,2 + and 4 +. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: α+ 20Ne with 20Ne internal functions of (80) SU(3) symmetry, ( K = 0 + band, and (82) SU(3) symmetry, ( K = 2 − band); 16O+ 8Be; and 23Na+p or 23Mg+n fragments with 23Na or 23Mg excitations in K = 3 2 and 1 2 rotational bands of SU(3) symmetry (83).

Excitation of the isoscalarE2 resonance in12C by proton inelastic scattering

Proton inelastic excitation spectra of12C have been measured imposing a coincidence with alpha decay to8Beg.s. and8Be2.9MeV. In plane angular correlations have been obtained for the main structures observed in the spectra. Comparison with DWBA correlation functions permits a 2+ assignment for all the groups in the 20–30MeV excitation range. The percentage of theE2-EWSR exhausted in the same range is in agreement, within the uncertainties indicated, with that derived from the inelastic scattering of other particles.

Radiative proton capture above the giant-dipole resonance in12C

Radiative proton capture above the giant-dipole resonance in12C

Study of the11B(p, n)11C reaction below the giant dipole resonance in12C

The11B(p, n)11C reaction has been studied for proton energies in the range (3 ÷ 6) MeV. Relative cross-sections were measured with a 4π counter in 15 to 20 keV steps. Absolute cross-sections were measured by using the activation technique to an accuracy of ± 10% at six different energies covering the range mentioned above. The observed resonance structure in the excitation function is compared with the predictions of an extended coupled-channel calculation.

The centre-of-mass spuriosity in continuum shell-model calculations

A method proposed previously to eliminate the centre-of-mass (CM) spuriosity in continuum shell-model (SM) calculations of 4He is generalised to adapt to the cases of heavier nuclei. It is applied to study the (p,p) and (p,n) reactions involving the one-particle-one-hole excitation of the dipole resonances in 12C and 16O. The effect is non-negligible and the results show features not observed previously. The Pauli term is also studied and is found to be less important in 16O as compared with the lighter nucleus 12C.