Isospin violation in α-induced reactions

A study has been made of the reactions ¹²C(α, α')¹²C and ¹⁰B(α, d)¹²C which lead to the 12.71 MeV T = 0 and the 15.11 MeV T = 1 levels in ¹²C. Significant structure is observed in the yield curves of the reactions ¹²C(α, α') ¹²C for both the isospin allowed and forbidden reactions up to the maximum available α-energy of 27 MeV; this structure is attributed to compound nucleus formation. No significant structure is observed in the reaction ¹⁰B(α, d)¹²C.     

The role of the Coulomb interaction in isospin-violating direct nuclear reactions

We investigate possible sources of isospin mixing in direct nuclear reactions. We find that there are mainly two effects which enter coherently into the direct reaction amplitude : “induced isospin mixing” caused by the Coulomb interaction between the target and the projectile, and “wavefunction effects” of the target nuclear states. These arise mainly through the difference of corresponding neutron and proton single-particle wave functions. These differences are especially noticeable just in the surface region where direct reactions take place. As illustrative examples we perform model calculations for the pick-up reactions ¹³C(d, ³H)¹²C¹(1⁺, 15.11 MeV) and ¹³C(d, ³He)¹²B_g.s.(1⁺) and the inelastic scattering ¹²C(d, d′)¹²C¹ leading to the 1⁺ states at 12.71 MeV and 15.11 MeV. These model calculations are compared with the corresponding experimental data.     

Indication of Δ-hole configurations in 12C(15.11 MeV)

A strong energy dependent enhancement is seen in inelastic pion scattering from ¹²C to the 1⁺, T = 1 state at 15.11 MeV, but not to the 1⁺, T = 0 state at 12.71 MeV. This enhancement may be interpreted as evidence for the direct excitation of delta-hole (Δ-h) components in the wave function of the T = 1 state. The required Δ-h amplitude is estimated and found to be in agreement with calculations of Bohr and Mottelson.     

A test of a model t-matrix for direct reaction inelastic scattering

Differential cross sections and analyzing powers from the inelastic scattering of 65 MeV protons leading to the 1⁺T=0 (12.71 MeV) and 1⁺T = 1 (15.11 MeV) states in ¹²C have been analysed as tests of a model two-nucleon t-matrix.     

Excited states of 10B from the 6Li(α, γ) and 9Be(p, γ) reactions

Excitation functions for the (α, γ) and (p, γ) reactions leading to ¹⁰B have been measured at θ = 0° in the energy range from E_x = 6.7 to 7.6 MeV. Two resonances corresponding to levels at 6.88 and 7.44 MeV are observed. Branching ratios extracted from γ-ray spectra are the same in both reactions for the 6.88 MeV (1^?, T = 0 + 1) level, but different at 7.44 MeV. The T = 0 + 1 level at 7.44 MeV (Γ = 90±10keV) is assigned 2^? or 2⁺ from its strong branch to the 3⁺ ground state. We find no evidence for a second isospin mixed 1^? state.     

Isospin mixing in 12C

Gamma-ray decays of the 12.71 and 16.11 MeV states of ¹²C are investigated in a coincidence study of the ¹⁰B(τ, pγ) reaction, and using the 163 keV ¹¹B(p, γ) resonance. This information together with existing data on M1 transitions and stripping and pickup spectroscopic factors is used to determine the isospin mixing between the 12.71 and 15.11 MeV levels. A charge dependent mixing matrix element of 110 ± 30 keV is deduced.     

Electron scattering studies of magnetic isovector transitions in 12C at high momentum transfer

The inelastic electron scattering cross sections for the M1 transition to the 15.11 MeV (1⁺, T = 1) level and for the M2 transition to the 16.58 MeV (2^?, T = 1) level in ¹²C have been measured in the momentum transfer region q = 0.4–3.0 fm^?1, with emphasis on precise data at high momentum transfers. Additionally, a broad state near 15.4 MeV excitation has been observed and its excitation energy and natural width have been established as 15.44 ± 0.04 MeV and 1.5 ± 0.2 MeV, respectively. The Fourier-Bessel technique for determining the Mλ transition current density has been applied to the M1 and M2 transitions. Particular attention has been paid to the Coulomb corrections required to deduce the PWBA form factors. The M1 radiative width is Γ_γ0 = 38.5 ± 0.8 eV.     

Isospin mixing observed in the reaction 12C(6Li, α)14N

The reaction ¹²C(¹²Li, α)¹⁴N was studied to investigate the isospin mixing of high-lying levels in ¹⁸F. Excitation functions and angular distributions of the α-transitions to the ground, first and second excited states in ¹⁴N were measured for bombarding energies from 3.2 to 8.0 MeV. The isospin-forbidden cross section for the excitation of the lowest T = 1 state in ¹⁴N at 2.31 MeV was found to lie between 1–2 % of that of the allowed transitions. A partial wave analysis of the α₁ angular distribution data revealed a strong resonance with J^π = 2⁺ at E_x = 15.99 MeV. Arguments are presented which tentatively identify this resonance as being due to two close-lying 2⁺ levels with different isospin.     

A new determination of the partial widths of the 16.11 MeV state in 12C

The partial widths of the second T = 1 state of ¹²C, at 16.11 MeV excitation energy, have been determined by measuring the ¹¹B(p, γ) and ¹¹B(p, α) cross sections at the E_p = 163 keV resonance corresponding to this state. These measurements result in the new values of Γ_p = 21.7 ± 1.8 eV and Γ_γ = 21.6 ± 3.3 eV, for the partial widths of this state; approximately 3 times smaller and larger, respectively, than the present values in the literature. The new result for the proton width eliminates a serious discrepancy found in an earlier comparison of the partial widths of the T = 1 analogue states of the A = 12 system. Measurements were also made of the ¹¹B(d, n)¹²C¹ reaction to compare the proton widths of the 15.11 and 16.11 MeV T = 1 states; these measurements confirm the new, smaller proton width for the 16.11 MeV state. An attempt was also made to determine the γ-width of the 16.11 MeV state by measuring the γ-branching ratio in the ¹⁰B(³He, p)¹²C¹(γ)¹²C reaction.     

A study of the 12N 2.43 MeV level

We have measured the differential cross sections for the reactions ¹²C(τ, τ′)¹²C(17.77 MeV 0⁺T=1) and ¹²C(τ, t)¹²N(2.43 MeV) at E_τ=44 MeV. The similar shapes of the angular distributions and the relative magnitudes of the cross sections suggest that the ¹²N 2.43 MeV level is the 0⁺T=1 analog to the ^q12C 17.77 MeV level. We have also studied the reaction ¹⁴N(p,t) ¹²N(2.43 MeV) at E_p=52 MeV. The strength with which this level is excited in this reaction is consistent with reasonable two-step calculations assuming the 2.43 MeV level to have J^π=0⁺.     

Two-nucleon T = 0 transfer reactions in the 0p shell

The ¹⁶O(d, α)¹⁴N, ¹⁴N(d, α)¹²C and ¹²C(d, α)¹⁰B reactions at E_d = 40MeV and the ¹²C(α d)1¹⁴N at E_α = 55 MeV were investigated. A total of seventeen transitions are analysed in terms of one-step, zero-range DWBA calculations, using the two-particle coefficients of fractional parentage obtained from the Cohen-Kurath Op shell wave functions. For most transitions, fair agreement is obtained between experiment and calculation, possible exceptions being the transition to the E_x = 4.43 MeV, J^π = 2⁺ state in ¹²C and to the E_x = 2.15 MeV, J^π = 1⁺ state in ¹⁰B, for which the calculations predict too much L = 0 strength. Where possible, a comparison with previous (p, ³He) results is made. In ¹⁴N a state at E_x = 11.04 MeV was observed for which the values (J_π; T) = (3⁺; 0) are suggested. In ¹²C we found, in addition to the well known T = 0 states, two relatively sharp T = 0 states at E_x = 19.50 ± 0.10 and 20.55 ± 0.10 MeV. The shape and strength of the angular distribution for the transitions to these states can be approximately accounted for by the calculations, although no one-to-one correspondence between observed and predicted levels could be established.     

Isospin-forbidden β-decay of 28Mg

We have measured the branching ratio for the isospin-forbidden Fermi β-decay of ²⁸Mg to the 0.972 MeV 0⁺, T = 1 level in ²⁸Al. This decay occurs through an admixture of the 0⁺, t = 2 analog state at 5.992 MeV into the anti-analog level at 0.972 MeV. A charge-dependent matrix element of 17.0_?5.8^+4.3 keV is deduced from the observed (0.21 ± 0.12)% branch. Comparisons are made with matrix elements deduced in other nuclei. An analysis based on a simple shell model with fourfold degenerate Orbitals indicates the importance of the two-body Coulomb interaction in isospin mixing in nuclei with more than one valence proton.     

The T = Tz + 2 GDR and the dipole states of the A = 6 and 14 nuclei

The isospin properties of the giant dipole resonance (GDR) built on states with isospin T = T_z + 1 are discussed. Results of a shell-model calculation with realistic interactions for dipole transitions to various low-lying states in ⁶Li, ⁶He, ¹⁴N and ¹⁴C are presented. The T = T_z + 2 component of the GDR in ¹⁴N decaying to the 0⁺T = 1 state is predicted at the surprisingly low energy E_x = 26.0 MeV.     

A particle-hole calculation for pion production in relativistic heavy-ion collisions

A differential cross section for π-meson production in peripheral heavy-ion collisions is formulated within the context of a particle-hole model in the Tamm-Dancoff approximation. This is the first attempt at a fully quantum-mechanical particle-hole calculation for pion production in relativistic heavy-ion collisions. The particular reaction studied is an ¹⁶O projectile colliding with a ¹²C target at rest. In the projectile we form a linear combination of isobar-hole states, with the possibility of a coherent isobar giant resonance. The target can be excited to its giant M1 resonance (J^π = 1⁺, T = 1) at 15.11 MeV, or to its isobar analog neighbours, ¹²B at 13.4 MeV and ¹²N at 17.5 MeV. The theory is compared to recent experimental results.     

Testing effective nucleon-nucleon forces to describe diagonal spin-transfer coefficients for the scattering of polarized protons with the excitation of the 1+ levels in 12C

The diagonal coefficients of spin-transfer D _ii in the small-angle inelastic scattering of polarized protons with the excitation of the two lowest 1⁺ levels in ¹²C are analyzed. The isoscalar (T = 0, E* = 12.71MeV) and isovector (T = 1, E* = 15.11 MeV) transitions are considered. The coefficients D _ii are calculated within DWBA using different effective nucleon-nucleon (NN) interactions between an incident proton and the nucleons of the nucleus. We consider the Franey-Love interaction and the Geramb effective interactions based on the Paris NN potential, and also the effective NN potential based on the chiral perturbation theory, etc. The impact of the wave function antisymmetrization is studied from the coefficients D _ii in a system that includes a projectile and nucleons of the nucleus, along with the impact of other effects.     

The width of the 5.11 MeV state in 10B and isovector parity mixing

We review estimates for effects of parity mixing on the α-capture of vector polarized ⁶Li to the 5.16 MeV, 2⁺, T = 1 state in ¹⁰B. The cross section depends on the ⁶Li polarization direction because of isovector parity mixing with the 5.11 MeV, 2^?, T = 0 state. The effect is enhanced due to isospin conservation. The α-width of the 5.11 MeV state, an important parameter for calculating the enhancement, has been measured to be 0.98 ± 0.07 keV. The consequences of parity mixing are reevaluated using best available values for the relevant parameters.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

The hyperspherical harmonics method applied to 12C

We apply the hyperspherical harmonics method to the low-lying T = 0 states in ¹²C, using the 3-α model. With the results from ref. ¹) we are able to investigate all states up to the 4⁺ level at 14.1 MeV, except for the broken symmetry 1⁺ state at 12.7 MeV. Antisymmetrization effects are included by adopting the local potential approximation²). Energy levels and electron scattering form factors are calculated.     

Alpha-particle unstable states in12C

Alpha particle unstable states in¹²C have been investigated using the three reactions¹⁴N(d, α′)¹²C,¹⁴N(d, α′α)⁸Be and¹²C(α, α′)¹²C. Excitation cross sections and angular distributions have been measured for the reactions¹⁴N(d, α′) at 52 MeV and¹²C(α, α′) at 90 MeV. For a few angle pairs the α-decay of excited states in¹²C have been observed in a¹⁴N(d, α′α) correlation measurement. The reactions selectively excite onlyT=0 states. A previously undetected level with a large α-decay width (Γ=1.2 MeV) has been observed at 15.62 MeV excitation. This level shows up clearly in both reactions and is further distinguished from the nearby 14.08 state in the correlation measurement because of the distinctly different energy distributions of the decay products. On the basis of a particle angular distributions the 15.62 MeV level was assigned spin and parity 4⁺ and the level at 14.08 was assigned 3^?. The latter differs from the value suggest by earlier work. Comparison with DWBA calculations indicates that angular distributions of all other prominent levels are in agreement with their earlier assignments. Two levels at 19.20 and 20.30 MeV (both Γ?0.4 MeV) and three further levels at 21.81, 22.7 and 24.24 MeV also decay predominantly by α-emission.     

Role of antisymmetrization in describing the excitation of the 1+, T = 1 level in the 12C nucleus by polarized protons

Inelastic polarized-proton scattering involving the excitation of the 1⁺, T = 1 level at 15.11 MeV in the ¹²C nucleus is described within the distorted-wave method. The effect of completely or approximately taking into account the antisymmetrization of the wave function for the projectile proton-intranuclear nucleons system on various observables, including the differential reaction cross section, the analyzing power, the difference of the polarization and analyzing power, and the depolarization parameter, is analyzed. The difference of the polarization and the analyzing power in the case of the excitation of anomalous-parity levels is shown to be especially sensitive to taking into account the above antisymmetrization. The reason for a large value of this difference for the level being studied and the sensitivity of this value to the parameters of the effective nucleon-nucleon interaction used are analyzed.