Levels in 156Gd studied in the (n, γ) reaction

Levels up to 2.3 MeV in ¹⁵⁶Gd have been studied using the (n, γ) reaction. Energies and intensities of low-energy γ-rays and electrons emitted after thermal neutron capture have been measured with a curved-crystal spectrometer, Ge(Li) detectors and a magnetic electron spectrometer. High-energy (primary) γ-rays and electrons have been measured with Ge(Li) detectors and a magnetic spectrometer. The high-energy γ-ray spectrum has also been measured in thermal neutron capture in 2 keV resonance neutron capture. The neutron separation energy in ¹⁵⁶Gd was measured as S_n = 8535.8 ± 0.5 keV.About 600 transitions were observed of which ~50% could be placed in a level scheme containing more than 50 levels up to 2.3 MeV excitation energy. 42 of these levels were grouped into 15 excited bands. In addition to the β-band at 1050 keV we observe 0⁺ bands at 1168, 1715 and 1851 keV. Other positive-parity bands are: 1⁺ bands at 1966, 2027 and 2187 keV; 2⁺ bands at 1154 (γ-band) and 1828 keV; and 4⁺ bands at 1511 and 1861 keV. Negative-parity bands are observed at 1243 keV (1^?), 1366 keV (0^?), 1780 keV (2^?) and 2045 keV (4^?). Reduced E2 and E0 transition probabilities have been derived for many transitions. The ground band, the β- and γ-bands and the 0⁺ band at 1168 keV have been included in a phenomenological four-band mixing calculation, which reproduces well the experimental energies and E2 transition probabilities.The lowest three negative-parity (octupole) bands of which the 0^? and the 1^? bands are very strongly mixed, were included in a Coriolis-coupling analysis, which reproduces well the observed energies. The E1 transition probabilities to the ground band are also well reproduced, while those from the higher-lying 0⁺ bands to the octupole bands are not reproduced. Absolute and relative transition probabilities have been compared with predictions of the IBA model and the pairingplus-quadrupole model. Both models reproduce well the E2 transitions from the γ-band, while strong disagreements are found for the E2 transitions from the β-band. The IBA model predicts part of the decay features of the higher lying 2⁺₂, 4⁺₁ and 2^?₁ bands.     

Investigation of giant E3 resonances by (N, γ) reactions

Effects related to the presence of giant E3 resonances are investigated by nucleon radiative capture according to the direct-semidirect model. The γ-ray angular distributions from the ²⁰⁸Pb(N, γ₀) reactions are calculated in the energy region above the giant dipole resonance and the influence of the E1–E3 and E2–E3 interferences is discussed. The results provide indications of an appreciable effect on the 90° photon emission when a collective isovector E3 excitation is present.     

7 Be(p, γ) 8 B cross section from indirect breakup experiments

The amplification of the E2 and M1 electromagnetic transitions in the radiative capture reaction⁷ Be(p, γ)⁸ B is investigated. This amplification occurs in Coulomb dissociation experiments. Interference between the excitation amplitudes of E1, E2 and M1 multipolarities leads to anisotropy effects in the angular distribution of the fragments. Dynamical coupling which could affect the direct correspondence between the Coulomb breakup and the radiative capture cross sections are studied by means of a coupled-channels approach.     

7Be(p, γ)8 B cross section from indirect breakup experiments

The amplification of the E2 and M1 electromagnetic transitions in the radiative capture reaction ⁷Be(p, γ)⁸ B is investigated. This amplification occurs in Coulomb dissociation experiments. Interference between the excitation amplitudes of E1, E2 and M1 multipolarities leads to anisotropy effects in the angular distribution of the fragments. Dynamical coupling which could affect the direct correspondence between the Coulomb breakup and the radiative capture cross sections are studied by means of a coupled-channels approach.     

Microscopic analysis of the 12C(α, γ)16O reaction

Electric transition probabilities in the ¹⁶O spectrum, and the ¹²C(α, γ_o,3¹⁶O capture cross sections are calculated with antisymmetric wave functions by the generator coordinate method. The influence of bound states on radiative capture is shown to be automatically included in the model. The reduced α-widths of the ¹⁶O bound states are discussed, and compared with previous theoretical and experimental estimates. The microscopic E2 capture cross sections to the O⁺₁ and 2₁⁺ states yield an astrophysical S-factor of 0.09 MeV · b at 0.3 MeV. An attempt to treat the El multipolarity by relaxing the long-wavelength approximation leads to a large underestimation of the γ-widths. Adopting the experimental γ- width and the theoretical reduced α-width of the 1₁^? state provides s_E1 = 0.30 MeV · b at 0.3 MeV.     

Study of the 208Pb(n, γ0)209Pb reaction between 0.8 and 7.7 MeV

The reaction ²⁰⁸Pb(n, γ₀)²⁰⁹Pb was studied from 0.8 to 7.7 MeV to investigate relative contributions of the compound-nucleus and direct and semidirect processes in this energy range. Compound-nucleus reactions dominate below about 5 MeV and semidirect processes above 6 MeV. The direct-semidirect (DSD) model with a complex particle-vibration coupling describes the experimental data in the giant resonance region. A relatively large imaginary term is necessary to obtain a good fit to the data indicating either that the reactions proceed to a large extent in more complicated ways than the simple two-step semidirect reaction or that the model has a serious defect in its present formulation. A second objective was to search for a possible excitation of the isoscalar E2 and the M1 giant resonances by measuring asymmetries around 90° in the angular distribution of the γ-rays. The results indicate no (or very weak) asymmetry effects.     

A singularity in E1 matrix elements at the neutron threshold: Evidence from (d,p)-(n, γ) correlations

There are several independent effects which tend to suppres correlations of (d, p)-(n, γ) type. When a near-perfect correlation is found, as in the case ³⁷Cl with thermal capture, it follows that all the effects are small. This has important implications, such as showing that the dominant thermal capture process can be ‘direct’, thereby settling a long debate. Further, the data establishes the E_γ^?1 singularity in E1 matrix elements for thermal capture that was derived theoretically in 1960.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

The E0 component of the 689 keV 2β → 2g transition in Sm

The electric monopole contribution to the 689 keV 2_β → 2_g transition in ¹⁵²Sm is studied by measuring the 689K-122γ directional correlation. The result for the directional correlation coefficient is a₂ (Kγ) = 0.10±0.05. This value is used together with earlier electron and γ-ray intensity data to evaluate the E0/E2 electron amplitude and the M1 penetration parameter. The corresponding E0/E2 mixing ratio is compared with recent theoretical predictions.     

Vibrational band structure in 184W populated in the decay of 184Re

The decay of ^184mRe has been investigated through γ-ray and conversion electron studies. The band head of the K^π = 2^? octupole band has been established at 1130.0 keV. The E2/M1 mixing ratios of three transitions from the γ-vibrational band to the ground state band have been determined by angular correlation measurements. A mixing of El, M2 and E3 multipolarity has been derived for the 921 keV transition combining angular correlation and conversion electron data. A value B(E3, 0⁺ → 3^? = (25 ± 5) × 10⁴e² · fm⁶ was obtained from the measured E2/M1 mixing of the 91 keV 3^? → → 2^? transition and γ-branchings. The data are discussed in terms of the collective model taking into account band mixing.     

High-resolution (e,e') study of isovector M1 and M2 transitions in the oxygen isotopes: (I). 16O

The M1 and M2 transition strength distribution for ¹⁶O in the excitation energy range from 16 to 20 MeV has been measured in a high-resolution electron scattering experiment. The M1 strength is concentrated in three sharp states at E_x = 16.22, 17.14 and 18.79 MeV (± 0.01 MeV) with B(M1, k)↑ = 0.20 ± 0.02, 0.32 ± 0.03 and 0.13 ± 0.03 μ_N², respectively. An additional strength of 0.35 ± 0.09 μ_N², distributed over eight weakly excited states with excitation energies E_x = 17.4 to 18.0 MeV, brings the total measured M1 strength to B(M1, k)↑ = 1.0 ± 0.1 μ_N². The experimental M2 strength is distributed over states at E_x = 16.82, 17.78, 18.50 and 19.0 MeV (± 0.01 MeV) with B(M2, k)↑ = 19 ± 2, 13 ± 2, 59 ± 7 and 341 ± 51 μ_N² · fm², respectively. Electric transitions were also measured to states at E_x = 16.45 MeV (2⁺, E2), 17.30 MeV (1⁺, E1) and 18.20 MeV (2⁺, E2). Calculations were performed using the modified surface delta interaction in a 2p-2h shell model for the M1 transitions and the random phase approximation for the M2 transitions. The results show the sensitivity of the M1 strength as a measure of ground-state correlations and compare well with results from the ¹⁵N($\text{p}$, γ) reaction.     

Radiative strength functions in odd-A spherical nuclei

The radiative strength functions for the partial γ-transitions from neutron resonances to the ground and low-lying states of odd-A spherical nuclei are calculated within the quasiparticle-phonon nuclear model. The fragmentation of one-quasiparticle and quasiparticle-plus-phonon states is calculated. This allowed one to calculate γ-transitions between the one-quasi-particle components (valence transitions) and γ-transitions between the quasiparticle-plus-phonon and one-quasiparticle components of the wave functions. The energy dependence of the strength functions $\text{C}$(E1, η) and $\text{C}$(M1, η) is calculated near the neutron binding energy B_n for ⁵⁵Fe and ^{59, 61}Ni. The corresponding experimental data are described qualitatively. The contribution of the valence E1 transitions to the strength function is shown to be from 20% to 90%, and M1 transitions about 1%. The influence of the M1 giant resonance is important for M1 transition probabilities.     

ISobaric analog state excitation in proton radiative capture

The direct-semidirect model for proton radiative capture so far formulated is unable to describe the observed (p, γ) excitation functions in the energy region where the isobaric analog resonances are located. To remove this difficulty, an extension of the model to include capture proceeding via isobaric analog state (IAS) excitation is here proposed. The calculated results are compared with the measured 90° excitation curve of the ²⁰⁸Pb(p, γ₁)²⁰⁹Bi reaction and satisfactory agreement is achieved. A detailed analysis of the three mechanisms involved in the El dominant capture process is presented. In the case considered the model seems to provide a useful tool for study of the striking effects arising from IAS excitation.     

Finite-range nucleon-nucleon interaction in the radiative capture of fast nucleons

The direct-semidirect model for nucleon radiative capture has so far been formulated assuming a zero-range nucleon-nucleon interaction. An extension of the theory to finite-range forces is proposed here. The usual δ-function in the interaction is replaced by a range-dependent gaussian function and then the radial form factor in the particle-vibration coupling (responsible for excitation of the E1 and E2 giant resonance states) is derived. Calculations are performed for the ¹⁴²(p, γ) reaction in the 5–30 MeV energy region. A detailed analysis provides indications on effects related to the interaction range as regards both the E1 and E2 integrated cross sections and the forward-backward asymmetry of the γ-ray angular distributions. Sensitivity to the interaction range shows connections with the proton final-level spin.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Radiative Ml capture in light nuclei

The importance of semi-direct processes in E1 and E2 capture reactions has been well documented. Little is known, however, about M1 capture although a vast body of data indicates a non-statistical nature. We discuss here the importance of the semi-direct M1 process and concentrate in particular on recent experimental results claiming that the M 1 strength in²⁹Si isnearly one order of magnitude smaller than in ²⁸Si, the target nucleus. We use shell model arguments to demonstrate that this reduction is indeed consistent with the semi-direct reaction process and that other mechanisms like2p-2h fragmentation and phonon coupling are not likely to be instrumental in elucidating further the non-statistical nature of the²⁸Si+n reaction.     

Microscopic investigation of electric dipole transitions in the α + 16O system

A microscopic calculation of forbidden E1 transitions is presented in the framework of the generator coordinate method. Isovector and isoscalar origins of E1 transitions are studied in the case of the α + ¹⁶O system. Two-cluster T = 0 and T = 1 configurations are coupled by the exact microscopic Coulomb interaction. The γ- widths of the 1₁⁻ and 3₂⁻, states of ²⁰Ne are fairly reproduced by the model but the anomalous branching ratios observed experimentally remain unexplained. Simplified formulas for the isospin-mixing rates and reduced E1 transition probabilities are compared with the microscopic results and are employed to discuss them. The non-resonant E1 contribution to the ¹⁶O(α, γ)²⁰Ne reaction is shown to be almost negligible at astrophysical energies.     

A study of 75Se by neutron capture and the SU(3)-SU(5) transition in the quadrupole-phonon representation

The γ and e^? spectra following thermal neutron capture in ⁷⁴Se were studied with curved-crystal, β, and pair spectrometers. Precise energies have been obtained for the transitions and levels at low energies. Two primary E2 transitions were found. The neutron separation energy for ⁷⁵Se was determined as 8027.6 keV. Precise γ-energies following the electron capture decay of ⁷⁵Se were also measured, resulting in precise level energies in ⁷⁵As. The calculation of the energy levels in ⁷⁵Se has been performed in the SU(6) particle-vibrational model (PTQM) and 27 theoretical states have been tentatively assigned to the experimental levels. The spectrum of the core nucleus ⁷⁴Se has been calculated in the SU(6) quadrupolephonon model (TQM). The structure of theoretical states, the relation to SU(3) and SU(5) limits, and potential energy surface are discussed. The E2, M1 and E1 transitions have been calculated in PTQM and compared to the experiment. Also, an overview is presented of theoretical explanations of the I = j, j?1, j?2 anomalous triplet emphasizing the rule with shell-model classification corrected for quadrupole phonons.     

On the direct capture to unbound states

Recently a discrepancy between the theory of direct radiative capture to unbound states and experimental results for the reaction ¹²C(p, γ₁)¹³N (2366 keV, unbound) has arisen at low γ-energies (150 keV < E_γ < 500 keV). It is shown that this discrepancy can be removed by a careful evaluation of the theoretical expression for the usual theory of direct capture to unbound states.     

Electromagnetic capture into theE x=7.56 MeV resonant state in15O

We have studied the¹⁴N(p, γ)¹⁵O reaction leading into thej ^π=1/2⁺ resonance atE _cm =260 keV in the proton channel. Our calculation is based on a potential model for nuclear bremsstrahlung allowing both fragments to have non-vanishing spins. Our study reproduces consistently the total width of the final resonance as well as the capture cross sections into this state thereby not confirming a contradiction between these two experimental data sets as discussed recently.