Thermal effects on neutrino-nucleus inelastic scattering in stellar environments

Thermal effects for inelastic neutrino-nucleus scattering off even-even nuclei in the iron region are studied. Allowed and first-forbidden contributions to the cross sections are calculated within the quasiparticle random-phase approximation, extended to finite temperatures within the Thermo-Field-Dynamics formalism. The GT₀ strength distribution at finite temperatures is calculated for the sample nucleus ⁵⁴Fe. The neutral-current neutrino-nucleus inelastic cross section is calculated for relevant temperatures during the supernova core collapse. The thermal population of the excited states significantly enhances the cross section at low neutrino energies. In agreement with studies using a large scale shell-model approach the enhancement is mainly due to neutrino up-scattering at finite temperatures.     

Energieverteilung und Wirkungsquerschnitt der Photoprotonen aus N15

The energy spectra of photo protons from highly enriched N¹⁵ were investigated with the bremsstrahlung from the Heidelberg betatron running at six different endpoint energies between 19 and 30.5 MeV. The protons were detected at 90° to theγ-beam by means of a CsJ-spectrometer with pulse shape discrimination. The energy spectra show pronounced maxima atE _p =3.2; 4.6; 9.5 and 13.3 MeV. Proton yields are given as a function of endpoint energy, the yield value atE ₀=30.5 MeV being (7.0±0.8) μb/MeV · ster. Because the first excited state in the daughter nucleus C¹⁴ lies 6.09 MeV above the groundstate, the cross section for groundstate transitions of the process N¹⁵(γ, p)C¹⁴ could be derived from the upper 6 MeV of the single proton spectra. The main contribution to the cross section comes from the region between 18 and 26 MeV excitation energy with maxima at 19.5; 20.4; 22.7 and 24.5 MeV. A “pygmy resonance” occurs at 15.2 MeV with further less pronounced structures at 13.6 and 17.0 MeV. The integrated cross section for groundstate transitions up to 30.5 MeV is (22±3) MeVmb assuming isotropic angular distribution. The ratios of protons from transitions to excited states and from the (γ, n p)-reaction to those of groundstate transitions rise from 0.45 atE ₀=24.5 MeV to 0.70 atE ₀=30.5 MeV.     

55Mn(n,n'γ) cross-section studies for En = 1.0–3.6 MeV

Absolute ⁵⁵Mn(n, n′γ) γ-ray production cross sections have been measured for 19 transitions from levels up to and including the 2429 keV state in ⁵⁵Mn over the energy range E_n = 1.0–3.6 MeV. Angular distributions were also measured for 6 of the transitions. Branching ratios were extracted and total inelastic neutron cross sections were inferred for these ⁵⁵Mn excited states. The measured and inferred cross sections are compared with calculated cross sections using the statistical compound nucleus theory.     

A statistical theory of nuclear neutrino capture

A statistical theory is proposed for the calculation of the total capture cross section of a neutrino by a nucleus. Close references are made to the statistical theory of β-decay and electron capture developed by Yamada and his collaborators. As a test of the theory, we calculate the total cross section for the capture of a solar neutrino by a ³⁷Cl nucleus.     

The 12C(α, γ)16O cross section at stellar energies

The capture reaction ¹²C(α, γ)¹⁶O has been investigated at E = 0.94 to 2.84 MeV with the use of an intense α beam and implanted ¹²C targets of high isotopic purity. The studies involved NaI(Tl) crystals and, for the first time, germanium detectors. The measurement of absolute cross sections, γ-ray angular distributions and excitation functions is reported. A cross section of 48 pb is found at E = 0.94 MeV. The data provide information on the E1 and E2 capture amplitudes involved in the transition to the ground state as well as to excited states. The S-factor at stellar energies has been determined by means of theoretical fits. The results verify the previous report of a substantial higher S-value compared to the value recommended in 1975. The present uncertainty in the S-value as well as possible improvements are discussed. This S-value is of crucial importance to nuclear astrophysics.     

Potential cluster approach to the description of the 7Li + γ ai p6He reactions

Angular distributions for the ⁶He(p, γ_{0 + 1})⁷Li process at the energy E _γ = 40 MeV are calculated within the potential cluster approach. It is shown that the observed cross section is well reproduced when E1 and E2 transitions are taken into account; in this case, unlike the case in the RGM calculations, the dominating mechanism is direct capture to the ground state of the ⁷Li nucleus. Total cross sections for direct photodisintegration ⁷Li (γ, p₀)⁶He in the energy interval E _γ = 22–30 MeV are calculated.     

The photoproton reaction of 25Mg

The proton yields from the ²⁵Mg(e, p) reaction have been measured for E_p > 3 MeV, at θ = 90°, using an enriched ²⁵Mg sample in the electron energy range 15–28 MeV. Partial photoproton cross sections to the ground and excited states in ²⁴Na have been deduced and a lower limit is placed on the ²⁵Mg(γ, np) cross section. The derived photoproton cross section combined with existing photoneutron data allows the ²⁵Mg absorption cross section to be estimated. Configuration splitting of the ²⁵Mg GDR is confirmed, and the effects of isospin splitting are considered.     

On the mechanism of formation of excited states of the 8Be nucleus in the reaction 12C(γ, 3α)

The reaction ¹²C(γ, 3α) was studied with the aid of a diffusion chamber placed in a magnetic field, filled with a methane-helium mixture, and irradiated with bremsstrahlung photons of endpoint energy 150 MeV. The total reaction cross section was measured in the energy range E _γ < 40 MeV. The ground state; the first, second, and unseparated third and fourth excited states; and highly excited states (in the range 19.9 < E _x < 25.2 MeV) of the ⁸Be nucleus manifested themselves in the distribution of events with respect to the energy of the relative motion of two alpha particles. A resonance that is characterized by the energy of E₀ = 0.72 MeV and the width of Γ = 0.80 MeV and which was identified as a ghost anomaly was found between the ground state and the first excited state. Partial cross sections were measured for various channels. Excited states are formed in narrow photon-energy intervals, and their partial cross sections are of a resonance shape. It is found that the energy corresponding to the maximum of the partial cross section for the ith level, E _m ⁱ , and the excitation energy of the next level, E ₀ ⁱ⁺¹ , are correlated: E _m ⁱ = E ₀ ⁱ⁺¹ + ?, where ? is the reaction threshold. The results are qualitatively explained on the basis of a model that assumes photon absorption by an alpha-particle pair.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Electrofission of238U and232Th

Absolute electrofission cross sections for²³⁸U and²³²Th in the energy regionE _e =7 ?65 MeV and fission fragment angular distributions forE _e =7–30 MeV have been measured. The angular distributions show strong anisotropies for low energies. The relative dipole and quadrupole contributions as a function of excitation energy are discussed in terms of the low lying fission transition states above the fission barriers. The cross sections show significant deviations from the results of some earlier measurements, in particular in the energy region above the giant dipole resonance. From the difficulties of absolute electrofission cross section measurements and the ambiguities in their interpretation it is concluded that by this time the quantitative analysis of electrofission cross sections with respect to the contributions of the giant quadrupole resonances to the fission decay channel should be regarded as rather tentative.     

Elastic and inelastic scattering of π mesons on 7Li nuclei

Within the diffraction theory of multiple scattering, the differential cross sections for elastic and inelastic pion scattering on a ⁷Li nucleus are calculated for the case where the final nucleus is either in the ground or in the first excited state. The nuclear wave function is set to that in the αt cluster model. The sensitivity of the calculated observables to variations in the type of the wave functions for the alpha-particle and the triton cluster and for their relative motion is investigated. Various multiplicities of scattering and rescattering on the clusters constituting the ⁷Li nucleus are taken into account, and their contributions to the cross section are revealed. The results of the calculations are compared with experimental data at E _π=143, 164, and 194 MeV.     

The structure of 26Mg investigated with the (d,p) reaction

Angular distributions have been measured for the ²⁵Mg(d, p)²⁶Mg reaction at 13 MeV leading to excited states between E_x = 0 and 8 MeV. Experimental cross sections are compared with DWBA calculations and extended shell-model calculations in the full sd shell. Spin and parity restrictions are obtained for several levels in the region E_x = 6?;8 MeV. Spectroseopic factors for transitions to the lowest four positive-parity states of each spin are well reproduced by the shell-model calculations; however, in mixed configurations the largest component is systematically underestimated by the shell model. Only 60% of the strength for $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transfer is observed.     

Energy levels of 14C

The ⁹Be (⁶Li, p)¹⁴C reaction has been studied using 20 MeV ⁶Li ions and the Penn multiangle spectrograph. Proton groups are reported corresponding to thirty excited states of ¹⁴C with E_x < 18.2 MeV. The total cross section for formation of the six bound excited states, whose J^π are known, is proportional to 2J_f + 1. Possible new spin assignments are suggested for several unbound levels of ¹⁴C, based on the 2J_f + 1 rule and a comparison of the experimental widths and widths predicted from neutron penetration of a centrifugal barrier.     

Coulomb dissociation of 8B and solar neutrino problem

We measured the cross section for Coulomb dissociation of ⁸B using a radioactive ⁸B beam of 46.5 MeV/u energy with a ²⁰⁸Pb target. The corss section for the ⁷Be(p,γ)⁸B capture reaction was deduced at E_cm = 0.6 – 1.7 MeV. The extracted astrophysical S₁₇ factors were consistent with the values measured by Vaughn et al. and Filippone et al. Possible corrections due to ⁷Be excited state population, E1 and M2 contribution, nuclear contribution and post acceleration effects are considered.     

Untersuchung der Reaktion Si28 (γ,p) AI27

A silicon semiconductor detector was irradiated with betatron bremsstrahlung of different end point energies and the energy distributions of the protons originating in the detector itself by the reaction Si²⁸(γ,p) Al²⁷ were measured with good statistical accuracy. The end point energies were varied in 1 MeV steps from 15 to 30 MeV. Using the known spectral distribution of theγ-rays the energy dependence of the total cross section of the studied reaction could be derived from the measured proton spectra. The resulting cross section shows a peak at 20, 5 MeV and a half width of 4 MeV. Approximate values for the branching ratios for transitions to excited states of the residual nucleus could also be obtained.     

A study of the 90Zr(6Li, 6He)90Nb reaction at E6Li = 93 MeV

The energy spectra of ⁶He nuclei from the ⁹⁰Zr(⁶Li, ⁶He) reaction at E_{⁶Li = 93 MeV} have been measured over the angular range of 7 ° ? θ_lab ? 20 °. The theoretical DWBA analysis of these spectra and angular distributions was performed employing transition densities of bound and resonance states obtained on the basis of the theory of finite Fermi systems. It is shown that up to excitation energies of E_x ≈ 10 MeV in ⁹⁰Nb a direct charge-exchange mechanism dominates in this reaction, while at higher E_x the contribution made by multistep processes increases significantly. It is also shown that the quasi-elastic cross section is determined by a sum of partial contributions of spin-isospin-flip transitions with multipolarities L=0 through L=6.     

A study of coupled-reaction channel effects in the36S +37Cl system,hybridization between single particle orbits

Elastic and inelastic scattering as well as transfer transitions involving a valence proton in thesd- andfp- shell orbits are studied in the interaction of³⁷Cl +³⁶S at E_CM=50 MeV. Experimental angular distributions of single particle states of³⁷Cl (elastic and inelastic transfer) are presented with a CRC analysis. In the CRC calculations the effects of inelastic and transfer couplings are studied using known spectroscopic information. In the CRC analysis six single particle bound states and the collective 2⁺ excitation of³⁶S are included in the coupling scheme. Higher order coupling effects are found to be important. A distinct effect, the mixing of single particle states (of different parity) due to direct and transfer interactions is observed to produce an enhancement of the transfer cross section to the low lying states. This feature is due to a change of the asymptotically defined single nucleon orbits via polarization in the field of the other nucleus, an effect which is analogous to hybridization, known from atomic physics.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

The58Ni(12C,γ)70Se reaction

The⁵⁸Ni(¹²C,γ)⁷⁰Se capture reaction was studied with beam energies ofE _12C=30 to 42 MeV. The capture events were identified by means of the residual activity produced in the reaction. At a beam energy of 38 MeV the capture cross section has been determined to 1.5±0.7 μb. AtE _12C=30, 34 und 42 MeV we established upper limits of 0.3, 0.5 and 0.6 μb, respectively. The experimental results are compared with a statistical model calculation.     

Proton direct capture on 40Ca

Excitation functions for the ⁴⁰Ca(p, γ)⁴¹Sc reaction have been measured at 0° and 90° in the proton energy range E_p = 2.1–3.1 MeV. The experimental results have been interpreted in terms of the direct capture process to the first excited state of ⁴¹Sc. The direct capture transition to the ground state has been observed only at a few proton energies. The spectroscopic factor of the first excited state in ⁴¹Sc has been found to be 1.0 ± 0.3. The direct capture cross section to the ground state is consistent with the spectroscopic factor reported from stripping reactions.