On the Yrast levels of106–108Sn

The isotope shift in the Ca-intercombination line withλ=6,573 Å was measured for all isotopes between⁴⁰Ca and⁴⁸Ca with the only exception of 47Ca. The combination of the results with muonic x-ray data yields highly accurate values for the changes of the mean square nuclear charge radii. In addition, the nuclear quadrupole moments of the three isotopes⁴¹Ca,⁴³Ca and⁴⁵Ca have been determined from the hyperfine structure splitting of the 4s 4p ³ P ₁ state.     

T=1, spin-dipole strength in40Ca

Spin-dipole strength in⁴⁰Ca has been studied by inelastic scattering of 500-MeV protons and the dipole response in⁴⁰Ca is compared with the spin-dipole data from the⁴⁰Ca(p, n) reaction and nonspin-dipole data from photonuclear studies.     

Investigation of large angle structure in α-scattering from calcium isotopes betweenE α=36–61 MeV

Elasticα-scattering angular distributions have been measured atE _α=36.2 MeV, 39.6 MeV, 42.6 MeV, 49.5 MeV, 61.0 MeV for⁴⁰Ca and atE _α=36.2 MeV, 42.6 MeV, 49.5 MeV and 61.0 MeV for⁴⁴Ca, respectively. At backward angles the data display an oscillatory structure forE _α<50 MeV and more smoothly decreasing slopes atE _α =61.0 MeV resembling the data obtained at higher energies. The⁴⁰Ca data belowE _α =50 MeV show the well known backward enhancement, which at 42.6 MeV and 49.5 MeV can be fitted by aP ₁₄ ² and aP ₁₆ ² respectively. Together with previous data,P _L ²-structures have now been observed for allL-values betweenL=8 andL=16. The slope of the curveL(L+1) versus excitation energy is slightly smaller forL>12 than forL<12. Optical model analyses (within a Woods-Saxon-folding model) lead to large differences between the⁴⁴Ca and⁴⁰Ca parameters. Furthermore, in our parametrization, the⁴⁰Ca real potential depth shows dramatic changes with energy. This feature seems outside the domain of the optical model and requires consideration of additional effects (e.g. antisymmetrization) not included in the standard optical model. Present microscopic calculations on the basis of the Resonating Group Method are discussed in connection with the characteristic features ofα-scattering from⁴⁰Ca.     

Levels of 41Sc from the 40Ca(p,p)40Ca reaction

Excitation functions have been measured for ⁴⁰Ca(p, p)⁴⁰Ca, in the energy range from E_p = 2.35 to 4.85 MeV at four angles. The R-matrix formalism for multilevel cross sections was used to analyse the data; spins, parities, proton widths and reduced widths were extracted for thirty levels. Several new spin values have been deduced. A detailed comparison of the levels in the mirror system ⁴¹Ca?⁴¹Sc is given.     

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.     

Structures in pp → ππ

A Barrelet-zero analysis is presented of data on $\text{p}\text{p}\text{→ π π}$ in the momentum range 1 to 2 GeV/c. With π^?π⁺ data alone, the slope for ambiguity is very large, but the addition of π⁰π⁰ information enables the number of solutions to be reduced to just a few. Although the alternative solutions differ considerably, they significant common features, in particular, with plausible extra assumptions, all solutions appear to be dominated by resonances in all spin states from J = 1 to 5.     

Variation of the α-particle pick-up spectroscopic factor from 12C to 40Ca

(³He, ⁷Be) cross sections have been measured on A = 4n target nuclei between ¹²C and ⁴⁰Ca. An α-particle pick-up spectroscopic factor is extracted from the data through a finite-range DWBA analysis. It is concluded that the overall changes of S_α between ¹²C and ⁴⁰Ca are moderate, but that local variations exist; S_α is lower in the middle of the sd shell and higher for ⁴⁰Ca.     

Coexistence of α-clustering and shell structure in40Ca

The energy spectrum and α-spectroscopic factors of⁴⁰Ca are calculated by using an α+³⁶Ar orthogonality condition model. Overall agreement is obtained with the experimental data. The model successfully produces the parity-doubletK ^π=O ⁺ and O^? α+³⁶Ar cluster bands. It is shown that the coexistence and interference of α-cluster states and shell-model states are indispensable to understand the structure of⁴⁰Ca.     

Thermonuclear reaction rates for proton induced reactions on 41K and neutron induced reactions on 41Ca

The yield of γ-rays from the reaction ⁴¹K(p, γ)⁴²Ca has been measured as a function of bombarding energy over the range 0.68–2.48 MeV and from the reaction ⁴¹K(p, αγ)³⁸Ar over the range 1.20–2.48 MeV, and the yield of neutrons from the reaction ⁴¹K(p, n)⁴¹Ca has been measured from threshold to a bombarding energy of 2.48 MeV. The energy dependence of the cross sections is compared with statistical-model calculations with global optical-model parameters in all particle channels. The calculations seriously overestimate the cross section for the neutron channel and underestimate those for the other channels. A reduction in the imaginary well depth in the neutron channel leads to good agreement with all the data. Statistical-model calculations with this modified set of parameters are then carried out to provide cross sections for the astrophysically interesting reactions ⁴¹Ca(n, p)⁴¹K, ⁴¹Ca(n, α)³⁸Ar, and ⁴¹Ca(n, γ)⁴²Ca. Thermonuclear reaction rates are calculated for all six reactions over the temperature range 5 × 10⁸–10¹⁰K which includes the range of temperatures of interest in nucleosynthesis calculations.     

Nuclear fragmentation in 35Cl-induced reactions at 11 MeV/u bombarding energy

The reactions ³⁵Cl + ⁵⁸Ni,⁴⁰Ca, ²⁷Al are studied at 385 MeV bombarding energy. The experiment employs 6 large-area ionization chambers which are set up to detect fragments with nuclear charge $\text{Z ≧ 4}$ in coincidence multiplicity m ≦ 6. The highest multiplicity observed is m = 4; a detailed analysis of the data is performed for m = 2 and m = 3 events. The ⁵⁸Ni data contain reactions with 2 fragments (σ = 1350±500 mb) and 3 fragmentes (σ = 175±90 mb) in the exit channel. The three fragments appear to have their origin in two different processes: a sequential-fragmentation process and a fast break-up process. A similar conclusion is reached for the ²⁷Al data, whereas in the ⁴⁰Ca data only the sequential fragmentation could be identified.     

Resonance spectroscopy of44Ti in the excitation energy range 9.05 to 10.28 MeV

The absolute differential cross sections for the⁴⁰Ca(α,α)⁴⁰Ca reaction have been measured in the bombarding energy range from 4.33 to 5.68 MeV at the four laboratory angles 85°, 125°, 141° and 165°. An analysis of the data using multilevelR matrix theory has provided the spin-parities and widths of 29 levels in the compound nucleus⁴⁴Ti. A comparison has been made with the levels deduced from the (α,γ) reaction and existing theoretical calculations of⁴⁴Ti levels.     

Cross section measurements and thermonuclear reaction rates for 48Ca(p, γ)49Sc and 48Ca(p,n)48Sc

Absolute cross sections have been measured for the reaction ⁴⁸Ca(p, γ)⁴⁹Sc for 0.579 MeV ≦ E_{p, lab} ≦ 2.670 MeV and for the reaction ⁴⁸Ca(p, n)⁴⁸Sc for 0.956 MeV ≦ E_{p, lab} ≦ 2.670 MeV. Substantial competition effects in the cross section for ⁴⁸Ca(p, γ)⁴⁹Sc were observed at the thresholds for neutron emission to the 623 keV (3⁺), 1143 keV (2⁺) and 1402 keV (2^?) excited states of ⁴⁸Sc. Thermonuclear reaction rates were calculated from the measured cross sections for 0.1 ≦ T₉ ≦ 10.0. The new rates differ considerably from those used in earlier calculations of the production of the rare, neutron-rich intermediate mass nuclides during explosive carbon burning. In particular, the new rates may change the predicted abundances for ⁴⁸Ca, ^{49, 50}Ti and ⁵⁰V substantially. The good agreement between current global Hauser-Feshbach models and the experimental data indicates that Hauser-Feshbach calculations can provide sufficiently reliable rates for astrophysical calculations in cases where experimental data are non-existent.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

Statistical analysis of the (d,p) and (d,d) reactions on 40Ca

Excitation functions of the ⁴⁰Ca(d, p)⁴¹Ca and ⁴⁰Ca(d, d)⁴⁰Ca reactions have been measured at 45°, 90°, 135° and 170° from E_d = 4.50 to 5.43 MeV in 10 keV steps. Angular distributions of these reactions have been taken at E_d = 4.70, 5.00 and 5.30 MeV from 25° to 170° in 5° steps. Transitions were observed to the excited states for the range 0.0 ≦ E_x ≦ 3.74 MeV in ⁴¹Ca. Rapid fluctuations in the excitation functions and strong variations of the angular distributions with the incident energy were observed, suggesting that the contribution from compound nucleus processes is very large. Various quantities extracted from the experimental data were compared to the predictions of the statistical theories combined with the DWBA theory for the calculation of the direct reaction amplitudes. The results of the present analysis are consistent with the predictions of the standard statistical theories based on the neglect of the channel-channel correlation.     

Isotope shift and hyperfine structure of43Ca by laser spectroscopy

The isotope shift⁴⁰Ca-⁴³Ca in the 4s ^{2 1} S ₀-4s4p ³ P ₁ intercombination line as well as the hyperfine structure splitting of the 4s4p ³ P ₁ state of⁴³Ca have been remeasured by saturation spectroscopy with a tunable stabilizedcw dye laser and an atomic beam of natural Ca as absorber. The nuclear charge radius of⁴³Ca obtained here reconciles our result with the radius obtained from measurements in muonic Ca-atoms and in the Ca resonance line. It reconfirms the fact that the charge radius of⁴³Ca is considerably smaller than the ones of both neighbouring even isotopes. The discrepancy of our previous measurement for this charge radius was due to a wrong assignment of so far unobserved absorption lines of probably molecular origin occuring in the neighbourhood of the atomic resonances under study.     

The 42Ca(α, γ)46Ti and 42Ca(α, p)45Sc cross sections and the mass-45 bottleneck

The yield of γ-rays from the reaction ⁴²Ca(α, γ)⁴⁶Ti has been measured as a function of bombarding energy over the range E_α = 3.42–5.62 MeV and from ⁴²Ca(α, pγ)⁴⁵Sc over the range E_α = 4.06–5.92 MeV, and the yield of protons from the reaction ⁴²Ca(α, p)⁴⁵Sc has been measured over the range E_α = 4.78–5.92 MeV. Cross sections for all three reactions have been extracted from the data and compared with global statistical-model calculations. The agreement is good. Thermonuclear reaction rates under stellar conditions appropriate for silicon burning are calculated and their significance for the approach to and bridging of the mass-45 bottleneck in the upward flow of nucleosynthesis is discussed.     

The reactions48Ca(d,t)47Ca and48Ca(3He, α)47Ca

The reactions⁴⁸Ca(d, t)⁴⁷Ca and⁴⁸Ca(³He, α)⁴⁷Ca have been measured at incident energies of 17 and 18 MeV, respectively and analysed by DWBA. Besides strong transitions to the groundstate and two unresolved states at aboutE _x =2.60 MeV relatively strong transitions withl=2 are observed at higher excitation energies in the (³He, α) reaction. The observedl=1 and higherl=3 transitions are rather weak indicating that particle-hole components in the⁴⁸Ca groundstate are relatively small.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.