Search for multiparticle-multihole states of Ca with the S(C,α) reaction

Levels of ⁴⁰Ca below E_x = 10 MeV have been populated with the ³²S(¹²C,α) reaction at an incident energy of 30 MeV. States which are thought to be based on 4p-4h and 8p-8h K = 0 configurations were more strongly populated than other low-lying states.     

Untersuchung von40Ca mit der Reaktion39K(p, γ0)40Ca

Excitation functions of the reaction³⁹K(p, γ ₀)⁴⁰Ca at 0° and 90° have been taken in the proton energy range 2.5–6.0 MeV corresponding to an excitation of⁴⁰Ca between 10.8 and 14.1 MeV. Positions and strengths of several resonances appearing in the excitation functions are given. The structure of⁴⁰Ca is compared with predictions from 1 particle — 1 hole calculations.     

Untersuchung von 0+−0+-Übergängen in12C,24Mg,28Si,32S und40Ca durch unelastische Elektronenstreuung

Transitions from the 0⁺ ground states to 0⁺ excited states at 7.65 (¹²C), 6.44 (²⁴Mg), 4.98 and 6.69 (²⁸Si), 3.78 (³²S) and 3.35 (⁴⁰Ca) MeV have been studied with 28 to 60 MeV electrons at scattering angles from 105 to 165°. Matrix elements and transition radii have been deduced, using DWBA-calculations. The monopole excitations can be uniquely distinguished from electric quadrupole excitations by the angular dependence of the cross sections. Some results forE2- andE3-transitions in¹²C,²⁸Si,³²S and⁴⁰Ca are given, too.     

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.     

Two-particle,two-hole Jπ=0+ states in 40Ca

Excited J^π=0⁺ states in ⁴⁰Ca have been identified by the observation of L=0 angular distributions in the ³⁸Ar(τ, n) ⁴⁰Ca reaction. Strong transitions are observed to the ground state, the known 2p–2h at 9.38 (T=1) and 11.98 MeV (T=2), and to states at 8.28 and 10.65 MeV. The strongest excited-state transition is to the 8.28 MeV state, which we identify as the 2p–2h T=0 state. The J^π=0⁺ state at 7.30 MeV which has been suggested as the 2p–2h T=0 state is not observed.     

Observation of weakly coupled 2p-1h states in 41Ca from proton transfer on 40K

The proton transfer on ⁴⁰K has been studied with the ⁴⁰K(³He, d)⁴¹Ca reaction at 13 and 21 MeV bombarding energy and with the ⁴⁰K(d, n)⁴¹Ca reaction at 6.5 MeV bombarding energy. The energy and angular distribution of outgoing particles have been measured. For transitions to 62 levels in ⁴¹Ca the l-values and spectroscopic factors have been derived with DWBA. The excitation energies of levels populated with l = 3 and the qualitative distribution of transfer strength strongly suggest their interpretation as 2p-1h states of the f_{$\text{7}\text{2}$}²d_{$\text{3}\text{2}$}^?1 configuration with weak coupling between the particle pair and the hole. The high-spin states of this configuration (with J^π up to $\text{15}\text{2}{}^{\mathrm{+}}$) are preferentially excited.     

The ground stateM1 strength in40Ca

The M1 gamma decay strengths of the ground state transitions of the 1⁺,T=1 states of⁴⁰Ca at 9.86 MeV and 10.32 MeV have been measured using the reaction³⁹K(p,γ)⁴⁰Ca. The measured ground state gamma decay widths of these levels are 1.06±0.15 eV and 5.8±0.8 eV respectively. These relatively large M1 strengths can be explained by a shell model calculation incorporating excited core configurations.     

Study of electric monopole transitions between the ground state and the first excited 0+ state in 40, 42, 44, 48Ca with high resolution inelastic electron scattering

Monopole transitions from the 0₁⁺ ground states to 0₂⁺ excited states at 3.353 MeV (⁴⁰Ca), 1.837 MeV (⁴²Ca), 1.884 MeV (⁴⁴Ca) and 4.272 MeV (⁴⁸Ca) have been investigated with high resolution inelastic electron scattering (FWHM ≈ 30 keV) at low momentum transfer (0.29 ≦ q ≦ 0.53 fm^?1). The respective monopole matrix elements are 2.53 ± 0.41 fm², 5.24 ± 0.39 fm², 5.45 ± 0.41 fm² and 2.28 ± 0.49 fm². These results are used together with known ground state charge radii and the average number of holes in the sd shell in the ground state to estimate the number of particle-hole excitations in the wave functions of the excited 0⁺ states.     

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.     

A mean-field description of (γ, pi) cross sections at medium energies

Differential (γ, p_i) cross sections on ¹⁶O and ⁴⁰Ca have been calculated within a single-particle direct knock-out model, for photon energies between 40 and 400 MeV. It is shown that generating the bound and scattered states in a Skyrme Hartree-Fock (HF) mean-field, one can account for the global features of the data. Hereby, the role of the velocity-dependent part of the nucleon-nucleon interaction is emphasized.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

Nuclear levels in43Sc at low excitation energies

Properties of levels up to 3.5 MeV in⁴³Sc were studied using⁴⁰Ca (α, p)⁴³Sc and⁴⁰Ca(α, pγ)⁴³Sc reactions atE _α =12 MeV. Level energies, branching ratios, mean lifetimes, spins and mixing ratios were obtained for a number of levels. Relevant results are compared with many-particle shell-model predictions.     

Beiträge von direkten und Compoundprozessen zur Reaktion40Ca(d, α)38K beiE d =5–10 MeV

For the reaction⁴⁰Ca(d,α)³⁸K differential cross sections for the excitation of the low lying states in³⁸K have been measured at bombarding energies between 5 and 10 MeV. Total cross sections have been calculated using the statistical theory. It was found, that in the whole energy region the isotropic background of the angular distributions gives a good estimation of the compound contribution to the reaction cross section.     

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.     

The isoscalar strength distribution in 24, 26Mg, 28Si and 40Ca obtained from inelastic alpha scattering at 120 Mev

The inelastic α-scattering reaction at E_α = 120 MeV with an energy resolution of 90–150 keV has been used to investigate isoscalar strength distributions in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca. For ^{24, 26}Mg and ²⁸Si the E2 strength between E_x = 14 and 27 MeV is strongly fragmented. In ⁴⁰Ca the E2 strength is mainly concentrated near $\text{E}{}_{\mathrm{<mtext>x</mtext>}}\text{~ 65 A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ MeV, although here the onset of fragmentation can be observed. The sum rule strength for the different multipolarities was obtained by applying for each nucleus an L-dependent normalization procedure. In this way we observed in total in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca for excitation energies up to 27 MeV an amount of (61⁺⁸_?6), (50⁺⁹_?8), (38⁺⁸_?6) and (94 ± 14)%, respectively, of the isoscalar E2 energy weighted sum rule (EWSR) of which (36⁺⁷_?5), (28⁺⁸_?7), (24⁺⁷_?5) and (74 ± 12)% was found between E_x = 14 and 27 MeV. In addition isoscalar E0, E3 and E4 strength was observed in this excitation energy region. A detailed comparison has been made between the isoscalar quadrupole strength distribution observed in the ^{24, 26}Mg(α, α') reaction and the E2 strength excitation function obtained from radiative α-capture measurements. In the low excitation energy region coupled channel effects have been observed, especially for the excitation of the 3⁺ states. Moreover, a considerable percentage of the 1?ω isoscalar dipole and octupole strength has been observed for excitations below 14 MeV.     

Study of the <Superscript>12</Superscript>C (<Superscript>8</Superscript>B, <Superscript>7</Superscript>Be)<Emphasis Type="Italic">X</Emphasis> knockout reaction at intermediate energies

The breakup reactions of ⁸B on a ¹²C target at 142, 285, 790, and 936MeV/nucleon have been studied. One-proton-removal cross sections, leading to the production of ⁷Be fragments in the ground and first excited states (at 0.429MeV), and the longitudinal momentum distributions of the ⁷Be fragments are obtained in the Eikonal approximation of the Glauber Model. The results of the calculations including the contribution of the ⁷Be to the ground and first excited states of ⁸B are compared with the available experimental data. One-proton-removal cross section for the ¹²C(⁸B, ⁷Be)X knockout reaction at 142, 285, 790, and 936 MeV/nucleon energy has been calculated. ⁸B and ⁷Be cross sections and momentum distribution are in a good agreement with available data.     

Antiproton-nucleus scattering with self-consistent model for medium corrections

The antiproton-nucleon t-matrix with propagation in the nuclear medium is calculated selfconsistently and applied to the construction of optical potentials for the elastic scattering of antiprotons from nuclei. We find that this treatment gives results that are sensitive to medium corrections even though the strong absorption acts to mask these corrections partially. The agreement with scattering experiments at 46.8 MeV on ¹²C is very good. We compare potentials containing medium corrections to those based on free $\text{p}\text{N}$ amplitudes for ¹²C and ⁴⁰Ca. The local approximation to the optical potential is found attractive at low energies, becoming shallower with increasing bombardment energy in the range considered here (up to about E_L = 120 MeV).     

Lifetime measurements in70Se and72Se

Mean lives and limits of lifetimes have been determined for some ten mostly yrast states in⁷⁰Se, by means of the recoil distance Doppler shift technique. The states were excited in the reaction⁴⁰Ca(³⁶Ar,α2p) at 115 MeV resp. the reaction⁵⁸Ni(¹⁴N,pn) at 39 MeV beam energy. The systematic decrease ofB(E2) values along the the ground band transitions indicates a band crossing consistent with theγ-ray energies. Effects of continuum feeding times in both reactions are being discussed. The lifetimes of the lowest three yrast transitions in⁷²Se have been remeasured by means of the reactions⁴⁰Ca(³⁶Ar,4p) and⁶⁰Ni(¹⁴N,pn).     

The decay of isoscalar giant resonances in 24Mg and 40Ca

In this paper we present data on the charged-particle decay of the isoscalar 2⁺ strength between 10 and 20 MeV excitation energy (E_x) in ²⁴Mg and ⁴⁰Ca. The isoscalar strength was excited by inelastic scattering of 120MeV α-particles at 14° and 12.5° for ²⁴Mg and ⁴⁰Ca, respectively. The charged particles originating from the decay were detected in coincidence with the α′ particles at several angles in the scattering plane. J^π assignments of the decaying states were made on the basis of the angular correlation pattern of the α₀ decay to the ground state of ²⁰Ne and ³⁶Ar, respectively, using a DWBA calculation for the m-state population of the decaying state.For ⁴⁰Ca, about 40% of the E2 EWSR is found to be located in the interval E_x = 13.5 ± 1.5 MeV, which is similar to what has been found from previous inelastic scattering experiments at E_x = 18 ± 2 MeV, but much more than such experiments located in the region E_x = 12–15 MeV. The difference for the region E_x < 16 MeV is due to the fact that from our α₀ angular correlation pattern we conclude that virtually no continuum is excited in the (α, α′) process up to E_x = 16 MeV while all previous inelastic hadron scattering experiments assumed such a continuum to be present. The E2 strength distribution for ⁴⁰Ca thus obtained is very different from what previous theoretical calculations predict. For ²⁴Mg about 30% of the E2 EWSR is present in the interval 12.5 ? E_x ? experiments. 16.5 MeV which again is about twice as much as deduced from previous inelastic scattering The observed branching ratios are compared with calculated ones assuming statistical decay. Reasonable agreement was obtained for ⁴⁰Ca, but for ²⁴Mg especially the α₀-decay branch and to a lesser extent also the p₁ one are much stronger than the statistical calculations predict, indicating that especially the α₀ decay occurs mainly in a non-statistical way.A similar conclusion can be drawn from the behaviour of the forward-backward asymmetry in the angular correlations of the decay particles as a function of the excitation energy FBA(E_x). For ⁴⁰Ca, FBA(E_x) for all decay channels increases smoothly on the average once E_x is above a well-defined threshold, which is due to the onset of knock-out processes. For ²⁴Mg, however, the FBA(E_x) for the α₀ shows a large fluctuation as a function of E_x, indicating an interference process between semi-direct decay and knock-out processes.