Alpha capture to the giant dipole resonances of 42Ca, 44Ca and 52Cr

Differential cross sections for the ${}^{38}\text{Ar}\text{(α, γ}{}_0\text{)}{}^{42}\text{Ca}\text{,}{}^{40}\text{Ar}\text{(α, γ}{}_{\mathrm{0,\; 1}}\text{)}{}^{44}\text{Ca and}{}^{48}\text{Ti}\text{(α, γ}{}_{\mathrm{0,\; 1}}\text{)}{}^{52}\text{Cr}$ reactions were measured at 90° to the beam direction in 50 or 100 keV steps over the bombarding energy ranges 6.0–15.0 MeV, 5.5–11.1 MeV and 6.0–12.0 MeV respectively. Gamma-ray angular distributions were measured at forty bombarding energies. These show that the (α, γ₀) reaction proceeds through 1^? levels and to a lesser extent 2⁺ levels, whereas the (α, γ₁) reaction most probably proceeds through 1^? and 3^? levels. It is deduced that 〈Γ〉/〈D〉 ≦ 1 for the ⁴⁰Ar(α, γ)⁴⁴Ca. reaction whereas the fine structure observed in the ⁴⁸Ti(α, γ)⁵²Cr reaction is probably due to fluctuations. From a comparison with other data it is shown that the (α, γ) reaction is most probably statistical in nature. Using Hauser-Feshbach theory it is deduced that the ³⁶Ar(α, γ)⁴⁰Ca. reaction is inhibited by isospin selection rules and an estimate is made of isospin mixing in the ⁴⁰Ca giant dipole resonance. The ${}^{38}\text{Ar}\text{(α, γ)}{}^2{}^{42}\text{Ca and}{}^{40}\text{Ar}\text{(α, γ)}{}^{44}\text{Ca}$ data are considered with respect to theories of isosopin splitting of the giant dipole resonance.     

Spectroscopy of 42Ca from 41Ca(d,p)

Energy levels in ⁴²Ca up to 7.8 MeV have been studied in the neutron capture reaction ⁴¹Ca(d, p)⁴²Ca with 12 MeV bombarding energy. Ninety-four excited states have been identified and angular distributions have been measured in the interval from 5° to 110° by means of a broad-range magnetic spectrograph. The angular distributions together with DW calculations have been used to determine I_n values and spectroscopic factors. The $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ strength sum agrees with shell-model expectations if the f_{$\text{7}\text{2}$} spectroscopic factors are renormalized by $\text{1}\text{0.75}$, in line with other $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$. transfer experiments on ⁴⁰Ca and ⁴¹Ca. A similar renormalization of the l_n = 1 spectroscopic factors brings this strength sum in accordance with the shell-model calculations. The effective ($\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^2$) matrix elements for ⁴²Ca are compared with the corresponding matrix elements of ⁴²Sc and ⁴⁸Sc. The differences between the three sets of matrix elements are of the order of a few hundred keV or less. The monopole centroid energy of the ($\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^2$ multiplet is shifted downwards in the mass-42 nuclei compared to ⁴⁸Sc, possibly indicating the importance of the monopole pairing force near ⁴⁰Ca.     

High-spin states of 39K and 42Ca

High-spin states of ³⁹K and ⁴²Ca have been investigated with the ²⁸Si(¹⁶O, αpγ)³⁹K and ²⁸Si(¹⁶O, 2pγ)⁴²Ca reactions at a beam energy of 45 MeV. Gamma-gamma coincidence, γ-ray angular distribution and linear polarization measurements were performed with a Ge(Li)-NaI(Tl) Compton suppression spectrometer and a three-crystal Ge(Li) Compton polarimeter. High-spin states of ³⁹K at E_x = 7.14,7.78and8.03 and of ⁴²Ca at E_x = 7.75MeV are established. Unambiguous spin-parity assignments of $\text{J}{}^{\mathrm{\pi }}\text{=}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{13}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{+}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{,}\text{17}\text{2}{}^{\mathrm{+}}\text{and}\text{19}\text{2}{}^{\mathrm{?}}$ to the ³⁹K levels at E_x = 5.35, 5.72, 6.48, 7.14, 7.78 and 8.03 MeV and of 6^?, 7^?, 8^?, 9^? and(8, 10)^? to the ⁴²Ca levels at E_x = 5.49, 6.15, 6.41, 6.55 and 7.37 MeV, respectively, have been obtained. Further spin-parity restrictions, lifetime limits, excitation energies, branching ratios and multipole mixing ratios are reported. Discrepancies with previous J^π assignments are discussed in detail.     

Wave functions of 0+ states in 42Ca

Ratios of cross sections in ⁴¹Ca(d,p) and ³⁸Ar(⁶Li,d) leading to 0⁺ states of ⁴²Ca allow determination of the coefficients in wave functions of the type a(2p)+b(4p?2h) + c(6p?4h), and an independent evaluation of the intrinsic amplitude for (sd)²(fp)² and (fp)⁴ α transfer.     

Direct transfer and two-step processes in the 42Ca(α, 3He)43Ca reaction

The ⁴²Ca(α, ³He)⁴³Ca reaction has been studied at 36 MeV incident energy. Angular distributions have been measured from 4° to 42° using a split-pole spectrometer and position sensitive Si detectors, for about 40 levels located up to 6 MeV excitation energy. A local zero-range DWBA analysis has been carried out; l = 3 and 4 assignments are tentatively proposed for levels located above 4 MeV excitation energy, indicating a strong fragmentation of the $\text{1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength between 4 and 6 MeV and the location of the main component of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ strength above 6 MeV. A number of weakly excited levels cannot be reproduced by DWBA analysis. Their angular distributions have been compared with the results of coupled-reaction-channel calculations assuming two-step excitation of weak coupling states with a [⁴²Ca¹ ? $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ structure. A reasonable agreement has been obtained, confirming that the two-step process cannot be neglected in the analysis of the (α, ³he) reaction.     

High resolution proton scattering from 42Ca

Differential cross sections were measured for ⁴²Ca(p, p) at four angles between E_p = 1.2 and 3.0 MeV, with an overall energy resolution of 325 eV. Spins, parities and proton widths were extracted for 170 resonances. Two analogue states were identified and spectroscopic factors determined. The nearest neighbor spacing distributions were analyzed. Proton strength functions were determined for $\text{1}\text{2}$⁺, $\text{1}\text{2}$^? and $\text{3}\text{2}$^? resonances.     

The mean life of the second 0+ state in 42Ca

The mean life of the second excited state in ⁴²Ca (1.84 MeV, O⁺) was measured by a direct electronic timing technique to be 558 ± 8 ps. This result compares with a previous measurement of 480 ± 30 ps which yields a high B(E2) value. The present result gives a B(E2; 0₂⁺ 1.84 MeV → 2₁⁺ 1.52 MeV) value of 484 e² · fm⁴ or 55 single-particle units; the theoretical implications of this are discussed.The accurate mean life was extracted using a convoluted function to describe both the inherent time resolution of the experimental system and the exponential decay of the state of interest.     

On the predictions of the coexistence model for the reaction 42Ca(p,t)40Ca

The coexistence model as formulated by Gerace and Green for ⁴⁰Ca has been shown to predict cross sections for the reaction ⁴²Ca(p,t)⁴⁰Ca in strong disagreement with experiment. In the present letter we demonstrate how a much improved agreement can be obtained by introducing additional kinds of basis states. Especially important are triaxially deformed components, which contain admixtures of the $\text{1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states.     

Second backbending in the yrast line of 156Er

High spin yrast states of ¹⁵⁶Er were investigated using the reactions ¹⁴¹Pr(¹⁹F,4nγ) and ¹²³Sb(³⁷Cl, 4nγ), the latter in connection with a sum-crystal. In addition to the backbending at $\text{I = 12}\text{h}\text{?}$, a second one is found at $\text{I = 26}\text{h}\text{?}\text{;}$ and the yrast band is extended up to $\text{I = 32}\text{h}\text{?}\text{;}$. These results are interpreted in terms of a Hartree-Fock-Bogolyubov Cranking (HFBC) method. It is demonstrated that for deformations in the vicinity of the Strutinsky equilibrium deformation, both a 2qp proton band crossing the yrast band or a 4qp neutron band crossing the yrast band can cause strong secondary backbending.     

40Ca+58Fe,58Ni反应中的径向膨胀流研究

利用同位旋相关的Boltzmann-Langevin方程研究了⁴⁰Ca+⁵⁸Fe和⁴⁰Ca+⁵⁸Ni两个反应系统在53,100,150和200MeV/u入射能量下对心碰撞的径向膨胀流.发现对于丰中子系统⁴⁰Ca+⁵⁸Fe的径向膨胀流系统性地小于稳定系统⁴⁰Ca+⁵⁸Ni的径向膨胀流.在假定轰击能量与反应体系的压缩密度呈抛物线关系时,能够解释入射能量和径向膨胀流之间呈现的直线关系.提取了出现径向膨胀流的轰击能量阈值,发现对丰中子系统⁴⁰Ca+⁵⁸Fe得到的能量阈值小于稳定系统⁴⁰Ca+⁵⁸Ni所得到的能量阈值.     

Two-step processes in the 40Ca(α, 3He)41Ca reaction

The ⁴⁰Ca(α, ³He) reaction has been studied at 36 MeV incident energy. About fifty levels have been observed up to 7.1 MeV excitation energy and angular distributions were measured from 6–60° using a split-pole spectrometer. A local zero-range DWBA analysis has been carried out, and the deduced l-assignments and spectroscopic factors are compared with those obtained from previous neutron stripping experiments. Core-excited states in ⁴¹Ca with a [3^? ? f_7,2], [2⁺ ? f_7,2] and [5^? ? f_7,2] component previously observed in inelastic scattering experiments, are selectively excited by the (α, ³He) reaction. Their angular distributions are compared with coupled-reaction-channel calculations, assuming a pure two-step reaction mechanism. The agreement between theory and experiment may be considered as rather satisfactory for a number of levels. In particular the $\text{1}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}$ levels and the high-spin states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{+}}\text{,}\text{15}\text{2}{}^{\mathrm{+}}\text{and}\text{17}\text{2}{}^{\mathrm{+}}$ are successfully described within the framework of the weak-coupling model.     

Estimate of the branching to the excited 0+ state in42Ca in the β+-decay of 42Sc

The β⁺-branch of the decay of the ⁴²Sc 0⁺ ground state to the 1.836 MeV 0⁺ state in ⁴²Ca is estimated in a 1435 1098 simple Coulomb mixing model, which relates this branch to Coulomb displacement energies in 0⁺ isotriplets and off-diagonal Coulomb matrix elements. The estimates obtained are very small, ≈ 10^?4, which is consistent with current experimental data.     

Investigation of high-spin states in 47Ca through double-step processes in the 48Ca(τ, α)47Ca reaction

In the ⁴⁸Ca (τ,α)⁴⁷Ca reaction at 25 MeV, some angular distributions are well reproduced by CCBA calculations, assumping double-step excitation of $\text{[}{}^{48}\text{Ca}{}^1\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{]}$ states. Unambigous J^π assignments are extracted from the analysis.     

Giant resonances in the fused system induced by 40Ca + 40Ca reactios

The giant quadrupole resonance of the fused system obtained in a ⁴⁰Ca + ⁴⁰Ca reaction is investigated in the framework of the TDHF approximation. A large splitting of the resonance due to the deformation of the composite system is observed. These results are confirmed by a direct fluid-dynamical calculation of the resonance. An estimation of the energy stored in the resonance is also presented.     

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.     

Atomic antiproton states in 16O, 18O, 32S, 40Ca, 44Ca and 122Sn

Atomic levels for the systems p? plus ¹⁶O, ¹⁸O, ³²S, ⁴⁰Ca, ⁴⁴Ca and ¹²²Sn are calculated in optical potentials based on the N?N interaction of Dover and Richard.     

Particle-hole multiplets in 40Ca observed in the 41Ca(τ, α) reaction

Energy levels in ⁴⁰Ca up to 10.2 MeV have been studied in the neutron pickup reaction ⁴¹Ca(τ, α)⁴⁰Ca with 20 MeV bombarding energy. Thirty excited states have been identified and angular distributions have been measured in the interval from 5° to 40° by means of a split-pole magnetic spectrometer. The angular distributions together with DW calculations have been used to extract l_n values and spectroscopic factors. The l_n = 2 strength distribution for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole levels is compared to the l_p = 3 strength distribution from pr stripping data.     

Analogue states in 47Ca

The ⁴⁸Ca(³He, ⁴He)⁴⁷Ca and ⁴⁸Ca(p, d)⁴⁷Ca reactions were used to observe six levels in ⁴⁷Ca above 12 MeV excitation. Analysis of the data has yielded precise excitation energies for the lowest $\text{T =}\text{9}\text{2}$ levels in ⁴⁷Ca; which are analogs of low-lying levels in ⁴⁷K. Comparison of experimental and calculated Coulomb displacement energies for the K-Ca isotopes is made.     

Spin-parity assignments to high-spin states of 41K and 41Ca

Yrast states of ⁴¹K and ⁴¹Ca have been investigated with the ²⁶Mg(¹⁸O, p2nγ)⁴¹K and ²⁶Mg(¹⁸O, 3nγ)⁴¹Ca reactions at a beam energy of 34 MeV. Gamma-gamma coincidence, γ-ray angular distribution and linear polarization measurements were performed with a Ge(Li)-NaI(Tl) Compton suppression spectrometer and a three-crystal Ge(Li) Compton polarimeter. Unambiguous spin-parity assignments of $\text{J}{}^{\mathrm{\pi }}\text{=}\text{7}\text{2}{}^{\mathrm{+}}$, $\text{11}\text{2}{}^{\mathrm{+}}$, $\text{11}\text{2}{}^{\mathrm{?}}$, $\text{13}\text{2}{}^{\mathrm{+}}$, $\text{15}\text{2}{}^{\mathrm{?}}$ and $\text{19}\text{2}{}^{\mathrm{?}}$ to the ⁴¹K levels at E_x = 1.68, 2.53, 2.76, 2.77, 4.27 and 4.98 MeV and of $\text{9}\text{2}{}^{\mathrm{+}}\text{,}\text{11}\text{2}{}^{\mathrm{+}}\text{and}\text{15}\text{2}{}^{\mathrm{+}}$to the ⁴¹Ca levels at E_x = 3.20, 3.37 and 3.83 MeV, respectively, have been obtained. Excitation energies, branching ratios, multipole mixing ratios and transition strengths are reported. The main features of the ⁴¹K and ⁴¹Ca level and decay schemes are reproduced in a 2p-1h and 3p-2h shell-model calculation.     

Study of low-lying levels in 47Ca with the 48Ca(d, t)47Ca reaction

Angular distributions of cross sections [α(θ)] and vector analyzing powers [iT₁₁(γ)] have been measured for seven low-lying states or groups of states excited by the ⁴⁸Ca($\text{d}$, t)⁴⁷Ca reaction with 13.5 MeV deuterons and analyzed by the DWBA. On the basis of comparison of vector analyzing powers with DWBA calculations, spin-parity assignments have been made or confirmed for several states. Spectroscopic factors have been extracted. Angular distributions for weak states at 3.30 and 3.57 MeV excitation in ⁴⁷Ca could not be reproduced by DWBA calculations. Investigations of compound nucleus and multi-step contributions to the cross sections and analyzing powers for these states have been made by means of Hauser-Feshbach and CCBA calculations. Optical model parameters were obtained from analysis of 13.5 MeV deuteron elastic scattering cross sections and analyzing powers.