Proton polarization observables for the elastic and inelastic scattering of 500 MeV protons from Ca and Pb

Measurements for the elastic and inelastic scattering of 500 MeV protons from ⁴⁰Ca and ²⁰⁸Pb at small momentum transfers are reported. The induced proton polarization P and the spin rotation parameter Q were measured for the elastic scattering. The spin rotation parameters D_SS′, D_SL′, D_LL′, d_LS′ and the induced polarization P were measured for transitions to the 3⁻(3.37 MeV) and 5⁻(4.48 MeV) states in ⁴⁰Ca and the 3⁻(2.61 MeV) state in ²⁰⁸Pb. Comparisons of the data with the theoretical calculations were carried out in the framework of nonrelativistic and relativistic approaches. We extracted the spin-up and spin-down channels for the elastic scattering cross sections and found that predictions of the relativistic and nonrelativistic approaches agree well with the spin-up channel data and differ considerably in the spin-down channel.     

Proton pick-up from Mo

The reaction ⁹²Mo(t, α)⁹¹Nb has been carried out at a triton bombarding energy of 12 MeV. Angular distributions of the emitted α-particles were obtained and compared with DWBA predictions. Relative spectroscopic factors were obtained for six low-lying states and are discussed with reference to shell-model calculations.     

Proton and neutron occupation numbers forfp-shell nuclei

Spectroscopic factors for single-particle transfer are calculated from many-particle shell-model wave functions for 23 different transfer reactions onfp-shell nuclei. A comparison of the present theory with the available experimental data is very successful. Subshell occupation numbers of target ground states are studied in detail. Some systematic deficiencies for low seniority shell-model wave functions are revealed. In several cases the experimental information appears to be rather incomplete.     

Proton induced resonances on 21Ne

Excitation curves for the ${}^{21}\text{Ne}\text{(}\text{p}\text{, γ)}{}^{22}\text{Na}\text{,}{}^{21}\text{Ne}\text{(}\text{p, p}\text{′γ)}{}^{21}\text{Ne and}{}^{21}\text{Ne}\text{(}\text{p, p}\text{)}{}^{21}\text{Ne}$ reactions have been obtained for E_p = 0.4–1.6 MeV. Neon gas enriched to 92 % in ²¹Ne was recirculated in a differentially pumped gas target system. The fifteen previously reported (p, γ) resonances were established and nineteen new (p, γ) resonances found. Anomalies in the elastic scattering yield were observed for fourteen resonances. The reported state at E_x = 7278 ± 7 keV in ²²Na was resolved into a doublet separated by 1 keV. All unbound states in ²²Na, observed previously in other reactions, have been confirmed as resonance states in the energy range covered, with the exception of the E_x = 7942 ± 7 keV state. The new E_p = 663, 694, 1235, 1432 and 1543 keV resonances correspond to new unbound states in ²²Na. Excitation energies, γ-ray decay schemes, resonance widths and strengths as well as limits on J^π assignments are reported for all the resonances. From the Coulomb excitation of the E_x = 350 keV, first excited state in ²¹Ne a value of B(E2) = 0.014 ± 0.002 e² · b² is deduced. The astrophysical as well as the nuclear structure implications of the present results are discussed.     

Proton stripping to 14N

The ¹³C(³He, d) reaction at a beam energy of 43.6 MeV was used to examine levels of ¹⁴N up to 11.7 MeV over an angular region including the main stripping peaks. Many spectroscopic factors were determined reliably for known states and found to be mostly in good agreement with calculations for the stronger levels. Several new spin or parity assignments are made at high excitation.     

Proton orbit sizes of the isotopes of tin

Root-mean square radii of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ in the isotopes of tin with A = 112, 116, 118, 120 and 124 have been determined from a DWBA analysis of crosssection data from the sub-Coulomb (t, α) reaction. The differential cross sections for the (t, α) reaction were measured at lab angles in the range from 60° to 160° for triton energies in the range from 4.75 MeV to 5.25 MeV. Spectroscopic factors of the populated states were obtained from a sum rule analysis of published proton stripping and pickup reactions on the isotopes of tin. The measured orbit sizes are compared with the results of Hartree-Fock calculations and the systematic features of the asymptotic proton wave functions are discussed.     

Proton capture by 15N at stellar energies

Excitation functions of the ¹⁵N(p, γ)¹⁶O proton capture reaction have been obtained at θ_γ = 45° and E_p = 150–2500 keV. Below E_p = 400 keV, the reaction is dominated by capture into the ground state of ¹⁶O. The observed excitation function for the latter process can be explained if, in addition to the two well-known J^π = 1^? resonances at E_p = 338 and 1028 keV, a direct radiative capture process (DC → 0) is included in the analysis. The direct capture component in the capture reaction is enhanced through interference effects on the tails of the two resonances. From the observed direct capture cross section, a single-particle spectroscopic factor of C²S(1p) = 1.8 ± 0.4 has been deduced for the ground state in ¹⁶O. The extrapolated astrophysical S-factor of S(0) = 64 ± 6 keV · b for the ¹⁵N(p, γ₀)¹⁶O reaction is a factor of 2.5 larger than previously reported. This result amplifies the role of the oxygen side cycle in the CNO hydrogen burning process.The observed excitation function of the ¹⁵N(p, α₁γ₁)¹²C reaction at E_p = 150 – 2500 keV shows that this reaction makes a negligible contribution to hydrogen burning at stellar energies [S(0) ≈ 0.1 keV · b] compared to ${}^{15}\text{N}\text{(}\text{p}\text{, γ}{}_0\text{)}{}^{16}\text{O and}{}^{15}\text{N}\text{(}\text{p}\text{, α}{}_{\mathrm{<mtext>o</mtext>}}\text{)}{}^{12}\text{C}$.     

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.     

Proton resonant and direct capture on 28Si

Excitation functions for the ²⁸Si(p, γ)²⁹P capture reaction have been measured in the proton energy range E_p = 1.3–2.3 mMeV. The analysis of the data reveals the presence of the direct capture process to the ground state and first excited state of ²⁹P. The strengths of the resonances at E_p = 1.65, 2.09 and 2.88 MeV and the spectroscopic factors of the ground state and first excited state in ²⁹P are deduced.     

The 42Ca photoneutron cross section

The reaction ⁴²Ca(γ, n_t)⁴¹Ca has been measured from 10.5 MeV to 28 MeV using an enriched metal target and the yield curve technique. The resultant cross section shows gross structure which is shown to be consistent with predictions of isospin splitting of the giant dipole resonance.     

Proton capture by 11B above the giant resonance

The cross sections for proton capture by ¹¹B to the ground and excited states of ¹²C have been measured in the proton energy interval between 18 and 43 MeV. The ground-state cross section shows good agreement with theoretical calculations including correlations. Capture photons have also been observed to all the residual 1p-1h states of ¹²C having a dominant $\text{1}\text{p}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole: the corresponding cross sections systematically show a giant resonance whose energy increases with the increasing excitation energy of the “background” level. The resonances at 27.4, 31, 33.2, 37 and 43 MeV, seem to show observable interference effects.     

Resonant neutron capture in 40Ca

The neutron capture cross section of ⁴⁰Ca has been measured with ≈ 0.2 % energy resolution below E_n = 300 keV. Resonance parameters have been extracted for many new p- and d-wave resonances. Gamma-ray spectra were also measured following capture in one doublet and two resolved resonances below 50 keV. Strong feeding of low-lying p-wave levels was observed in all cases. Calculations showed that valence transitions were inadequate to account for the observed dominance of these transitions and a further mechanism is required. The average resonance parameters obtained from the data are as follows: 〈D〉 = 37 + 4keV, 10⁴S₁ = 0.16 ± 0.05, 10⁴S₂ = 2.0 ± 0.7. The average radiative widths and standard deviations of their distributions were found to be strongly l-dependent as follows: 〈Γ_γ〉_s = 1.5 ± 0.9 eV, 〈Γ_γ〉_p = 0.36 ± 0.09 eV and 〈Γ_γ〉_d = 0.7 ± 0.4 eV.     

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.     

A study of the Ca(d, p)Ca reaction (I). The single-particle states

The reaction ⁴⁰Ca(d, p)⁴¹Ca has been studied with a resolution 30 keV. Excitation functions for the first three strong states have been measured in the energy interval 9.80 to 12.12 MeV. Cross section fluctuations are found to be entirely within statistics, i.e. < 5 %, and it is concluded that σ_CN(θ)/(2J_f+1) < 5 μb/sr. Differential cross sections have been measured for elastic scattering, and the (d, p) transitions to the ground state and the strong single-particle states at E^* = 1.949, 2.471, 3.623 and 3.954 MeV at E_d = 12.00 MeV and, over a limited angular range, at E_d = 11.00 MeV. The angular distributions have been analysed by the DWBA method and spectroscopic factors have been determined. It is suggested that the 3.623 MeV state may be the third state predicted by Gerace and Green rather than as assigned by earlier studies.     

Cross sections and thermonuclear reaction rates for 42Ca(p, γ)43Sc, 44Ca(p, γ) 45Sc, 44Ca(p,n) 44Sc and 45Sc(p,n)45Ti

The yield of γ-rays from the reaction ⁴²Ca(p, γ)⁴³Sc has been measured as a function of bombarding energy over the range 0.63–3.01 MeV, from ⁴⁴Ca(p, γ)⁴⁵Sc over the range 0.775–4.00 MeV, from ⁴²Ca(p, p'γ)⁴²Ca over the range 2.24–3.01 MeV, and from ⁴⁴Ca(p, p'γ)⁴⁴Ca over the range 1.90–5.03 MeV. The cross section of the reaction ⁴⁴Ca(p, n)⁴⁴Sc has been measured from threshold to a bombarding energy of 5.05 MeV by observation of the 1157 keV γ-ray associated with the residual ⁴⁴Sc activity, and the cross section of the reaction ⁴⁵Sc(p, n)⁴⁵Ti has been measured from threshold to a bombarding energy of 4.00 MeV both by observation of the annihilation radiation associated with the residual ⁴⁵Ti activity and by measurement of the total neutron yield with a wide-angle BF₃ tube and paraffin detector. All these data are compared with statisticalmodel calculations and satisfactory agreement is achieved. Thermonuclear reaction rates for the (p, γ) and (p, n) reactions are calculated for the temperature range 5 × 10⁸-10¹⁰K and the significance of these results for explosive nucleosynthesis in stars is discussed.     

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.     

Proton polarization and differential cross section for the (3He,p) reaction on 6Li and 9Be at 14 MeV

Angular distributions of the proton polarization and the differential cross section have been measured for the reaction (³He, p) initiated by 14 MeV incident ³He particles and proceeding to the ground and the first excited states of the final nuclei ⁸Be and ¹¹B. Large polarization values were observed, especially for the ⁹Be(³He, p)¹¹B reaction leading to both the ground and the first excited states in ¹¹B. The experimental results have been analysed in terms of a two-nucleon transfer spindependent distorted-waves theory using finite-range formalism and including corrections due to the non-locality of the optical potentials. A proper coherent summation over L and S, whenever necessary was included in the DWBA calculations of the polarization and the differential cross section as implied by the presence of the spin-orbit terms in the optical-model potentials used to generate the distorted waves.     

Anomalous 3He scattering in the Ca region

Elastic ³He scattering on ⁴⁰Ar, ³⁹K, ⁴¹K, ⁴⁰Ca and ⁴²Ca was investigated at $\text{E(}{}^3\text{He) = 28}\text{MeV}$. A comparison of the scattering on neighbouring nuclei shows differences in backward angle cross sections up to one order of magnitude. This variation is clearly outside the domain of the standard optical model. This anomalous backward angle scattering is discussed in connection with similar anomalies observed in elastic α-particle scattering.     

Proton spectroscopy of 96Tc from the (3He,d) reaction

Energy levels of the even-mass odd nucleus ⁹⁶Tc have been populated with the ⁹⁵Mo(³He, d)⁹⁶Tc reaction at a bombarding energy of 33.6 MeV and with 28 keV resolution (FWHM). Thirty levels were observed below 2.10 MeV excitation. Comparison of experimental angular distributions with DWBA calculations allowed l-value assignments and the extraction of spectroscopic factors for most levels. Over eighty-five percent of the observed spectroscopic strength is located in the lowlying $\text{π1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{-}\text{v}\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ configuration multiplet. A simple residual interaction shell model calculation reproduces the observed low-lying positive parity multiplet relatively well although the experimental spectrum indicates much configuration mixing is present.