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.     

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.     

12C(7Li,t)16O and stellar helium fusion

The reaction ¹²C(⁷Li, t)¹⁶O has been studied at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$ with the LASL tandem accelerator and QDDD magnetic spectrometer. Angular distributions to levels with E_x < 11 MeV have been obtained from 0° to 90°, including 0°. The results have been analyzed with finite-range distorted-wave Born approximation theory. The α-particle spectroscopic factors and reduced widths obtained are compared with those calculated with group theory (SU(3)) and other models. The analysis of data for the 7.1 and 9.6 MeV J^π = 1^? levels, which are of great importance in stellar helium buring, yields a ratio, R, of dimensionless reduced α-widths $\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(7.1}\text{MeV}\text{)}\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(9.6}\text{MeV}\text{)}\text{= 0.35b ± 0.13}$. The observed line width of the 9.6 MeV level (Γ_c.m. = 390 ± 60 keV) is less than the accepted value (Γ_c.m. = 510 ± 60 keV) and implies θ²_a(9.6 MeV) ≈ 0.6. These results as well as data for the 6.92 MeV J^π = 2⁺ and 10.35 MeV J^π = 4⁺ “α-cluster” states indicate 0.09 < θ²_a(7.1 MeV) < 0.33 with a mean value θ²_a(7.1 MeV) = 0.14 ± 0.04. The implication for stellar helium burning is discussed.     

Spin assignments from the 142Nd(7Li, 6He)143Pm and 144Sm(7Li, 6He)145Eu reactions at 52 MeV

Angular distributions have been measured for transitions to low-lying states in ¹⁴³Pm and ¹⁴⁵Eu populated by the ¹⁴²Nd(⁷Li, ⁶He)¹⁴³ and the ¹⁴⁴Sm(⁷Li, ⁶He)¹⁴⁵Eu reactions at $\text{E(}{}^7\text{Li}\text{) = 52}$ MeV. Elastic scattering of ⁷Li at 52 MeV on ¹⁴²Nd and ¹⁴⁴Sm, and ⁶Li at 46 MeV on ¹⁴²Nd and at 45 MeV on ¹⁴⁴Sm, were measured. Optical-model parameters extracted from fits to the scattering data were used in a finite-range DWBA analysis of the angular distributions for levels below 1.40 MeV excitation energy in ¹⁴³Pm and 1.84 MeV in ¹⁴⁵Eu. The reaction cross sections forward of 6° c.m. allow unambiguous distinction to be made between 2d_{$\text{5}\text{2}$} and 2d_{$\text{3}\text{2}$} final states. Final-state spins have been assigned to d-states in ¹⁴³Pm at 1.40 MeV($\text{3}\text{2}$⁺)and in ¹⁴⁵Eu at 1.042 MeV ($\text{3}\text{2}$⁺). Existing assignments to other levels in both residual nuclei have been confirmed.     

Investigation of the level schemes of 73,75,77As via the (3He,d) reaction

The reactions ^{72, 74, 76}Ge(³He, d) were investigated at E_lab = 23 MeV with a multigap and a Q3D magnetic spectrograph. Some 30 new levels up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ have been found. The level schemes of the odd As isotopes ^{73, 75, 77}As up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ seem to be rather independent of the neutron number. The good agreement of the low-lying level structure with the Coriolis-coupling model including a pairing force was verified and the vacancies of low-lying shell model states were extracted and compared with the simple pairing theory.     

Spin and parity assignments for 23Na levels from the 19F(α, p)22Ne reaction

Resonances were found in the 120° and 160° excitation functions for the ¹⁹F(α, p_o)²²Ne reaction between E = 2.5 and 5.0 MeV corresponding to ²³Na levels at excitation energies between 12.56 and 14.51 MeV. Twenty-one on-resonance angular distributions were analysed with single-level and two-level theory to extract ²³Na spin and parity information. The results of an earlier experiment were analysed by the same procedure, extending the diagnostics down to a ²³Na excitation energy of 11.55 MeV. The analysis incorporated an optical potential for the α-particle consistent with previous channel-spin-$\text{1}\text{2}$ reaction studies and α-induced reaction data.     

New highly excited 4He levels found by the 2H(d,p)3H reaction

The differential cross section, the vector- and the tensor-analyzing powers of the reaction ²H($\text{d}$, p)³H have been measured. The polarization data were obtained at 11 energies between 1.0 and 13 MeV at lab angles between 5° and 160°. The data were fitted with Legendre polynomials and the resulting coefficients analyzed for resonances in ⁴He. Overwhelming evidence for a 1^? level at 24.1 MeV and a strong indication of a 4⁺ level at 24.6 MeV excitation energy have been found.     

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 polarization of 3He elastically scattered from 27Al and 28Si at 21 MeV

The polarization of 21 MeV ³He elastically scattered from ²⁷Al and ²⁸Si has been measured in an angular range of θ_lab = 25°–55°. Differential cross-section data have been obtained out to angles of approximately 100°. The small values observed in the polarization distributions differ somewhat from optical-model predictions based on fits to the differential cross-section data and cannot be used to obtain significant information about the optical-model spin-orbit potential. It is concluded that statistically significant, non-zero ³He polarization measurements will not be possible using traditional double scattering techniques for ³He energies ≦ 27 MeV and targets of $\text{Z ≧ 13}$.     

Proton scattering from 9Be between 6 and 30 MeV and the structure of 9Be

Differential cross-section excitation functions at lab scattering angles 86.9°, 120.0°, 140.0° and 160.0° were measured for ⁹Be(p, p_o)⁹Be, ⁹Be(p, p₂)⁹Be and ⁹Be(p, d₀)⁸Be at proton lab energies from 6 to 15 MeV in 100 keV steps. A broad anomaly was observed in the ⁹Be(p, p₀)⁹Be excitation functions. Differential cross-section angular distributions were measured for ⁹Be(p, p₀)⁹Be and ⁹Be(p, p₂)⁹Be at lab energies of 13.0, 14.0, 15.0, 21.35 and 30.3 MeV and for ⁹Be(p, d₀)⁸Be at 13.0, 14.0, 15.0 and 21.35 MeV. Angular distributions of polarization analysing powers for ⁹Be($\text{p}$,p₀)⁹Be, ⁹Be(p, p₂)⁹Be and ⁹Be($\text{p}$, d₀)⁸Be were measured at 8.0, 11.0, 12.0, 13.0 and 15.0 MeV. A spherical optical-model (SOM) analysis of the elastic scattering angular distribution data from 13.0 to 30.3 MeV showed that an energy dependence of only V_R and W_s (volume real and surface imaginary depths) is sufficient to reproduce the measurements. Coupled-channels (CC) analyses were made with a quadrupole-deformed optical-model potential and strong coupling of $\text{3}\text{2}{}^{\mathrm{?}}$, $\text{5}\text{2}{}^{\mathrm{?}}$ and $\text{7}\text{2}{}^{\mathrm{?}}$ levels of a $\text{K =}\text{3}\text{2}$ ground-state rotational band of ⁹Be. The ⁹Be(p, p₀)⁹Be and ⁹Be(p, p₂)⁹Be data from 13.0 to 30.3 MeV were analyzed simultaneously at each energy, varying only V_R and W_s with energy, for a potential deformation of β = 1.1. Both SOM and CC analyses indicated the same energy dependence in V_R, while W_s averaged 3.5 MeV lower in CC than in SOM, with both energy dependences consistent with previous analyses of nucleon scattering from 1p shell nuclei.     

The tensor analyzing power AzzATθ = 0° for the 3He(d, p)4He reaction

The tensor analyzing power f_zz has been measured for the ³He($\text{d}$, p)⁴He reaction at 0 = 0° over an incident deuteron energy range E_d = 6.6–15.8 MeV in steps of 0.5 MeV. The present results agree with and extend the previous measurements of Grüebler et al. The present results indicate that this reaction is a very good tensor analyzer for polarized deuteron beams with energies up to 15.8 MeV.     

Study of 11B at high excitations with the 9Be(3He,p)11B and 9Be(α, d)11B reactions

The nucleus ¹¹B has been studied over the excitation energy range from 8.5 MeV to 21.5 MeV with the ⁹Be(³He, p)¹¹B / reaction at / E_{³He = 38 MeV}. The analogs of the parent states in ¹¹Be have been located at 12.56, 12.92, 14.40, 16.44, 17.69, 18.0, 19.15 and 21.27 MeV. A complementary measurement with the ⁹Be(α, d)¹¹B reaction at E_α = 48 MeV demonstrates that the 16.44, 17.69, 18.0 and 19.15 MeV resonances have rather pure isospin $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$. The 14.40 MeV state is a strongly isospin-mixed analog of the $\text{5}\text{2}{}^{\mathrm{+}}\text{1.78}\text{MeV}$ state in ¹¹Be. It is argued that spin S = 1 transfer is involved in the excitation of the 16.44 MeV state and its 3.887 MeV parent in ¹¹Be in a two-step stripping process. The $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ states and the lowest three $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$ states are compared with the predictions of DWBA utilizing shell-model form factors. It is concluded that the $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ strength is more strongly fragmented than is implied by the calculations of Teeters and Kurath.     

Spin-parity assignments for 66Cu levels via the 68Zn(d, α)66Cu reaction

The ⁶⁸Zn($\text{d}$, α)⁶⁶Cu reaction populating low-lying states in ⁶⁶Cu has been studied at θ_lab = 4° using deuteron beams in the energy range 9.0 to 10.5 MeV. Tensor analyzing powers were calculated and natural- or unnatural-parity assignments were made for thirteen states in ⁶⁶Cu. By combining these results with existing limits unambiguous J^π assignments of 2⁺, 2⁺, 2⁺ and 1⁺ have been made for the levels at 186, 465, 822 and 1344 keV respectively. The previous tentative assignments to seven other levels have been confirmed while that for the 1247 keV level has been shown to be incorrect. The identification of the quartet of levels based on the $\text{π(}\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)v(}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ configuration has been confirmed.     

Study of 20Ne(3He,n)22Mg at 3He energies between 2.6 and 4.0 MeV

The ²⁰Ne(³He, n) reaction leading to the ground state of ²²Mg has been investigated in the ³He⁺ energy range of 2.6 to 4.0 MeV. Angular distributions were determined with a neutron time-of-flight spectrometer at average incident energies (lab) of 3.27, 3.69, and 4.01 MeV between 0° and 120° (lab). Excitation functions for the energy region were measured at 0° and 80° (lab). The observed differential cross sections are explained by coherent contributions from direct interaction and compound-nucleus formation. A spectroscopic factor was extracted for the DWBA calculation from the absolute cross-section measurements and found to be $\text{? = 0.43±0.21}$. Resonances in the compound-nucleus formation were found at 3.00 and 3.33 MeV (c.m.) with widths of 0.28 and 0.21 MeV and spins of $\text{5}\text{2}{}^{\mathrm{+}}\text{and}\text{1}\text{2}{}^{\mathrm{?}}$, respectively.     

Three-nucleon transfer on 12C: The 12C(α, p)15N reaction at 96.8 MeV

Angular distributions of protons from the ¹²C(α, p)¹⁵N reaction have been measured over the angular range from 10–70° at an α-particle bombarding energy of 96.8 MeV. Well defined particle groups are observed up to an excitation energy of 18 MeV in ¹⁵N. The relatively small number of states excited implies a selectivity both in the reaction mechanism and in structure effects. DWBA calculations using a semi-microscopic three-nucleon form factor have been performed using several different sets of wave functions. Good agreement in the ratio σ_exp/σ_th is obtained for most states using the ¹⁵N wave functions of de Meijer. The strongest state in the (α, p) spectrum is observed at 15.397 MeV in ¹⁵N and DWBA calculations give good agreement for a $\text{13}\text{2}{}^{\mathrm{+}}$ assignment. This state has been observed only in other three-nucleon transfer reactions involving heavy ions. The recent discovery of a $\text{9}\text{2}{}^{\mathrm{+}}$ state at 10.693 MeV in a p+¹⁴C resonance measurement is supported by our analysis.     

Evidence for assignment of 14.0 MeV state in 11B from 10B(n,n)10B

The differential cross section and polarization for neutrons scattered from ¹⁰B have been measured at E_n = 2.63 MeV (E_x = 13.85 MeV). The results of this experiment and other available neutron scattering data in the range 1 < E_n < 4 MeV are interpreted through a single-level R-matrix calculation over the region 12 < E_x < 15 MeV. Based on this analysis the most probable J^π assignment for the 14.0 MeV level in ¹¹B is $\text{11}\text{2}{}^{\mathrm{+}}$. The anomaly near E_x = 13.1 MeV can only be explained in terms of two overlapping levels having assignments of ($\text{5}\text{2}$, $\text{7}\text{2}$)^? and ($\text{3}\text{2}$, $\text{5}\text{2}$, $\text{7}\text{2}$)⁺.     

Study of the 91Zr(d, 3He)90Y reaction

The ⁹¹Zr(d, ³He) reaction was studied at a deuteron energy of 28 MeV. Angular distributions were measured from 13° to 47°; l_p values were extracted for the prominent lines of ⁹⁰Y. The l_p values and transition strengths were determined by DWBA analysis. The angular distributions for the $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ doublet (g.s. and 0.20 MeV state) exhibit the characteristic l = 1 shape. States at 1.42, 1.57, 1.64 and 1.81 MeV were also populated strongly in the (d, ³He) reaction; the 1.42, 1.57 and 1.81 MeV levels contain l= 1 transition strength and are most likely members of the $\text{(π}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ multiplet. The 2.03 MeV state has a characteristic l = 3 angular distribution and is suggested to be the only member of the $\text{(π}\text{f}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ sextet to be unambiguously observed in this study, most probably the 5^? or 4^? member. The members of the $\text{(π}\text{g}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)(ν}\text{d}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}$ sextet were populated weakly (less than 100 μb/sr) in this reaction.     

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.     

The radial distribution of the 1f72 neutron in 41Ca from the 40Ca(13C, 12C)41Ca reaction

The reaction ⁴⁰Ca(¹³C, ¹²C)⁴¹Ca leading to the ground and low-lying $\text{3}\text{2}$^? levels has been studied at bombarding energies of 18.5 and 19.0 MeV, close to the Coulomb barrier. The cross sections have been analysed using the DWBA with previously measured calibrations to obtain the rms radii of 1f_{$\text{7}\text{2}$} and 2p_{$\text{3}\text{2}$} orbits in the ⁴¹Ca levels. The rms radius of the 1f_{$\text{7}\text{2}$} point neutron orbit in the ground state relative to the ⁴⁰Ca core was determined to be 3.89 ± 0.12 fm. This is compared with various theoretical predictions based on Hartree-Fock theory. The 1f_{$\text{7}\text{2}$} orbit radius gives the point neutron excess size to a good approximation for comparison with the value of 3.45 fm deduced from Coulomb energy differences. The consistency of the results with ⁴⁰Ca(t, d)⁴¹Ca experiments using a (t/d), zero-range normalization of 3.26 × 10⁴ MeV² · fm³ is demonstrated, and trends in neutron size parameters through the Ca isotopes are discussed.     

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.