Cross-section measurements and thermonuclear reaction rates for 46Ti(p, γ)47V, 47Ti(p, γ)48V, 47Ti(p,n)47V and 48Ti(p, γ)49V

The yield of γ-rays from the reaction ⁴⁶Ti(p, γ)⁴⁷V has been measured as a function of bombarding energy over the range 0.72–3.00 MeV, from ⁴⁷Ti(p, γ)⁴⁸V over the range 0.74–3.50 MeV, and from ⁴⁸Ti(p, γ)⁴⁹V over the range 0.72–4.40 MeV. The yields of γ-rays following (p, p') reactions on all three targets were also measured and (p, p') cross sections were deduced for the first excited state proton groups for ⁴⁶Ti and ⁴⁸Ti and for the first ten proton groups for ⁴⁷Ti. The yield of neutrons from the reaction ⁴⁷Ti(p, n)⁴⁷V has been measured over the range from threshold to 4.40 MeV. All these data are compared with statistical-model calculations, and good agreement is achieved. Thermonuclear reaction rates for the (p, γ) and (p, n) reactions are calculated for the temperature range 5 × 10⁸–10¹⁰ K which includes the range of temperatures of interest in nucleosysnthesis calculations.     

High-resolution proton scattering on 50Ti

Differential cross sections were measured for ⁵⁰Ti(p, p) at four angles for E_p = 1.83 to 2.97 MeV, with an overall energy resolution of about 350 eV. Spins, parities and total widths were extracted for 212 levels. An energy region near E_p = 1.37 MeV was also examined in order to study the analogue of the ground state of ⁵Ti. Coulomb energies and spectroscopic factors were determined for the analogues of the ground and first excited states of ⁵¹Ti. The latter analogue was highly fragmented. The s-wave spacing and width distributions were analyzed and the number of missing levels estimated. The $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton strength functions were determined.     

Limitation to complete fusion in the reactions 12,13C+48Ti and 30Si+30Si

Excitation functions of the reactions ^{12, 13}C+⁴⁸Ti and ³⁰Si+³⁰Si were measured by in-beam γ-ray spectrometry in the energy ranges 20–60 MeV for the ^{12, 13}C induced reactions and 55–126 MeV for the ³⁰Si+³⁰Si reaction. Light-particle angular distributions were measured at 46 MeV and 47.5 MeV for the ¹³C and ¹²C induced reactions. Measurements of elastic scattering angular distribution and particle-γ coincidences were carried out for the system ¹³C+⁴⁸Ti at 46 MeV. The limitation to complete fusion detected for the system ³⁰Si+³⁰Si appears to be related to entrance channel effects and is well reproduced by a barrier penetration calculation using the KNS potential. The angular distribution measurements carried out for the ¹²C+⁴⁸Ti and ¹³C+⁴⁸Ti systems allowed to identify an incomplete fusion mechanism with emission of direct α-particles before the formation of a fully equilibrated system.     

A study of 50V using the direct reactions 49Ti (3He,d) and 51V(d,t)

Energy levels in ⁵⁰V up to 4.3 MeV have been studied using the ⁴⁹Ti(³He, d)⁵⁰V and ⁵¹V(d,t)⁵⁰V reactions with ³He particles of 22 MeV and deuterons of 19.5 MeV incident energy. More than eighty levels are seen, with angular distributions taken for forty-one levels in the (³He, d) reaction and for the ten lowest levels in the (d, t) reaction. The angular distributions are compared with the distorted-wave Born approximation (DWBA) to extract the l-values of the transferred nucleons and obtain the spectroscopic strengths. In the stripping reaction, a small amount of l = 0 and l = 2 strength is seen, indicating the presence of s and d proton holes in the g.s. of ⁴⁹Ti. The results are compared with a recent shell-model calculation based on an $\text{(}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{n}}$ configuration, and show qualitative agreement.     

The deformation of 46, 48, 50Ti from 104 MeV α-particle scattering

Differential cross sections have been measured for the elastic and inelastic scattering of 104 MeV α-particles from^{46, 48, 49}Ti. The experimental results are analyzed in terms of coupled channels on the basis of various limiting models of the collective behavior of these nuclei: symmetric rotator (⁴⁶Ti), asymmetric rotator (⁴⁸Ti) and anharmonic vibrator (⁵⁰Ti). The analysis uses both the usual extended optical model and a semimicroscopic folding model. Prolate-oblate and γ-asymmetry effects are studied and confirm prolate deformation of ⁴⁶Ti and ⁴⁸Ti. Hexadecapole transitions (0⁺ → 4₁⁺) are found.     

Electromagnetic transitions in 42Ti

Levels in ⁴²Ti up to 4 MeV have been investigated using the ⁴⁰Ca(³He, n)⁴²Ti reaction and a neutron time-of-flight method. Using the DSA method, lifetimes of 750±300, > 200, 350±250, > 2000 and < 250 fs have been measured for levels at E_x = 1.56, 1.85, 2.40, 2.68 and 3.74 MeV respectively. The level at E_x = 3043.0±1.5 keV is tentatively identified as the 6⁺ member of the $\text{(f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^2$ configuration, and its mean life has been measured as 26±5 ns by a direct timing method. Using isospin formalism, transition strengths are compared with theoretical and experimental values for ⁴²Ca and ⁴²Sc.     

High-resolution measurements of beta-delayed protons from 37Ca and 41Ti

Protons with energies from 870 keV to 5.4 MeV have been observed following bombardment of a ⁴⁰Ca target with ³He at beam energies of 29.5, 36.5 and 60 MeV, as well as from 40 MeV ³He bombardment of an ³⁶Ar gas target. These data, and those resulting from 20 MeV proton bombardment of ⁴⁰Ca, permit accurate identification of proton unbound levels in ⁴¹Sc, ³⁷K, and ⁴⁰Ca fed by allowed beta decay from ⁴¹Ti, ³⁷Ca or ⁴⁰Sc, respectively. Absolute ft values have been determined for beta decay to these levels. The half-life of ⁴¹Ti has been remeasured to be 80±2 ms and the log ft for its superallowed decay branch has been found to be 3.35±0.02, indicating an isospin purity for the lowest $\text{T =}\text{3}\text{2}\text{state in}{}^{41}\text{Sc of}\text{≈ 91 \%}$. The $\text{ft}\text{values for}{}^{37}\text{Ca}\text{β}{}^{\mathrm{+}}$ decay are compared to shell-model calculations for beta-decay in A = 37 nuclei.     

Absolute residue cross sections for 46–50Ti + 13C reactions at 36, 46 and 56 MeV

Absolute cross sections for nuclei produced in the reactions ^46–50Ti + ¹³C at 36, 46 and 56 MeV (lab) were measured. Complete identification in mass and atomic number for the evaporation residues was obtained by means of in-beam γ-ray spectroscopy techniques. In the entire energy range, an overall satisfactory account of the observed product nuclei is given by the predictions of the fusion-evaporation model. Direct channels like inelastic scattering and n-transfer appear to be noticeable and contribute ~ 15 % to the total cross section.     

The reactions 50,52Cr(d, 6Li) 46,48Ti at Ed = 651 MeV

The ^50,52Cr(d, ⁶Li) ^46,48Ti reactions have been studied at E_d = 65 MeV bombarding energy. Angular distributions of outgoing Li particles were measured for final states in ^46,48Ti nuclei from 15° to 50° (lab). These were compared with zero-range and finite-range DWBA calculations in an α-cluster pick-up approximation to obtain relative α-spectroscopic factors.     

Reaction and fusion cross sections for 32S on 27Al and 48Ti

Elastic scattering and evaporation residues have been measured for the system ³²S + ²⁷Al at E_c.m. = 66.4, 73.2 MeV and ³²S + ⁴⁸Ti at E_c.m. = 96.0 MeV. Reaction cross sections have been obtained by use of the optical theorem and are found to be about 60 % larger than the fusion cross sections.     

High-resolution proton scattering on 46Ti

Differential cross sections were measured for ⁴⁶Ti(p, p) and ⁴⁶Ti(p, p₁) at four angles between E_p = 1.5 and 3.1 MeV, with an overall energy resolution of about 300 eV. Spins, parities, total and partial widths were extracted for 144 resonances. Six analogue states were identified. The s-wave states have expected spacing and width distributions, while the $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states behave anomalously. The $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ strength functions were determined.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

The 48Ti(t,d)49Ti reaction: A comparison with magnetic electron scattering

The reaction ⁴⁸Ti(t, d)⁴⁹Ti leading to the ground and first excited states of ⁴⁹Ti has been studied at triton energies of 2.75 and 3.0 MeV. The cross section to the ground state of ⁴⁹Ti has been analysed using the DWBA with a previously determined bound-state well geometry to obtain a value for the (t, d) normalization factor of D² = (3.29 ± 0.40) × 10⁴ MeV² · fm³. This value is in agreement with that obtained from a comparison of the (d, t) reaction with heavy-ion single-neutron transfer reactions. Using this value of the normalization factor the rms radius of the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ component in the $\text{3}\text{2}{}^{\mathrm{?}}$ first excited state of ⁴⁹Ti is found to be 4.42 ± 0.07 fm (point neutron), corresponding to the use of a local bound-state potential well.     

Levels of 209Po and 211Po populated in one-neutron stripping and pickup from 210Po

Energy levels of ²⁰⁹Po have been populated with the ²¹⁰Po(d, t)²⁰⁹Po and ²¹⁰Po(p, d)²⁰⁹Po reactions at bombarding energies of 17.0 and 17.8 MeV respectively. Fifteen levels were observed below 2.7 MeV of excitation. Energy levels of ²¹¹Po were populated with the ²¹⁰Po(d, p)²¹¹Po reaction, also at 17.0 MeV. Thirty-five levels, almost all new, were observed below 3.9 MeV of excitation. Comparison of experimental angular distributions with DWBA calculations allowed l-value assignments and extraction of spectroscopic factors for many levels. In ²⁰⁹Po the observed level structure is well described in terms of a simple particle-vibration coupling model. In ²¹¹Po the level structure is more complex and the simple model is not adequate.     

An investigation of the 144Sm(α, 3He)145Sm reaction

The ¹⁴⁴Sm(α, ³He)¹⁴⁵Sm stripping reaction has been studied up to 3 MeV excitation energy with a 40 MeV α-beam. Angular distributions have been recorded, and spectroscopic factors are deduced using a standard DWBA procedure. The reaction favours high-l transfers, and is found to be very useful for the investigation of large-j states. From a comparison with the spectroscopic factors known from the ¹⁴⁴Sm(d, p)¹⁴⁵Sm reaction the normalization factor for the (α, ³He) reaction is found to depend strongly on the optical model parameters and on the transferred angular momentum l.     

Level structure of 51Cr from the (d,p) reaction on 50Cr

The level structure of ⁵¹Cr is studied through the ⁵⁰Cr(d, p) reaction at E_d = 12 MeV using the Van de Graaff accelerator and multi-channel magnetic spectrograph at AERE, Harwell. A total of 174 levels was observed up to E_x ≈ 8.1 MeV. The stripping angular distributions are analysed in terms of the DWBA model with NLFR corrections. Spins, parities and spectroscopic factors are obtained for various levels and a sum rule analysis is made. Hauser-Feshbach calculations are done for the non-stripping levels and the levels showing a poor DWBA fit. Finally, the level spectrum is compared with the MBZ and MS models.     

Neutron hole states in 138La and 140Pr

Protons accelerated to 30 MeV were used to investigate low-lying states in the odd-odd nuclei ¹³⁸La and ¹⁴⁰Pr with (p, d) reactions. The elastic scattering of 30 MeV protons and 23 MeV deuterons was also studied to determine optical potentials. Experimental angular distributions are compared with distorted-wave Born approximation calculations to extract spin, parity, and spectroscopic factors for levels up to 432 keV of excitation in ¹⁴⁰Pr and 530 keV in ¹³⁸La. Comparisons with the simple shell-model predictions and extended shell-model calculations are presented. The ¹⁴⁰Pr levels appear experimentally to have an almost pure particle-hole structure whereas the ¹³⁸La levels exhibit substantial mixing.     

A study of the 106Pd(p,d)105Pd and 106Pd(3He,d)107Ag reactions

The ¹⁰⁶Pd(p, d)¹⁰⁵Pd reaction has been studied at 22.9 MeV with an energy resolution of 13 keV. Angular distributions permitted the assignment of l-values and the extraction of spectroscopic factors for 13 states including several previously unresolved l = 2 transitions. The ¹⁰⁶Pd(³He, d)¹⁰⁷Ag reaction has also been studied at 32.8 MeV with a resolution of 20 keV. Angular distributions were obtained, l-values assigned and spectroscopic factors extracted for 14 levels including many not observed previously in a proton transfer reaction. The level structure of ¹⁰⁵Pd and ¹⁰⁷Ag is discussed particularly in terms of quasirotational bands.     

High-resolution study of the 118Sn(d,p)119Sn reaction at 17 MeV

Energy levels in ¹¹⁹Sn up to 4.75 MeV excitation have been studied with the ¹¹⁸Sn(d, p)¹¹⁹Sn reaction at an incident deuteron energy of 17 MeV. The scattered particles were analysed by a magnetic spectrograph and detected in nuclear emulsions with a resolution of ≈ 9 keV. Seventyseven energy levels were identified. Angular distributions were compared to DWBA predictions allowing the identification of transferred angular momenta and the determination of spectroscopic factors for 49 states. The results obtained are compared with pairing theory and the weakcoupling model.