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.     

The reaction 55Mn(d, t)54Mn

Neutron pick-up cross sections and vector analyzing powers have been measured for the reaction ⁵⁵Mn($\text{d}$, t)⁵⁴Mn at 17 MeV. The mixture of $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ to $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ transfer to the low-lying l_n = 1 states has been found. Evidence of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole nature of several strong l_n = 3 states above 1 MeV has been obtained.     

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.     

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.     

Study of the 58Ni(τ, α)57Ni reaction at 25 MeV

The ⁵⁸Ni(τ, α)⁵⁷Ni reaction has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 50° with a split-pole spectrometer up to 13.5 MeV excitation energy. A local zero-range DWBA analysis has been carried out, allowing l-assignments for about eighty levels, most of them previously unknown. An isospin-dependent potential has been used in the calculation of the neutron form factor for both T_<and T_> states, and the C²S values deduced using this procedure are compared to those obtained with the usual separation energy method. Analog states of eleven ⁵⁷Co levels have been identified and the eventuality for isospin mixing in ⁵⁷Ni has been discussed. A sum rule analysis has been carried out and energy centroids of hole states have been determined. About 60% of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ strengths and the full $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole strengths are observed. It is shown that the two excess neutrons in the ⁵⁸Ni ground state mainly populate the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbitals, whereas the occupancy number of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ subshell is found to be smaller than 0.1%. Some non-pickup angular distributions have also been observed and a CRC analysis assuming two-step processes in the (τ, α) reaction and weak-coupling wave functions for final states has been attempted. Assignments of J^π values are proposed for four ⁵⁷Ni levels, based on this analysis.     

The structure of 26Mg investigated with the (d,p) reaction

Angular distributions have been measured for the ²⁵Mg(d, p)²⁶Mg reaction at 13 MeV leading to excited states between E_x = 0 and 8 MeV. Experimental cross sections are compared with DWBA calculations and extended shell-model calculations in the full sd shell. Spin and parity restrictions are obtained for several levels in the region E_x = 6?;8 MeV. Spectroseopic factors for transitions to the lowest four positive-parity states of each spin are well reproduced by the shell-model calculations; however, in mixed configurations the largest component is systematically underestimated by the shell model. Only 60% of the strength for $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transfer is observed.     

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.     

Experimental and shell-model studies of the reactions 91Zr(d,p)92Zr and 90Zr(t,p)92Zr

The results of high-resolution studies of the ⁹¹Zr(d, p) reaction at E_d = 12 MeV and the ⁹⁰Zr(t, p) reaction at E_t = 11.85 MeV are presented. Absolute cross sections have been measured for both reactions and (d, p) spectroscopic factors determined. A comparison of these results with earlier data has been made, and although many of the previous assignments have been confirmed, many new features concerning the structure of ⁹²Zr have been discovered. Shell-model calculations have been performed for ⁹¹Zr and ⁹²Zr using a neutron space which includes the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{1}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbits and a proton space comprising the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits. Realistic proton-neutron and neutron-neutron interactions based on the Sussex matrix elements were used in the calculations. Spectroscopic factors have been calculated for the ⁹⁰Zr(d, p) and ⁹¹Zr(d, p) reactions and cross sections calculated for the ⁹⁰Zr(t, p) reaction. In general, good agreement between the theoretical and the experimental results has been obtained.     

Structure study of 12B from the elastic scattering of neutrons from 11B

Differential cross sections for neutrons scattered from ¹¹B have been measured for 2.2 MeV < E_n < 4.5 MeV. The differential cross section σ(θ) is fitted reasonably well by R-matrix parameters for broad states in ¹²B with assignments 1 ^? and (1) ⁺ at excitation energies E_x = 5.8 and 6.8 MeV respectively. The broad 1 ^? state has not been previously observed and is believed to be the 1 ^? member of the $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ particle-hole multiplet predicted to exist by earlier shell model calculations. Its existence completes the identification of all of the levels of this multiplet (3 ^?, 2 ^?, 4 ^?, 1 ^?). The broad (1)⁺ level at E_x = 6.8 MeV has not been previously observed. States at excitation energies E_x = 5.61, 5.73 and 6.6 MeV have been assigned spins and parities of 3⁺, 3^? and (1)⁺ respectively. These states had previously been assigned spins of 2, 3 and $\text{≧ 1}$ respectively. Work on T = 1 states in ¹²C¹ has been compared with the present work.     

The energy dependence of the spectroscopic factors for the 208Pb(p,d)207Pb reaction

The ²⁰⁸Pb(p,d)²⁰⁷Pb reaction has been studied at 26.3 MeV and data at 121 MeV reanalyzed. These data, along with the data of others at 22, 35, 41 and 55 MeV, have been compared with zero- and exact-finite-range DWBA calculations carried out in a consistent fashion to determine the energy dependence of the spectroscopic factors for the six strong single-neutron-hole states in ²⁰⁷Pb. Strong energy dependencies were noted for the spectroscopic factors, particularly for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{,}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$and$\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ states. Variations in the calculations provided no satisfactory understanding of the problem.     

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.     

Energy dependence of the reaction mechanism of 11B induced single nucleon transfers on 26Mg

Angular distributions for elastic scattering and for single nucléon stripping reactions induced by a 31 MeV ¹¹B beam on ²⁶Mg have been measured. The DWBA calculations provide a good account of the shape and magnitude of the proton transfer data and of the neutron transition to the $\text{j-}\text{favoured}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ level in ²⁷Mg, but fail to reproduce the features of the $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ transitions to ²⁷Mg. The j-dependent effects and l-matching conditions are investigated as a function of beam energy and their role in determining the reaction mechanism is examined.     

The 1h92 proton orbit size in 209Bi

Angular distributions of α-particles from the reaction ²⁰⁹Bi(t, α)²⁰⁸Pb (ground state) have been measured at bombarding energies E_t = 8.5 MeV and E_t = 9.0 MeV. Zero-range (ZR) DWBA analyses of the data are used to determine the radial extent of the wave function of the $\text{lh}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ orbit in which the transferred proton is bound in ²⁰⁹Bi. The applicability of the sub-Coulomb ZR DWBA treatment is investigated by comparison of ZR and exact finite-range DWBA calculations. A value of the (t, α) normalization constant of (20.8 ± 3.1) × 10⁴ MeV² · fm³, based on forward dispersion relations, has been obtained from this comparison. The asymptotic amplitude of the wave function is measured directly and the rms radius is extracted via a Woods-Saxon model. A value of √〈r²〉 = 6.10_?0.08^+0.12 fm, corresponding to a point proton and to a local Woods-Saxon potential, is obtained. The rms radius and radial wave function of the $\text{1}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton are compared with the results of electron scattering and muonic atom data on targets of ²⁰⁹Bi and ²⁰⁸Pb and with the results of Hartree-Fock calculations.     

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.     

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-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.     

Spectroscopic study of 55Co via the 54Fe(τ, d)55Co and 54Fe(τ, dp̃)54Fe reactions

The ⁵⁴Fe(τ, d)⁵⁵Co reaction has been studied at 25 MeV incident energy with a split-pole spectrometer. About one hundred levels have been observed in ⁵⁵Co up to 10 MeV excitation energy. Angular distributions have been measured and analyzed with DWBA and Gamow functions as form factors for unbound levels. The ⁵⁴Fe(τ,dp?)⁵⁴ reaction has been investigated at 24 MeV incident energy. The angular distributions of the emitted protons were measured in coincidence using method 2 of Litherland and Ferguson, with 0 detection of deuteron groups. Spins, population parameters, branching ratios and proton partial widths for the transitions to the ground and excited states of ⁵⁴Fe were determined from the analysis of the angular correlation data. The results of these two experiments provide a large number ofspectroscopic properties of unbound proton states and in particular of analog states of ⁵⁵Fe low-lying levels. The IAS of the $\text{3}\text{2}{}^{\mathrm{?}}$ ground state of ⁵⁵Fe is observed to be split between two individual levels. The amplitude of neutron coupling to the first 2⁺ excited state of ⁵⁴Fe is obtained for the $\text{lg}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{d}\text{5}\text{2}$ low-lying parent statfes in ⁵⁵Fe. summed spectroscopic factors and the centroid energies of the proton states in ⁵⁵Co are obtained. A comparison is made with previous (τ, d), (d, p) and (p, p) results.     

An investigation of 86Sr wave functions with the (p, α) reaction at Ep = 35 MeV

Wave functions of low-lying states in ⁸⁶Sr have been calculated in a model space including $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ sub-shells but neglecting the proton-neutron residual interaction. These wave functions have been tested by the ⁸⁹Y(p, α)⁸⁶Sr reaction at E = 35 MeV by applying a DWBA analysis with microscopic form factors.     

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.     

Spectroscopic study of 15N states with the reaction 14C(d,n)

Energy and angular distributions of neutrons from the reaction ¹⁴C(d, n)¹⁵N have been measured at 6.5 MeV deuteron energy. The DWBA analysis yielded l-values and absolute spectroscopic factors for fifteen states in ¹⁵N below 10 MeV excitation energy. For the 9.23 MeV level J^π is determined to be $\text{3}\text{2}$⁺ or $\text{5}\text{2}$⁺, for the 9.93 MeV level the data suggest $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$. The spectroscopic factors are in qualitative agreement with pure jj coupling and in semi-quantitative agreement with shell-model calculations.