Study of the (3He,d) reactions on 58, 60Ni and 56Fe near the Coulomb barrier

Using spectroscopic information gained by earlier measurements of the proton bound states populated by stripping reactions, (³He, d) reactions on ^{58, 60}Ni and ⁵⁶Fe targets are studied at energies near the Coulomb barrier and evaluation is made of the vertex function . This value is then used to determine spectroscopic factors for low-lying states in ⁵⁷Co.     

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.     

β-delayed charged particles from 9Li and 11Li

β-delayed emission of α-particles from ⁹Li and of both α and ⁶He particles from ¹¹Li is observed. Singles energy spectra and two-dimensional energy spectra of coincident particles are measured. A time-of-flight versus energy measurement is used to identify the mass of the particle. New β-branches are observed which populate high-energy levels in the daughter nuclei. The branching ratios are measured and the β-delayed neutron emission probabilities $\text{P}{}_{\mathrm{<mtext>n</mtext>}}\text{for}{}^9\text{Li and}\text{P}{}_{\mathrm{3n}}\text{for}{}^{11}\text{Li}$ are deduced.     

The 54Fe(3He,t)54Co reaction at 70 MeV,Gamow-Teller strength

The ⁵⁴Fe(³He, t)⁵⁴Co reaction has been studied at 70 MeV with an energy resolution around 70 keV (FWHM). The triton spectra are characterized by sharp peaks up to 10 MeV excitation energy superimposed on a continuum. Most of the sharp peaks have a forward-peaked angular distribution and 38 peaks or groups of peaks are found to have an angular distribution corresponding to an angular momentum transfer of 2. Model considerations lead to the conclusion that most of these states are 1⁺ states. A shell-model calculation with parameters that account for the Gamow-Teller strength distribution in ⁴⁸Ca-⁴⁸Sc divides the β-strength in ⁵⁴Co in a ratio 5.7:6.8:1.3 for the T = 0, 1 and 2 states. A comparison is made with the 1⁺ spectrum in ⁵⁴Mn (T = 2 states) and a tentative assignment of T = 2 states in ⁵⁴Co is reached. The cross section has been calculated for the 0⁺, 1⁺ and 3⁺ states in ⁵⁴Co assuming a pure ($\text{π}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{ν}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) configuration finite-range DWBA is used and the conclusions are that the (³He, α, t) and (³He, d, t) processes give significant contributions to the cross sections.     

Strong coupled-channels effects in the 9Be(α, t)10B reaction

Differential cross sections were measured for the reactions ${}^9\text{Be}\text{(α, α')}{}^9\text{Be}\text{,}{}^9\text{Be}\text{(α,}\text{t}\text{)}{}^{10}\text{B and}{}^9\text{Be}\text{(α,}{}^3\text{He}\text{)}{}^{10}\text{B at}\text{E}{}_{\mathrm{\alpha }}\text{= 65}\text{MeV}$ for angles ranging from θ_lab = 6° to 48°. Optical-model analysis was performed for elastic α-scattering from ⁹Be at E_α = 48, 65 and 104 MeV, and DWBA and CC calculations were done for the inelastic α-scattering at E_α = 65 MeV. DWBA calculations for the ⁹Be(α, ³He) reactions do not fit the transfer data so well and extracted spectroscopic factors are in disagreement with those of Cohen and Kurath and with values obtained from other reactions. Full CRC calculations assuming a band structure for the low-lying states of ¹⁰B and employing a modified set of Cohen and Kurath spectroscopic factors yield globally better fits both in shape and in absolute cross section for differential cross sections to low-lying states in ¹⁰B obtained in ⁹Be(α, t)¹⁰B at $\text{E}{}_{\mathrm{\alpha }}\text{= 65}\text{MeV and}{}^9\text{Be}\text{(}{}^3\text{He, d}\text{)}{}^{10}\text{B at}\text{E}{}_{\mathrm{<mtext>d</mtext>}}\text{= 17}\text{MeV}$. In general, strong coupled-channel effects mainly affecting the distorted waves are observed both in entrance and exit channels.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

The GT matrix elements in the decay of the mirror nuclei 47Cr, 51Fe and 55Ni

Three new mirror nuclei, ⁴⁷Cr, ⁵¹Fe and ⁵⁵Ni, have been identified in (³He, 2n) reactions. The measured half-lives were as follows: ${}^{47}\text{Cr}\text{, 452 ± 18}\text{ms}\text{;}{}^{55}\text{Fe}\text{, 245 ± 7}\text{ms}\text{;}{}^{55}\text{Ni}\text{, 189 ± 5}\text{ms}$. Known mass data were utilized to deduce log $\text{?t}$ values and Gamow-Teller matrix elements for the three mirror β-decays. The experimental GT matrix elements are compared to the results of shell-model calculations.     

Resonances in the reaction 56Fe(p, γ)57Co

Resonances in the reaction ⁵⁶Fe(p, γ)⁵⁷Co have been surveyed over the energy range 1.2 ? E_p ? 1.5 MeV wherein the analogues of the ground state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}\text{, 0.014}\text{MeV}$ state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$ and 0.136 MeV state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}\text{)}$ of ⁵⁷Fe are expected to occur. Gamma-ray angular distributions have been used to establish resonance and bound-state spins, and decay schemes have been determined. The analogue resonances appear to be severely fragmented, however the density of resonances of a given spin correlates quite well with (³He, d) results and with the expected analogue-state positions.     

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.     

Low-lying levels of 92Nb from the 92Zr(3He,t) and 92Zr(3He,p2nγ) reactions

The structure of ⁹²Nb has been investigated using the 33.8 MeV ⁹²Zr(³He, t) and (³He, p2nγ) reactions. Several previously unobserved levels, including several belonging to the $\text{π(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)ν(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$ multiplet, are reported. The results are discussed in terms of the shell model.     

Half-life of the ground state of 53Co

The half-life of ⁵³Co(g.s.) was measured by observing its positron emission following the ³⁹K.( ¹⁶O, 2n) reaction induced by a chopped ¹⁶O beam. The contributions to the half-life of positrons from competing reaction products were considered. The final spin distribution and the isomeric ratio values for ${}^{\mathrm{53m}}\text{Co}{}^{53}\text{Co(}\text{g.s.}\text{)}$ and ${}^{\mathrm{53m}}\text{Fe}{}^{53}\text{Fe(}\text{g.s.}\text{)}$ were calculated by the spindependent nuclear evaporation model and found to be different, the former much smaller than the latter. The ${}^{\mathrm{53m}}\text{Fe}{}^{53}\text{Fe(}\text{g.s.}\text{)}$ isomeric ratios were measured for ³⁹K.+ ¹⁶O as well as for ⁴⁰C + ¹⁶O reactions and were found to be in agreement with the above theoretical prediction. On the basis of the smallness of the calculated ${}^{\mathrm{53m}}\text{Co}{}^{53}\text{Co(}\text{g.s.}\text{)}$ ratio, the half-life of ⁵³Co(g.s.) was determined to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>\; =\; 262\; \pm \; 25\; </mtext><mtext>ms</mtext>}}$.     

Deuteron induced pickup reactions on 41Ca

The ⁴¹Ca(d, t)⁴⁰Ca and ⁴¹Ca(d, τ)⁴⁰K reactions have been investigated at a bombarding energy of 40 MeV. A distorted-wave analysis of the measured angular distributions and a sum-rule analysis of the resulting spectroscopic factors has enabled the identification of members of various particle-hole multiplets. Values obtained for the matrix elements of the $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ effective interaction are in poor agreement with values obtained from other nuclei, but are reasonably well reproduced by calculations with a simple force.     

Low-lying levels of 140Pr

The doubly odd nucleus ¹⁴⁰Pr has been investigated by means of the ¹⁴¹Pr(d, t)¹⁴⁰Pr and ¹⁴⁰Ce(p, nγ)¹⁴⁰Pr reactions. Twenty-eight levels, up to 1300 keV excitation, were observed in the pickup study. DWBA analysis was used to determine l-values and spectroscopic factors for all but a few which are very weakly populated. Gamma-ray angular distributions, measured at E_p = 4.78 MeV for the five strongest γ-rays, show appreciable nuclear alignment and demonstrate the feasibility of such experiments in this mass region. Taken together, the two studies have permitted the identification of the 12 levels expected from the low-lying ($\text{π2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{ν2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$), ($\text{π2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{ν3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$), ($\text{π1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{ν2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) and (π1g_{$\text{7}\text{2}$}ν3s_{$\text{1}\text{2}$}^?1) configurations. Tenta assignments for the strong odd-parity states are suggested on the basis of their spectroscopic factors.     

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.     

Angular distributions of the 2h(d, γ)4he reaction

Angular distributions of γ-rays from the ²H(d, γ)⁴He reaction have been measured at the deuteron energies E_d = 6.05, 8.96 and 11.67 MeV with a 12.7 cm × 15.2 cm NaI(Tl) crystal enclosed in a Cerenkov anticoincidence shield. A least-square fit of the angular distributions indicates that the differential cross section is proportional to sin²θ cos²θ and that the process proceeds through an E2 transition of the type ${}^1\text{D}{}_2\text{→}{}^1\text{S}{}_0$.     

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 (g92)2 residual interaction from 87Sr(d,t)86Sr

Differential cross sections for ⁸⁷Sr(d, t)⁸⁶Sr transitions to the $\text{(1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?2}}$ states of ⁸⁶Sr were obtained with the Pittsburgh 18 MeV deuteron beam and the Enge split-pole spectrograph. States of ⁸⁶Sr up to 3.82 MeV in excitation were studied with a total resolution of 12 keV. Successful distorted-wave Born approximation (DWBA) predictions for ⁸⁷Sr(d, t) ⁸⁶Sr angular distributions permitted the extraction of l-values and spectroscopic strengths. The sum-rule value agrees with the observed value for the $\text{(1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?2}}$ configuration. The observed $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ strength is spread over 13 states. Contrary to an earlier interpretation, the 0⁺ ground state is found to contain only 65% of the strength. Similarly, the full 4⁺ strength is not located in a single state. The new data change the interpretation of the $\text{(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?2}}$ spectrum of ⁸⁶Sr. They significantly alter the deduced low-spin matrix elements and bring them into much closer agreement with those derived from ⁸⁸Y. Several new negative-parity states dominated by l = 1 orbital angular momentum transfer have also been identified.     

Ground-state properties of 3h 184Ir and 14h 185Ir

The ground-state spectroscopic quadrupole moments of ${}^{184}\text{Ir [J}{}^{\mathrm{\pi }}\text{=(5}{}^{\mathrm{\pm }}\text{);t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{=3.00]}$ and ${}^{185}\text{Ir (J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}\text{;t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 14}\text{h}\text{)}$ have been determined by nuclear orientation as +2.2(4) b and ?2.03(3) b, respectively. The negative QM of ¹⁸⁵Ir can be explained only by a $\text{J}{}^{\mathrm{\pi }}\text{K=}\text{5}\text{2}{}^{\mathrm{?}}\text{1}\text{2}$ ground-state configuration. The positive QM of ¹⁸⁴Ir implies K ? 4 in contradiction to expectations of K=0, 1 in analogy to ¹⁸⁶Ir.     

The (6Li, 6He) spin-isospin-flip reaction

A formulation of the (⁶Li, ⁶He) spin-isospin-flip scattering problem is presented. The method is applicable to quasielastic collisions between⁶Li described in pureLS coupling scheme and any target nucleus which can be described in a shell model or an adiabatic deformed-nucleus model picture. The effective interaction responsible for the (⁶Li, ⁶He) reaction involves an integration of the (σ₁ · σ₂) (ρ₁ · ρ₂) compo nent of the central part and the (τ₁· τ₂) tensor part of the nucleon-nucleon interaction over the internal wave function of the projectile. The ⁴⁸Ca(⁶Li,⁶He)⁴⁸Sc reaction populating the ($\text{πf}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{νf}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) multiplet in ⁴⁸Sc is analysed. It that the tensor force makes some contribution to the transitions to high spin states.