The structure of 209Bi: (I). Microscopic structure from analog resonances

Excitation functions for the ²⁰⁹Bi(p, p′) reaction have been measured for incident proton energies from 14.0 to 15.5 MeV to study the population of states in ²⁰⁹Bi via decay of the isobaric analog resonances in the compound nucleus ²¹⁰Po. The analogs correspond to parent states in the lowest one MeV of excitation in ²¹⁰Bi. Strong resonances are observed in the excitation functions for twenty proton groups corresponding to levels between 2.75 and 3.65 MeV in ²⁰⁹Bi. From these results, levels which possess microscopic 2p-1h structure involving the orbitals are identified and their ²¹⁰Bi parentage determined. The resonant scattering results together with other direct inelastic scattering data allow the spins and parities for many of the levels to be deduced. The results of a microscopic calculation, in which empirical two-body matrix elements are employed to describe the interactions between the orbitals, are also reported and compared with the experimental results for levels in ²⁰⁹Bi. The excellent agreement between theory and experiment demonstrates that the general character of these levels can be understood microscopically in terms of their 2p-1h structure.     

The 208Pb(α, 3He)209Pb reaction at 58 MeV

The ²⁰⁸Pb(α, ³He)²⁰⁹Pb reaction at 58 MeV has been used to search for high-spin states in ²⁰⁹Pb. Only three levels are excited with appreciable intensity: the ground state $\text{(2}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}$ and levels at $\text{0.781 (}\text{li}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}\text{and}\text{1.426}\text{MeV}\text{(}\text{lj}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{)}$. The angular distributions for these levels have been measured and analyzed using standard DWBA calculations to obtain spectroscopic strengths. The ²⁰⁸Pb(α, α) elastic scattering was measured and optical parameters deduced from the data. A normalization value N = 50 yields spectroscopic values which are close to the values measured in the (d, p) reaction. The (α, ³He) reaction should easily pick out any appreciable components of the $\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}$ shell model state, which weak-coupling calculations predict should be fragmented. However only three weak transitions previously seen in a (d, p) experiment are observed.     

The distribution of 3p12 strength in 209Bi

An optimized Woods-Saxon potential, which gives excellent fits to the observed proton states in ²⁰⁹Bi and ²⁰⁷Tl, is used to calculate the excitation energy of the unbound $\text{3p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton state in ²⁰⁹Bi. Using the wave functions given by the above potential, the strength of the core-particle interaction is calculated. The effect of the vibration of the core on the fragmentation of the $\text{3p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state is estimated. It is found that the $\text{3p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state at 5.123 MeV loses more than 80% of its strength to five $\text{1}\text{2}{}^{\mathrm{?}}$ collective states in ²⁰⁹Bi and the observed $\text{3p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state at 3.64 MeV is actually an almost equal mixture of the $\text{3p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ single-proton state and the ($\text{4}{}^{\mathrm{+}}\text{, 1}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$) collective state.     

Gamma decay of particle-core states in 209Pb

A γ-decay scheme for levels in ²⁰⁹Pb up to 4.13 MeV of excitation has been established by means of the reaction ²⁰⁸Pb(d, pγ)²⁰⁹Pb. In high efficiency p-γ coincidence measurements γ-cascades have been observed from the single-particle states and from core-excited states with very small single-particle strength. Assuming a qualitative validity of the weak-coupling model spins and main configurations of particle-core states can be deduced from their γ-decay. The $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{5}\text{2}{}^{\mathrm{?}}\text{or}\text{7}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{)}$ members of the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?3}{}^{\mathrm{?}}$ multiplet could be located. A systematic manner of doublet splitting is found for the lowest states with main configuration $\text{(}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{?3}{}^{210}\text{Pb}\text{(0}{}^{\mathrm{+}}\text{, 2}{}^{\mathrm{+}}\text{, 4}{}^{\mathrm{+}}\text{, 6}{}^{\mathrm{+}}\text{, 8}{}^{\mathrm{+}}\text{)}$. A new decay branch of the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ single-particle state is attributed to an admixture of quadrupole core vibration.     

Quantitative evidence of weak isospin mixing in the low-lying isobaric analog resonances in 209Bi

The excitation functions of ${}^{208}\text{Pb}\text{(}\text{p}\text{,}\text{p}{}_0\text{)}{}^{208}\text{Pb}$ have been measured in the energy range E_p = 14.2 to 17.4 MeV in 50 keV steps at θ_lab = 120°, 140° and 160°. The isobaric analog resonances of the parent states in ²⁰⁹Pb up to E_x = 2.5 MeV and the optical-model background were fit simultaneously at all energies and angles. The spreading widths and the values of a parameter β², which measures the isospin purity of the IAR, were determined for the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{,}\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{,}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, and $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ resonances. An average value of the isospin purity of β² = 66% was found.     

7 MeV dipole ground state transitions in 207Pb, 208Pb and 209Bi

The Doppler-broadened 7.117 MeV line from the ¹⁹F(p, αγ)¹⁶O reaction has been used to resonantly excite levels in ²⁰⁸Pb at 7071±2 and 7091±2 keV, in ²⁰⁷Pb at 7186±5 and 7206±5 keV and in ²⁰⁹Bi at 7179±5 and 7202±5 keV. On the basis of angular distribution measurements the 7071 and 7091 keV levels of ²⁰⁸Pb are assigned spins of 1 and assuming 100% ground state branching the widths are calculated to be 31±3 and 17±2 eV respectively. It is suggested that the states in ²⁰⁷Pb and ²⁰⁹Bi arise from the weak coupling of a $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron hole and an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton respectively to one or the other of the ²⁰⁸Pb levels. The widths obtained in terms of _gΓ_o²/Γ are 15±4 and 25±5 eV for the 7186 and 7206 keV levels of ²⁰⁷Pb and 24±5 and 30±5 for the levels of ²⁰⁹Bi respectively. These values are consistent with the weak-coupling suggestion.     

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.     

The mass and kinetic energy distributions in the fission of 237Np, 232Th, 238U, 235U and 209Bi induced by 110 MeV electrons

Fission of ²³²Th, ²³⁷Np, ²⁰⁹Bi, ²³⁵U and ²³⁸U induced by 110 MeV electrons has been studied by means of surface barrier detectors. The resulting mass and kinetic energy distributions are presented. Comparison with the liquid drop model predictions shows reasonable agreement in the case of ²⁰⁹Bi. The data are analysed in terms of a two component model of fission and the mean total kinetic energies of the components are shown to depend linearly on $\text{Z}{}_1\text{Z}{}_2\text{(A}{}_1{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{+ A}{}_2{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{)}$. Interesting differences are found when the present results are compared with the recent photofission experiments of Areskoug et al. and features in both sets of data correlate with changes of fragment deformation implied by the calculations of Wilkins et al.     

Shell-correction approach to nuclear state densities and the competition between fission and neutron emission of 210Po

Starting from the Hartree-Fock approximation to the grand canonical partition function we formulate a consistent renormalization of the ground-state energy and the intrinsic state density as a function of deformation. The competition between fission and neutron emission, $\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{(E)}$, of ²¹⁰Po is studied within the framework of the statistical theory as an example. Calculations using renormalized state densities are compared with usual shell-model calculations and experimental data. We find that the usual calculations reflect the incorrect uniform deformamation dependence of the shell-model spectral function. As important changes due to renormalization we find: there is a rapid change of the shape of the transition state at ≈ 45 MeV excitation energy, $\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{(E)}$ remains smaller than unity for all excitation energies and the deformation of the transition state increases after the “shape transition” at 45 MeV monotonically towards the liquid drop saddle-point deformation.     

Shell model study of N = 50 nuclei

Measured E2 and M4 transitions and energy levels in the N = 50 isotones with Z > 38 are satisfactorily reproduced by a shell model with proton configurations $\text{(2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{n}}$. Four sets of two-body matrix elements are found by least-squares fitting to energy levels and transition rates in the N = 50 isotones. These interactions include one that exactly conserves seniority and another that fits the strongly inhibited 8⁺→ 6⁺ transition in ⁹⁴Ru. Slight seniority nonconservation is required to predict inhibited N = 50 transition rates. The sign of the off-diagonal matrix element is determined by comparison with experimental M4 rates. The seniority conserving interaction is found to be equivalent to the best seniority nonconserving interaction for prediction of energy levels.     

Generalized neutron particle-hole states in an extended unified model

Negative-parity levels in the doubly even N = 82, Z nuclei, with 3.0 MeV ? E_x? 6.0 MeV are described in an extended unified-model approach, where neutron hole states in the Z = 50, N = 82 closed shell core, (i.e. ) are coupled to the low-lying levels (E_x ? 2.0 MeV) of the odd-neutron N = 83, Z nuclei. This particular configuration space of generalized neutron particle-hole states (GNPH) is particularly suited for describing negative-parity levels obtained in proton inelastic scattering through isobaric analogue resonances (IAR), corresponding to the N = 83, Z low-lying nuclear levels. Level schemes as well as partial decay widths and angular distributions are calculated and compared extensively with the available experimental data. Also spectroscopic factors, as well as wave functions, deduced from the experimental results are studied in detail. Thus in the cases of ¹³⁶Xe, ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd and ¹⁴⁴Sm, some of the important neutron particle-hole configurations can uniquely be determined in the energy region 3.0 MeV ?E_x ? 6.0 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.     

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.     

Proton-neutron excitations in the high-spin states of 95Tc

The high-spin states of ⁹⁵Tc have been studied in the reaction ⁹³Nb(α, 2n)⁹⁵Tc using inbeam spectroscopy of both γ-rays and conversion electrons. A new sequence of negative-parity states extending up to angular momentum $\text{I =}\text{29}\text{2}$ was found to exist within an excitation energy interval of 4.1 MeV. The positive-parity states are in remarkable agreement with the predictions of a simplified shell-model approach on the basis of coupled excitations of $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton and $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}$ as well as $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ neutron configurations. A similar analysis for the negative-parity states shows qualitative agreement with the experimental results.     

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.     

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.     

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.     

Total reaction cross sections of deformed nuclei: A study of the 233, 238U + α systems

The cross sections for α-particle scattering and α-particle induced fission of ^{233, 238}U were measured at bombarding energies of 15 to 27 MeV. For these fissionable systems, the fission cross sections are very nearly equal to the total reaction cross sections. These experimental reaction cross sections are compared with various theories based on spherical and deformed potentials in order to investigate the effect of static target deformation on the reaction cross sections. From such comparisons no effect of target deformation is established. An interaction barrier (defined by the condition of 22.34 MeV is obtained from a spherical optical model fit to the experimental reaction cross-section data of uranium. This value agrees within 2.3 % with values deduced by a number of other methods.