The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

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.     

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 ($\text{3}\text{2}$, $\text{5}\text{2}$, $\text{7}\text{2}$)⁺.     

The (7Li, 8Li) reaction to the (h92)−1 state in 207Pb

Relative differential cross sections for the reaction ²⁰⁸ P(⁷Li, ⁸Li) leading to the predominantly single-hole states in ²⁰⁷Pb have been analysed using the DWBA to determine the rms radius of the 1h_{$\text{9}\text{2}$} neutron orbital in ²⁰⁸Pb by comparison with known sizes of the 3p_{$\text{1}\text{2}$} and 2f_{$\text{7}\text{2}$} orbits. The experiment was performed at a beam energy of 52 MeV. The insensitivity of the technique to unknown input parameters to the DWBA analysis is demonstrated and a value of 5.94±0.11 fm for the rms radius of the 1h_{$\text{9}\text{2}$} orbit obtained assuming 70% of the hole strength is concentrated on the $\text{9}\text{2}{}^{\mathrm{?}}$, 3.41 MeV state in ²⁰⁷Pb. Effects due to fragmentation of the different hole strengths are examined and a value of 6.00 ± 0.11 fm is extracted as the best value for the rms radius of the neutron excess in ²⁰⁸Pb. The relevance of these data to mean-field calculations of nuclei is discussed.     

Axially symmetric time-dependent Hartree-Fock study of the 208Pb + 208Pb reaction

A time-dependent Hartree-Fock calculation assuming axial and reflection symmetry constraints is performed for the head-on collision of ²⁰⁸Pb + ²⁰⁸Pb systems at E_lab≈1600 MeV. The calculation suggests the excitation of surface modes in the reaction and the energy loss characteristic of a deep inelastic process. An estimate of neck-radius and neck-formation time is given.     

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.     

Yrast levels of 220Ra populated in the 208Pb(14C, 2n) reaction

Yrast states in the nucleus ²²⁰Ra were studied by means of the ²⁰⁸Pb(¹⁴C, 2n) reaction at 61 and 64 MeV. A staggering sequence of levels of positive and negative parity has been observed up to spin and parity I^π = 16⁺ (18 ⁺) and from I^π = 5^? to I^π = 17^?, respectively. These states are connected by strong E1 transitions competing with the stretched E2 transitions, the $\text{B(}\text{E}\text{1)}\text{B(}\text{E}\text{2)}$ ratio being ~ 10 ^?6 fm^?2. The ratio of the excitation energy of the 4⁺ state to that of the 2⁺ state is close to the vibrational limit. The moment of inertia associated with the negative-parity yrast states is slightly increasing with the rotational frequency ω. It is considerably higher than that of the positive-parity states at lower spins, the difference decreasing monotonically with increasing ω. The data are discussed with reference to the octupole vibrational picture as well as to the results of recent models predicting reflection-asymmetric shapes in the Ra-Th region.     

Gamma-spectroscopic investigations on 67Ge

By γ-γ coincidence measurements following the ⁵⁷Fe(¹²C, 2nγ) reaction at E_12C = 40 MeV several new states above 1.5 MeV excitation energy in ⁶⁷Ge have been established. Spin and parity assignments on the basis of the angular distribution, linear polarization and γ-ray yield function indicate very similar structures in ^{67, 69}Ge. The positive-parity states can be followed up to the $\text{17}\text{2}{}^{\mathrm{+}}$ state at E_x = 3.07 MeV followed by a sequence of negative-parity high-spin states at nearly the same excitation energy relative to the $\text{9}\text{2}{}^{\mathrm{+}}$ single-particle state as in the neighbouring nucleus ⁶⁹Ge where these states were found to have strong single-particle admixtures. A reinvestigation of the spin of the E_x = 2.75 MeV level in ⁶⁹Ge resulting in a change of its spin from $\text{15}\text{2}{}^{\mathrm{+}}\text{to}\text{17}\text{2}{}^{\mathrm{+}}$ and for all spins above, removed the discrepancy concerning the spin assignments of corresponding levels in ^{67, 69}Ge. The excitation pattern of the Ge isotopes with 34 ≦ N ≦ 39 clearly indicate same structures probably due to the strong competition between collective and single-particle excitations along the whole chain similar to the results for the Zn isotopes.     

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.     

Giant-resonance excitation by 130 MeV 3He

Energy spectra of 130 MeV ³He scattered from ²⁴Mg, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb have been measured. The spectra exhibit a pronounced giant resonance (GR) structure in the excitation energy region around $\text{E}{}_{\mathrm{<mtext>x</mtext>}}\text{≈ 63A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$. The GR angular distributions as well as those corresponding to the first 2⁺ levels in ²⁴Mg and ¹²⁰Sn have been obtained for angles 7° ≦ θ_L ≦ 35°. Distorted wave calculations using the optical model parameters fitting the elastic data resulted in good fits to the 2⁺ levels. For ²⁴Mg, ⁹⁰Zr and ¹²⁰Sn the shapes of the GR angular distributions are well fitted by L = 2 curves alone. However, for ²⁰⁸Pb both L = 2 and L = 4 curves give fits of comparable quality.     

12C1 and 8Be production in 12C + 208Pb collisions

The mechanisms involved in the production of fast α-particles in ¹²C-induced reactions have been studied for the ¹²C + ²⁰⁸Pb system at the bombarding energies of E_12c = 132, 187 and 230 MeV. Absolute cross sections for the reactions ²⁰⁸Pb(¹²C. ¹²C¹→α + ⁸Be), ²⁰⁸Pb(¹²C, ⁸Be(g.s.)) and ²⁰⁸Pb(¹²C, ⁸Be(2.94 MeV)) have been determined by coincidence measurement of two or three correlated α-particles. Inclusive α-particle production cross sections were also measured at E_12c = 187 MeV. It is found that the inelastic process (¹²C, ¹²C¹→α + ⁸Be) does not contribute significantly to fast α-particle production but that the production of ⁸Be by projectile fragmentation is an important source of α-particles. At the highest bombarding energy (230 MeV) it appears that the ¹²C → 3α fragmentation reaction becomes more prominent at the expense of the ¹²C→α + ⁸Be fragmentation channel.     

High-spin states of 39K and 42Ca

High-spin states of ³⁹K and ⁴²Ca have been investigated with the ²⁸Si(¹⁶O, αpγ)³⁹K and ²⁸Si(¹⁶O, 2pγ)⁴²Ca reactions at a beam energy of 45 MeV. Gamma-gamma coincidence, γ-ray angular distribution and linear polarization measurements were performed with a Ge(Li)-NaI(Tl) Compton suppression spectrometer and a three-crystal Ge(Li) Compton polarimeter. High-spin states of ³⁹K at E_x = 7.14,7.78and8.03 and of ⁴²Ca at E_x = 7.75MeV are established. Unambiguous spin-parity assignments of $\text{J}{}^{\mathrm{\pi }}\text{=}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{13}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{+}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{,}\text{17}\text{2}{}^{\mathrm{+}}\text{and}\text{19}\text{2}{}^{\mathrm{?}}$ to the ³⁹K levels at E_x = 5.35, 5.72, 6.48, 7.14, 7.78 and 8.03 MeV and of 6^?, 7^?, 8^?, 9^? and(8, 10)^? to the ⁴²Ca levels at E_x = 5.49, 6.15, 6.41, 6.55 and 7.37 MeV, respectively, have been obtained. Further spin-parity restrictions, lifetime limits, excitation energies, branching ratios and multipole mixing ratios are reported. Discrepancies with previous J^π assignments are discussed in detail.     

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.     

Alpha cluster states in 16O

A very successful cluster-core model for the rotational bands of light nuclei has been extended to treat excited core states. The resulting coupled-channels problem has been solved for the ${}^{16}\text{O }{}^{12}\text{C + α}$ system. As well as the known + ve and ? ve parity bands many new levels are predicted and compared with experiment. The agreement between theory and experiment is very good both for the excitation energies and the decay properties. We predict the positions of two low-spin non-natural parity levels with E_x < 20 MeV and the positions of many high-spin states. In particular, we explain why the 8⁺ level seen in α-transfer at 22.5 MeV could not be found in the α-scattering cross sections and predict a second 8⁺ at 24.4 MeV. We discuss how the levels may be regarded as members of rotational bands and determine the terminating J-values for these bands. Finally we show that the usual rotational model would be a poor approximation for the cluster bands of ¹⁶O.     

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.     

Half-lives of two-neutron-hole O2+ states in 206Pb and 208Po

Half-lives of O₂⁺ states in ²⁰⁶Pb and ²⁰⁸Po, 770±40 and 465±20ps, respectively, are determined using direct-timing techniques. The corresponding monopole strength parameter values,$\text{ρ(}{}^{206}\text{Pb}\text{) = 0.034±0.002}$ and $\text{ρ(}{}^{208}\text{Po}\text{)=0.030?0.037}$, indicate that the O₂⁺ states in both nuclei are mainly of similar two-neutron-hole character.     

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.     

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.