Statistical analysis of24Mg+24Mg elastic and inelastic scattering

The data on the excitation functions of²⁴Mg+²⁴Mg elastic and inelastic (²⁴Mg +²⁴Mg^*(2⁺),²⁴Mg^*(2⁺)+²⁴Mg^*(2⁺),²⁴Mg+²⁴Mg^*(4⁺),²⁴Mg^*(4⁺)+²⁴Mg^*(2⁺),²⁴Mg+²⁴Mg^*(6⁺)) scattering fromE _c.m=42 to 56 MeV have been subjected to a statistical analysis consisting of calculations of deviation function, cross-correlation function, cross-channel correlation coefficients, coherence widths, and the distribution of cross sections. On the basis of the analysis resonant structures atE _c.m=45.70, 46.65, 47.35 and 47.75 MeV have been confirmed. Two new resonant structures atE _c.m=44.55 and 50.50 MeV have been identified.     

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of²⁰Ne(¹⁶O,¹²C)²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(1.37, 2⁺),²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(4.12, 4⁺+4.24, 2⁺) +²⁰Ne(¹⁶O,¹²C^*(4.44, 2⁺))²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(6.01, 4⁺+6.43, 0⁺),²⁰Ne(¹⁶O,²⁰Ne)¹⁶O,²⁰Ne(¹⁶O,²⁰Ne^*(1.63, 2⁺))¹⁶O, and²⁰Ne(¹⁶O,²⁰Ne^*(4.25, 4⁺))¹⁶O reactions atθ _lab=13° fromE _c.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atE _c.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atE _c.m. =25.6 MeV.     

High-spin states in48Ti

The⁴⁵Sc(α, p γ) reaction has been investigated atE ^α=11, 12 and 13MeV. Theγ-decay of 198 levels in⁴⁸Ti up to 8,323 keV excitation energy has been observed. High-spin states were investigated by proton-γ ray angular correlation measurements atE=11 and 13MeV and by DSAM lifetime measurements atE=11 MeV. From the combined evidence spin (-parity) assignments were obtained for the levels atE _x =8,323 keV (J= 10,8,6), 8,091(12, 10, 8, 6), 7,668(10, 8), 7,427(9, 7), 7,374(11, 9, 7), 6,906(10, 8, 6), 6,172(8⁺,6⁺), 6,102(10⁺,8⁺), 6,039(6), 6,034(9⁺, 7⁺), 5,630(7), 5,197(8⁺), 5,169(7⁺), 5,155(5), 4,404(5), 4,398(6⁺) and 4,046keV (5). Most of the ambiguous spin assignments become unique if the 8,091 keV level hasJ=12, an assumption which is favoured by its excitation function. The level spectrum thus obtained is well reproduced by shell model calculations in the pure (f _7/2)⁸ configuration space. Discrepancies exist in the reproduction ofγ-decay modes. The reason is found in low-lying high-spin intruder states which include the 7,427 and 8,323 keV levels. The spectrum of negative-parity states is understood qualitatively by a comparison with⁴⁶Ti and⁴²Ca.     

Non-statistical structures in12C(15N,4He)23Na reaction

The data on the? _lab=7° excitation functions of¹²C(¹⁵N,⁴He)²³Na reaction betweenE _cm=9.42 and 17.33 MeV for 28 states upto an excitation energy of 8.940 MeV in²³Na have been subjected to statistical analysis. In addition to statistical fluctuations, the results of the analysis indicate the existence of non-statistical structures atE _cm=10.66, 10.93, 11.38, 12.62, 13.16, 15.32 and 16.18 MeV.     

Non-statistical effects in the 12C(12C, α)20Ne reaction near Ec.m. = 15 MeV

The ¹²C(¹²C, α)²⁰Ne reaction is studied near E_c.m. = 15 MeV. Angular distributions for three energies and excitation functions at θ_{lab = 30°} over an energy range E_c.m. = 14.5?15.4 MeV for about 20 levels in ²⁰Ne (E_ex = 0–13 MeV) are examined. The statistical analysis yields the results that a correlated resonance is present at E_c.m. = 14.75 MeV. A nonstatistical contribution to the reaction is also apparent when energy-averaged cross sections are compared with the Hauser-Feshbach model predictions. Strong population of the 0⁺₃ band in ²⁰Ne is observed.     

Structure of28Si from the spectroscopy of high-spin states

A search for high-spin states in²⁸Si has been performed byn?y coincidence measurements in the²⁵Mg(α,nγy) reaction atE _α=14 and 15.5 MeV. Spin-parity assignments of the observed levels were obtained fromn?γ angular correlation and lifetime measurements atE _α=14.5 MeV. Theγ-decay of the 9,164 keV level was investigated separately with the²⁷Al(p, γ) reaction at theE _p=2,160 and 2,312 keV resonances. Rotational bands withK ^π=3^? (comprising levels atE _x=6,879, 8,413, 10,188 and 12,204 keV),K ^π =5^? (comprising levels atE _x=9,702, 11,577 and 13,741 keV) andK ^π=0⁺ (comprising levels atE _x=6,691, 7,381, 9,164 and 11,509 keV) were observed. The finding of the latter band supports the idea of coexisting oblate and prolate shapes in²⁸Si. A level at 14,643 keV excitation energy has the properties of theI ^π=8⁺ member of the ground state band. There are additional positive-parity high-spin states which do not fit into rotational bands. All types of positive-parity states are well accounted for by shell model calculations.     

Oscillations in the excitation function for complete fusion of 6O+12C at low energies

The excitation function of the complete fusion of ¹⁶O + ¹²C has been measured in the range E_c.m.=8.5?12.9 MeV. It contains oscillations which have already been observed at higher energies. Some of these oscillations are tentatively in terms of a rotational band.     

Mechanism of reactions induced by 7 MeV deuterons on9Be [(d,p), (d,d), (d,t), (d,4He)]

Angular distributions of protons, deuterons, tritons and alpha-particles emitted from the reactions in thed+⁹Be-system atE _d =7 MeV as well as excitation functions at selected angles in the energy rangeE _d =6.5–7.5 MeV (LAB) were measured. The potential part of the elastic scattering is described by the phenomenological optical model. The compound nucleus contribution to all exit channels is determined using the Hauser-Feshbach model. The collective excitation of the 2.43 MeV excited state of⁹Be and transfer processes are analysed within the DWBA formalism. The analyses suggest a significant contribution of five-nucleon transfer to the (d,⁴He) channel.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

Investigation of large angle structure in α-scattering from calcium isotopes betweenE α=36–61 MeV

Elasticα-scattering angular distributions have been measured atE _α=36.2 MeV, 39.6 MeV, 42.6 MeV, 49.5 MeV, 61.0 MeV for⁴⁰Ca and atE _α=36.2 MeV, 42.6 MeV, 49.5 MeV and 61.0 MeV for⁴⁴Ca, respectively. At backward angles the data display an oscillatory structure forE _α<50 MeV and more smoothly decreasing slopes atE _α =61.0 MeV resembling the data obtained at higher energies. The⁴⁰Ca data belowE _α =50 MeV show the well known backward enhancement, which at 42.6 MeV and 49.5 MeV can be fitted by aP ₁₄ ² and aP ₁₆ ² respectively. Together with previous data,P _L ²-structures have now been observed for allL-values betweenL=8 andL=16. The slope of the curveL(L+1) versus excitation energy is slightly smaller forL>12 than forL<12. Optical model analyses (within a Woods-Saxon-folding model) lead to large differences between the⁴⁴Ca and⁴⁰Ca parameters. Furthermore, in our parametrization, the⁴⁰Ca real potential depth shows dramatic changes with energy. This feature seems outside the domain of the optical model and requires consideration of additional effects (e.g. antisymmetrization) not included in the standard optical model. Present microscopic calculations on the basis of the Resonating Group Method are discussed in connection with the characteristic features ofα-scattering from⁴⁰Ca.     

Alpha-heavy-ion angular correlations from 28Si + 12C

Alpha particles have been measured in coincidence with heavy recoil nuclei from the ²⁸Si + ¹²C reaction. At E_lab = 87 MeV angular correlations for alphas between 15° and 55° and heavy ions at angles ?9°, ?12° and ?15° have been taken. An excitation function of coincidence events with θ_α = 30° and θ_HI = ?12° has been measured for 84 MeV < E_lab < 91.5 MeV. The results are well described by a statistical-model calculation for compound nucleus decay. No evidence is found for additional processes.     

Decay properties of very-high-spin states in transitional Er nuclei aroundA=154

Theγ ray continuum structures of the transitional Er isotopes withA～154 are studied using the reaction⁷⁴Ge(⁸⁴Kr,xn)^158?xEr atE _lab=340 MeV. The measurements include energy spectra, total energies, multiplicities, angular distributions and lifetimes using the DSAM method. The analysis of data confirms the previously observed two-bump structure of the continuum radiation. A meticulous subtraction of discrete contributions proves the persistence of the low-energy bump even at high spins, i.e.I>40?. The angular-distribution measurements assign predominant dipole structure to the bump atE _γ=0.65 MeV, whereas the bump atE _γ=1.3 MeV is of almost pure quadrupole character at high spins. The lifetime measurements give evidence for a strong enhancement of theB(E2) values of the upper bump,B(E2)/B _sp>130. Spin-selection studies reveal, in the spin rangeI=30?50? an almost constant energy for the 1.3 MeV bump,ΔE<60 keV.     

Intermediate width structures in the 12C(12C,8Beg.s.)16O reaction at E c.m. =20 to 30 MeV

The ¹²C(¹²C,⁸Be_g.s.)¹⁶O reaction cross section has been measured at center-of-mass energies between 20 and 30 MeV. Intermediate width structures have been observed for the reactions leading to the ground state and two doublets of states, 6.05/6.13 MeV and 6.92/7.12 MeV, in ¹⁶O. For the ⁸Be_g.s.+¹⁶O_g.s. channel the dominant angular momenta contributing to several structures have been deduced by the analysis of the excitation functions at selected center-of-mass angles. Correlations between the structures in the ⁸Be_g.s.+¹⁶O_g.s. channel and in other inelastic scattering channels in the E _c.m. = 30 MeV region are discussed. An interpretation of the resonances in terms of current structural models is given     

Search for resonances in 12C(9Be, α)17O

Excitation functions at 7° (lab) have been measured from E_c.m. = 5.1 to 11.4 MeV in approximately 114 keV steps for 15 groups of final states in ¹⁷O populated by the ¹²C(⁹Be, α) reaction. Statistical tests have been used to locate possible non-statistical structure in the excitation functions. Possible anomalies were found near E_c.m. = 6.3, 7.5, 8.9 and 9.7 MeV. Angular distributions were measured at E_c.m. = 9.20, 9.71 and 10.23 MeV for the three lowest excited states in ¹⁷O. The data have been compared with Hauser-Feshbach calculations in addition to the following reaction mechanisms: compound plus a single resonance, compound plus interfering resonances and compound plus direct reactions.     

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.     

Molecular orbital theory for intermediate structure in the excitation function of heavy-ion reactions

In the excitation function for the elastic scattering between an α-conjugate target and projectile, there often exist intermediate structures which cannot be interpreted easily either by conventional optical potential model or statistical theory. A nuclear molecular-orbital approximation theory for the α-transfer mechanism has been formulated and applied to the ²⁴Mg(¹⁶O, ¹²C)²⁸Si reaction. The excitation function at θ_c.m. = 0° and differential cross section in the whole angle region at three different energies E_c.m.= 27.8, 30.8 and 36.2 MeV are calculated. The calculations reproduce well these experimental curves with a common set of parameters. The intermediate structures shown naturally in the excitation function and the anomalous oscillatory structures appear in the whole angle region of the differential cross section.     

Resonances in low energy40Ca(α, α)-scattering and quasimolecular band in44Ti

The elasticα-scattering from⁴⁰Ca has been studied betweenE _α=7.035 MeV and 7.405 MeV. Angular distributions and excitation functions have been measured in 5 keV steps. The data display a resonance atE _α=7.26 MeV which by its width and angular correlation is clearly distinguished from strong Ericson fluctuations in this region. From the analysis of the angular distributions and excitation functions a spinJ ^π=1^? is assigned to this resonance. The resonance parameters areΓ _α=31 KeV,Γ _total=51keV. By its spin and excitation energy this state is interpreted as a member of a quasimolecular band in⁴⁴Ti the higherl-members of which are known from⁴⁰¹Ca(α, α) scattering betweenE _α=18 MeV and 50 MeV. The experimental data are compared with recent microscopic calculations within a fully antisymmetrized reaction theory.     

High-spin states in68Ga

The⁶⁸Ga nucleus has been studied via the reactions⁶⁵Cu(α, nγ)⁶⁸Ga atE _α=12–21 MeV and⁶⁶Zn(α, p nγ)⁶⁸Ga atE _α=25–40 MeV. The level scheme has been established by means of relative yield functions, electronic timing measurements, prompt and delayedγ-γ coincidences, angular distributions and directional orientation coÏncidences. Spins up to 11⁺ were assigned to levels up to 4 MeV excitation and the higher ones were interpreted by coupling a⁶⁷Ga core with a (v 1 g_9/2) neutron.     

12C(12C, 8Be)16O angular distributions and excitation functions between 35 and 69 MeV bombarding energy

An array of eight detectors has been developed for identifying the particle unstable ⁸Be nucleus from nuclear reactions with high detection efficiency. Absolute cross sections have been measured for the reaction ¹²C(¹²C, ⁸Be_g.s.)¹⁶O to the ground state and to several excited states in ¹⁶O. Excitation functions at seven angles from 15° to 45° (lab) in 5° steps have been measured for bombarding energies between E¹²_C(lab) = 35 and 69 MeV. Excitation functions were obtained for the following states in the residual nucleus ¹⁶O which were found to be strongly populated: g.s.(0⁺); 6.1 MeV (0⁺, 3^?); 6.9 MeV (2⁺); 10.4 MeV (4⁺); 11.1 MeV (4⁺); 14.7 MeV (6⁺,…) and 16.3 MeV (6⁺,…). The energy range is covered in 250 keV (c.m.) steps; at certain energy ranges in ¹²⁵ keV or 50keV steps. All excitation functions exhibit a strong energy dependence of the cross section; pronounced gross structures with superimposed fine structures, similar to those observed for ¹²C+¹²C elastic and inelastic scattering at these energies, are observed. At 19.3 MeV, where resonant structures were observed in the reactions ¹²C(¹²C, p)²³Na, ¹²C(¹²C, n)²³Mg and ¹²C(¹²C, d)²²Na, no resonance is found for the reaction studied here. At 60, 61 and 63 MeV angular distributions have been measured in 1° and 2.5°(lab) angular steps. The excitation functions have been analyzed in terms of Ericson fluctuations and cross-correlation functions.     

Structure of the mirror nuclei21Ne and21Na

Theγ-decay of levels in²¹Ne up to 10 MeV excitation energy has been investigated byn — γ coincidence measurements initiated with the¹⁸O(α, nγ) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining then — γ angular correlation measurements performed atE _α=11, 11.82 and 13.6 MeV with a consideration of lifetimes, neutron penetrabilities of the unbound states, and information from the mirror nucleus²¹Na. The resulting values of E_x[keV]?J ^π are as follows: 4525-5⁺, 4686-3⁺, 5431-7⁺, 5549-3⁺, 5819-7^?, 6175-7⁺, 6268-9⁺, 6550-9, 6639-9, 7006-7⁺, 7041-9, 7356-7 or 9, 7422-11^(?), 7648-7⁺, 7981-11 or (7⁺), 8154-9, 8240-11, 8664-9^? or 11 or 13^?, 9401-13^?, 9867-13^? or 15⁺, 9941-13^? or 15 or 17⁺. The assignment of mirror levels in²¹Ne —²¹Na has been extended to the 6175 keV level of²¹Ne. Excitation energies, electromagnetic properties, Gamow?Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unifieds—d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 —1s _1/2—0d_3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands atJ=17/2 or 19/2. The spectrum of intruder states in²¹Ne is observed to begin with a 5628 keV,J ^π=7/2⁺ state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.