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.     

High-spin states in26Mg

Theγ-decays of levels in²⁶Mg have been investigated up to 12.5 MeV excitation energy by proton-γ-ray coincidence measurements in the²³Na(α, pγ) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-γ-ray angular-correlation measurements were performed at E_α=14.2 MeV. Many high-spin states were observed, among them levels at 6,978 (5⁺), 7,283(4^?), 7,395(5⁺), 7,953(5^?), 8,202(6⁺), 8,472(6⁺), 9,065(5), 9,112(6⁺), 9,169(6^?), 9,383 (6⁺), 9,542(5), 9,829(7⁺), 9,989(6⁺) and 12,479(8⁺, 7^?) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by 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. Members of five inferred rotational bands, withK ^π=0⁺, 2⁺, 3⁺, 0⁺ and 3^? have been observed up to at leastI=6. TheK ^π=2⁺ band shows strong anomalies of excitation energies andE2 transition rates near theI=6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within theK ^π=2⁺ band and also the ground state band. The lowest lyingI ^π=4⁺ state appears to be “spherical” and cannot be associated with a rotational band.     

Shape coexistence and other aspects of nuclear structure in40Ar

Theγ-decay of⁴⁰Ar has been studied by particle-γ-ray coincidence measurements in the³⁷Cl(α, pγ) reaction at 12 and 13 MeV bombarding energy. Particle-γ-ray angular correlations and linear polarizations ofγ-rays were measured at 12 MeV. A lifetime measurement using the Doppler-shift attenuation method was performed at 11 MeV. The coexistence of spherical and deformed states in⁴⁰Ar could be concluded from the observation of aK ^π=0⁺ rotational band which has itsI ^π=0⁺ through 6⁺ members at 2,121, 2,524, 3,515 and 4,959 KeV excitation energy. The intrinsic quadrupole moment derived fromB(E2) values is ∥Q ₀∥=1,320 _?120 ⁺⁶⁰ mb. Negative-parity states with high spin were observed at 4,858(5^?), 4,494(5^?), 4,226(4^?) and 4,991 KeV(4^?) excitation energy. A complete account of all levels below 5 MeV excitation energy is obtained by a model in which twod _3/2 proton holes couple weakly to the⁴²Ca levels below 4.75 MeV excitation energy.     

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.     

Deformed states of high spin in42Ca

The⁴²Ca levels at 4,715 and 6,633 keV excitation energy have been investigated using the³⁹ K(α,pγ reaction atE _α=14 and 15 MeV. From particle-γ-ray angular correlations the spin assignmentsJ(4,715)=6, 4 andJ(6,633)=8, 6, 4 have been obtained. Lifetime measurements using the Doppler-shift attenuation method yieldedτ (4,715)=120±46 fs andτ(6,633)=52±21 fs. Both levels have positive parity and decay by enhancedE2 transitions. They are interpreted as theJ ^π=6⁺ and 8⁺ members, respectively, of theK ^π=0⁺ rotational band which has theE _x =1,837, 2,423 and 3,250 keV states as further members. The enhancement of inbandE2 transitions is 50 _?16 ⁺³⁵ W.u. (6→4) and 63 W.u. (8→6) respectively. The intrinsic quadrupole moments which have been derived on the basis of the coexistence model, areQ ₀=1.13?0.16/+0.37b(8→6) andQ ₀=1.36±0.25b(6→4), respectively. TheJ ^π=10⁺ member of the rotational band has possibly been observed as a level at 8,856±5 keV excitation energy.     

Evidence for the coexistence of spherical and deformed states in38Ar

The³⁸Ar levels at E_x=5350, 7289 and 9341 keV have been investigated using the³⁵Cl(α,pγ) reaction at E_α=l4 and 14.5 MeV. From particle-γ-ray angular correlations the spin assignments J(5350)=4, J(7289)=6,4 and J(9341)=8,6,4 have been obtained. Life-time measurements using the Doppler-shift attenuation method yielded τ(9341)=106±25 fs and τ(7289)=77±30 fs, while the lifetime τ(5350)=200±50 fs was known previously. All levels have positive parity and decay by enhanced E2 transitions. Hence we propose that they are the J^π=4⁺, 6⁺ and 8⁺ members, respectively, of a K^π=0⁺ rotational band which has the E_x=3377keV, J^π=0⁺ and the 3937 keV, J^π=2⁺ levels as further members. The enhancement of inband E2 transitions is 30 _?6 ⁺¹⁰ W.u. (4→2), 35 _?14 ⁺³⁰ W.u. (6→4) and 20–36 W.u. (8 → 6), respectively, yielding an average intrinsic quadrupole moment Q₀=850 _?125 ⁺²⁰⁰ mb. The moment of inertia is given by h²2θ=92 keV. The present data are in good agreement with the predictions of a deformed state in³⁸Ar that coexists with the spherical states.     

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.     

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.     

New aspects of the rotational model in25Mg

Spin assignments have been made to the²⁵Mg levels in theE _x=5–6 MeV region fromγ-ray angular distributions measured in the²²Ne(α, n y) reaction atE _α=8.0 and 8.8 MeV and fromp-γ angular correlations measured in the²⁴Mg(d, p γ) reaction atE _d=6 MeV. Unique spin assignments ofJ=7/2, 5/2, 5/2, and 9/2 could be made to the levels atE _x=5005, 5511, 5851, and 5967 keV, respectively. Ambigious assignments have been made to the levels atE _x=5245, 5524, 5785, 6032 keV (J=11/2, 7/2), 5455 keVJ=13/2, 9/2), and 5738 keV (J=3/2, 5/2). The present data confirm previous assignments ofJ=1/2 to the levels atE _x=5108 and 5466 keV, respectively. Lifetime estimates have been obtained, using the Doppler-shift attenuation method, for the levels atE _x=5245 keV (τ=30–60 fs), 5785 keV (τ=50–100 fs), 5967 keV (τ=50–100 fs), and 5455 keV (τ>1ps). All other levels in theE _x=5–6 MeV region haveτ<60 fs. A breakdown of theK-selection rule has been observed in theγ-decay of some high spin states, indicating a deviation from the strong coupling model.     

T=1 states in26Al

The resonance reaction²⁵Mg(p, γ)²⁶Al in the energy rangeE _p =300–400 keV was used to populate high-lying bound states in the self-conjugate nucleus²⁶Al. The existence of three resonances atE _p =304, 316 and 388 keV was verified, the spins of the ones at 316 and 388 keV were found to be 3^? and 2⁺, respectively. The spin of the bound level at 4,547 keV level was fixed to beJ ^π=2⁺. Several strong isovector Ml transitions were observed, which led toT=1 assignments for the levels atE _x =4,191, 4,547, 4,599, 5,141 and 5,542 keV. The results for excitation energies and values ofJ ^π,T together with previous experimental and theoretical data on²⁶Al and the neighboring |T _z |=1 nuclei²⁶Mg and²⁶Si are discussed in the framework of the isospin model.     

Recoil distance lifetime measurements in82Kr

The lifetimes τ=124±12, 6 _?2 ⁺⁴ and 380±100 ps of theE _x (I ^π )=3.46(8⁺), 2.92(6⁺) and 3.04(6^?) MeV states, respectively, populated by the reaction⁷⁶Ge(¹²C,α2n) were measured with the recoil distance method. In addition upper lifetime limits were obtained for nine states. The measured lifetimes and energies indicate a band crossing at aboutI ^π =8⁺, probably arising from the alignment of twog _9/2 neutrons. For the 3.04 MeV 6^? state as a second member of a band built on the 2.65 MeV 4^? state the measured lifetime points to a two-quasiparticle configuration. The positive-parity states have been discussed in the frame of the interacting boson approximation, nuclear field theory and the cranked shell model.     

The parity of the 3134 keV,J=1 State in18F

The¹⁶O(³He,?γ)¹⁸F reaction atE(³He)=2.95 MeV was used to study the low-lying states in¹⁸F belowE _x =3.2 MeV. A combination of γ-ray angular distribution and linear polarization measurements using a single planar Ge(Li) polarimeter resulted in aJ ^π =1^? assignment to the 3134 keV state. In addition, the positive parity assignments to the 937(3⁺) and 1702(1⁺) keV states have been verified. Information on branching and mixing ratios as well as on lifetimes are reported. The results are discussed in terms of the weak-coupling and strong-coupling models.     

High-spin states in38Ar

Theγ-decay of 93³⁸Ar levels between 6.84 and 10 MeV excitation energy has been measured using the³⁵Cl(α,pγ) reaction atE _α=14 MeV. A previous measurement of the same reaction could be exploited in the light of the present results, yielding spin(-parity) assignmentsJ ^π(7,070)=5^-, J(7,507)=7,5,J ^π(8,077)=7⁺, J(8,129)=5,6 and J(8,488)=7,5. Theγ-decay modes of yrast levels, which have been previously observed in heavy ion induced reactions, are revised leading to major changes in their spin-parity assignments. New candidates for theJ ^π=8^- and 9⁺ levels were found in the levels at 9,644 and 9,928 keV excitation energy, respectively. A comparison of yrast levels with shell-model calculations is satisfying.     

Quantum numbers of26Al levels above 6 MeV excitation energy

Measurements of resonance strengths and ofγ-ray angular distributions or anisotropies have been performed on selected resonances of the²⁵Mg(p, γ) reaction in the rangeE _p=2–4 MeV,E _x=8.2?10.1 MeV with an emphasis on high-spin andT=1 analog resonances. EightT=1 states are identified, among them high-spin states at 8747 keV (I=6), 9286 KeV (I=5), and 9986 keV (I ^π = 7⁺, 6⁺). Shell model calculations in thes-d basis space reproduce the branching ratios of these states and clarify the nature of final states. New high-spinT=0 states are observed at 9720 keV (I ^π = 7⁺), 8602 keV (I = 6), and 6695 keV (I ^π = 7⁺). TheI ^π assignments to severalE _x = 6–8 MeV states are revised and the role of two-particle excitations into thef-p shell is elucidated. A revised spectrum of 73 positive-parity,T = 0 states is compared to the predictions of shell-model calculations in thes-d basis space using the universals-d shell Hamiltonian.     

Transition probabilities and the structure of some negative-parity states in126,130Xe and132Ba

The lifetimes of several negative-parity states in^126,130Xe and¹³²Ba have been determined by means of the generalized centroid-shift method. The reactions^124,128Te(α,2n) and¹²²Sn(¹³C, 3n) have been used. Following results were obtained:T _1/2(2758 keV)=1.3±0.2 ns in¹²⁶Xe,T _1/2(2060 keV)=0.20±0.10 ns,T _1/2(2104 keV)=0.50±0.10 ns,T _1/2(2376 keV)=0.30±0.10 ns andT _1/2(2973 keV)=4.6±0.4 ns in¹³⁰Xe as well asT _1/2(2120 keV)=0.40 _?0.10 ^+0.20 ns in¹³²Ba. A systematics of the B(E2; 7 _? ¹ ?5 ₁ ^? ) values in theN=76 nuclei is presented. Electric dipole and quadrupole transition rates are discussed in terms of octupole and quadrupole collectivity. The structure of the 5 ₁ ^? and 7 ₁ ^? states is considered. Nuclear reactions:^124,128Te(α, 2 _n ),E=26 MeV,¹²²Sn (¹³C, 3n),E=53 MeV; measuredE _γ I _γ , γ-r.f. DeducedT _1/2, B(σL) in^126,130Xe and¹³²Ba. Ge detectors. Generalized centroid-shift analysis.     

High-spin states in109Sn and their decay to the ground state

An extended level scheme of¹⁰⁹Sn is presented showing high-spin states up to E_x≈ 8 MeV and spins up toJπ=(41/2+). Their decay to the 5/2+ ground state has been observed identifying a 12.8 keV 7/2⁺ → 5/2⁺ transition. A half-life of T_1/2=7(1) ns has been measured for the 17/2⁺ state atE _x =2114 keV. The experimental data are compared with the predictions of shell-model calculations.     

The low-lying states and configurations in138La

Tritons from the reaction¹³⁹La(d, t)¹³⁸La atE _d=16 MeV were analyzed at eleven reaction angles from 22 ° to 90 ° with a broad-range magnetic spectrograph. TheQ-value of the reaction is ?2522±5 keV. The nine lowest-lying states in¹³⁸La are interpreted in terms of the shell model configurations (πg _7/2)^?1 (vd _3/2)^?1, (πg _7/2)^?1 (vs _1/2)^?1 and (πg _7/2)^?2 (πd _5/2)^?1(vd _3/2)^?1. Seven levels in the energy range of 700–1300 keV are populated byl=5 transitions and are interpreted as coming from the (πg _7/2)^?1(vh _11/2)^?1 configuration. The ground state of¹³⁸La is shown to haveJ ^π=5⁺. Therefore, beta decay by unique second-forbidden transitions to the 2⁺ one-phonon states of¹³⁸Ce and¹³⁸Ba must be inferred in spite of unusually high logft values of 19.2 and 18.5, respectively.     

The 6− analog-antianalog states of 28Si

A resonance is observed in the ²⁷Al(p, γ)²⁸Si reaction at E_p=2876±2 keV, which corresponds to an excitation energy of 14356±2 keV. The 14.36 MeV level decays to a new level at 11577±2 keV, which is turn decays to the known level at 9701.8±0.5 keV. With previous information on the 9.70 MeV level and the present γ-ray angular distributions, obtained from singles spectra as recorded by a 40 cm³ Ge(Li) detector, the spins of the three levels can be limited to J=5, 6; J=6; and J=5, respectively. Transition strength arguments based on measurements of the strength of the 2876 keV resonance and the lifetime of the 11.58 MeV level indicate that the 14.36 MeV level has J^π=6^?, T=1 and that the 11.58 MeV level has J^π=6^?, T=0.     

On the yrast levels in204Pb

High-spin states in²⁰⁴Pb were populated in the²⁰⁴Hg(α,4n) reaction using α-particles in the energy region 42–51 MeV. Prompt and delayedγ-rays as well as conversion electrons were studied in addition to excitation functions, angular distributions andγ-γ coincidences. In this way a stretched cascade ofγ-rays from a level at 8125.9 keV was found to feed the previously known isomeric 9^? level at 2185.7 keV. Spins and parities were established for levels up to and including a 19^? level at 6098.0 keV. The levels with c= 17^2212; and 19^? at excitation energies of 5664.3 and 6098.0 keV are likely to be due to the simplep ₁ ^2/s-1 i ₁₃ ^2/?3 andf ₅ ^2/?1 i ₁₃ ^2/?3 configurations. The agreement between calculated and experimental energies for all observed levels in the regionJ=9–19 is very good in cases where the empirical two-particle interactions used are satisfactorily well known. Above the 19^? level there are three weakly populated levels at 7402.1, 7849.2 and 8125.9 keV, which are likely to haveJ≥20. None of these energies agrees with the calculated value 7695±20 keV for the 20⁺ state of thei ₁₃ ^2/?4 configuration which has the highest angular momentum produced by the four valence neutron holes. This apparent anomaly can be understood if the yrast levels withJ≥20 have angular momentum contribution from the core. It seems likely that the states at 7402.1, 7849.2 and 8125.9 keV are due to proton core excited states of the typeπh _9/2 h ₁₁ ^2/?1 ×νp ₁ ^2/?2 i ₁₃ ^2/?2 withJ ^π=20⁺ andJ ^π=21⁺ andπh _9/2 h ₁₁ ^2/?1 ×νp ₁ ^2/?1 f ₅ ^2?1 i ₁₃ ^2/?2 withJ ^π=22⁺ or 23⁺, respectively. The state at 8126 keV has the highest energy so far directly observed in a stretched cascade ofγ-rays from the decay of a heavy nucleus produced in (α, xn) reactions.     

The structure of28Si above 10 MeV excitation energy III: Level scheme and shell model interpretation

²⁸Si level scheme up to 14.5 MeV excitation energy is reevaluated using information from two preceding papers. It consists of approximately 250 levels which are almost completely characterized according to the quantum numbersI, π, T of the levels. The properties of positive-parity states are compared to the predictions of shell model calculations within the completes-d basis space using the unifieds-d shell Hamiltonian. A spectrum of 48 experimentalT=1 states between 9.3 and 16 MeV is reproduced with a rms deviation of only 150 keV. A calculation of radiative widths and γ-decay modes which uses free-nucleong-factors yields excellent agreement with experiment and confirms that quenching of M1 transitions is only marginal in²⁸Si. The detailed shell model analysis of theT=0 spectrum is extended to the limiting energy whereT=1 wave function admixtures, not contained in the theory, become important experimentally. This happens at 6–8 MeV above the yrast state, depending on the spin value. Altogether it appears that a spectrum of 171 levels below 14.5 MeV, which have positive or unassigned parity, is almost completely accounted for by the model. Apparent intruder states from outside thes-d shell space are observed atE _x =10 945 keV (I ^π=4⁺) and 12 860 keV (I ^π=6⁺) and are interpreted as members of aK ^π=0⁺ rotational band.