Determination of the static quadrupole moment of the first 2+ states of 122Te, 124Te,and 130Te by heavy-ion coulomb excitation

A Coulomb excitation experiment has been performed on the first 2⁺ states of ¹²²Te, ¹²⁴Te and ¹³⁰Te. The relative excitation probabilities of the first 2⁺ states were measured at backward and forward projectile scattering angles. Particle-γ coincidences were used to identify the inelastic events. The data were analyzed with the aid of the Winther-deBoer multiple Coulomb excitation program. Separate γ-ray angular distribution measurements were made as a function of target recoil velocity to determine the influence of the deorientation effect. The projectile and bombarding energy were chosen to minimize the effect on the experiment of higher state interference due to Coulomb excitation of the first 2⁺ state via the second 2⁺ state. For positive higher state interference the extracted quadrupole moments of the first 2⁺ states are Q₂₊ = ?0.43 ± 0.08 b, ?0.49 ± 0.08 b and ?0.08 ± 0.08 b for ¹²²Te, ¹²⁴Te and ¹³⁰Te respectively. These results and other measurements of Q_2⁺ for the doubly even Te isotopes are used to discuss the model dependent calculations of Q_2⁺.     

Dipole excitations in 122Te, 126Te and 130Te

Excited states of the nuclei ¹²²Te, ¹²⁶Te and ¹³⁰Te were populated via the (γ, γ') reaction at endpoint energies of the bremsstrahlung between 4.5 and 5.5 MeV. Gamma rays were detected with a EUROBALL-CLUSTER detector and a single detector. In all nuclei several dipole transitions were identified at energies around 3 MeV. The lowest corresponding J = 1 states are interpreted as two-phonon excitations. Quasiparticle-phonon-model calculations predict one 1^? state arising from the coupling of the first quadrupole and the first octupole phonon and one 1⁺ state arising from the coupling of the first and the isovector second quadrupole phonon at about 3 MeV. The calculated transition strengths are compatible with experimental ones.     

Effect of inelastic scattering processes on (p,t) reactions exciting the first 2+ states in Te,Sn and Cd isotopes

Differential cross sections of (p, t) reactions exciting the 2⁺₁ states in Te (A = 128 ? 120), Sn (116 and 114) and Cd (114 and 112) have been measured at E_p = 52 MeV. The observed differences of the angular distributions are interpreted by taking into account the two-step processes through inelastic scattering channels.     

A study of the reaction 12C(α, α′)12C exciting the 1+T = 0 level at 12.71 MeV

The differential cross section for the excitation in the inelastic scattering of 36 MeV α-particles of the 1⁺T = 0 level in ¹²C has been measured. Calculated angular distributions suggest that the transition proceeds primarily by two-step reactions rather than by the one-step reaction involving the two-body alpha-nucleon spin-orbit potential.     

Channel coupling and exchange of an alpha-particle cluster in deuteron scattering on 6Li nuclei

Existing experimental data on elastic and inelastic deuteron scattering on ⁶Li nuclei in the energy range from 8 to 50 MeV were analyzed within the approach of coupled reaction channels. The coupling of elastic scattering and inelastic scattering accompanied by the transition to the 3⁺ state at E _x = 2.186 MeV and the mechanism involving the exchange of an alpha-particle cluster were taken into account in respective calculations. The phenomenological potentials obtained from the present analysis describe well experimental angular distributions at all energies and in full angular ranges. The depths of the real and imaginary parts of the potentials in question depend smoothly on energy at fixed values of the remaining parameters. The energy dependence of relevant volume integrals agrees well with similar data for the p + ⁶Li, ?? + ⁶Li, and ¹²C + ¹²C systems and with the predictions of a microscopic theory.     

Evidence for inelastic processes in the 24Mg(13C, 12C)25Mg reaction at elab = 30 MeV

The ²⁴Mg(¹³C, ¹²C)²⁵Mg reaction has been studied at 30 MeV using a magnetic spectrometer. Differential cross sections for transitions to several final states in ²⁵Mg have been measured and analysed using an exact finite range DWBA code. The DWBA predictions have fitted the bell-shaped distributions satisfactorily, yielding spectroscopic factors which are in reasonable agreement with those obtained using (d, p) reactions. The exceptions are the $\text{3}\text{2}$⁺ state at 0.97 MeV which displays a marked departure from the bell-shaped angular distribution obtained for the other $\text{3}\text{2}$⁺ state at 2.80 MeV, and the $\text{7}\text{2}$⁺ state at 1.61 MeV whose angular distribution has an unusual shape, displaying a deep minimum located at the grazing angle. A semiquantitative model has been used to suggest that the angular distribution for the 0.97 MeV state is evidence for the coupling of inelastic processes in this transition. In the case of the 1.61 MeV state it is suggested that the angular distribution shows the influence of indirect Coulomb excitation on the transfer cross sections.     

Analysis of inelastic scattering of3He on14C at 37.9 MeV

The differential cross sections of elastic and inelastic scattering of³He ions on the¹⁴C nucleus have been measured at an energy of 37.9 MeV. By fitting the shape of the measured angular distribution of the elastic scattering the parameters of the optical model have been found. These parameters have been used for the standard DWBA calculations of angular distributions corresponding to excitations of the¹⁴C levels 6.73(3^?), 7.01(2⁺) and 8.32(2⁺) MeV and for coupled channels calculations of the level 8.32(2⁺) MeV. The vibration parametersβ _L of the¹⁴C nucleus have been deduced.     

Observation/confirmation of hindered E2 strength in 18C/16C

We have measured the lifetime of the first excited 2⁺ state in ¹⁸C using an upgraded recoil shadow method to determine the electric quadrupole transition. The measured mean lifetime is 18.9±0.9 (stat)±4.4 (syst) ps, corresponding to B(E2;2₁ ⁺ $ \rightarrow$ 0⁺ _gs) = 4.3±0.2±1.0e ² fm^4, or about 1.5 Weisskopf units. The mean lifetime of the first 2⁺ state in ¹⁶C was remeasured to be 18.3±1.4±4.8 ps, about four times shorter than the value reported previously. The discrepancy is explained by incorporating the $ \gamma$ -ray angular distribution obtained in this work into the previous measurement. The observed transition strengths in ^{16, 18}C are hindered compared to the empirical values, indicating that the anomalous E2 strength observed in ¹⁶C persists in ¹⁸C .     

Nuclear spin relaxation of Xe in liquid Te

By the method of time differential perturbed angular distribution following a nuclear reaction, the relaxation rateT _r ^?1 of the 8 msI ^π=10⁺ isomer of¹³²Xe has been measured in liquid Te. Between 670 °K (supercooled liquid) and 1,000 °K the rate decreases from about 720/s by about a factor of two. From existing experimental material it is concluded thatT _r ^?1 is mainly due to quadrupolar interaction (T _r ^?1 ≈T _Q ^?1 ). Its magnitude is discussed considering the metallic and the noble gas limit as models for the Xe-Te-interactions. The temperature dependenceT _Q(T) apparently does not correlate with the diffusion constant of Te in contrast to a simplified theoretical treatment. — The nuclearg value of the isomer has been determined to be g=(?)0.195(5) thus confirming the configuration (vh_11/2)².     

Observation of the nuclear rainbow scattering for12C+12C atE Lab =300 MeV

The elastic and inelastic scattering of¹²C on¹²C has been measured in the angular range between 2.8° and 70.4° in the c.m. system atE _Lab =300 MeV. Optical model calculations have been performed with Woods-Saxon and folded potentials, the ground state and the first 2⁺-state were coupled in the calculations. The large cross sections of the elastic scattering at large angles is related to the nuclear rainbow scattering, which is centered at about 56°. This requires a potential depth of 100 MeV at a distance of 3 fm, the fit to the data is sensitive down to this region. The calculations with the folded potential show a better agreement with the data than those with the Woods-Saxon shape. The total reaction cross section of 1,420 mb, obtained from the optical model analysis, corresponds to the geometrical value; no transparency is observed.     

Isospin mixing observed in the reaction 12C(6Li, α)14N

The reaction ¹²C(¹²Li, α)¹⁴N was studied to investigate the isospin mixing of high-lying levels in ¹⁸F. Excitation functions and angular distributions of the α-transitions to the ground, first and second excited states in ¹⁴N were measured for bombarding energies from 3.2 to 8.0 MeV. The isospin-forbidden cross section for the excitation of the lowest T = 1 state in ¹⁴N at 2.31 MeV was found to lie between 1–2 % of that of the allowed transitions. A partial wave analysis of the α₁ angular distribution data revealed a strong resonance with J^π = 2⁺ at E_x = 15.99 MeV. Arguments are presented which tentatively identify this resonance as being due to two close-lying 2⁺ levels with different isospin.     

Measurement of nuclear deformation parameters from elastic and inelastic scattering of α and 3He ions on Te isotopes

Cross sections for the elastic scattering of ⁴He by ^{122, 124, 126, 128}Te and ³He by ¹²⁸Te and for inelastic transitions to the lowest 2⁺ states of Te isotopes were measured for several scattering angles at bombarding energies in the vicinity of the Coulomb barrier. The data were analyzed in the framework of the optical model and the DWBA from which optical potential and deformation parameters were extracted. A detailed study of the fit procedure is presented with emphasis on the significance of the extracted parameters and the correlations among them.     

Determination of nuclear parameters by inelastic electron scattering at low-momentum transfer

The second-order Born-approximation treatment of Cutler and Schucan was applied to inelastic electron scattering data on ⁶Li, ⁶⁰Ni, and ¹¹⁴Cd acquired at low momentum transfers. The form factors as a function of momentum transfer q in the range of 0.25–0.57 fm^?1 were obtained by angular distribution measurements performed at incident energies of 30 to 60 MeV. The correlation between two parameters deduced from the measurements, the reduced transition probability B(E2↑) and the transition radius R⁽²⁾_tr, is discussed. It is suggested that inelastic electron scattering data at low-q is best used either in conjunction with an accurate value of B(EL↑) (available from the model-independent analysis of “photon” experiments at zero momentum transfer) to allow accurate determination of R⁽²⁾_tr, or in conjunction with high-q inelastic electron scattering data to allow accurate determination of B(EL↑) as well as R⁽²⁾_tr.     

Rotational and vibrational states in 115Te

High-spin states of the ¹¹⁵Te were studied by in-beam spectroscopy with the ⁸⁹Y (²⁹Si, p2n) fusion-evaporation reaction at a beam energy of 108 MeV. γ?γ coincidence and γ?γ angular correlation analyses were employed for determining the level scheme of ¹¹⁵Te. We have identified two vibrational-like bands built on the νh_11/2 and νg_7/2 quasiparticle states and the noncollective oblate states from the full alignment of quasiparticle configurations. In addition, a regular ΔI = 2 sequence with positive-parity was found for the first time in odd-A Te nuclei. This sequence is interpreted as a deformed structure resulting from three-quasiparticle alignment having the [π(g_7/2, h _11/2) ? ν(h _11/2)] configuration. Calculations of total Routhian surfaces and cranked shell model were performed and were used for assigning quasiparticle configurations to the states in ¹¹⁵Te.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

Analyses of inelastic proton scattering from 20Ne

Differential cross sections and analyzing powers for inelastic proton scattering to the 2⁺₁, 4⁺₁ and 6⁺₁ states of ²⁰Ne are analyzed using an antisymmetrized distorted wave approximation in direct reaction theory. The spectroscopy of these states was obtained by angular momentum projection from an axially symmetric minimal-energy Hartree-Fock intrinsic state.     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

Analysis of inelastic scattering of 3He on 13C at 37.9 MeV

The differential cross section of elastic and inelastic scattering of ³He ions on the ¹³C nucleus has been measured at an energy of 37.9 MeV. By fitting the shape of the measured angular distribution of the elastic scattering the parameters of the optical model have been found. These parameters have been used for the DWBA calculations of angular distributions corresponding to excitations of the ¹³C levels 3.09(1/2⁺) MeV, 3.68(3/2^–) MeV, 3.85(5/2⁺) MeV, 7.55(5/2^–) MeV, 8.84(1/2^–) MeV and 11.85(7/2⁺) MeV. Several sets of transition densities calculated with different effective nucleon-nucleon interactions and six different M3Y interactions between a projectile and target nucleon have been tested. Analysis of the inelastic scattering of 135 MeV protons on ¹³C is also presented, which enabled us to obtain additional information about the tested structure models.     

Study of 122Te with charged particle reactions

The reactions ¹²²Te(d,d′)¹²²Te, ¹²³Te(d,t)¹²²Te, ¹²³Te(³He, ⁴He)¹²²Te, and ¹²¹Sb(³He,d)¹²²Te were measured with the Q3D magnetic spectrograph of the Munich Tandem Accelerator. The level scheme of ¹²²Te was extended up to about 4 MeV using also previous results and new ¹²²Te(γ,γ′)¹²²Te data. The level scheme is compared with IBA and QPM calculations. An intruder band is proposed with the 0⁺ band head at 1746 keV.     

Resonant effects in the12C+12C→8Be gs +16O gs reaction aroundE cm=32.5 MeV

The¹²C+¹²C→⁸Be _gs +1¹⁶O _gs reaction has been studied at c.m. energies of 27.9, 32.5 and 35.0 MeV. The energy dependence of the cross section is consistent with a resonant behaviour like the one observed for two¹²C nuclei excited in a very deformed state in the final channel. The angular distributions for the two reactions show also a similar oscillatory behaviour. The analysis suggests that the reaction proceeds through the formation of an intermediate state with a complex nature, involving largely deformed configurations as well as almost spherical ones.