Transfer reactions and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems ⁴⁰Ca + ^90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target ⁹⁶Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data. Received: 2 May 2002 / Accepted: 4 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: montagnoli@pd.infn.it, Fax +39049 8277102, Tel. +39049 8277117. RID="b" ID="b"On leave from the China Institute for Atomic Energy, 102413 Beijing, China. Communicated by C. Signorini     

Time-dependent quantum description of few-nucleon transfers upon nuclear reactions 40Ca + 96Zr, 40Ca + 208Pb, and 90Zr + 208Pb

The time-dependent Schrödinger equation is solved numerically using the difference approach for outer nucleons of the spherical nuclei ⁴⁰Ca, ⁹⁰Zr, and ²⁰⁸Pb upon their grazing collisions. The neutron and proton transfer probabilities are determined for energies near the Coulomb barrier as functions of the minimum internuclear distance and quantum numbers of initial nucleon states.     

Comment on fusion cross sections in the40Ar+40Ca and40Ca+40Ca systems

Using a strongly mismatched transfer reaction,¹³⁸Ba (¹⁴C,¹⁵N), the spin orbit potential for¹⁵N projectiles has been derived in terms of the reaction asymmetry. The strength and sign of the L·S-potential are consistent with a previous determination using an (¹⁶O,¹⁵n) reaction; the signis opposite to that for nucleons and agrees with a model where the last P_1/2 nucleon is responsible for the L·S potential.     

The quadrupole momentQ 2+ of32S

The static quadrupole moment of the first excited 2⁺ state in³²S was determined by comparing, in coincidence with³²S ions backscattered from⁶⁰Ni, the gamma-ray yields of the 2 ₁ ⁺ →0 ₁ ⁺ transitions in both nuclei for bombarding energies around 70MeV. Depending on the sign of the interference term for transitions via the second excited 2⁺ state in³²S, the following two values were determined:Q ₂ ⁺ =(?18±4)e·fm² andQ ₂₊=(?15±4)e·fm².     

Correlations between nucleon transfer and fusion at near-barrier energies for the systems32S +100,101Ru and33S +90,91,92Zr

Transfer reactions at two near-barrier energies for the systems³²S +^100,101Ru have been studied. Differential cross sections have been extracted for a large variety of channels, with a set-up yielding good mass, nuclear charge and energy resolutions. A steeper decrease of the measured angular distributions at backward angles with respect to the prediction of a semiclassical theory is interpreted as a loss of transfer flux feeding more complex channels and/or fusion. Coupled channels calculations, which use the transfer form factors derived from the experiment, reproduce the fusion cross sections at sub-barrier energies. Multi-nucleon transfer seems to play an essential role for the fusion process, as evidenced by the found strong correlations. A systematic comparison is made with the systems³³S +^90,91,92Zr, which have been the object of a previous experimental study with the same set-up.     

Near-barrier transfer and fusion of the systems33S +90,91,92Zr

Double differential cross sections of all prominent transfer channels have been measured in the systems³³S +^99,91,92Zr at two energies close to the nominal Coulomb barrier. In addition the fusion excitation functions of these systems have been measured below and around the barrier. The angular- andQ-distributions of the most important transfer reactions have been analysed in the framework of a simple semiclassical formalism. Particularly the two-nucleon transfer angular distributions exhibit strong multi step coupling effects which manifest themselves in reduced cross sections at large angles corresponding to close distances. From the angular distributions at forward angles, where a single step character of the transfer reaction can be assumed, approximate form factors have been extracted employing a first order perturbation theory. Within the uncertainties of a schematic coupled channels calculation the isotopic differences of the sub-barrier fusion enhancement can be understood on the basis of the isotopic differences of the transfer form factors andQ-values.     

Intermediate mechanisms in fission-like fragmentation in the 32S + 59Co and 32S + 63Cu reactions

The fission-like fragmentation of the ³²S + ⁵⁹Co and ³²S + ⁶³Cu composite systems has been studied at incident energies E/A ≈ (4–5) MeV/nucleon. Mass, energy and angular distributions of the fission-like fragments were obtained from time-of-flight measurements. The mean total kinetic energies of the fragments are found to be fully relaxed, whereas a strong angular dependence is observed in the mass distributions. The data are interpreted in terms of a dynamical model based on the transport theory.     

近垒能区32S+90,96Zr势垒分布的研究

精确测量了³²S+^90,96Zr两系统的背角准弹散射激发函数, 总体误差小于1%, 从中分别抽取了它们的势垒分布, 对比观测到³²S+⁹⁶Zr的势垒结构扁平且向低能区展宽, 这种 势垒可导致在垒下能区该体系的熔合截面的大大增强. ³²S+⁹⁶Zr与³²S+⁹⁰Zr相比 存在较强的中子转移反应, 且转移Q值为正. ³²S+⁹⁶Zr势垒的扁平结构可能是中子转移道耦合所致, 这会导致³²S+⁹⁶Zr垒下熔合截面大的增强.     

Resonating-group study of the N + 40Ca system

The scattering of nucleons by ⁴⁰Ca is studied with the resonating-group method. The ⁴⁰Ca wave function used is a translationally invariant antisymmetrized product of single-particle wave functions of (1s)⁴(1p)¹²(1d)²⁰(2s)⁴ configuration in a harmonic-oscillator well having an appropriately chosen width parameter. The nonlocal interaction between the nucleon and the ⁴⁰Ca cluster is computed with the help of a generator-coordinate technique. Calculated results are compared with experimental data on bound states in ⁴¹Ca, as well as n + ⁴⁰Ca and p + ⁴⁰Ca differential cross-section and polarization data at various energies. In each of these comparisons, it is found that our results are generally quite satisfactory; in fact, the fits to experimental data on cross sections and polarizations are of similar quality as those obtained by conventional optical-model analyses which employ a large number of adjustable parameters. The importance of the Pauli principle is also examined in detail. Here we find that, at relatively high energies, the knockout exchange term is quite significant, but the heavy-particle pickup exchange term has a rather minor contribution.     

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

We present studies of mixed Coulomb crystals of ⁴⁰Ca⁺ and ⁴⁰Ca²⁺ ions in a linear Paul trap. Doubly charged ions are produced by photoionization of trapped ⁴⁰Ca⁺ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled ⁴⁰Ca⁺ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with ⁴⁰Ca²⁺ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al. (Phys Rev A 87:052304, 2013) and Li and Lesanovsky (Phys Rev Lett 108:023003, 2012) using ions excited to Rydberg states.     

Preliminary frequency measurement of the electric quadrupole transition in a single laser-cooled 40Ca+ ion

The trapping and laser cooling of ⁴⁰Ca⁺ ion on the way toward optical frequency standards have been developed. A single ⁴⁰Ca⁺ ion is trapped in the miniature Paul trap and laser cooled by two frequency-stabilized diode lasers. A commercial Ti:Sapphire laser system at 729 nm is referenced to a high-finesse cavity to meet the requirements of ultra narrow linewidth of the 4s²S_1/2-3d²D_5/2 electric quadrupole transition. Its center frequency is preliminarily measured to be 411 042 129 686.1 (2.6) kHz. The attempt to finally lock the 729-nm laser system to atomic transition is made. Further work to improve the accuracy of measurement and the stabilization of system locking is in consideration and preparation.     

Element distributions for the reactions32S+100Mo,32S+93Nb and28Si+93Nb near the coulomb barrier

The element distributions for the reactions³²S+¹⁰⁰Mo,³²S+⁹³Nb, and²⁸Si+⁹³Nb have been measured atE/B～1.4. The correlations between the first moment of the measured distributions and TKEL are consistent with the predictions of the liquid drop potential energy surfaces showing the charge equilibration of the dinuclear systems. The measured second moments are compared with a recent systematics.     

Directed and elliptic flows in 40Ca + 40Ca and 112Sn + 112Sn collisions

The directed and elliptic flows for different light particles and fragments in collisions of ⁴⁰Ca + ⁴⁰Ca and ¹¹²Sn + ¹¹²Sn at energies from 30MeV/nucleon to 100MeV/nucleon were studied in the isospin-dependent quantum molecule dynamics model (IQMD). With increasing incident energy, the directed flow rises from negative to positive, while the elliptic flow decreases with increasing the incident energies. The directed flow for the ⁴⁰Ca + ⁴⁰Ca system is not sensitive to the nuclear equation of states (EOS), but the directed flow for the ¹¹²Sn + ¹¹²Sn system is sensitive to the EOS. However, the elliptic flows for both ⁴⁰Ca + ⁴⁰Ca and ¹¹²Sn + ¹¹²Sn systems are not sensitive to EOS. A study of the dependence of directed and elliptic flows on the fragment charge (mass) is also performed. Received: 15 March 2002 / Accepted: 14 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: Zhanghy@sinr.ac.cn; Permanent address: Shanghai Institute of Nuclear Research, Chinese Academy of Sciences, P.O. Box 800-204(2), Shanghai 201800, China. Communicated by W. Henning     

Precision mass measurements of 40Ca17+ and 40Ca19+ ions in a Penning trap

High-precision mass measurements on lithium-like and hydrogen-like ⁴⁰Ca-ions are reported. The obtained mass of the hydrogen-like and lithium-like ion is 39.952181819(29) u and 39.953272223(24) u, respectively. The corresponding mass of the ⁴⁰Ca atom is 39.962590858(22) u. This new value has a precision ten times higher than the literature value.     

Multifragmentation study on 30 AMeV32S+58Ni

In a multidetector experiment on 26 or 30 AMeV³²S+⁵⁸Ni, up to four coincident heavier or intermediate-mass fragments were observed. One of these occasionally has the characteristics of a projectile-like fragment, up to three may be attributed to the decay of the heavy reaction product. Taking the velocity of the fragments as a measure of the heavy-product excitation energy, one finds evaporation, fission and multifragmentation to follow one another with rising excitation. Model simulations of sequential decay with up to two binary fissions and, alternatively, of simultaneous statistical multifragmentation were performed for comparison with experimental distributions of mass, velocity and (for events with three slow intermediate-mass fragments) relative azimuthal angle. Though in the three-fragment events indications of simultaneous multifragmentation are present, the sequential binary decay predominates. Evaporated protons and α particles detected in coincidence have a mean multiplicity growing with excitation energy, while the temperature governing the spectra has a plateau with a value of about 5.5 MeV.     

Self-consistent analysis of sub-barrier fusion enhancement effect in Ca+Ca and Ni+Ni

The fusion dynamic mechanism of heavy ions at energies near the Coulomb barrier is complicated and still not very clear up to now. Accordingly, a self-consistent method based on the CCFULL calculations has been developed and applied for an ongoing study of the effect of the positive Q-value neutron transfer (PQNT) channels in this work. The typical experimental fusion data of Ca+Ca and Ni+Ni is analyzed within the unified calculation scheme. The PQNT effect in near-barrier fusion is further confirmed based on the self-consistent analysis and extracted quantitatively.     

Folding-model analysis of the inelastic scattering of 32S on 40Ca at 100, 120 and 151.5 MeV

The angular distributions for the 2⁺ level of ³²S at 2.24 MeV and 3⁻ level of ⁴⁰Ca at 3.74 MeV have been measured at 100, 120 and 151.5 MeV ³²S bombarding energies and the 3⁻ level of ³²S at 5.01 MeV at 120 and 151.5 MeV. The levels have been analysed by the coupled-channel approximation using real potentials and form factors deduced from the folding model. It has been found that the energy dependence of the folding-model renormalization coefficient decreases in comparison with that found in the elastic-channel analysis and that an overall energy-independent renormalization coefficient seems to be needed.     

中子与90,91,92,94Zr反应的理论计算和分析

根据中子与天然Zr及其同位素反应的总截面,去弹截面和弹性散射角分布的实验数据,得到一组普适的光学模型势参数;应用得到的光学模型势参数,光学模型,Hauser-Feshbach理论,预平衡反应的激子模型和扭曲波玻恩近似理论,系统计算和分析了中子与^90,91,92,94Zr反应的非弹散射角分布和双微分截面,理论结果与实验很好的一致.